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EUROPEAN COMMISSION

Directorate-General for Research and Innovation Directorate D— Industrial Technologies Unit D3 — Advanced Materials and Nanotechnologies

Contact: Hélène CHRAYE

E-mail: [email protected] [email protected]

European Commission B-1049 Brussels

What makes a material function? Let me compute the ways…

Modelling in H2020 LEIT-NMBP Programme Materials and Nanotechnology projects

Sixth version, 2017

Edited by

Anne F de Baas

Directorate-General for Research and Innovation 2017 Industrial Technologies EN

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ISBN 978-92-79-63185-6 doi 10.2777/417118

CONTENT

Introduction ...... 6 Importance of the projects to the European Industry ...... 6 Questions that can be answered by modelling ...... 7 Industrial impact of modelling ...... 7 Future research needs ...... 9 Conclusions ...... 9

Concepts, Language and Classification ...... 10 Concepts and Vocabulary ...... 10 What are models? What are simulations? ...... 10 Introduction of physics-based model types...... 11 Electronic models ...... 13 Atomistic models ...... 13 Mesoscopic models ...... 13 Continuum models ...... 14 Deterministic and Statistical models ...... 14 Solvers ...... 14 Choosing the right model and model workflow (multi-scaling) ...... 15 Post- and pre-processing ...... 17 Different uses of the same physics law ...... 17 MODA ...... 18 Metadata ...... 19 Modelling and characterisation ...... 19 Specification and classification of physics-based model types ...... 19

Chapter 1 Electronic models ...... 20 1.1. Schrödinger Equation based models ...... 21 1.1.1. Single particle Schrödinger models ...... 21 1.1.1.1. Ab initio quantum mechanical (or first principle) models ...... 21 1.1.1.2 Schrödinger equation with Hartree-Fock Hamiltonian model ...... 21 1.1.1.3 Higher level ab initio models ...... 22 1.1.2 Many body Schrödinger models ...... 22 1.1.2.1 Schrödinger equation with nearly free electron Hamiltonian model ...... 22 1.1.2.2 Schrödinger with semi-empirical tight binding Hamiltonian model ...... 22 1.1.2.3 Schrödinger equation with Hubbard Hamiltonian model ...... 22 1.1.2.4 Schrödinger equation with k⋅p effective Hamiltonian model ...... 23 1.1.3 Quantum mechanical time dependant Schrödinger models ...... 23 1.1.3.1 The time-dependent Schrödinger equation with k⋅p effective Hamiltonian model 23 1.1.3.2 Other time-dependent Schrödinger models ...... 23 1.2 Kohn Sham equation Density Functional Theory (electronic DFT) ...... 24 1.2.1 Kohn-Sham equation, Pseudopotentials, Projector Augmented Waves ...... 25 1.2.2 TD-DFT and TD(Spin)DFT ...... 25 1.3 Quantum Dynamic Mean Field Theory ...... 25 1.4 NEGF ...... 26 1.5 Representations of continuous media ...... 26 1.5.1 Polarisable continuum approximation ...... 26 1.5.2 Envelope function approximation ...... 27 1.6. Statistical charge transport model ...... 27 1.6.1 Statistical semi-classical transport model for drift-diffusion (BTE) ...... 27 1.6.2 Fermi Golden Rule (FGR) (hopping model) for quasi particle transport ...... 27 1.6.3 Percolation models ...... 28 1.7 Statistical spin transport model ...... 28

Chapter 2 - Atomistic models ...... 29 2.1 Classical Density Functional Theory and Dynamic Density Functional Theory ...... 31 2.2 Newton's equation based models...... 31 2.2.1 Molecular Mechanics ...... 31 2.2.2 Molecular Dynamics (MD) ...... 32 2.2.2.1 Classical Molecular Dynamics ...... 32 2.2.2.2 Ab initio Molecular Dynamics ...... 32 2.2.2.3 Quantum Mechanics/Molecular Mechanics (QM/MM) a workflow ...... 33 2.3. Statistical Mechanics atomistic models ...... 33 2.3.1 Monte Carlo Molecular Models ...... 33 2.3.2 Kinetic Monte Carlo Models ...... 34 2.4. Atomistic spin models ...... 34 2.4.1 Deterministics spin models ...... 34 2.4.2 Langevin Dynamic method for magnetic spin systems ...... 34 2.5 Statistical transport model at atomistic level ...... 35 2.6 Atomistic phonon-based models (Boltzmann Transport Equation) ...... 35

Chapter 3 Mesoscopic (particle) models ...... 37 3.1 Mesoscopic Classical Density Functional Theory and Dynamic Density Functional Theory .... 38 3.2. Coarse-Grained Molecular Dynamics and Dissipative Particle Dynamics ...... 38 3.2.1 Coarse-Grained Molecular Dynamics ...... 38 3.2.2 Dissipative Particle Dynamics (DPD) ...... 38 3.3 Statistical Mechanics mesoscopic models ...... 39 3.4 Micromagnetic models ...... 39 3.5 Mesoscopic phonon models (Boltzmann Transport Equation) ...... 40

Chapter 4 Continuum modelling of materials ...... 41 4.1 Solid Mechanics ...... 43 Materials Relations in solid mechanics...... 44 Model development in solid mechanics: new MR ...... 47 4.2 Fluid Mechanics ...... 47 Compressible vs incompressible flow ...... 47 Viscous vs inviscid flow ...... 47 Laminar vs turbulent flow...... 48 Newtonian vs non-Newtonian fluids and Rheology ...... 48 Materials Relations (MR) for flows ...... 49 Scales (micro and macro fluidics) ...... 49 4.3 Heat Flow and Thermo-mechanical behaviour ...... 50 4.4 Continuum Thermodynamics and Phase Field models ...... 50 4.4.1 Thermodynamics ...... 50 4.4.2 Phase Field models ...... 52 4.5 Chemistry reaction (kinetic) models (continuum) ...... 54 4.6 Electromagnetism (including optics, magnetics and electrical) ...... 55 4.6.1. Magnetics ...... 56 4.6.2 Elect(ron)ics...... 56 4.6.3 Optics ...... 56 4.7 Application of models to simulate Processes and Devices ...... 56

Chapter 5 Solvers and Databases ...... 58 5.1 Solvers ...... 58 Discretisation (FV and FE) ...... 58 Discrete Element Method ...... 58 Monte Carlo, a generic statistical method to solve different equations ...... 59 Smooth Particle Hydrodynamics (SPH) ...... 59 Automata (Lattice Gas, Cellular and Movable Cellular Automata) ...... 59 Accelerated simulations in molecular dynamics ...... 60 5.2 Databases ...... 60

Chapter 6 Model Development ...... 61 6.1 Model application ...... 61 6.2 Developmentof physics-based models ...... 61 Expanding models ...... 62 Reducing models ...... 63 6.3 Development of data-based models ...... 63 Post-processing leading to MR complementing PE ...... 63 Post-processing leading to self-standing data-based models ...... 64 6.4 Software engineering ...... 64 Software engineering and up-scaling for the industry ...... 64 Guidance on quality assurance for academic materials modelling ...... 64

Annex I Annotated template for MODA ...... 71

Annex II H2020 project MODA ...... 78 ALLIANCE: Crash-worthiness of car wheel-house ALMA: Heat in an electronic device AMPHIBIAN: Magnets for a flywheel ARCIGS COO: Optical and electrical behaviour of solar cell CRITCAT: Catalist performance of ultra-small metal alloys DEEPEN: Behaviour of LED structures EENSULATE: Sorption and permeation for windows with insulating material EIROS: Materials for extreme environments EXTMOS: New models for organic electronics FASTGRID: Superconducting fault current limiters FEMTOSPIN: Spin dynamics for storage of information GOFAST: Correlated materials in insulators and superconductors ICMEG: Elastic properties of polycrystalline polypropylenes High Throughput Discovery of Single Crystal Ferroelectrics Film INNOVIP: Insulation and dynamic behaviour of buildings IN-POWER: Mirror support design for thermoelectric plant INSPIRED: Reactor design for functionalised nanomaterials LOCOMATECH: Forming process for aluminium production LORCENIS: Reinforced concrete MODCOMP: Ectrical and thermal properties of fiber-based materials MODENA: Behaviour of polyurethane foams MOSTOPHOS: Stability of organic light emitting diodes N2B-patch: Drug delivery fot multiple sclerosis NANODOME: Gas-Phasesynthesis of complex nanomaterial structures. NANOPACK: Migration into food NEOHIRE COO: Permanent Magnets for Wind Energy Application NEWSOL: Thermal energy storage NEXTOWER: Solar towers NOVAMAG: Intermetallic compounds for permanent magnets PARTIAL-PGMs: Nanostructured materials for automotive after-treatment systems POROUS4APP: Nano-porous carbon fabrication PRODIA: Heat flow in an adsorber PROTECT: Piezo electric transducer emitting ultrasounds in liquid SIMPHONY: Flow in a micro or nano channel SINTBAT: Deformation and stresses within the battery anode STARCELL: Materials for photovoltaic cells WALL IN ONE: Heat and moisture transport in insulation products for buidlings

Annex III List of software codes used in NMP projects ...... 375

Introduction

Modelling is a powerful tool that supports materials research in the development of novel or improved applications. It provides the key information for identifying new materials, tailoring materials and design materials for structures and systems.

This is the sixth version of the Review of Materials Models (RoMM) illustrated by modelling projects funded under H2020 LEIT NMBP Programme in the unit Advanced Materials and Nanotechnologies. It is a follow-up of the first five versions which have received extensive appreciation. The European Commission has received numerous statements and inputs that have been taken into account to prepare this sixth version.

Based on the analyses of modelling done in projects in the H2020 and via numerous discussions with the field, this review aims to define the necessary concepts and to classify them. This Review proposes names for these concepts which harmonise the language of modelling subfields. The common language is hoped to foster dialogue and mutual understanding between industrial end- users, software developers and theoreticians. This common language can in the future form the basis for an ontology with a formal language of materials modelling and a definition of the relation between the concepts. Such an ontology can then be a basis for metadata development necessary for a Modelling Market Place.

The scope and achievements of the modelling in 36 projects are presented with this harmonised language. For a review of modelling in 100 projects funded in the 7th Framework Programme (2007-2013) by the NMP Programme we refer to the fifth version of this Review.

Definitions of concepts and a harmonised language are proposed in this Review of Materials Modelling.

This vocabulary will later on be the basis of metadata to describe models and databases with.

Importance of the projects to the European Industry

The use of materials modelling in industries is very versatile. Application addresses fields like Energy, Environment, Transport, Health, ICT and Manufacturing. It is supporting the creation of products like solar cells, sensors, car parts, tissues, computers, tools, coatings. Industrial application is the target of the H2020 LEIT NMBP programme and the projects show the continuous effort to move from model development to model application and finally upscaling for industrial application. It is important to note that, in general, models become most useful to industry when they have reached an advanced maturity. This requires strong interaction between the code developers and industry, and, because of the complexity and long timescale of the code development and validation process, the support of programmes such as NMP makes an important contribution to competitiveness.

The most crucial issue related to modelling in industrial applications is in the formulation of models that produce realistic results. In general, modelling and simulations can be the eyes of the experimentalists, helping them to access information that would not be available otherwise and interpret the experimental results. Modelling provides also invaluable predictions on the evolution of a system in a quicker or cheaper way than with trial and error methods. Industry uses modelling for:

 Saving costs by establishing a strategy for testing and by screening new material candidates, when a “try and fail” approach cannot be carried out in the industry or it would be too complicated, dangerous or expensive.

 Understanding results of measurements. This is particularly important at the nanoscale and at femtoscale where access to materials properties and processing methods is often difficult. The simulation can provide this information for every point in the sample at every time.  Reducing the time to market, by accelerating the time scales of understanding and developing new materials and of existing materials in new applications.  Suggesting new materials and experimental procedures to create them. Materials design by modelling is about investigation of relations between chemical and physical composition, microstructure and effective properties at a macroscale, so that a material can be designed with desired macro-properties. Modelling can be used to examine the properties of materials and devices that have not or cannot yet be created.

Questions that can be answered by modelling

To show the value of modelling, the achievements of the models beyond experiments have been listed. The models can answer questions like:

 What is the influence of the automotive catalytic converter’s shape on its performance?  Which hydrogen-microstructure interactions play a critical role in the degradation of materials and components?  Which are the dissipation mechanisms that contribute to the macroscopic adhesion between a metal and a polymer?  What is the role of thermodynamics and what are the reversal processes involved in ultrafast magnetisation processes?  Is it possible to control the parameters of the excitation process and of the metal oxides to create long-lived metastable phases with tailored physical properties?  Which is the role of the size of the systems in realistic nanometric devices? How is the dynamics influenced when the length scale is reduced to the nanometer size of devices (<20 nm)?  Which are the parameters that control the final state in a solar cell reached after the photo- excitation?  Which is the influence of biomedical devices on the surrounding tissues?  Which is the increase of electrical conductivity in composites upon addition of carbon nanotubes?

Industrial impact of modelling

From the description of the FP7 and H2020 projects in this Review of Materials Models (version 5 and 6) it transpires that an efficient materials modelling approach shortens the development process of materials-enabled products in all industrial sectors. According to the stakeholders, the future of the European industry is associated with a strong modelling capacity. Their opinion is that an efficient modelling approach is needed to shorten the development process of materials- enabled products. To predict properties of final products several models covering a wide range of physics and chemistry phenomena are used. This requires strong interaction between the different modelling communities and industry. Because of the complexity and long timescale of the code development and validation processes, the support of programmes such as FP7-NMP and H2020- NMBP makes an important contribution.

This Review provides insight and helps the reader to see the models as more than mere “black boxes”. It shows that:  Industry is a very active player both in modelling for production and in modelling research areas  Application areas of modelling span all industrial sectors. In each industrial sector all types of models are used except for Health where electronic modelling is

underrepresented and except for mesoscopic models which are predominantly used in ICT and Energy and Transport.  The majority of the projects performed modelling of the continuum type, corroborating the idea that modelling has reached a level of maturity that enables realistic simulation of macroscopic behaviour that can be used in industrial applications.  Electronic and atomistic models have a much respected position in industrial use and they are a traditionally a stronghold of the Europe.  Mesoscopic models are the least represented in this survey. This is probably due to lower level of maturity of these models which have to bridge the gap between the established concepts of "electrons" and "continuum”. In the medical area they are slowly finding their place.  Winners in frequency of use are: ab intio quantum mechanics, molecular dynamics and continuum mechanics (solid and fluid).  The bulk of the projects are applying existing models to new materials, which shows that the current state of the art of modelling can be characterised as "mature".  Model validation against a chain of experimental data of increasing complexity is an ongoing activity.  Development of the physics and chemistry models seems to progress steadily and there is a significant number of research groups that is constantly pushing the boundaries by developing models based on theoretical physics and chemistry.  Linking between models, especially through newly developed force fields and constitutive equations is extensive.

The modelling has lead to progress in many industrial sectors. Models can provide insights that experiments can not provide. Predictive design of novel materials optimised for specified applications is heavily used by industry e.g. to add properties and functionality to new materials. The modelling has generated improved control of materials development and an improved control of concerned industrial products and processes, minimising the environmental impact, reducing risk of product failure and increasing service life-time.

Fig 1 Industrial feedback on modelling use and benefits

Future research needs

From an analysis of modelling in H2020 projects it transpires that the projects on model development link the four types of models. In the application domain this is still very seldom.

The community, contributing to this Review, highlighted that future research could target linking of models to extending the width and breadth of the models. In parallel, it could be targeted to elaborate the physics and chemistry involved in existing codes to extend their application scales, especially an elaboration of mesoscopic would be welcome. Interface design to facilitate the future implementation in larger and extendable framework architectures would be of added value.

Conclusions

We hope that the analysis in this Review of Materials Models illustrated by results of NMP and NMBP projects bring insights. We hope that, with this insight, material behaviour and manufacturing processes across length and time scales can be better understood. This understanding of materials should then enlarge the application area and shorten the development process of materials-enabled products, which is key to increased global competitiveness of our industries.

In the following, a new terminology and classification will be discussed.

It is the hope that this Review of Materials Modelling will make it easier for modellers in different subfields to communicate!

Concepts, Language and Classification

Concepts and Vocabulary

It is not always clear whether expressions used by modellers to describe their work deal with the entity, the physics equation, the closure relation, the solver, the input, the output….and sentences are not always precise enough. This chapter first defines concepts used in simulations. Then it chooses words for these concepts: the vocabulary. In chapter 1-5 we will present the classifications.

Examples of unclear expressions: A model for atoms: Is the atom the entity or is it the output that describes an atom? A model for friction: Is friction the adaptation of the physics in the equation or is it the output describing these phenomena in the application? A laminate model: The material is the application, but what is the phsyics with which this is described? A FE model: This is the solver, but is this model dealing with solid mechanics, fluid mechanics, thermodynamics or electromagnetics?

What are models? What are simulations?

Materials are complex systems and the equations that describe the physical and chemical behaviour of real systems are often too complicated to be solved easily. In order to save computer time, which is a precious and limited resource, the description

Fig. 2 Simulation gives the numerical solution to the model applied to a specific 10 situation (Hans Fangohr, University of Southampton, UK)

of phenomena has to be simplified. Fortunately, often not all details need be taken into account in order to reproduce and predict experimental results. Key assumptions about reality can be made ignoring the complexity that is not necessary to describe the given situation. n this Review of Materials Models, an approximated Physics/chemistry Equation (PE) describing generic physics and its Materials Relations (MR) describing a specific material and its behaviour are called model.

The Physics Equation (PE) is by its nature generic and widely applicable and this is the strength of modelling! In this RoMM the chapters are dedicated to these generic PEs. But a physics equation alone can not be solved. The equation has to be applied to a specific case “documented” by the Materials Relation (MR). Only the system PE+MR is complete and can be solved. (Note that the PE, nor the MR, can be "run" in isolation.) Materials Relations include the concepts constitutive equation used in the continuum models. When a new MR is found, the combination PE+MR is called a new model.

Together the physics or chemistry equations and materials relations are called governing equations and they form one model.

Fig. 3 Model = Governing Equations = PE+MR

Introduction of physics-based model types

A new classification of existing models into four types is presented. Until now materials models were presented by the length and time scales of their applications, but as computers grow stronger the application areas started to overlap and the application area is no longer a good identifier of the model. In the new classification models are defined by the entity whose behaviour is described in the physics equation PE. The guiding thread in the RoMM V is the classical view of materials consisting of either electrons, atoms and molecules/nanoparticles, or considered as a continuum. In a full quantum approach, phenomena like electrons but also electromagnetic waves and lattice vibrations are entities with particle- and wave-like behaviour. The Quantum Mechanical wave representation will be considered when they become necessary to explain physical phenomena of interest. The entity itself is considered to be “frozen” and processes inside are not resolved.

It is the modeller who chooses to describe a certain phenomena. If very high accuracy is needed an electronic model is applied, but often solving this models requires too much computational resources and the less accurate continuum models are used user cases to be calculated should thus be described without any modelling information. Different modelling approaches can then be benchmarked.

Models are strictly classified according to the entity described by the physics and not according to the size (length scale) of the application or system!

The four natural categories of materials models consist of three discrete types and one continuum type of model:

Indicative Indicative Entity whose length scale time scale Model behaviour is Number of entities (depending on (depending on described current current computers) computers) Electronic electron 10-100 0.1 - 1 - models nm

Atomistic atom 102 - 109 0.1 - 100 nm fs - µs models

Mesoscopic nanoparticle, 106-unlimited 1 nm – 100 mm ms - s models grain, molecule, bead

Continuum continuum Unlimited (the model nm-m s - ks models volume equations are written up for finite volumes or elements)

Table 1: Overview of model classes

Fig.4 An illustration of entities in the different model types (Pierre Severin, Coexpair and Olaf van der Sluis, Philips) The length and time scales to which the models can be applied are indicated by ellipses but as computers grow they are overlapping more and more. Hence the new classification!

Electronic models

These models are based on physics/chemistry equations, the Schrödinger equations, describing the behaviour of electrons as quantum mechanical waves. Quantum mechanical methods describe the behaviour of the electrons and other quantum particles which determine the properties and structures of the material.

Examples of electronic model results: o electronic band structure giving conductive/dielectric and optical properties, o (magnetic) anisotropy, diffusion coefficient, activation energies, o thermodynamic stability and kinetic elementary processes for atomic defects and dopants o chemical reaction coefficients o force fields parameters for atomistic models

Atomistic models

These models are physics/chemistry equations describing the behaviour of atoms. When the electronic degrees of freedom are ignored, molecular mechanical models and classical mechanics are applied to describe the behaviour of atoms and molecules. Newton Dynamics can be used to describe effective interactions between atoms, called force fields or interatomic potentials. Interatomic potentials do not treat the quantum nature of electrons explicitly, which allows models using these potentials to be enormously faster than models using quantum methods. Such interatomic potential based modelling may not be as accurate as full quantum mechanical approaches, but can be used to simulate complex materials processes as radiation damage in nanocrystalline materials and friction between surfaces.

Examples of atomic model results: o trajectories, packing, stiffness, dynamical properties, o surface and interface energies, o constitutive equations parameters, o spectral properties, o heat transfer, o magnetism

Mesoscopic models

These models are physics/chemistry equations describing the behavior of nanoparticles, (parts of) molecules or grains. What happens inside these entities is not resolved. The entity is considered to be “frozen”. At the supra-atomic scale where uninteresting or fast details of the atomic motions are averaged out or replaced by stochastic terms, mesoscopic models concentrate on essential motions and large-scale structures.

A “mesoscale model" indicates the application domain is of nanometer size, but ….it does not tell whether the modeller looks at the behaviour of electrons, atoms, molecules or considers the material to be homogenous in larger volumes.

The word "scale" only relates to the size of an application domain and we do not be use it as an adjective to indicate "type of models".

Examples of mesoscopic model results: o morphology, domain formation and growth kinetics, o thermal stability, o magnetic behaviour

Continuum models

These models are physics/chemistry equations describing the behavior of a continuum in a finite volume. In this description, the material is assumed to be continuously distributed throughout this volume and the models disregard the discrete particle-based structures and smaller detail. Continuum models can be applied to situations with a wide range of length and time scales and the lower limit is growing smaller and smaller (nm). The models applied to at "micro-scale" phenomena can predict material decomposition, defect formation, crack propagation, solidification of liquids and applied to "macro-scale" continuum models can describe behaviour of thin films and realistic nano-devices with metallic contacts and other important variables for industrial manufacturing.

Examples for continuum model results: o macroscopic structural behaviour, o heat and mass transport, permeation times, o chemical reaction kinetics, o electromagnetic behaviour

Fig. 5 Number of projects in the FP7 NMP Programme performing modelling of the four different types.

Deterministic and Statistical models

Models can deterministically describe the behaviours (motion, energy) of the entities. Statistical models are based on statistical mechanics, statistical thermodynamics and other probabilistic theory. They consist in treating the many-entity system as a large statistical population, whose behaviour is determined by the forces applied to each single entity.

Note that such statistical models are still classified according to the entity whose distribution they describe.

Solvers

Simulation of models applied to new materials involves finding a solution to the equations of the model. Solvers can become very complicated and the computational power needed may become an issue. Solvers are numerical methods used to solve the Physics Equation complemented by the Materials Relations. In this Review of Materials Modelling there is a strict separation between the two concepts "solver" and "model".

E.g. Finite Elements Method is a solver technique. This method is used to solve physics equations in continuum models, but also for discrete models when continuum notions like distributions (electronics, atoms, particles) are used (SPH) is a solver (used to discretise the fluid dynamics model equations) and not a model. Monte Carlo is a way to solve mechanics equations. Care should taken with Green’s functions: they can be helpful in solving equations, but they also appear in PEs (see Ch 1.4) and KMC is a model (see Ch 2.3.2). Ch 5 will go into some more detail.

Solvers are numerical methods, not models (equations). Solvers do not determine the model class!

Choosing the right model and model workflow (multi-scaling)

When several (validated) models exist, the scientist/industry has to choose which one to use. This "testing of models" is also a valuable part of modelling. This consists in trying to answer questions like "which model gives properties that are closest to measurements for this material?" Here the researcher is investigating which physics is needed to describe the given situation. So a model that “approximate reality by considering the neighbours as point charges and ignore temperature effects” states what is the necessary physics to describe the measurements with. Sometimes the choice of a model depends on the balance between accuracy and simplicity. The outcomes of such testing might also be important because if none of the models are adequate the result of testing is that more physics/chemistry needs to be added to existing models. A particular user case can be described by a chain of different models and these approaches can be benchmarked. The standardised descriptions shouod facilitate this. In order to increase their predictive capability and applicability, continuum models need to be supplemented with descriptions of processes, which originate at the electronic, atomistic and nanoparticle-scale. It is in the very nature of the continuum models, that such effects are neglected. The great challenge in creating accurate and predictive models is that materials form a true multi-scale problem. A consistent hierarchy of simulations at different levels of representation is needed. With a chain of models the description of macro behaviour of materials in operation can be built up including the smallest detail.

For example, diffusivity of ions may first be simulated by modelling electron diffusion; then ion transport can be modelled at atomistic level resulting in particle formation; then particle transport through membranes and finally continuum models are used to simulate the electrical current.The large majority of projects combined models of different types.

Multi-scaling The word "multi-scaling" is a remnant of the naming of models after their application length scale and a more correct word would be "multi-equation- modelling".

The word method is reserved to indicate the way in which models are used. This is the workflow describing how models are put into a chain and are simulated either subsequently or concurrently and the workflow describes when and how to link in databases, with esperimental or simulated data. Finally, last but not least, in a multi-scale approach not only models should be connected but such an approach should also integrate experimental data in a clever way.

For sequential modelling we use the term linking models and this means running different models consecutively. For concurrent modelling we use the term coupling models. Two types of coupling exist: iterative coupling and tightly coupled equations solved together (running different

models for the same entity concurrently by solving one matrix). The linking of the models represents a considerable challenge and 80% of the projects linked different types of models.

Post- and pre-processing

A major issue in linking and coupling models is transfer of data from one model to another. The operation of reduction and extraction of model output is called post-processing. (Arbitrarily this can also be called pre-processing for the next model). Post processing is an operation on the data set resulting from the solution of the PE in order to extract useful information. Fortunately this usually takes substantially less computing resources than the solver itself!

The essential difference between a post-processor and a PE is that a PE calculates or generates a new physical system state, while a post-processor does not. A post-processor obtains more information about the same physical system state. A physical system state contains all the basic, fundamental information to describe a system. (This 'state' can also be a series of states (ensemble), such as a so-called trajectory of coordinates and velocities).

There are many types of post processors:

Visualizers read and visualize data (no change to the data, no addition of further data)

Converters change e.g. the numerical representation of a state (without altering the physical state itself)

Extractors enrich the dataset/state description by further information being calculated based on the information already contained in the state.  Calculating averages (T, v,….)  Calculating interpolated values  Calculating parameters (diffusivity from trajectories based on the Einstein relation, absorption coefficients,…)  Calculating other physics quantities applying their definitions  kinetic energy from velocities of the same state  electric potential from charge distributions of the same state  thermodynamic quantities from p,V,T series of the same state  thermodynamic properties like coefficient of thermal expansion, density, specific heat as a function of temperature and composition from Gibbs energy

Different uses of the same physics law

The same physics can be used as PE or in post-processing:  When the Poisson equation makes charges act on potentials and thus might and will alter the charge distribution and thus generate a new state then it’s a (part of a system of tightly coupled) PE describing the evolution of the charge distribution.  When the Poisson equation is used to calculate the electric potential for the same state it is a PP. Another example is:  When thermodynamics equations (the equation dG=0) provide information about the driving forces to reach an “equilibrium state” they are used as PE. This classifies them as a PE allowing modelling a state change, see e.g. phase change models.  When definitions of thermodynamic variables are used they are PP.

There is physics is involved in both PE and Post Processing! Thus the same equation/physics can be used as PE or as Post Processing.

MODA

The information of models is very different in different fields. Some name the solver, some the application, some the lengthscale and seldomly the complete physics is given. It is since the Work Programme 2016-2017 obligatory in the NMBP programme to give information about the PE, the MR, the solver and the post processor for each model in the workflow and the exchange between models;

To collect the information in a standard way across all fields a new fiche called MODA has been developed. The annotated version can be found in Annex I and on www.emmc.info under “Advice for LEIT proposers”. The MODA is meant to guide the documentation step by step and by following this guidance all necessary aspects will be presented. The use of this fiche is to increase the information in project descriptions of modelling, so that we can grow the field. The MODA will also help to inform the industry. The workflow pictures are very intuitive presentations of what modellers are doing. The MODA will enable the later preparation of these metadata.

H2020 projects with a substantial modelling part are documented with these MOODA in Annex II. A single example is given here.

Fig. 7 Workflow example from H2020 project ALMA

Metadata

In conjunction with the data, a vocabulary should be included for describing the data. This Metadata are data that describe and give information about other data. Metadata can be used to describe models, databases and platforms.

Metadata are under development for all the concepts important to describe models and data (see www.emmc.info for more information).. A starting point is the terminology and classification put forward in this Review. The MODA can be regarded as a schema that describes all aspects of a user case and metadata can be built on that basis. The aim is to move forwards towards a semantic level of interoperability. As standards they will facilitate interoperability.

This vocabulary will contain a formal language and the RoMM vocabulary is in fact an ontology describing the formal language of this specific domain.

Such metadata will enable exchange of information between materials modelling codes. Data should be put in a form that allows models to properly recognize it along with its meaning. This can be done based on semantic metadata schema. Metadata can deal with the complexity of (correctly, safely and maintainably) sharing data between multiple tools (in-house and commercial; proprietary and open).

The metadata can also be used for validating correctness (avoid confusion about types, units, dimensions etc.), and automatic configuration of generic file import/export filters. Furthermore, it can be used for code generation (meta-programming of classes and structures), and even generation of source code that can be used to extend existing software. The establishment of metadata is a topic under research at the moment.

Another aspect is how to make the data available. Simulation data is encoded in documents containing text, table, images, etc. Metadata allow modellers to publish their simulation data in a structured, semantic (knowledge-based) way that is requested by journals or open access databases, and that will enable others to find and use the data.

Metadata make it possible to do science in a new collaborative way.

Modelling and characterisation

The industry only wants validated models. The co-operation between modelling and characterisation is thus always very tight. And it goes both ways. The interpretation of experimental data often relies on models as well. In Fig 2 "experimental results" contains BOTH the "getting the signal" phase and "making the interpretation" phase. This includes deciding which physics (model) to use to convert the signal into a property. It can also involve the post- processing of measured quantities into other physical/chemistry properties.

Specification and classification of physics-based model types

The description of the four classes of model types will be presented in the next four chapters. The RoMM will be concluded by a chapter dedicated to model application and development.

Chapter 1 Electronic models

Electronic models are physics/chemistry equations describing the behaviour of electrons (entity). The theoretical framework of most electronic models is the Schrödinger equation (PE), with which the evolution at the quantum level of any atomic or molecular system with time is described. The electronic wave function is a function which represents, at each moment in time, the positions, momenta and spins of all electrons in the system. However, if the focus is not on magnetic properties than the spin part of the wave function is not explicitly carried. The most crucial element is H, the Hamiltonian operator, which represents the total energy of any given wave function and takes different forms depending on the forces acting on the material. In magnetics, the Hamiltonian includes terms expressing energy due to exchange interaction, spin- orbit interaction, and Zeeman interaction.

A model based on the Schrödinger equation i approximates either the Hamiltonian operator or the wave-function of the quantum system (MR).

When a new MR is complementing the PE we call the combination PE+MR a new model.

In this RoMM we dedicate the chapters only to the generic PEs.

To solve the Schrödinger equation numerically the concept of basis sets of wave functions is introduced. The orbitals are expanded as a linear combination of such functions with the weights or coefficients to be determined. Often a simple and effective basis set is made of linear combinations of atomic orbitals (LCAO) centered on the nuclei. Basis sets composed of Gaussian functions centered on the nuclei are also popular because of their flexibility in implementation and, only if needed, functions centered on bonds or lone pairs are added.

In solids and other systems that can be represented by a unit cell with periodic boundary conditions, it is common, and sometimes more appropriate to use basis sets composed of plane waves up to a cutoff wavelength. These functions are naturally periodic and independent of the atom positions and are therefore appropriate to describe the delocalized electrons in solid crystal (electron gas).

In all cases, the choice of the most appropriate basis functions depends on the system under consideration and the level of accuracy that is needed in the final result. A large number of ready- made basis sets are available and implemented in commercial codes, but new basis set are sometimes generated to study systems that present new challenges.

Fig.1.1 Number of FP7 projects that used one of the four main types of electronic models treated here.

Often the output of ab initio quantum mechanical models is post processed to develop parameters for atomistic, mesoscopic or continuum models, in the development of interatomic

potentials or to calculate partial atomic charge distribution. This ensures the incorporation of crucial quantum effects and properties for larger, more realistic, systems simulations at a reduced computational costs and time.

There are six main Physics Equations (PE) are: the Schrödinger equation, the Kohn Sham equation, Dynamic Mean Filed Theory, Non-Equilibrium Green’s Functions and statistical charge and spin models.

Single particles can be described by the ab-initio Schrödinger equation. Quantum mechanical calculations can only be performed for isolated systems (in vacuum) and at zero temperature.

The many-body problem is a general name for a vast category of physical problems where a large number of equations for a large amount of particles need to be solved in order to provide an accurate description of the system. This is e.g. the case in a large many-electron system or when it is necessary to include the effect of the surroundings on the system of interest (for example, transport of electrons in devices or solvation where there is weak interactions of the (small) quantum system with the (many) solvent molecules). Models using the Schrödinger equation exist but also many other approaches for many particle systems exist and these will also be discussed.

To study electronic and spin dynamics under the effect of external time dependent electric or magnetic fields, time dependent models are needed.

1.1. Schrödinger Equation based models

1.1.1. Single particle Schrödinger models

1.1.1.1. Ab initio quantum mechanical (or first principle) models

The Schrödinger equation can be solved exactly only for a few problems of limited interest. To solve the equation for systems of practical use, approximations are in general required. Ab initio models may be based on a series of approximations that do not include fitting the model to experiments. This is also called a first principle approach because the model is using the Schrödinger equation and is still based purely on fundamental principles of physics.

The ab-initio Schrödinger equation can be solved for small molecular systems if one considers that the mass of the nuclei is much larger than the mass of the electrons, the Born-Oppenheimer approximation. This assumption is valid if the electrons move much faster than the nuclei and the electrons feel the electric field of the nuclei as if the nuclei are in a fixed position. The electronic wavefunction of the electrons depends then only on the position of the nuclei and not on their momenta.

Quantum mechanical chemistry models are routinely used to calculate the ground state of atomic and molecular systems and the energy and configurations (electronic structure) of the excited states. This can be applied to several problems of practical use.

1.1.1.2 Schrödinger equation with Hartree-Fock Hamiltonian model

Several approximations are applied in a Hartree-Fock (HF) calculation. A new H (MR) is derived. First, the Born-Oppenheimer approximation is assumed and relativistic effects are neglected. Moreover, each particle is thought to be subjected to the mean field created by all other particles. This means that the method is neglecting the electron-electron correlation terms in the Hamiltonian. This method thus fails to represent strongly correlated systems, and systems close to the dissociation limit, as well as the weak dispersion interactions between molecules.

In so-called wave-function based approaches, the Hartree–Fock (HF) model is the conceptual starting point of molecular poly-electron structure calculations. The orbitals of the system are expressed in a set basis functions (discussed in the previous section) and the coefficients of this expansion are obtained numerically using a variational procedure that iteratively refines the

individual electronic solutions to obtain the configuration that yields the lowest total energy (also known as the SCF, self-consistent field method).

1.1.1.3 Higher level ab initio models

The Hartree-Fock method has fundamental limitations. It provides a localised representation of molecular orbitals which is not appropriate in highly dispersive systems and electron correlation is neglected. Higher level quantum chemical methods have been developed to overcome these simplifications and provide the most accurate calculation results of electronic structure.

These methods include: Configuration Interaction (CI), which includes the excited states in the description of the electronic state. Coupled Cluster (CC) takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Møller–Plesset perturbation theory (MP2, MP3, MP4, etc.) improves on the Hartree–Fock method by adding electron correlation effects as a second order perturbation of the Hartree-Fock Hamiltonian. These methods devise schemes which can, at least in principle, be infinitely refined by the addition of higher level terms. For example, a CCSD(T) calculation simply means a calculation done using a coupled-cluster method, which includes singles and doubles fully and triples are calculated non-iteratively. Note that due to their higher computational cost, these methods can only be applied to systems very limited in size.

1.1.2 Many body Schrödinger models

Depending on the characteristics of particular system at hand, more drastic approximations on the Hamiltonian or wave functions representation are made. Except in few simple cases, models that treat many-body electron interactions require the definition of an "effective" Hamiltonian. This is a simplified representation of the true Hamiltonian where some parameters are derived from empirical data. These methods are very popular because they allow to treat large systems (up to millions of non-equivalent atoms), where a full ab-initio method without the approximations would often be computationally too expensive.

1.1.2.1 Schrödinger equation with nearly free electron Hamiltonian model

The electronic band structure of metals can be described by the simplest effective Hamiltonian, which treats electrons in a solid as moving almost freely through the crystal lattice.

1.1.2.2 Schrödinger with semi-empirical tight binding Hamiltonian model

The opposite extreme to the nearly-free electrons is the case where the electrons in the crystal are tightly bound and behave much like the atoms, as in the tight binding model (TB). The method is closely related to the LCAO method used in ab initio models. Electrons are viewed as occupying the standard orbitals of their atoms, and then 'hopping' between atoms during conduction. Tight binding models are applied to a wide variety of solids. The approximation often works well in materials with limited overlap between atomic orbitals and limited overlap between potentials on neighbouring atoms. Band structures of materials like Si, GaAs, GaN, SiO2 and diamond for instance are well described by TB-Hamiltonians.

1.1.2.3 Schrödinger equation with Hubbard Hamiltonian model

The Hubbard model is the simplest model of interacting particles in a lattice, with only two terms in the Hamiltonian: a kinetic term allowing for tunneling ('hopping') of particles between sites of the lattice and a potential term consisting of an on-site interaction, which stems from the Coulomb repulsion between electrons occupying the same atomic orbital. For electrons in a solid, the Hubbard model can be considered as an improvement on the tight-binding model, which includes only the hopping term. The Hubbard model is actually the simplest model able to describe the interaction-driven transition from a metal to an insulator, commonly known as the Mott transition. Mott insulators are commonly found within transition metal oxides and organics,

where the Coulomb repulsion overwhelms the very narrow bandwidth. More recently, the Bose- and Fermi-Hubbard models has been used also invoked to describe the behavior of ultra-cold atoms trapped in optical lattices. The Hubbard model is a good approximation insofar the effect of all other bands but the conduction ones can be neglected, which corresponds to low enough temperature and energy so that all interband transition are uninfluential. If interactions between particles on different sites of the lattice are included, the model is often referred to as the 'extended Hubbard model'.

The fact that the Hubbard model cannot be solved analytically in arbitrary dimensions has led to intense research into numerical methods for strongly correlated electron systems.

1.1.2.4 Schrödinger equation with k⋅p effective Hamiltonian model

This is a technique that allows a band structure to be approximately described in terms of just a few parameters. The technique is commonly used for semiconductors, and the parameters in the model are often determined by experiment.

1.1.3 Quantum mechanical time dependant Schrödinger models

1.1.3.1 The time-dependent Schrödinger equation with k⋅p effective Hamiltonian model

This quantum kinetic model describes the time evolution of the multi-band electronic state and is a linearly coupled system of Schrödinger equations. The evolution is governed by the k∙p Schrödinger operator which as an extension to the single-band models describes a system of bands of the band structure, usually the four topmost valence bands.

1.1.3.2 Other time-dependent Schrödinger models

The time-dependent approach based on the Gutzwiller wave function and approximation is a very simple tool that allows simulating for quite long times the non-equilibrium evolution of correlated electron models. It is in essence an improvement of the time-dependent Hartree-Fock approximation, endowing a Hartree-Fock Slater determinant with local many-body correlations that better capture the collective nature of the Mott localization phenomenon. It is a rigorous variational approach in the limit of large lattice-coordination, but seems to provide qualitatively correct results also beyond that limit.

The Blonder-Tinkham-Klapwijk model is used to describe the normal-superconducting microconstriction contacts at the crossover from metallic to tunnel junction behavior. The Blonder-Tinkham Klapwijk (BTK) model in its simplest form does not require any input from other models. In its 3D extension, the BTK model requires in input the shape of the Fermi surface. In any case, this model allows fitting the gap features of the point-contact Andreev-reflection (PCAR) spectra and thus obtaining the amplitude and the symmetry of the superconducting gap(s).

The multiband Eliashberg theory includes interband spin-fluctuation interactions and describes superconductivity-induced infrared optical anomalies. The multiband Eliashberg model requires some input from band structure calculations (normal DOSs at the Fermi levels) and contains 2 free parameters (namely the coupling strengths) that can be adjusted to reproduce the gaps provided by the BTK fit of the spectra and the experimental critical temperature.

In particularly good contacts, the point-contact spectra also contain electron-boson structures that cannot be fitted by the simple BTK model; in these cases, since one of the outputs of the Eliashberg model is the whole energy-dependent gap function, this may be put in the extended BTK model to calculate theoretical point-contact spectra that feature electron-boson structures that can be compared to the experimental ones.

1.2 Kohn Sham equation Density Functional Theory (electronic DFT)

When the system size increases the calculations required become very quickly unfeasible. In addition, ab initio models are based on approximations which limit their accuracy. Often solving the Schrödinger equation within an independent electron scheme fails to reproduce experimental results. A popular and versatile model that includes (some of) the effect of electron correlation (albeit approximately) is quantum Density Functional Theory (DFT).

Quantum DFT is based on the Hohnberg-Kohn theorem that states that ground-state energy is uniquely defined by the electron density. The properties of a many-electron system are then determined by using functionals. These are functions of the spatially dependent electron density. The Kohn–Sham equation (PE) is the Schrödinger equation of a fictitious system (the "Kohn– Sham system") of non-interacting particles (typically electrons) that generate the same density that the real system of interacting particles would generate. This simplifies the formulation greatly because instead of explicitly including the real potential of many interacting electrons, the Kohn–Sham equation contains a local effective (fictitious) external potential of non-interacting particles. Spin polarized quantum DFT is an extension of quantum DFT which includes both the electron density and the up and down spin densities explicitly in the Kohn-Sham equations.

A little side note: Continuous notions like electron density are used. But these models are still describing the behaviour of electrons model and are thus called "electronic" and not “continuum”. DFT models that use the probabilistic density of atoms are classified as atomistic (Chapter 2) and if the model uses densities for nanoparticles the models is mesoscopic (Chapter 3).

Typically, the biggest additional modelling necessary in quantum DFT is the formulation of the exchange-correlation functionals (MR), which need to model not only the electron exchange and correlation energy terms but also the difference between the kinetic energy of the fictitious non- interacting system and the real one.

The simplest approximation in quantum DFT is using the local density approximation (LDA) where the functional depends only on the density at the place where the functional is evaluated. A further refinement is obtained considering the generalized gradient approximation (GGA) which is still local but also takes into account the gradient of the density at the same place.

For many solid-state systems, and in calculations of electron behaviour in molecules (chemistry), more sophisticated functionals are often needed, and a huge variety of exchange-correlation functionals have been developed. For calculation of electron behaviour in molecules, the so-called B3LYP functional is widely used, and is mentioned as an example of a hybrid functional in which the exchange energy, in this case from Becke's exchange functional, is combined with the exact energy from Hartree–Fock theory. The adjustable parameters in hybrid functionals are generally fitted to a 'training set' of molecules. Although the results obtained with these functionals are sufficiently accurate for many applications, there is no obvious systematic way of improving them (in contrast to some of the higher level ab initio methods like configuration interaction or coupled cluster theory). In the current quantum DFT approach, error is estimated comparing the results to other methods or experiments. Improving quantum DFT calculations by modifying the functional or by the addition of terms to overcome these problems is an active research topic.

The equations are then solved using an iterative self-consistent approach based on the variational principle. Computational costs are relatively low when compared to higher level ab initio methods based on the complex many-electron wave function. However, there are still difficulties in using quantum Density Functional Theory to properly describe charge transfer excitations; transition states, global potential energy surfaces and strongly correlated systems; and there are inaccuracies in quantum DFT calculations of the band gap in semiconductors, to mention a few examples.

In Ch 2 and in Ch 3 it is presented how the theory can be extended to atoms and particles.

1.2.1 Kohn-Sham equation, Pseudopotentials, Projector Augmented Waves

DFT models (PE) often include pseudopotentials. These are a MR providing an approximation of the full Hamiltonian. They can be developed to approximate the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential. This approach considers the nuclear charge as effectively screened by tightly bound core electrons. This has two consequences: only the chemically active valence electrons are treated explicitly, and the potential profile they experience is much smoother, thereby reducing the number of electrons and the size of basis sets.

The projector-augmented wave (PAW) method is another kind of MR used in ab initio electronic structure calculations. Like pseudopotentials, it is essentially a method to remove the core electrons from the problem, and allows for DFT (PE) calculations to be performed with greater computational efficiency. However, it is based on different and more general principles than pseudopotentials. The actual wavefunctions of density functional theory tend to have rapid oscillations near ion cores, requiring large basis sets to be expressed. The PAW method uses a set of linear operators to link those valence wave functions to a set of smoother ones that can be conveniently expressed on more compact bases. All properties can then be computed in terms of those smoother wave functions.

1.2.2 TD-DFT and TD(Spin)DFT

Time-dependent density functional theory (TDDFT) is a quantum mechanical model used to investigate the properties and dynamics of many-body systems in the presence of time- dependent potentials, such as electric or magnetic fields. The effect of such fields on molecules and solids can be studied with TDDFT to extract features like excitation energies, frequency- dependent response properties, and photo-absorption spectra.

As TDDFT is an extension of DFT (PE), the conceptual and computational foundations are analogous and use the effective potential of a fictitious non-interacting system which returns the same density as any given interacting system (MR). Numerically, this TDDFT model is much more complex than DFT, most notably because the time-dependent effective potential at any given instant depends on value of the density at all previous times. At present most of the implementations assume a local time-dependence of the potential (adiabatic approximation).

1.3 Quantum Dynamic Mean Field Theory

The many body Dynamical Mean Field Theory (DMFT) uses a quantum analogue of the classical mean field theory as PE, where the Weiss field becomes a fully dynamical one that has to be self- consistently determined. The many body Hamiltonian (MR) can e.g. be approximated in a localized basis or a Wannier function basis representation with short-range interaction. It provides frequency dependent but momentum independent single-particle self-energies.

A basis of Wannier orbitals are orbitals centred on lattice sites. There are two different ways to implement electronic structure calculations, either using plane waves or using more localised basis sets, as muffin tin orbitals. One can apply DMFT only in the latter representation. In reality there are several codes that construct Wannier orbitals from the Kohn-Sham single particle wave functions. In a basis of Wannier functions, any lattice system is described by a more or less involved Hubbard-like Hamiltonian. DMFT is devised to deal with such a Hamiltonians and in essence is the quantum analogue of the classical mean field theory. In the latter, one represents the effects of the coupling between one site and its neighbours by a so-called Weiss field acting on that site. One then solves the classical problem of a site in an external field, under a self- consistency condition that, in brief, implement the fact that the action of a neighbouring site on the site under investigation must be the same as the reverse. In DMFT the Weiss field is a dynamical one, the local problem that must be solved becomes a quantum problem of a site

coupled to a quantum bath, but the self-consistency condition has just the same meaning: the site under investigation must at end be identified with any other site of the bath.

DMFT is in principle applicable to any crystalline material. There is however a caveat. For the approach to have meaning, one needs that in the Wannier basis the tight-binding parameters must be fairly short range. This condition identifies that class of materials that people call “strongly-correlated” ones, which includes transition metal oxides, actinides , so-called heavy fermion compounds, molecular compounds, etc.

Therefore DMFT is designed to deal with strongly correlated materials where the approximation of independent electrons, which is used in Density Functional Theory band structure calculations, breaks down. DMFT can account better than DFT for the contribution of sizeable short range interactions between electrons and bridges the gap between isolated atoms and dense condensed-matter bulk systems; in the paradigmatic example of metallic hydrogen the bridge from Heitler-London to Slater. For instance, DMFT is able to model the phase transition between a metal and a Mott insulator, a collective phenomenon that escape any independent particle description.

1.4 NEGF

For the transport problem, described as a many-particle system (a many-electron system in particular) H cannot be formulated and, even if it could, the Schrödinger equation could not be solved. The total wave function (as argued by W. Kohn) is not a physical object in that case, and therefore the Schrödinger equation cannot be said to be the PE. Another PE is established called the NEFG. The definition of the Green’s function is a correlation of field operators in the Heisenberg picture (the wave functions are constant, the operators are time-dependant).Thus the Ψ symbols in the correlation do not refer to wave functions coming from the Schrödinger equation, but to creation and annihilation operators.

The form for H chosen by modellers is the MR.The H in the equation for the retarded Green's function is not the Hamiltonian for the global system but only its projection on a limited subset of degrees of freedom. The self-energies appearing in the definition are the key in this formulation as they contain the influence of the rest of the system. The initial Hamiltonian matrix in NEGF is an infinite matrix that contains the Hamiltonian of the considered material or device that is used in the PE and two semi-infinite Hamiltonians that describe the environment around the considered material or device. To reduce the size of the Hamiltonians into something that is solvable, the concept of boundary self-energies has been introduced and the original Hamiltonian matrix is modified.

The solvers are the set of mathematical techniques for computing Green's functions and related variables, of which there are many, including diagrammatic expansions, real-space iterative methods, etc.

Although the Green’s function is a concept often use as solver, here it is a major physics variable in a new physics equation.

1.5 Representations of continuous media

1.5.1 Polarisable continuum approximation

The polarisable continuum representation (PCM) is commonly used to model a solvent-mediated chemical reaction. For a system with very many solvent molecules, the computational cost of modeling would grow prohibitively high, if it were necessary to consider each solvent molecule as a separate molecule. Instead the solvent reaction field (MR) is simulated by a set of apparent charges self-consistently determined on the basis of the electric potential generated by the

solvated molecules. The solvated molecules electronic field is modelled with one of the available electronic PEs.

1.5.2 Envelope function approximation

This is a model that proposes an approximation of the wavefunction (MR), based on the fact that the wave function varies very quickly close to the cores of the atoms of the lattice. In the he envelope approximation only the slowly varying "envelope" modulating the rapidly varying part of the wavefunction is considered. The boundary conditions are applied to the envelope function directly, rather than to the complete wave function. The PE can be any of the above.

1.6. Statistical charge transport model

To describe the transport of charge carriers in solids or liquids, statistical methods can be used. It should be noted that the underlying methodology can be applied to other entities like atoms and molecules.

1.6.1 Statistical semi-classical transport model for drift-diffusion (BTE)

In simple homogeneous materials transport can be described by a continuum description of a diffusion-advection equation (also called drift-diffusion) with a well-defined diffusivity coefficient (Ch 4.2) However in disordered material this does not work accurately and therefor a statistical semi-classical model to describe the transport of particles (here electrons but in Ch 2 and Ch 3 resp. the equation is used to describe the motion of atoms and particles) in solids has been developed. The Boltzmann Transport Equation (PE) model has been used in the analysis of transport in semiconductors. This is an equation for the probability of particle occupation of energy at position and time. The particle density distribution can be modelled using quantum mechanical Fermi-Dirac statistics or Boltzmann statistics. The solution to the BTE is cumbersome but the equation can be solved numerically by a stochastic Monte Carlo method. This describes hopping of the entity on a lattice of sites (hopping rate (MR)). The necessary input parameters like band gap, carrier mobility and electron diffusion coefficient are obtained empirically or with separate theoretical calculations, using the Einstein relation. Disorder has to be taken into consideration if the sites of lattice are randomly distributed and hopping rates might depend on energy states on the sites. External forces might be added to the equation. To arrive at the behaviour at longer time and length scales a process of averaging is applied.

1.6.2 Fermi Golden Rule (FGR) (hopping model) for quasi particle transport

In quantum mechanical models for hopping transport of quasi-particles (like electrons, holes and excitons) the underlying PE is Fermi’s Golden Rule (FGR), which is derived from time-dependent perturbation theory. Fermi's Golden Rule is an equation for the probability of transition per unit time (transition rate) from one energy eigenstate of a quantum system to other energy eigenstates affected by a perturbation. The energy eigenstates are often states that are localized at different positions in the material. Equations for the material-specific rates k of all hopping transfer process to complete BTE (MR). By applying FGR the Marcus or Miller-Abrahams rate for charge transfer, and the Förster or Dexter rate for exciton transfer can be derived. For future models for other quasi particles we can already mention that other final equilibrium statistical properties, like the Fermi-Dirac distribution for fermions or the Bose-Einstein distribution for bosons also follow from the specific forms of Fermi’s Golden Rule. This is because all rates satisfy the principle of detailed balance, which guarantees the obedience of equilibrium statistical physics as we know it. Kinetic Monte Carlo (kMC) uses a MC solver for the time evolution of the quantum system by generating a Markov chain of eigenstates. In the kMC procedure, at each step the rates of all possible transitions are calculated by applying Fermi’s Golden Rule to all these transitions and one transition is chosen with a probability proportional to its transition rate.

1.6.3 Percolation models

Statistical approaches for electrical conductivity are also applied in percolation models. Transport due to percolation is represented as movement through a three-dimensional network of vertices in which the edge or "bonds" between two neighbors may be open (allowing the particles through) or closed (PE) with a certain defined probability (MR). Electron tunnelling is described with quantum mechanical percolation models which assume the charge transport between carbon nanotubes are partly through physical contacts and partly through electron tunneling between carbon nanotubes with a given probability.

1.7 Statistical spin transport model

Irradiation of a ferromagnetic metal layer with a femtosecond laser pulse causes a sudden demagnetization within a few hundred femtoseconds. The non-equilibrium spin transport model (PE) describes the laser-induced non-equilibrium transport occurring on the nanoscale using statistical principles. It treats explicitly the laser-created distribution of highly energetic, spin- polarized electrons, which immediately start to move randomly through the material (typical velocities of several nm/fs). These hot non-equilibrium electrons undergo random scattering with other electrons or with phonons and thereby they loose energy, i.e., the process of electron thermalization.

Chapter 2 - Atomistic models

Atomistic models are physics/chemistry equations that describe the behavior of atoms (entities) and are simulating the behaviour of larger e.g. molecular systems (typically between 102 and 109 atoms) maintaining individual atomistic detail, but removing an explicit representation of the electrons. Although the application systems are not always large enough to be considered macroscopic, they are often sufficiently large to reproduce experimental results within the desired accuracy and at the same time detailed enough to detect their microscopic origin. The different physics equations will be discussed in the separate chapters. Deterministic models rely on Material Relations (MR) for forces and the concept "force field" will be introduced first. Statistical models rely on Material Relations (MR) probability functions.

Fig.2.1 Number of FP7 projects that used one of the four main types of atomistic models treated here.

Input to atomistic models: Force fields and Interatomic potentials Many atomistic models use the Newton Equations (PE) and need as physics input a description of the forces on the entities (atoms) (MR). The interaction forces between the atoms can be expressed by interatomic potentials. Interatomic forces are forces of attraction and repulsion which act on atoms. Interatomic forces may be represented by the Lennard-Jones potential, which contain an attractive term and a repulsive term. The attractive term approximates dipole-dipole forces, ion-dipole forces, van der Waals forces (Keesom force, Debye force, and London dispersion force). The repulsive term approximates the Pauli repulsion. This input to the atomistic models (interatomic potential functions and parameter sets) can be derived from experiments or calculated by electronic models (see Ch 1) for a small number of appropriate test atoms. Validation of parameter sets is done against experimental results on larger and more diverse systems. Often an iterative procedure for the refinement of the parameters is needed. The most important aspect in the development of the interatomic potentials is to ensure transferability of parameters across a diverse range of systems and test the accuracy limits of the parametrisation. From the force field the potential energy of the atom and surrounding atoms can be calculated. To describe the potentials in molecules, typically, first each atom is modelled by assigning a radius (usually the van der Waals radius), a polarisability and a constant net charge (generally derived from quantum calculations and/or experiment). Force fields usually consist of a sum of additive terms. The terms represent both bonded interactions (between atoms that are actually covalently bonded) and non-bonded interactions. Terms between bonded atoms include: bond terms between 2 atoms, bend terms between 3 atoms, and torsional (dihedral) terms between 4 atoms. Bond and bend terms are often treated as springs with an equilibrium distance equal to the experimental or calculated value. The dihedral or torsional terms have multiple minima and cannot be modeled as springs, and their specific functional form varies in different force fields. Additionally, "improper torsional" terms may be added to enforce the planarity of aromatic rings and other conjugated systems, and "cross-terms" may be added that describe coupling of different internal variables, such as angles and bond lengths. Some force fields also include explicit terms for hydrogen bonds.

The non-bonded terms are much more computationally costly to calculate in full, since a typical atom is bonded to only a few of its neighbors, but interacts with every other atom in the system. The electrostatic force between charged particles is a typical non-bonded interaction and is given by Coulomb's law. Long-range electrostatic interactions are often important features of the system under study (especially for proteins) but the electrostatic terms are notoriously difficult to calculate precisely l because they do not fall off rapidly with distance. A variety of approximations are used to address this problem; the simplest approximation consists in using a cut-off range for these interactions and atom pairs whose distances are greater than the cutoff have a van der Waals interaction energy of zero. Other more sophisticated but computationally intensive methods are known as Particle Mesh Ewald (PME) and the multipole algorithm. To account for electronic polarisability and in order to produce better agreement with experimental observations, parameters can be buffered or scaled by a constant factor. Other non-bonded forces are London dispersive interatomic forces (attractive) and electron- electron short range forces (repulsive). These are typically put together using the so-called Lennard-Jones potential. Notwithstanding their simplicity, force fields can reproduce quite well a wide variety of chemical and biological problems, including drugs binding, protein folding kinetics and protonation equilibria. Bond order potentials belong to a class of analytical potentials which are used in molecular simulations. Examples include the Tersoff potential, the Brenner potential, the Finnis-Sinclair potentials, ReaxFF, and the second-moment tight-binding potentials. They have the advantage over conventional molecular mechanics force fields in that they can, with the same parameters, describe several different bonding states of an atom, and they may thus, to some extent, be able to describe chemical reactions correctly. The potentials were developed partly independently of each other, but share the common idea that the strength of a chemical bond depends on the bonding environment, including the number of bonds and possibly also angles and bond length. In classic polymer solution theory, the Flory-Huggins interaction potential gives an expression for the Gibbs free energy change ΔG m for mixing a polymer with a solvent and approximates three molecular interactions: solvent-solvent, monomer-monomer (not the covalent bonding, but between different chain sections), and monomer-solvent. In Ch 3 these force fields are extrapolated to interactions between nanoparticles or beads or grains.

Deterministic and Statistical models

Models can deterministically prescribe the behavior of the entities. The Ch 2.1 and Ch 2.2 address such models.

Many of the models described in this chapter, are based on statistical mechanics, statistical thermodynamics and other probabilistic theory. They consist in treating the many-atoms system as a large statistical population, whose behaviour is determined by the forces applied to each single atom. Simulations are performed keeping the number of particles, temperature and total energy constant (the so-called microcanonical ensemble); the number of particles, temperature and volume constant (the so-called canonical ensemble) or the chemical potential, temperature and pressure (the so-called grand canonical ensemble).

In statistical approaches kinematic constraints (MR) express the limits on the movement (barostats and thermostats). This can be due to the properties of the material like incompressibility, but more frequently kinematic constraints reflect the requirement of internal kinematic compatibility of motion of the particles (e.g. across boundaries between different constituents of a heterogeneous material). Compatibility with external boundary conditions of kinematic type (e.g. including periodic boundary conditions) is considered to be computational implementations of the physics boundary conditions.

Statistical mechanics provides the framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life. These models explain macroscopic structural, thermodynamical and dynamical

observables (e.g. temperature, pressure, work, heat, free energy, entropy and spectra of these variables) based on classical and quantum-mechanical descriptions of statistics and mechanics at the microscopic level. For example, a macroscopic observable like temperature is due at microscopic level to the collisions between particles and can therefore be mathematically derived sampling the velocities of the atoms. For the statistical mechanics formulation to be valid, the averaging has to be done over all possible configurations of the system, i.e. all possible positions and momenta of all particles (ergodic condition). This is true if the simulation is infinitely long, and approximately true if the system is allowed to evolve for a sufficient amount of time. The ergodic condition may be more difficult to achieve in systems with many degrees of freedom, or with large energy barriers between possible configurations, as the systems may be trapped in one local energy minimum. Computational methods to overcome this problem and speed up the configurational sampling are an active field of research.

To determine whether or not to use continuum models or discrete statistical mechanics, depends on the accuracy to be obtained. If full accuracy is necessary the Knudsen number may be evaluated for the problem. The Knudsen number is defined as the ratio of the molecular mean free path length to a certain representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. More simply, the Knudsen number is how many times its own diameter a particle will travel on average before hitting another particle. Problems with Knudsen numbers at or above unity are best evaluated using finer (atomistic and mesoscopic) statistical mechanics for reliable solutions.

Atomistic models need post-processing equations that are used to obtain the macroscopic properties in small volumes that can be compared with experiments.

2.1 Classical Density Functional Theory and Dynamic Density Functional Theory

Density Functional Theory (DFT) using the Kohn-Sham equations (PE) (see Ch 1.2) can also be used to describe the behaviour of atoms using classical potentials (MR). In classical DFT, the forces acting upon the atoms are described by an external (effective) free energy potential (similar to the ground state energy in the electronic model) which is a unique functional of the atomistic density profiles. As in the quantum equivalent, the modelling challenge is to formulate approximate density functionals for atoms in complex situations such as inhomogeneous complex fluids. Classical DFT is used to study colloids, fluids at interfaces or in presence of an external potential, and phase transition phenomena.

The time-dependent extension of the classic DFT is Dynamic Density Functional Theory (DDFT). The time evolution of the average density of Brownian particles (atoms) is given by the generalization of Fick's law to the diffusion of interacting particles in terms of the equilibrium Helmholtz free energy functional (or the grand canonical functional).

DDFT resolves density variations on length scales down to the particle size but only works for slow relaxing dynamics close to equilibrium.

2.2 Newton's equation based models

2.2.1 Molecular Mechanics

Molecular mechanics is a screening method to find an atomic constellation that has minimal energy in a given force field. It uses classical mechanics to calculate the global energy of the molecule. The code then tries different atomic positions (user cases) to find the lowest energy conformation of the atoms in a molecule. The (local) minimum is searched for by an appropriate algorithm (e.g. steepest descent). Global energy optimization can be accomplished using simulated annealing, the Metropolis algorithm and other Monte Carlo methods, or using different deterministic methods of discrete or continuous optimization. Molecular mechanics can be used to prescreen small molecules as well as large biological systems or material assemblies with many thousands to millions of atoms. Molecular Mechanics is thus not a model in the sense of a PE+MR being solved to find a new physical state.

2.2.2 Molecular Dynamics (MD)

The purpose of Molecular Dynamics is to deterministically calculate atomic motions. The equations used in Molecular Dynamics are the Newton equations of motion for all atoms in the system (PE). The MR specify the specific the interatomic forces. The effect of a thermostat or barostat can be simulated by limiting movements (MR). Note that the use of stochastic methods like Langevin dynamics that add friction and random forces to account for molecular collisions (and thus adding a statistical note to the model) is dicussed in Ch 2.4.2 and Ch 3.2.2

Molecular Dynamics equations are solved by simulating molecular trajectories by integrating the equations of motion. The time evolution of the simulation is broken down in small time steps. Using a numerical integration scheme, the dynamics of each atom in the system under the effect of the interatomic forces is calculated for each time step. The length of the time step chosen is a compromise between a value large enough to allow a reasonably long simulation time for the purpose of the study and a value small enough to capture all the required fundamental frequencies of motion in the system and conserve the energy between integrations steps. Typically this is in the range of 1-10 fs, but it depends on the range of motions allowed in the system. Multiple time scale calculations, where motions due torapidly changing forces are updated more frequently than motions due to slowly changing forces, are also possible in order to reduce the required computational time.

Large systems which are repetitive at a certain scale can be simulated using unit cells with periodic boundary conditions. In these, forces are calculated only for atoms contained in a unit cell and then replicated across 1, 2 or 3 dimensions to simulate the effect of particles entering and leaving the unit cell. The size of the unit cell needs to be large enough so that each particle does not feel the influence of its mirror image in one of the replicated cells.

The results are post-processed with the help of Statistical Mechanics which provides the mathematical expressions that relate macroscopic properties to the distribution and motion of the atoms and molecules of the N-body system. In doing so molecular dynamics simulations can provide both thermodynamic properties and/or time dependent (kinetic) phenomenon.

The main advantage of molecular dynamics with respect to some other molecular simulation methods is that not only does it allow obtaining equilibrium macroscopic properties (e.g. temperature, pressure, work, heat, free energy, and entropy) , but also the trajectory of the system during the simulation from which dynamical and structural quantities can be obtained.

The MD models can be used to give chemical information. This application is often part of a "microkinetics" workflow. But we do not name models (physics) after their application and thus say "an MD model can be applied to describe chemical reactions". Continuum chemical reaction models (also called kinetics) are discussed in Ch 4.5.

2.2.2.1 Classical Molecular Dynamics

Molecular Dynamics (MD) calculations performed using force fields (whose precise form is given in MR) and integrating the classical Newton's equations of motions for atoms (PE) are called classical MD. If the force fields parameters are derived from experimental data, classical Molecular Dynamics is often called empirical Molecular Dynamics.

2.2.2.2 Ab initio Molecular Dynamics

With the progress of computational speed and memory, it is possible to perform calculations of Molecular Dynamics with the Newton's equations of motions (PE) which take into consideration explicitly the effect of the electrons in the calculation of the forces, whose precise form is given in MR, (ab initio MD). Although still limited to smaller systems and shorter periods of time than classical MD, a significant advantage of using ab-initio methods is the ability to study, without

empirical parameters, reactions that involve breaking or formation of covalent bonds, tunneling and proton transport mechanisms.

The main challenge consists in calculating efficiently and accurately the forces acting on the nuclei due to the electrons. Since many electrons are in the system their potential energy is represented by a multidimensional surface for each nuclei configuration. Assuming that it is possible to decouple the motion of the electrons from the motion of the nuclei (Born- Oppenheimer approximation), the classical equations of motion for the nuclei are integrated using the sum of the interatomic potential and the forces derived from the electron potential energy surface. At each time step, the ground-state electronic potential surface can be calculated using standard quantum mechanical methods (Born-Oppenheimer Molecular Dynamics) or introducing fictitious dynamics for the electrons which follow adiabatically the nuclei and are subjected to small readjustments "on the fly" during the nuclei evolution to keep them close to the ground state potential surface (Car-Parrinello Molecular Dynamics).

2.2.2.3 Quantum Mechanics/Molecular Mechanics (QM/MM) a workflow

For systems in which full consideration of electrons is not feasible, it may still be possible to perform calculations that retain some quantum mechanical details. Quantum Mechanical/Molecular Mechanics methods (QM/MM) consist in finding a subdivision of the system into a part that needs to be calculated at quantum mechanical level and a (larger) part that can be calculated using classical force fields.

In the strictest sence this is thus a workflow encompassing an electronic and an atomistic model. They are used to model atoms for energy optimization calculations, calculation of reaction paths and other explorations of the potential energy landscape, and molecular dynamics simulations. For example, a QM/MM scheme can be used to calculate the reactions occurring between a drug and the target protein binding site atoms, while the rest of the protein is simulated with classical molecular dynamics. The challenge is to define the forces at the interface between the region treated with QM and the region treated with MD (coupling of models).

2.3. Statistical Mechanics atomistic models (Monte Carlo and kMC methods)

2.3.1 Monte Carlo Molecular Models

In the framework of statistical mechanics, it is not necessary to follow the dynamics of the systems to calculate macroscopic observables. A new state of a system (called move) is calculated by employing a Markov chain (PE) with appropriate probabilities (given by MR) (the statistical physics in the model) Equilibrium conditions are imposed on the new state. The macroscopic observables are then derived from an accurate sampling of all equivalent microscopic configurations of the system.

First a model of the potential energy (MR) of the system, like in Molecular Dynamics is established. To solve the system of equations the Metropolis Monte Carlo technique, which creates a Markov chain of states which biases the generation of configurations towards reasonable potential energies (so-called importance sampling). (Monte Carlo is a solver technique and does not describe the dynamics of a system). Each move generates a new equilibrium configuration which is accepted if its energy is lower or its normalised Boltzmann factor is larger than a random number between zero and one, and otherwise rejected. Monte Carlo allows the simulation with energy potentials that would not be possible in Molecular Dynamics.With MC technique the sampling efficiency can be increased, which is particularly important where the potential surface contains many local minima (as in close to state transitions, in large proteins etc). Note also that the random sampling of Monte Carlo based methods fulfills the ergodic condition intrinsically. Hybrid Monte Carlo methods introduce an acceptance criterion into Molecular Dynamics simulations, allowing the use of large time steps.

Statistical thermodynamics equations are subsequently used to derive the macroscopic observables (e.g. temperature, pressure, work, heat, free energy, and entropy) from the positions of the atoms in all configurations sampled (this is a post-processing operation)

The success of this statistical model has led to various generalisations, such as the method of simulated annealing for energy optimisation of a system, in which a fictitious high temperature is introduced to obtain a fully random sample and then the temperature is gradually lowered to obtain a configuration close to the ground state.

2.3.2 Kinetic Monte Carlo Models

Statistical models are used to simulate chemical reactions between atoms. Transition states (“rare” events for the reaction to occur) are identified on the potential energy surfaces (e.g. determined by electronic DFT or MD) to get an estimate of the energy barriers/free energy differences. The progress of a reaction is followed on a potential energy surface. The rate of a reaction is determined by the motion of the system through the col or saddle points, which is caused by vibrational modes responsible for the conversion of an activated complex to the product. The study hereof is also called “vibrational analysis”. When the transition states are identified and thus the preferred reaction path, Transition State Theory (TST) allows computing the reaction rate constant. This is faster than "manipulated MD" (doing thermo-dynamical integration methods on MD results). Both these TST-based and MD approaches are based on the statistical mechanics equations expressing reaction equilibrium (PE) and rates in terms of the statistical distribution of molecular velocities (MR). KMC and MD models are often part of a microkinetic workflow (see also Ch 4.5). kMC can solve electronic, atomistic or mesoscopic or continuum models for transitions and in order to do so we need to specify the appropriate transition to simulate the time evolution (the non-equilibrium is expressed by the word kinetics) of chemical processes. (see Ch 1.6.2 and Ch 3.3)

Note that any Monte Carlo technique is a solver. The probability distribution has to be given by the physics/chemistry model. Monte Carlo solvers are described in more detail in Ch. 5.1.

2.4. Atomistic spin models

2.4.1 Deterministics spin models

Spin models are used to describe magnetic material properties. A spin here normally represents the magnetic moment of an atom, the energy of which is typically parameterized within a Heisenberg formalism, though even relativistic interactions, like Dzyaloshinskii-Moriyam interactions or anisotropies can be taken into account. The fact that magnetic structures are described on an atomic level allows for an investigation of ferromagnets as well as ferrimagnets and antiferromagnets or even heterostructures composed of different materials. In the classical limit the equation of motion (PE) is the Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation describes the spin precession that follows from Heisenberg’s equation of motion and its relaxation into an equilibrium direction via a damping term (either after Landau and Lifshitz or after Gilbert) with a corresponding damping parameter (MR). Though the LLG equation is partly phenomenological this approach turns out to be very successful.

2.4.2 Langevin Dynamic method for magnetic spin systems

The Landau-Lifshitz-Gilbert equation is an equation used to solve time-dependent micromagnetic problems. When augmented by a stochastic term describing thermal fluctuations as random fields (a statistical approach), the LLG equation is converted into the Langevin equation (PE) of the problem. Langevin Dynamics (LD) is the principal method for dynamic models of atomistic and mesoscopic spin systems at non-zero temperature. It allows for the calculation of thermal equilibrium and non-equilibrium properties of magnetic systems where the heatbath can be described by phononic or electronic degrees of freedom. With that approach equilibrium

properties like magnetic phase transitions can be described and investigated as well as ultra fast phenomena like optically induced switching events. The properties of the random field, whose precise form is given by the MR, are determined via the fluctuation-dissipation theorem. Following this approach the random field values are determined by a correlator dependent on the damping constant representing the coupling of the spin system to the heat bath, and also the magnitude of the spin. LD is used on two lengthscales. It was first introduced to model temperature dependent properties in the mesoscopic formalism (micromagnetics see Ch 3.4) and later to atomistic spin models. In using LD it is necessary to ensure that the time integration follows Stratonovich calculus, which is generally achieved using the Heun integration scheme, although normalization of the spin after each timestep fulfills this basic requirement.

2.5 Statistical transport model at atomistic level

The same statistical methodology that can be used to simulate electronic transport (Ch 1.6) can be adapted to simulate transport of atoms (transport at atomistic level). This can again be used for diffusion or percolation phenomena.

In physics, specifically non-equilibrium statistical mechanics, the Boltzmann equation (or Boltzmann Transport Equation (BTE)), the PE, describes the statistical behaviour of a fluid not in thermodynamic equilibrium, i.e. when there are temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random (and biased) transport of particles..The equation expresses the probability that a number of particles all occupy a very small region of space centered at the tip of the position vector, and have very nearly equal small changes in momenta from a momentum vector, at an instant of time. The set of all possible positions and momenta is called the phase space of the system. In the equation there is a collision term. It is a statistical term representing the particle collisions, and requires knowledge of the statistics the particles obey, like the Maxwell-Boltzmann, Fermi-Dirac or Bose-Einstein distributions (MR).

The probabilistic Boltzmann equation can be used to derive the fluid dynamic conservation laws for mass, charge, momentum and energy when the results are averaged into values for a continuum. In Ch 4 the continuum equivalent (Navier–Stokes, Nernst-Planck and there approximations diffusion, diffusion and convection (advection) equations for scalar tansport will be discussed.

2.6 Atomistic phonon-based models (Boltzmann Transport Equation)

Heat transport in periodic systems of atoms is explained through the dynamics of phonons. Phonons are entities with dual wave/particle characteristics arising in the quantum description of the field of atomic vibrations in such an ordered system, much in the same way as photons arise from a quantum description of the electromagnetic field. They are characterised by their energy (frequency), their displacement pattern (polarisation vector) and propagation direction.

The equilibrium arrangement of atoms and the properties of these springs determine the phonon spectrum of a particular material. The model is thus an atomistic model (entity). The solvers for atomistic and mesoscopic phonon models are identical (much like MD and CGMD are analogous), but the material problem to be solved is essentially different and this guides the classification of the models.

In a typical semiconductor crystal the phonon wavelength stretches over 2 to 1000 atoms. The dominant phonon wavelength in Si is 1.4 nm (10-9 meters) at T=300 K or 4 μm at T=0.1 K and the distance between atoms in a bulk Si crystal is 2.22 angstroms (10-10 meters). Hence, phonons are a phenomenon happening in the mesoscale. Nevertheless, these models are not mesoscopic, as mesoscopic models deal with movements of entities in which several atoms remain frozen with respect to each other. In Ch 3.5 mesoscopic phonon models are described that consider vibrations of nanoparticles/molecules (with the internal degrees of freedom inside the molecule frozen).

Deviations from the harmonic approximation come from a variety of factors: impurities, imperfections, intrinsic anharmonicities, surface effects, alloy disorder and so on and so forth. Such deviations limit heat transport by phonons as phonons can only be sustained in materials with a homogeneous lattice. The way phonons are perturbed by inhomogeneitites (defects) comprising more-than-one-atom is described in chapter Ch 3.5 about mesoscopic models. Considered together, the phonon spectrum and all sources of anharmonicities control familiar macroscopic variables like the thermal conductivity.

Examples of other properties calculable from knowledge of the phonon spectrum include the entropy, specific heat, macroscopic elastic coefficients, Raman and Ir spectra, and the speed of sound. Electron-phonon interaction is of critical importance for charge transport in solids, and is even an important factor in determining electronic structure in materials like diamond.

"Phonon spectra can be computed from a Fourier analysis of molecular dynamics trajectories or by characterizing the linear response of the system to periodic perturbations"

A perturbation such as a temperature gradient can propel phonons out of thermodynamical equilibrium. An important tool for studying out-of-equilibrium phonons is the Boltzmann Transport Equation (BTE) which is the PE. The BTE deals with the space and time evolution of the statistical distribution of phonons over their possible states, while this evolution is driven by advection and scattering. Due to the wide applicability of this equation - originally designed for particles in a gas and later adapted to phonons by Peierls - it can go by many names, including advection-diffusion equation, drift-diffusion equation and general scalar transport equation. It is thus necessary to state whether the phenomena are modelled by an equation for electrons, atoms, particles or continuum in finite volumes.

Many different approximations have been devised for use depending on the context, from homogeneous materials to inhomogeneities with sizes from the angstrom to the µm, from the static case to the high-frequency regime, etc. Worthy of note is the relaxation time approximation (RTA) which greatly simplifies the scattering term by considering that the populations of each phonon mode relax to equilibrium with a single characteristic time scale. Methods for solving the BTE can be either deterministic (iterative solution or specialized finite element solvers) or stochastic (direct simulation and variance reduced Monte Carlo).

Prior to solving the BTE, the elements of phonon dynamics in the material under study must be known (MR). Ideally this knowledge would come in the form of phonon spectra and a full description of anharmonicites; however, when operating under the RTA, phonon spectra and a set of relaxation times can suffice. Even though traditionally semiempirical parameterizations have often been used, nowadays this connects phonon-based models with other classes of models. Specifically, combinations of electronic DFT with the BTE have demonstrated a large predictive power. Other sources of information about phonons include ab-initio and classical molecular dynamics.

For historical reasons, "lattice dynamics" is the name given to the study of the physics governing the motion of ordered lattices, and in particular particularly the quantum mechanics of phonons.

Note that “lattice dynamics” is the generic name for the physics governing the motion of lattices, and particularly the quantum mechanics of phonons. This should not be confused with structural mechanics models (Ch 4.1) or the solvers Lattice Automata or Lattice Boltzmann see (Ch 5.1)

Chapter 3 Mesoscopic (particle) models

Mesoscopic models are (approximated) physics/chemistry equations describing the behaviour of entities like nanoparticles, grains, agglomerates, large bio-molecules or macrospins. These particles are considered to be frozen, and the detail inside is not resolved. The models are e.g. applied to beads consisting of 106 up to unlimited number of atoms, particles with length scales of 10nm-mm and the phenomenon could have timescales of ms-s. The length scale of the entity does not determine the type of model, if the inside of te entity is not resolved it is a mesoscopic model!

Molecular models, if they group more than one atom together in an entity, belong to this class of models describing the behaviour by a physics or chemistry equation (PE). For example, in order to speed up the calculations, in certain cases certain atoms may be combined and considered as one entity: a single particle or bead. These are called united-atom force fields and some atoms, like hydrogen and carbon atoms in methyl and methylene groups, are treated as a single unit. This approach has been extended into general mesoscopic considerations where grouping of larger atomic moieties are made to simulate larger systems for longer times and this is treated in this chapter. These mesoscopic models need as input Materials Relations (MR), which give the description of forces between the particles. Potentials and force fields for mesoscopic interactions are defined in an analogous way as for atomistic potentials (see introduction to Ch. 2).Their output is the position and velocity of the entities. The macroscopic bulk observable properties of materials are given by conformational sampling relating the calculated positions and velocities with pressure, temperature, density and free energies.

Also micro-magnetics is classified in this group (Ch 3.4) as it describes a group of coupled spins as one macrospin. Even if the physics of many models may be similar to the ones already discussed and doesn't need to be repeated here, some implications and unique aspects of mesoscopic models will be highlighted in this Chapter. Also DFT for molecules (Ch 3.1) and phonon models for molecules/particles (Ch 3.5) are described.

Mesoscopic and mesoscale Mesoscopic models are categorised into one class based on the type of entity they describe. This is not necessarily directly related to the size of the application domain the model can simulate. When the application domain is of nm size, we say that the model is applied to the meso-scale. We strictly classify models according to the entity described, not according to the size of the application and thus warn the reader for the different way in which words can be used.

Note that in micromechanics and in materials engineering in general the term "mesoscale modelling" is used for a continuum model applied to an application domain of nm-mm lengthscale. We want to stress that this use of the word relates to the size of the application domain, while the model remains continuum.

Fig.3.1 Number of FP7 projects that used one of the main types of mesoscopic models treated here.

3.1 Mesoscopic Classical Density Functional Theory and Dynamic Density Functional Theory

Classical Density Functional Theory (DFT) with the Kohn Sham equations as PE (see Ch 1.2) can also be used to describe the behaviour of mesoscopic entities using specially defined classical potentials.

In mesoscopic classical DFT, the forces acting between parts of molecules (e.g. segments of polymer chains), molecules, groups of molecules or grains particles (these mesoscopic entities are further on called "particles") are described by an external (effective) free energy potential (MR) which is a unique functional of the particle density profiles. As in the atomistic equivalent, the modelling challenge is to formulate approximate density functionals for with complex shapes and internal degrees of freedom.

Also Dynamic DFT can be expanded to mesoscopic versions.

3.2. Coarse-Grained Molecular Dynamics and Dissipative Particle Dynamics

3.2.1 Coarse-Grained Molecular Dynamics

Coarse-Grained Molecular Dynamics (CG-MD) is a particular kind of classical (deterministic) molecular dynamics where the entity whose behaviour is described is a group of atoms forming a large single unit, also called pseudo-atom (the entity). The behaviour is decribed by Newton Equations (PE) a particular force field (the physics equation of the model) whose precise form is given in a MR.

The simplest form of coarse-graining is the "united atom" (sometimes called "extended atom") and was used in most early MD simulations of proteins, lipids and nucleic acids. For example, instead of treating all four atoms of a CH3 methyl group explicitly (or all three atoms of CH2 methylene group), one represents the whole group with a single pseudo-atom. This pseudo-atom must, of course, be properly parameterized so that its van der Waals interactions with other groups have the proper distance-dependence. Similar considerations apply to the bonds, angles, and torsions in which the pseudo-atom participates. In this kind of united atom representation, one typically eliminates all explicit hydrogen atoms except those that have the capability to participate in hydrogen bonds ("polar hydrogens"). This approximation can provide substantial savings in computer time as coarse-grained models can provide a simpler representation of nucleotides and acids which are large molecular units for the simulation of larger systems: DNA/RNA strands, long chain polymer, membrane lipids and proteins.

The modelling challenge is in the calculation of the forces, in the determination of the pseudo- atoms charge distribution and in the parametrisation of these coarser-grained potentials.

3.2.2 Dissipative Particle Dynamics (DPD)

The Newton equation can also be applied to beads with a stochastic Force Field. This model is called the Dissipative Particle Dynamics (DPD). It is a stochastic Lagrangian model (PE) technique describing a set of beads (entity) moving in continuous space and discrete time. In the DPD model, a bead may represent many atoms, whole molecules or even fluid regions. The forces between the beads consists of simplified pairwise dissipative and random forces (MR), so as to conserve momentum locally and ensure correct hydrodynamic behaviour (model). The model is used to simulate the dynamic and rheological properties of fluids at the mesoscale. DPD forces are parametrized in order to recover macroscopic properties, while CGMD forces are parametrized in order to reproduce the free energy surface of a reference MD (all-atom) simulation.

3.3 Statistical Mechanics mesoscopic models

Statistical models based on the theory discussed before (see Ch 1.6 and Ch. 2.3) can also be used to describe entities like nanoparticles and grains. It describes the motions of the entities as stochastic (not deterministic). These models can be used to describe diffusion and percolation at the mesoscale and using conformational sampling also thermodynamic properties are derived. Statistical theories are also used in chemistry by describing the reaction between molecules (mesoscopic entities). These models then form part of the model workflow used in "microkinetic". The statistical models described in Ch. 2.3 together with their solvers (MC for static equilibrium situations and non-equilibrium/time evolution) can also be applied to mesoscopic entities. Using statistical mechanics and thermodynamics the Arrhenius or Eyring relations for the reaction rates can be derived. These relations are used as MR in the Law of Mass Action models (see

Ch_4.5) with the value of the activation energy appearing in this MR calculated with electronic models like DFT. More involve approaches use a workflow that could encompass MD to get the structure of the molecules or the surface where most reactions take place. Transition states (“rare” events for the reaction to occur) are identified on the potential energy surfaces (e.g. determined by electronic DFT or MD) to get an estimate of the energy barriers/free energy differences. The progress of a reaction is followed on a potential energy surface. The rate of a reaction is determined by the motion of the system through the col or saddle points, which is caused by vibrational modes responsible for the conversion of an activated complex to the product. The study hereof is also called vibrational analysis. When the transition states are identified and thus the preferred reaction path, Transition State Theory (TST) allows computing the reaction rate constant. This is faster than "manipulated MD" (doing thermo-dynamical integration methods on MD results). Both these TST-based and MD approaches are based on the statistical mechanism equations (PE) expressing reaction equilibrium and rates in terms of the statistical distribution of molecular velocities given by specific MR. Also this probability density function can be used in the kMC approach.

3.4 Micromagnetic models

The underlying assumption in micromagnetics is that the spins at electronic and atomic level are coupled to one "macro-spin" (entity). The interactions between the macrospins are described by several competing energy terms (whose precise form is given in the MR). Exchange interaction (responsible for the very existence of ferro- and antiferromagnetic materials) ‘attempts’ to align adjacent magnetic moments (in ferromagnetic materials) or antiparallel (in antiferromagnetic materials). Magnetodipolar contribution accounts for the energy of a magnetic moment in the (dipolar) field created by all other moments of a magnetic body. Anisotropy energy is mainly due to the spin-orbit interaction and the anisotropy of the crystal lattice: it is low when the magnetic moments are aligned along a particular crystallographic direction. Zeeman energy describes the interaction between magnetic moments and external magnetic field and is at its lowest when the moments lie parallel to this external field. The competition of these interactions under different conditions is responsible for the overall behavior of a magnet.

Since the equilibrium arrangement of magnetic moments (“magnetisation configuration”) is usually (but not always!) the one in which the total magnetic energy is lowest, the sum of these four energy terms will ‘attempt’ to become as small as possible (with some energy terms decreasing at the expense of the others), yielding complex physical interactions.

A form of the Landau-Lifshitz-Gilbert equation (PE) is used to describe time-dependent micromagnetic problems. An essential merit of the micromagnetic theory concerns the answer to the question, how the effective magnetic field depends on the relevant interactions, namely, (i), on the exchange interaction; (ii), on the so-called anisotropy interaction; (iii), on the magnetic

dipole-dipole interaction creating the internal field; and, (iv), on the external field (the so-called "Zeeman field").

Usually the exchange interaction and the magnetic dipole-dipole interaction term play the dominating role, usually a competing one. In particular: due to the last term the effective field is a nonlocal function of the magnetisation, i.e. although the Landau-Lifshitz-Gilbert equation looks relatively harmless, one is actually dealing with a complicated nonlinear set of integro-differential equations.

The necessary material constants can either come from measurements or from electron-spin and atomistic ab-initio models (10-10m). These electronic models can e.g. give the lattice distortions near interfaces and compute the anisotropy as function of lattice constant. They also give the reversal curves.

The micromagnetic models are used to describe the magnetics at the nanoscale in domains (which have an magnitude of the order of 10-6m) nucleation of domains, pinning and expansion behavior of magnetic domains and wall motion.Input to the model can be grain size, shape, boundary type and boundary phases. Outcome will be the macroscopic properties coercivity, remanence, max energy product and thermal stability (thermal dependance of coercivity).

3.5 Mesoscopic phonon models (Boltzmann Transport Equation)

Phonon models that describe how “atomistic” phonons scatter on defects consisting of more than on atom are classified as mesoscopic. The models that describe how frozen molecules in an ordered system vibrate also fall in this category. These models are used when the atomistic phonons have - too many degree of freedom or - fast-oscillating degrees of freedom (e.g., a C-H bond) and basically amount to a cut-off in the phonon spectrum. The solvers for atomistic and mesoscopic phonon models are identical (much like MD and CGMD are analogous), and the reader is referred to Ch 2.6.

Chapter 4 Continuum modelling of materials Parts of this text have been taken from Wikipedia

This chapter is concerned with the designing of materials with desired macroscale (nm-mm) properties. Modeling for materials design is about investigation of relations between chemical composition, microstructure and effective properties.

Materials, such as solids, liquids and gases, are composed of molecules separated by empty space. Physical and chemical processes at the smallest scale are modeled by electronic, atomistic or mesoscopic models as addressed in Ch 1 and Ch 2. However, certain physical phenomena can be modeled assuming the materials exist as a continuum, meaning the matter in the body is continuously distributed and fills the entire region of space it occupies. Many physical phenomena are multi-scale in nature and researchers must look to multi-scale methods that couple electronic, atomistic, mesoscopic and continuum simulations. In this Chapter continuum models (approximated physics/chemistry equations) describing the behaviour of continuum unit cells will be presented.

The entity in a continuum model is the continuum material. Numerically this is divided into finite volumes/elements/cells. Sometimes we will take a short-cut and instead of saying that the continuum material is the entity we will call the finite volume/entity/cell the entity.The length scale for the (numerical) entity (unit cell) modelled in continuum models has two limits: the lower limit is related to the notion "continuum" and this lower limit is so big that even heterogeneous materials can be considered to vary in a continuous fashion; the upper limit is related to the requirement that the model adequately describes reality and this upper limit is thus smaller than any spatial variation in material properties. When the spatial variation length scales are not much greater than that of inter-atomic distances or when a continuum of a finer resolution is to be established statistical mechanics is used and modellers employ statistical volume elements and random continuum fields linking continuum mechanics to statistical mechanics. Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

In continuum modeling it is possible to apply a chain of modelling that uses the same physics and chemistry equations applied to different scales. Often the application of models to a smaller scale is called "micro-modeling" and the results of these models are, after being post-processed, fed into "macro-models" in the form of new macroscopic constitutive equations (MR).

This chapter will deal with 4.1 Solid Mechanics 4.2 Fluid Mechanics 4.3 Heat Flow and Thermo-mechanical behaviour 4.4 Continuum Thermodynamics and Phase Field models 4.5 Chemistry reaction (continuum kinetic) models 4.6 Electromagnetism (including optics, magnetics, electrical) 4.7 Process and device modelling (being an application of the above)

The text has been rigorously organised along the concepts: 1. Physics and chemistry equations (often the conservation equations) 2. Materials relation: specification of the particular material in parameters, constitutive equations and constraints

Fig.4.1 Number of FP7 projects that used one of the seven main types of continuum models

Elasticity and visco-elasticity Solid mechanics Describes materials that return to their rest The study of the shape after an applied stress. Continuum physics of continuous mechanics materials with a Plasticity Rheology defined rest shape. Describes materials that The study of The study of permanently deform after materials with the physics of a sufficient applied stress. both solid and continuous fluid Fluid mechanics materials Non-Newtonian fluids characteristics. The study of the

physics of continuous materials which take Newtonian fluids the shape of their container.

Continuum Thermodynamics

The study of energy conversion

Conservation equations (Phyics Equations PE)

Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy are including the physical principles that govern the mechanical response of a continuous medium. These laws allow us to write mathematical equations of physical quantities like displacements, velocities, temperature, stresses and strains in mechanical systems. The solution to the equations, once closed with a constitutive equation, represents the material behaviour. The equations of motion and equilibrium e.g. are derived from the fundamental principle of conservation of linear momentum. Heat flow is derived from the energy conservation law.

Constitutive equations (Materials Relations MR)

Information about the particular material studied and its response to external agents (e.g. forces fields) is added through a constitutive equation, expressing that the material is homogeneous or inhomogeneous, isotropic or anisotropic, linear or nonlinear or thermo-elastic or that the material shows plasticity, visco-elasticity, or visco-plasticity. In more general terms the constitutive equations relate the primary field variables (like density, temperature, displacement and velocity) to secondary field variables (energy, heat and stress). The detail employed may be macroscopic or microscopic, depending upon the level necessary to the problem under scrutiny.

These MRs might be derived from experiments or they might be "phenomenological". The relations might also be derived from theory, models applied to a finer scale whose output is processed into a formula. The theoretical derivation of a material's constitutive equations is a common, important, and sometimes difficult task in theoretical materials science and includes physics considerations.

Phenomenology goes beyond purely empirical data as it involves a certain concept. A phenomenological constitutive equation is not completely based on physical mechanisms responsible for the behaviour.

Constitutive equations can take the form of simple formulas like Hooke's law, complicated formulas like REAFF force fields, a system of equations (of algebraic, differential or integral type) with a number of parameters (or functions) to be identified from experiments.

Kinematic constraints

The model equations are the conservation equations (PE). Material information enters the system via constitutive equations (MR) and material information can also enter via constraints on the solution (and this physics information is thus considered to be part of the MR). In statistical approaches kinematic constraints express the limits on the movement. This can be due to the properties of the material like incompressibility, but more frequently kinematic constraints reflect the requirement of internal kinematic compatibility of motion of the continuum (e.g. across boundaries between different constituents of a heterogeneous material) or compatibility with external boundary conditions of kinematic type (e.g. periodic boundary conditions). The internal or external constraints are independent of the properties of the material and constitute a part of the formulation of a micromechanical model of the material.

Geometric changes in a continuous medium (in static or dynamic equilibrium under mechanical and/or thermal forces) are expressed by the conservation laws, constitutive equations and kinematic constraints considered jointly. The solution describes how each little part of a material moves and where it will go and how large a space will be occupied in a certain place and time. (People involved in continuum mechanics call this solution “the kinematic equations”.) Kinematic behavior as expressed in the solution is often a necessary basis for the formulation of constitutive equations for models applied to larger scales. Also the temperature gradient can be part of this description.

4.1 Solid Mechanics

Solid mechanics is the branch of mechanics, that is concerned with properties and behavior of solid matter under external actions like external forces, temperature changes, applied displacements.

Contact mechanics is the study of deformation and behaviour of bodies that touch each other and may undergo relative motion and contact phenomena such as friction, lubrication, wear, heat transfer.

Modeling of materials behavior under service conditions is about predicting materials behavior under e.g. mechanical (static or dynamic) loading, thermo-mechanical loading, chemically aggressive environment (e.g. all types of corrosion) and combinations thereof.

The PE can be a simple equation relating the displacement to the force via the stiffness matrix (MR) (Hooke’s law).

In continuum modeling also a chain of modeling can be applied that uses the same physics and chemistry equations applied to different scales but with different MR. When continuum mechanics is applied to the smaller (nm and µm) scale it is called "continuum micro-mechanics" (note this name refers to the dimensions of the sample only) and the larger scale case is called "macro- mechanics".

Micromechanics (continuum solid mechanics applied to microscale) Heterogeneous materials, such as composites, solid foams, poly-crystals and human intervertebral discs, consist of clearly distinguishable constituents (or phases) that show different mechanical and physical material properties. Micromechanics of materials predict the response of the heterogeneous material on the basis of the geometries and properties of the individual phases. The results are then "homogenised" to describe the properties and behaviour of a heterogeneous material. Such properties and behaviour are often difficult to measure experimentally, and micromechanics models can avoid expensive tests that would involve a large number of permutations of constituent material combinations; fibre and particle volume fractions; fibre and particle arrangements and processing histories.

Micromechanics of materials can also evaluate the local (stress and strain) fields in the phases for given macroscopic load states, phase properties, and phase geometries. Such knowledge is especially important in understanding and describing material damage and failure.

Macro-mechanics (continuum solid mechanics applied to macroscale)

The same continuum mechanics physics equations (conservation equations) can be applied to larger (macro) scales and this is called "continuum macro-mechanics". The constitutive equations can either be derived by postprocessing results of micromechanics simulations or experimental or phenomenological constitutive equations can be used.

Materials Relations in solid mechanics

A material has a rest shape and its shape departs away from the rest shape due to stress (force per unit area). The amount of departure from rest shape is called deformation; the proportion of deformation to original size is called strain. The strain induces stresses in the material (and vice versa) and how they exactly do this in a particular material is expressed in the constitutive equations for solid mechanics relating the strain to the stress.

Here we discuss MR used in continuum models that describe how a solid responds to an applied stress. The relations used in macromechanics are often found by postprocessing of continuum solid mechanics applied to microscale. The relations used in micromechanics are often found by post processing of discrete modelling.

This chapter does not cover MR expressing non-mechanical effects. Among them, heat conduction and temperature effects play an important role in a number of applications. Ch 4.3 treats briefly this issue.

1. Elastically – If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity. This region of deformation is known as the linearly elastic region. When an applied stress is removed, the material returns to its un-deformed state, i.e. no permanent strain remains after unloading. Linearly elastic materials, those that deform proportionally to the applied load, can be described by the linear elasticity constitutive equations such as Hooke's law. When the strain becomes larger the material might react non-linearly and this is called hyper-elasticity.

2. Viscoelastically – These are materials that behave elastically, but also have damping: when the stress is applied and removed, work has to be done against the damping effects and is converted in heat within the material resulting in a hysteresis loop in the stress–strain curve. This implies that the material response is time dependent or rate sensitive. This is modeled by constitutive equations resulting from the superposition of the elastic (spring) and viscous (dashpot) models, which can be joined in series (Maxwell solid) or in parallel (Kelvin solid) or as various combinations of spring-dashpot assemblies.

3. Plastically – Materials that behave elastically generally do so when the applied stress is less than a yield value. When the stress is greater than the yield stress, the material behaves plastically and does not return to its previous state. That is, deformation that occurs after yield is permanent. This is modeled by constitutive equations in which the total strain is decomposed into elastic and plastic part. The onset of plastic flow is characterised by a yield condition and the elastic strains are related to the stresses by Hooke’s law, whereas the constitutive equation for the plastic strain increment (flow rule) is obtained from the plastic potential, often assumed the same as the yield function. The plastic potential specifies the components (to within a multiplier) and the direction of the vector of plastic strain increment (exterior normal of the flow surface) through the system of partial differential equations.

4. Rheologically - Rheology is the study of the flow of ''soft solids' or solids which respond plastically rather than deforming elastically in response to an applied force (see also Ch 4.2). It applies to substances which have a complex molecular structure, such as muds, sludges, suspensions, polymers and other glass formers (e.g. silicates), as well as many foods and additives, bodily fluids (e.g. blood) and other biological materials. This is modeled by constitutive equations of non-Newtonian fluid mechanics or linear or nonlinear viscoelasticity and plasticity.

5. Fatigue/damage -In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. If the loads are above a certain threshold, microscopic cracks will begin to form. In homogeneous materials, like metals, eventually a crack will reach a critical size, and the structure will suddenly fracture. In heterogeneous materials fatigue damage can be distributed and material can still bear load notwithstanding excessive micro-cracking. The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets are therefore important to increase the fatigue strength of the structure. Fatigue can be modeled with the solid mechanics equations (the energy equations formulated to describe the energy balance which accounts for the stress transfer at a fine scale) complemented by MR (constitutive equations) for damage like Paris's or Goodman's rule. This system describes how so-called damage variables change under applied stress-strain state and give the change of the load-carrying ability (for example, material stiffness) with the changing damage variables.. The post-processed results can then be fed as MR into a mechanics model applied to macroscale. As for all phenomena it is the modeller who chooses how to model the physics and some extract damage information via applying criteria to the output of continuum models (thus via a post- processing operation). The onset of damage might be modelled with discrete models, which can then give a MR (constitutive equation) to micromechanics (continuum solid mechanics applied to nm scale).

6. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. In modern materials science, fracture mechanics is an important tool in finding materials and components with improved mechanical performance. Fracture mechanics is a typical multi-scale problem: the initial crack starts at a very small scale (having a very small process zone) and this might be modeled with atomistic models sprouting expressions for the atomistic driving force on a crack and the atomistic material resistance ro fracture. The propagation of the fracture can then be simulated with continuum solid mechanics

models at microscale sprouting a MR for the model applied to macroscale. The models are employed to predict the response of a structure under loading and its susceptibility to various failure modes may take into account various properties of the materials.

7. Creep In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of stresses. It occurs as a result of long term exposure to high levels of stress that are below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods, and near melting point. Creep always increases with temperature. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function. But moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking. The rate of this deformation is a function of the material properties, exposure time, exposure temperature and the applied structural load. Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long- term stress. Creep is a "time-dependent" deformation. The constitutive equations for creep are those of the plastic flow (cf. above) with the concept of yield condition and associated flow rule or a creep potential function different than the yield function.

8. Wear In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface. Wear is related to interactions between surfaces and more specifically the removal and deformation of material on a surface as a result of mechanical action of the opposite surface (see also chemical diffusion under CFD in Ch 4.2) Impulse wear e.g. can be described by a constitutive equations based on a synthesized average on the energy transport between two travelling solids in opposite converging contact. The micro-scale calculations are performed to obtain the averaged activation parameter for the oxidation process. The macro-scale calculations are done to explicitly model wear and oxidation. But the time dependent parameters needed to do that are obtained from micro-scale calculation. The temperature distribution around a single asperity can reach very high values. This might be lost in homogenisation as on the macro level, the averaged temperature in the unit cell containing the asperity, can be well below the oxidation threshold. Thus micro scale calculations are needed to obtain the exact temperature distribution around the asperity. To do that standard heat conduction models can be applied with the heat flux acting on the upper surface of the conical asperity. Having this micro-scale temperature, an averaged activation factor for oxidation can be calculated, which allows the oxidation to take place for relatively low temperatures on the macro scale.

9. Corrosion (oxidation) is to be included in wear phenomena, when the damage is amplified and performed by chemical reactions rather than mechanical action. The constitutive equations can be chemical, but can also be purely phenomenological without any account of the underlying chemical process. In such models the rate of change of mass of the corrosion product (oxide) is related to temperature and time based on experimentally observed relations from thermo- gravimetric analysis (TGA). Chemical properties of the oxide layer are considered through parameters in the phenomenological function approximating results of the TGA.

There is also the option to couple the solid mechanics equation to full-fledged chemistry reaction equations (Ch 4.5); this is the choice of the modeller!

10. Other chemical reactions No specific comments are made.

Model development in solid mechanics: new MR

Model development for solid mechanics usually addresses the MR. These come from data mining in simulated or experimental databases (See Ch 6.3).

4.2 Fluid Mechanics

Fluid mechanics is the study of the motion of fluids due to forces. (Fluids include liquids, gases, and plasmas if sufficiently dense to be a continuum). The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). These can be reworked to give the Navier–Stokes equations PE, named after Claude-Louis Navier and George Gabriel Stokes, which are a non-linear set of differential equations that describe the flow of a fluid whose stress depends linearly on velocity gradients and pressure. The solution to a fluid dynamics problem typically involves solving these equations calculating speed, pressure, density and temperature.

Magnetohydrodynamics Flow of electrically conducting fluids (e.g. fluids including plasmas, liquid metals, and salt water) in electromagnetic fields need to be described by coupled Navier-Stokes equations and Maxwell's equations of electromagnetism, which need to be solved simultaneously. This part of fluid dynamics is called magneto-hydrodynamics.

Different Flow models

In contrast to solid mechanics, modelling efforts in computational fluid dynamics often simplify the principle physical equations (PE). They do this in a number of ways, and these approximations (PE) will be discussed.

Drift-Diffusion

The simplest continuum model for diffusive mass transport is the differential equationdescribing the phenomena at macro scale by balancing diffusion and advection. A tightly coupled set of models consisting of the Drift-Diffusion equation, the Poisson equation and the continuity equation is often used to describe the functioning of electronic devices including OLEDS.

Compressible vs incompressible flow

All fluids are compressible to some extent, that is, changes in pressure or temperature will result in changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modeled as an incompressible flow. Otherwise the more general compressible flow equations must be used.

Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.

Viscous vs inviscid flow

Viscous problems are those in which fluid friction has significant effects on the fluid motion. The Reynolds number, which is a ratio between inertial and viscous forces, can be used to evaluate whether viscous or inviscid equations are appropriate to the problem.

Stokes flow is flow at very low Reynolds numbers, Re<<1, such that inertial forces can be neglected compared to viscous forces. On the contrary, high Reynolds numbers indicate that the inertial forces are more significant than the viscous (friction) forces. Therefore, one may assume the flow to be an inviscid flow, an approximation in which viscosity is neglected completely, compared to inertial terms. This idea can work fairly well when the Reynolds number is high. However, certain problems, such as those involving solid boundaries, may require that the viscosity be included. Viscosity often cannot be neglected near solid boundaries because the no-slip condition can generate a thin region of large strain rate (known as boundary layer) which enhances the effect of even a small amount of viscosity, and thus generating vorticity. The standard equations of inviscid flow are the Euler equations. Another often used model, especially in computational fluid dynamics, is to use the Euler equations away from the body and the boundary layer equations, which incorporates viscosity, in a region close to the body. The Euler equations can be integrated along a streamline to get Bernoulli's equation. When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field. Such flows are called potential flows.

Laminar vs turbulent flow

Turbulence is flow with a high Reynolds number and is characterized by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds decomposition, in which the flow is broken down into the sum of an average component and a perturbation component. Equations for the perturbation component are subject to different models (k-eps, second order models etc).

Newtonian vs non-Newtonian fluids and Rheology

If fluids can be characterized by a single coefficient of viscosity for a specific temperature they are called Newtonian fluids. Although this viscosity will change with temperature, it does not change with the flow rate or strain rate. Only a small group of fluids exhibit such constant viscosity. For a large class of fluids, the viscosity change with the strain rate (or relative velocity of flow) and are called non-Newtonian fluids. The behaviour of non-Newtonian fluids is described by rheology. These materials include sticky liquids such as latex, honey, and lubricants. For example, ketchup can have its viscosity reduced by shaking (or other forms of mechanical agitation, where the relative movement of different layers in the material actually causes the reduction in viscosity) but water cannot. Ketchup is a shear thinning material, as an increase in relative velocity caused a reduction in viscosity, while some other non-Newtonian materials show the opposite behaviour: viscosity going up with relative deformation, which is called shear thickening or dilatant materials. Rheology is the study non Newtonian-fluids or otherwise describes as the flow of matter, primarily in the liquid state, but also as 'soft solids' or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. It applies to substances which have a complex molecular structure, such as muds, sludges, suspensions, polymers and other glass formers (e.g. silicates), as well as many foods and additives, bodily fluids (e.g. blood) and other biological materials. Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (e.g., the orientation and elongation of polymer molecules), and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity.

Two phase flows Without the wish to be complete it should be stated that many flows need their own models like e.g. two-phase flows where interactions between the phases have to be modeled.

Materials Relations (MR) for flows

Besides modeling of the fundamental physics equations (PE), there are also different constitutive equations in use and some projects have developed new ones.

Constitutive equation for the diffusion of chemical species Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). This constitutive equation is used to close the conservation of mass (flow) equations reduced to diffusion only. Diffusion of interstitial atoms due to chemical potential gradients can be described by an extended Fick’s diffusion equation with added terms due to chemical potential gradients (stress and temperature).The Nernst–Planck equation is a constitutive equation used to close the conservation of mass equations to describe the diffusion of charged chemical species in a fluid in an electric field. It relates the flux of ions under the influence of both an ionic concentration gradient and an electric field. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces. If the diffusing particles are themselves charged they influence the electric field on moving. Hence the Nernst–Planck equation is applied in describing the ion-exchange kinetics. Please see also the diffusion equation described at atomistic level.

Constitutive equation for the poro-elastic flow When fluids are streaming through a porous medium a combination of solid mechanics and fluid mechanics is to be applied. Two mechanisms play a key role in this interaction (i) an increase of pore pressure induces a dilation of the porous solid, and (ii) compression of the solid causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. The fluid transport in the interstitial space can be described by the well-known Darcy’s law, which is an empirical (phenomenologically) derived constitutive equation that describes the flow of a fluid through a porous medium (see also Ch 4.2). Darcy's law works with variables averaged over several pore-widths. It can also be derived from Navier-Stokes equations by dropping the inertial terms, so this is an example of a constitutive equation being derived from the physics equations. Darcy's law is a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid and the pressure drop over a given distance.

Scales (micro and macro fluidics)

Also in this part of continuum mechanics, constitutive equations can be created for the behaviour at different scales and also in this discipline a chain of flow models applied to different scales might be used. State-of-the-art models for flow at the smallest scale are using the so called "atomistic" finite elements solverwhich can be applied to length scales of 100 nm – mm and timescale of ms to s. (This scale is called meso by electronic modellers and micro by continuum modelers.)

The calculated properties can be used as constitutive equations in the flow models applied to larger scales.

4.3 Heat Flow and Thermo-mechanical behaviour

On the crossing point of micromechanics and fluid dynamics there is the domain of heat flow and its influence on mechanical properties.

Heat flow

The conservation of energy equation contains the energy change due to heat flow. The first law of thermodynamics states that the change in internal energy ΔU of the system is equal to the amount of heat Q supplied to the system minus the amount of work W done by system on its surroundings.Heat transfer may take place due to conduction (also called diffusion), convection (energy taken away by the surroundings solids or fluids) or radiation (PE). The heat equation is an important partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time

Heat capacity and heat conductivity are parameters playing a roleand these can be modeled by different assumptions and in different MR (constitutive equations) might be used A MR for conductive heat flow is the Fourier's law that states that the heat flow is proportional to the temperature gradient. A MR for convective heat flow can be Newton's law of cooling.

Thermo-mechanics

Thermomechanics studies the properties of materials as they change with temperature. The materials might show a change of dimension (expressed in the calculated macroscopic thermal expansion coefficients) or of a mechanical property. The bonding in the material determines this response. Crystallinity and fillers introduce physical constraints to motion. Cross-linking between molecules will restrict the molecular response to temperature change since the degree of freedom for segmental motions is reduced as molecules become irreversibly linked.

A MR for radiative heat flow is the Stefan Boltmann's law.

The thermo-elastic constitutive equation defines a relationship between stress, strain and temperature, and thermal conductivity equation relates the heat flux density to temperature gradient. For anisotropic solids, both have to be written in a tensor form. Coefficients of these equations depend themselves of the temperature and represent thus material functions rather than constant parameters for a specified material. Other material functions determine temperature dependence of parameters in constitutive equations of plasticity, visco-plasticity and rheology. Such material functions are usually determined empirically.

4.4 Continuum Thermodynamics and Phase Field models

4.4.1 Thermodynamics

The two fundamental principles of thermodynamics are summarized in the first and second law of thermodynamics referring to conservation of energy and positive production of entropy, respectively.

Different types of energy are distinguished in thermodynamic models. The portion of the internal energy associated with the kinetic energies of the atoms/molecules (rotation and vibration of the atoms about the center of mass) is called sensible energy. The internal energy associated with the atomic bonds in a molecule is called chemical energy. Mutual potential energy of the atoms as they change their distance inside the molecules is part of the internal energy. Stresses in the material can be regarded as part of the internal energy. The energy associated with the phase –

change process related to the bonds between molecules/atoms and is called latent heat. Nuclear energy is not considered in NMP projects.

The second law – requiring a positive rate of entropy production in a closed system for any process - is probably explained best and easiest as the tendency of a system to relax towards the most probable state under given conditions. An instructive example are atoms of two species A and B being in a container (volume) being divided into two parts by a wall. All A atoms are in one part and all B atoms are in the other part. The entire container is at the same temperature, which is high enough that any bond energy between the atoms A-A, B-B and A-B can be neglected. Under these given conditions this system is in equilibrium. When removing the wall, the energy of the system is not changed, but the atoms will start to mix until they reach the most probable state – a homogeneous distribution of all A and B atoms in the entire volume.

Reduction of the temperature in this example then will make the interactions between the atoms become dominant and bound states of a number of atoms will form first as clusters and eventually as solid phases. Depending on the relative strength of the A-A, B-B and A-B bonds either a demixing or the formation of superstructures will occur. In case A-A and B-B bonds are stronger than A-B bonds regions of a phase containing only A elements and regions of a phase containing only B elements will from. In contrast, in case A-B bonds are stronger – an AB compound phase will form.

These two principles thus can be used to describe the equilibrium state of a system comprising a large number of interacting atoms ( which may be the same or different chemical elements) under given external conditions like e.g. temperature, pressure (or also electric/magnetic fields) and especially thermodynamics can describe the new equilibrium state being established when changing these external conditions.

Thermodynamics equations are often used as post processor. Data-mining operations fit these relations to the (experimental or simulated) data and rules are obtained for dependencies. The calculation by electronic or atomistic models is today possible for low temperatures and for simple systems, which only have few different chemical elements (see atomistic models). In the current state of the art, thermodynamic databases integrate the results obtained from theoretical calculations using discrete simulations and from experimental data (e.g. measurements of specific heat, heat capacity etc.). Collection and assessment of these data and subsequent decisions on exclusion or inclusion or modifications of the databases is a very difficult task requiring a fundamental understanding of the phenomena involved.

Thermodynamic equations (PE) can also be used to calculate a new physical system state. The equations rely on a description of the Gibbs energy as a function of external and internal system conditions (p, V, T, relative composition). This describes the equilibrium of the system under given conditions and the equations are used to study materials being processed. There are several types of equations available to describe the Gibbs Energy of a phase and how it changes as function of (T, p, V, relative composition). These relations in general are in the form of polynomials and other functional dependencies (e.g. sublattice model, ideal mixtures, Redlich- Kister polynomials). The parameters occurring in these equations (MR) the polynomial coefficients - have to be derived from other sources of knowledge (experimental, empirical or theoretical).

From the notion of the Gibbs energy a number of further thermodynamic entities (e.g. specific heat capacity, thermal expansion coefficient, latent heat of fusion, latent heat of vaporization, molar volume, density and many more) can be derived by applying their respective definition, which usually involves partial derivatives of the Gibbs energy.

From the Gibbs energy nucleation models and crystal growth models (PE) can be derived.

4.4.2 Phase Field models

Thermodynamic databases in general are limited to equilibrium data and can thus be used to predict equilibria and also metastable equilibria. Thermodynamics however does not provide any information about the time requested to reach the equilibrium and also no information about the spatial distribution of the phases. The challenge for modelling the microstructure thus is describing the kinetics of the relaxation process from non-equilibrium to equilibrium in a spatially resolved way (PE). Respective models – called phase field models and describing this relaxation processes are also derived from the basic principles of thermodynamics.

Phase Field models are a recent approach to address phenomena at small scales, like microstructure formation.

Microstructures The term “microstructure” is not uniquely defined. Typical perceptions are e.g. “what you see under the microscope” or “all defects in a material”. At the state of current knowledge a possible and meaningful definition would read: “All internal structural features in a Representative Volume Element (RVE) affecting the properties of the material”. In other words microstructure is a spatial distribution of elements/atoms and defects. Nature helps to reduce this very general description by the self-assembly of regular structures (crystals/phases/grains/molecules) allowing to treat thousands or even millions of atoms as a single object. Microstructure thus is an “arrangement of objects in a RVE”. The objects may be 1D, 2D or 3D like e.g. phases, grains, precipitates, defects, dislocations, nano-precipitates, atoms and much more. This definition at least comprises following phenomena: phases and phase boundaries (phase transformations), grains and grain boundaries (recrystallization, grain growth), precipitates, point defects, vacancies (diffusion, phase transformations), dislocations (crystal plasticity, recovery), crystal structure of the phases (defect properties), crystal orientation (anisotropy, texture), elemental distribution (chemical composition, segregation) and probably much more. It is important to note that microstructure is – besides the overall chemical composition - the state variable of material properties. There are no direct “Processing–Property relationships” but the relation goes via “Processing– Microstructure relationships” and “Microstructure– Property relationships”. Post processing of the phase fractions already allows for estimation of effective properties of the RVE e.g. by using volume averaging concepts. A next refinement of the microstructure description are distribution functions for the different objects e.g. grain size distributions or precipitate size distributions, orientation distribution functions etc. A number of current models refer to the calculation of such distribution functions and their evolution during processing. The microstructure can be characterised by objects: sizes, aspect ratios, positions, orientations and mutual arrangement of all individual objects in the microstructure i.e. the topology is described. The properties of materials follow from their crystal structures on an atomic (or Å) length scale and from their microstructure (i.e. “the arrangement of phases and defects”) on the nm-cm length scale. In a microstructure interfaces appear between phases. The equilibrium nature of microstructures can be interpreted by considering the phase diagram, which itself can be predicted by computational thermodynamics.

Phase Field models were originally developed to predict fundamental properties of extended defects, such as interface and critical nucleus, and the associated energy and nucleation and migration, whose chemical and structural inhomogeneity occurs at length scale usually between 1 and 100 nm. The coarse-grained phase field, subsequently developed to describe collective behaviours of "large" mesoscale assemblies, covers length scales up to mm for the heterogeneity during dendritic solidification, grain growth, domain coarsening and coalescence, and various phase transformations events. A large number of models for microstructure evolution exist for the different levels of detail. In the following some models for 2D/3D description and prediction of

microstructure topology (phase field models, phase field crystal models and crystal plasticity models) will be shortly addressed. These models can be applied up to mm in coarse-grained models, where the quantum physics meets the classical physics, or where systems are on the boundary between interacting and isolated systems

Phase field models are constructed to predict the microstructure formation in time and space. Microstructure formation in time and space during phase transitions can be calculated with these models if complemented by a diffusion equation. Note that thermodynamics does NOT comprise any information about structures as thermodynamics do not comprise time/length scales and this should be alleviated by these Phase Field models.

The evolution of the phases (solid, liquid) in a continuum model is described by a number of coupled differential equations (PE) which all can be derived from thermodynamic principles: energy conservation equations expressed as an equation for temperature, diffusion equations for all alloy elements concentration, and phase field equations for each of the phases describing the evolution of the local equilibrium state in the application area, often called RVE. Phi is describing the existence or non-existence of a specific phase at a point in space a time (e.g. phi=1 is solid, phi is 0 is liquid) under given external conditions (e.g. temperature)). Numerically this is described for the continuum material in "finite volume/elements also called “cells” (the entities).The continuum Phase-field equation for Phi contains a diffusion, stabilising and interface moving term.

These models have been extended to multi-phase field models at the end of the last century allowing the description of multicomponent, multiphase alloys as used in engineering applications. The conditions for the local stability of the phases are calculated e.g. on the basis of thermodynamic data and respective databases for all phases being present in the application area. These coupled equations for Phi, T and C and describe phase changes due to the temperature being different from the phase equilibrium temperature (which itself is – amongst others - defined by the local concentration conditions of all alloy elements). The dynamics of one or more order parameter (s), that is the evolution of the microstructure with time, are governed by set of non-linear partial differential equations (MR) (i.e. Cahn-Hilliard, time-dependent Ginzburg-Landau, and other Newtonian based dynamics) through a minimization of phenomenological free energy functional (or potential or driving force). This functional (potential) is expressing the influence of the Gibbs free energy (where thermodynamics plays its role), interfacial energy, elastic energy and other contributions executed by external fields including electrical, magnetic and applied stress fields, etc). In order to do so, the free energy functional is written in terms of the order parameters including composition and other fields (temperature, pressure, strain, electrical, magnetic, etc). Phase field models derive the potential "driving force" usually from the difference in Gibbs energy across the interface.

Application area “RVE”

The application area is often called RVE and to give just one example: numerically it is described by up to 100*100*100 cells (finite volumes) with a size ranging from 1 mm via 1 micron down to a few nanometers (1000 atoms) allowing the continuum view of for “solid” or “liquid” of the cell. The collective outcome of the simulation done for a number of interacting finite volume elements is called the "microstructure". This describes the morphology which in general is polycrystalline and polyphase. Thus the RVE/domain comprises different objects "grains" (typical diameter 20-50 micron) and precipitates (nms to microns) of different phases for mm^3 type RVEs. Together with the other results the output is called the "microstructure". Temperature, concentration of alloy elements ci or other fields like dislocation densities, stresses, orientations etc. may vary across the grains. There are phase-field models simulating nucleation and e.g. polymer crystallization at the nm scale.

Post-processing

In a first approximation these objects (found in the raw output) each have homogeneous properties (e.g. same concentration of alloy elements anywhere in the object), which may however change from object to object. In a further refinement down to full spatial resolution (e.g. down to a single voxel in a numerical representation or down to the continuum in real world) takes local variations inside the objects into account.

The highest level of detail comprises data for each voxel, which themselves have been simulated/ calculated considering the single voxel itself again as an RVE but at a much smaller scale. Examples for the latter are e.g. size distributions of nano-precipitates within a grain.

Phase field models calculate how many grains are formed. The grains are thus the output, and not the entities in mesoscopic models, whose behaviour as frozen particles is described.

Crystal-plasticity model

Another type of continuum model is the crystal-plasticity model describing the deformation of poly- or single crystalline materials (the output) based on the description of the slip-systems (PE) within the individual objects. Interesting output is the interfaces between objects at the nanoscale, the formation and evolution of defects like e.g. dislocations resp. dislocation densities and data about plasticity after experimental calibration. Promising developments currently show up in the combination of crystal-plasticity and phase-field models.

Phase field crystal model

The phase field crystal model can both be considered as a higher order expansion of the phase- field model equations and also as a homogenized solution of a density functional theory model. It thus naturally bridges the scales between atoms/lattices and the objects in the microstructure. It opens pathways to investigate “interacting lattices” (interfacial energies etc.) at the nanoscale of grain boundaries and phase boundaries.

4.5 Chemistry reaction (kinetic) models (continuum)

Chemical reaction (kinetics) models are equations that describe the characteristics of a chemical reaction, for example to study the effect of a catalyst. Such models can be used for a wide range of operating conditions and are more versatile than purely empirical phenomenological methods (“operational” kinetics).

A mass balance model (PE), also called a material balance, is an application of the conservation of mass. In the case of chemical reactions the mass balance equation must be amended to allow for the generation or depletion (consumption) of each chemical species.

This equation is complemented by stoichiometry model (PE),which calculates relative quantities of reactants and products in chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products. Describing the quantitative relationships among substances as they participate in chemical reactions is known as reaction stoichiometry.

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. The rates (MR) can be determined experimentally or via electronic and atomistic models.

Mass transfer models (PE) find extensive application in chemical engineering problems. The driving force for mass transfer is typically a difference in chemical potential, when it can be

defined, though other thermodynamic gradients may couple to the flow of mass and drive it as well. A chemical species moves from areas of high chemical potential to areas of low chemical potential. While thermodynamic equilibrium determines the theoretical extent of a given mass transfer operation, the actual rate of mass transfer will depend on additional factors including the flow patterns within the system and the diffusivities of the species in each phase. This rate can be quantified through the calculation and application of mass transfer coefficients (MR) for an overall process. These mass transfer coefficients are typically published in terms of dimensionless numbers, often including Péclet numbers, Reynolds numbers, Sherwood numbers and Schmidt numbers, among others.

In macrokinetics studies the Law of Mass Action equations (PE) for the overall chemical reaction is established. This equation states that the speed of a chemical reaction is proportional to the quantity of the reacting substances through the reaction rate constant. As MR the Arrhenius or Eyring relation is used. In “first principles microkinetics” the input value for Ea is calculated with DFT (Ch 1.2) otherwise measured values are used.

In microkinetics Law of Mass Action (LMA) equations are established for all relevant elementary reaction steps underlying the mechanicsm. The set of LMA equations form a large set of coupled equations. Based on the assumption of steady states for the intermediates the reaction rate for elementary reactions is recalculated for a given set of thermodynamic condistions. Finally the system of the elementary reactions will deliver the concentrations of the product in the reactor as well as insight into dominant reaction pathways in the underlying mechanisms such as rate- controlling steps. As MR the Arrhenius or Eyring relation is used to obtain values for the reaction rate constants.

Often the term (micro) kinetics is used for workflows that describe chemistry. These workflows are linking electronic, atomistic, mesoscopic and continuum models.

Electrochemistry reactions are chemical reactions which take place in a solution at the interface of an electron conductor and an ionic conductor (the electrolyte) e.g in batteries. These reactions involve electron transfer between the electrode and the electrolyte or species in solution where oxidation and reduction reactions are separated in space or time, and may be connected by an external electric circuit. To model such reactions the forward reaction rate coefficient for each reaction is usually calculated by a modified Arrhenius formulation incorporating also the influence of the electric potential difference. All reactions are considered surface reactions and are modelled to happen on defined interfaces between solid species and/or the liquid electrolyte.

The chemistry kinetic model should not be confused with the kinetic Monte Carlo method.

4.6 Electromagnetism (including optics, magnetics and electrical)

Electromagnetism is the branch of science concerned with the forces that occur between electrically charged particles. In electromagnetic theory these forces are explained using electromagnetic fields. The electromagnetic force is the one responsible for practically all the phenomena one encounters in daily life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting on the electrically charged atomic nuclei and electrons inside and around the atoms, together with how these particles carry momentum by their movement. This includes the forces experienced in "pushing" or "pulling" ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects. It also includes all forms of chemical phenomena. The behaviour of electrons based on this is described in Ch 1 and Ch 2. In this Ch 4 we then discuss the continuum EM model.

In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations (PE). The MR (constitutive equations) link the electrical and magnetic field to the electrical flux density (displacement) and the magnetic flux density. Each type of material (magnets, conductors, metamaterials etc.) has their own relation).

Most projects solve the EM equations via FE techniques but also ray tracing methods with Monte Carlo algorithms for the scattering are employed.

4.6.1. Magnetics

It is noted that electric fields and magnetic fields are different aspects of electromagnetism, and thus also described by the Maxwell equations

4.6.2 Elect(ron)ics

Electric circuit equations are also used in the form of Kirchhoff’s laws where electric conductivity plays a major role or relations expressing stress and currant can be used.

4.6.3 Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter. Because light is an electromagnetic wave, most optical phenomena can be accounted for using the classical electromagnetic description of light. Some times the continuum Schnell’s law and ray tracing models are used. Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics and this is discussed in Ch 1.

4.7 Application of models to simulate Processes and Devices

Manufacturing processes

Once the material has been designed it has to be produced. The manufacturing processes often have to be adapted for the new material and these processed too can be designed and optimised via modelling. The modelling thereof is considered part of materials modelling. Manufacturing processes that can be modelled are a.o.  deposition (isotropic (sputtering) or anisotropic),  etching (basic etching is treated as the opposite of deposition and is modeled as a pure geometric process, which is e.g. (an-)isotropic, of fourier-type, directional, crystallographic), oxidation (basic oxidation models only calculates a velocity however, the influence of mechanical stress can also be considered for oxidation and etching),  dopant diffusion during growth,  thermal induced reactions during annealing steps,  interface movements,  epitaxy (also reactions based on gas flows).  Most of the models rely on the physics described in the preceding chapters and no new physics needs to be discussed to describe projects. The simulation tool will allow the researcher to select operational parameters to be investigated and visualize the influence of each parameter, as well as to compute the influence of mechanical stresses in devices etc.

Devices

And, last but not least, the material will be used in applications and integrated in devices, and also this can be optimised via modelling, using the physics principles described above.

Chapter 5 Solvers and Databases

5.1 Solvers

Solvers are used to solve the physics equation. In this Review there is a strict separation between the two concepts "solver" and "model". Some aspects are highlighted but for a thorough review of solvers other texts should be consulted.

Note: Discrete solvers use concepts like "fictitious particles" but these are not to be confused with real particles and one should keep in mind the physics equations to be solved and for which physical entities these are established.

Discretisation (FV and FE)

Discretisation methods are used to allow numerical solving of the governing equations and these include  Finite difference methods (FD)  Finite volume methods (FV)  Finite element methods or analysis (FE, FEM or FEA or RVE)  Spectral element methods (SEM)  Boundary element methods (BEM)

In all of these approaches the same basic procedure is followed: 1. During preprocessing a. The geometry (physical bounds) of the problem is defined. b. The volume occupied by the material sample is divided into discrete points or cells (the mesh). The mesh may be uniform or non uniform. c. The physical modeling is defined – for example, the equations of motions + enthalpy + radiation + species conservation d. Boundary conditions are defined. This involves specifying the fluid behaviour and properties at the boundaries of the problem. For transient problems, the initial conditions are also defined. 2. The simulation is started and the equations are solved iteratively to converge to as a steady- state or to describe transient situations. 3. Finally a post-processor is used for the analysis and visualisation of the resulting solution. Extraction of data and Material Relations for further modelling can be done. This post-processing can involve further physics.

Discrete Element Method

A discrete element method (DEM), also called a distinct element method is any of a family of numerical methods for solving physics equations. The fundamental assumption of the method is that the material consists of separate, discrete particles. These particles may have different shapes and properties. He forces are given by the physics equation to be solved. An integration method is employed to compute the change in the position and the velocity of each particle during a certain time step.. Then, the new positions are used to compute the forces during the next step, and this loop is repeated until the simulation ends. DEM is very closely related to molecular dynamics, Today DEM is becoming widely accepted as an effective method of

addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics.

Monte Carlo, a generic statistical method to solve different equations

The Monte Carlo solver is a method intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with a given known rate. It is important to understand that these rates (derived from the PE) are inputs to the MC algorithm, the method itself cannot predict them.

Smooth Particle Hydrodynamics (SPH)

Smoothed-particle hydrodynamics (SPH) is a computational method used for solving fluid dynamics and structural dynamics equations. The smoothed-particle hydrodynamics (SPH) method works by dividing the fluid into a set of discrete elements, referred to as particles. These particles have a spatial distance (known as the "smoothing length") over which their properties are "smoothed" by a kernel function. This means that the physical quantity of any particle can be obtained by summing the relevant properties of all the particles which lie within the range of the kernel. The contributions of each particle to a property are weighted according to their distance from the particle of interest, and their density. Kernel functions commonly used include the Gaussian function and the cubic spline. The latter function is exactly zero for particles further away than two smoothing lengths (unlike the Gaussian, where there is a small contribution at any finite distance away). This has the advantage of saving computational effort by not including the relatively minor contributions from distant particles.

Automata (Lattice Gas, Cellular and Movable Cellular Automata)

Lattice gas automata (LGA) or lattice gas cellular automata (LGCA) solvers used to solve mechanics models used to simulate diffusion. I These Eularian models comprise of a lattice, where the sites on the lattice can take a certain number of different states. The various states are 'fictitious particles' with certain velocities (entities). Evolution of the simulation is done in discrete time steps. After each time step, the state at a given site can be determined by the state of the site itself and neighboring sites, before the time step. The state at each site is purely Boolean. At a given site, there either is or is not a particle that is moving up. At each time step, two processes are carried out, propagation and collision (model). In the propagation step, each particle will move to a neighboring site determined by the velocity that particle had. Barring any collisions, a particle with an upwards velocity will after the time step maintain that velocity, but be moved to the neighboring site above the original site. The so-called exclusion principle prevents two or more particles from travelling on the same link in the same direction. In the collision step, collision rules are used to determine what happens if multiple particles reach the same site. These collision rules are required to maintain mass conservation, and conserve the total momentum; the block cellular automaton model can be used to achieve these conservation laws. Note that the exclusion principle does not prevent two particles from travelling on the same link in opposite directions. When this happens, the two particles pass each other without colliding. Macroscopic quantities like the density at a site can be found by counting the number of particles at each site. If the particles are multiplied with the unit velocity before being summed, one can obtain the momentum at the site. However, calculating density, momentum, and velocity for individual sites is subject to a large amount of noise, and in practice, one would average over a larger region to obtain more reasonable results. Ensemble averaging is often used to reduce the statistical noise further.

A Cellular Automaton (pl. cellular automata, is a discrete solver. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, identifying a physics parameter value. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state is selected by assigning a state for each cell. A new generation is created according to the physics equation, which determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the physics for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. The Movable Cellular Automaton (MCA) method is another solver used in computational solid mechanics based on the discrete concept used for direct simulation of materials fracture including damage generation, crack propagation, fragmentation and mass mixing. The automata are mobile and the new concept is "neighbours" is based on the introducing of the state of the pair of automata (relation of interacting pairs of automata) in addition to the conventional one – the state of a separate automaton. As a result of this, the automata have the ability to change their neighbors by switching the states (relationships) of the pairs. The automata are ruled by the physics equations to be solved, which give the dynamics by their mutual forces and rules for their relationships.

Green Functions Green functions are often used as mathematical tool to solve phyiscs equations. We refer though to the chapter on electronic model where physics aproximations are made in the ”Green Function” space and this leads to the NEGF model (Ch 1.4).

Accelerated simulations in molecular dynamics

The main problem of standard molecular simulations is that the time of the simulation sampling is often not long enough to ensure complete statistical sampling (ergodic theorem not valid, see Ch_2). For example, "centuries" on their available supercomputer would be needed to simulate 1s of “a day in the life” of a polymer. For this reason, calculating free energy, reaction pathways and rare events may be not possible using standard molecular simulations. Advanced methods have thus been developed to increase the efficiency of the sampling and to obtain a more accurate answer in a limited amount of time, e.g. temperature accelerated molecular dynamics, metadynamics and kinetic Monte Carlo. Accelerated Molecular Dynamics (AMD) and Metadynamics are methods to increase the sampling in Molecular Dynamics simulations. Accelerated molecular dynamics (AMD) tricks MD into reducing the separation of timescales between fast and slow components of the dynamics and renormalizes the MD-time accordingly. Metadynamics is an artificial molecular dynamics method performed in the space defined by a few collective variables, which are assumed to provide a coarse-grained description of the system.

5.2 Databases

Models that are not worked up from quantum mechanical (ab-initio) principles need values for the parameters used in the model. Huge databases are created for each class of compounds in any medium (environment). These contain e.g. potentials parameters (e.g. for classic force fields) to use in electronic and atomistic models, polymer properties and thermodynamic phase diagrams for micromechanical modelling. Data can be compacted into relations used as MR in the models. Some of these relations can be used as self-standing models and this is discussed in the next chapter.

Chapter 6 Model Development

6.1 Model application

In this Review we talk about model application when we apply an existing physics equation and closure relation to a specific situation. The tuning of parameters in these equations (e.g. parameterisations in existing force fields expressions or in existing constitutive equations) is not considered to be model development.

The strength of physics based modelling is that the physics is widely applicable. The MR are ofcourse limiting the applicability as they have been developed by datamining in a dedicated database. A model is strong if it is transferable from one materials system to another within the limits of the model. Many NMP and NMBP projects are applying existing physics and chemistry models to new materials and manufacturing processes. This has generated a wealth of new information1. When applying an existing model to a new situation, unexpected results or new phenomena may be discovered, An overview of the extensive fields of model application in FP7 projects in described in the RoMM V.

6.2 Developmentof physics-based models

Model development is the act of finding the approximations in the physics and chemistry equations and in the materials relations. Materials Modelling is the establishing of governing equations (physics/chemistry equations and/or closure relations) between physical or chemical quantities. These governing equations contain the key assumptions of the model. Modelling does not include fitting parameters in existing governing equations to (simulated or experimental) data.

Modelling starts with an approximation of the physics which at first is seen as a good balance between complexity and computability. Development of models may either make the crude model more complex (and in principle the full physics equations will be retrieved again) or reduce the complexity of the model. Below (Fig. 6.1) is an illustration of model development, across time- and length scales.

1 Please note that the physical/chemical knowledge about the system or process needed to perform the model application goes beyond purely computational skills.

Fig. 6.1 Model development works by moving along the arrow upwards or downward. (based on Kersti Hermansson, Uppsala University, SE)

Expanding models

At times, models cannot be transferred from one physical situation to another (say from energy conversion to spin-dynamics). In such cases, research projects may want to increase the complexity of the model, by incorporating new physics and chemistry in the PE. This happens when new physics and chemistry is to be described. Modellers start from strongly approximated physics equations, and gradually add complexity to them until a satisfactory agreement with experiments is reached. For example, it has been necessary to develop new models in femtosecond dynamics: at the femto-scale new dynamics, physics or chemistry takes place and new opto-electronics/magnetics/ models have been developed. Other examples are the addition of more transition metal orbitals, ligand orbitals, Coulomb exchange, spin-orbit, phonons, and friction.

Modellers (more) often establish new MR (constitutive equations) either from measurements or by applying models of a finer type and transferring the results into a coarser type of model in the form of relations with new terms expressing the added physics phenomena now taken into account. This allows them to identify the critical relevant processes that lead to experimental results. Deriving a new force field by adding new terms to include physical or chemical properties previously disregarded and ignored in the approximations will be considered as a new MR and thus as a new model. In the continuum modelling world researchers develop new constitutive equations linking physical or chemical parameters in a new empirical equation, found by datamining in experimental or simulated results, and this is also included as new modeling. The basic phenomenon might not be completely understood but this new relation can at least be called a ‘hypothesis’.

Reducing models

The Schrödinger equation, Newton Dynamics and conservation equations are the foundations of materials physics and chemistry. But these equations can often not be solved and an approximated equation is taken instead. Development of models may also reduce the complexity of an existing model if the accuracy allows it. This is done to save computer time. A reduced model starts from a pre-existing detailed physical equation, which is systematically simplified by using expert knowledge or automatic mathematic procedures for extracting most relevant features (e.g. projection method, principal component decomposition, manifolds, etc). An example of using expert knowledge is the reducing the number of reactions considered to describe a chemical reactor.

6.3 Development of data-based models

“Model” throughout the RoMM means physics-based model.

Simulations with physics-based models can be computationally heavy and sometimes physics equations can‘t (yet) capture the complexity of phenomena (e.g. in the pharmaceutical world). Often data-mining based relations are then extracted from (simulated or experimental) data. They are best-fitting, phenomenological models. They are often called surrogate models in engineering. These simplified relations when used in isolation do not need complicated numerical solvers as they are able to find quick answers. E.g. In chemistry, biology and pharmaceutical fields relations between “descriptors or predictor variables” to the response variable established from experimental data are called quantitative structure–activity relationship models (QSAR) or quantitative structure–property relationships (QSPR). We will collectively call these relations data-based models. The database from which these relations are extracted should always be documented.

If confusion could arise the distinction between “physics-based model” and “data-based model” should be indicated.

Hence the difference in surrogate and reduced models is in the starting point. A reduced model starts with a detailed physical model, which is very accurate but too complicated. The surrogate model starts with a cloud of data points.

Post-processing leading to MR complementing PE

Post processing can be done to prepare input for the next model in the form of values like above. But also relations between descriptors can be extracted with data-mining. These values and relations can be used as MR in the next model. To do this the modellers have to have an idea (assumption, postulation) for what physics relation they are looking for. And when this relation is supported by the data in a testing operation, then it is adopted. An example of this is finding in the output of DFT a new template relation for a force field (MR). In continuum modelling, often the results of continuum models applied at meso-scale (nm) are fed into the continuum model applied at macro-scale model (μm) in the form of constitutive equations – which in the language of this Review are called “Material Relations” - or as boundary conditions. The establishment of such constitutive equations represents a big challenge in contemporary modelling.

Post-processing leading to self-standing data-based models

Extracted relations can also be used in isolation as data-based models in similar situations. Of course data-based models also allow the description and prediction of state changes. The quality of these relations is varying. The dataminer can postulate relations between aspects based on a physics understanding (like Hooke’s law). (If the wide community of physicists accept this new relation to be an omni-applicable law they will ofcourse be added to the RoMM as PE.) But as long as these data-based models fail to have the wide applicability of physics-based models they are not discussed in this RoMM. These relations should always be accompanied by the identification of the dataset they have been derived from. Data mining can e.g. be used to find the Gibbs energies as continuous functions of temperature, concentration/composition a pressure. These continuous functions allow the definition of a value of the Gibbs Energy, even in regions where no measurements or simulations are available.

6.4 Software engineering

Software engineering and up-scaling for the industry

Models and solvers and post-processors are coded up into software packages. Simulation software is a computational code, which solves the governing equations by numerical methods and requires information about the application (boundary and initial conditions). More than one model can be integrated into a single code (toolkit/framework/workbench).

Codes or simulation software are not equal to model. A code might contain several models plus solvers, plus pre-and post-processors.

The coding effort should not go lost and the software should be available to third parties. Upscaling to industry should be the focus of an industrial programme like the H2020 NMBP Programme appropriate maintenance, software code modularity and reusability are thus an issue. An integrated and user-friendly design environment must be created.

Software owners have written up guidance on software engineering, which is available at www.emmc.info.

Guidance on quality assurance for academic materials modelling

This chapter presents the advice of software owners, commercial and academic, on what academic software could do to generate better quality software, ready to be used by third parties. It can also be found on www.emmc.info.

Under Horizon2020, funding programmes have divided their scope by TRL levels

TRL 0: Idea. Unproven concept, no testing has been performed. TRL 1: Basic research. Principles postulated and observed but no experimental proof available. TRL 2: Technology formulation. Concept and application have been formulated. TRL 3: Applied research. First laboratory tests completed; proof of concept. TRL 4: Small scale prototype built in a laboratory environment ("ugly" prototype). TRL 5: Large scale prototype tested in intended environment. TRL 6: Prototype system tested in intended environment close to expected performance. TRL 7: Demonstration system operating in operational environment at pre-commercial scale. TRL 8: First of a kind commercial system. Manufacturing issues solved. TRL 9: Full commercial application, technology available for consumers.

1. The European Research Council is addressing TRL1-3. They fund bottom-up research, usually in individual grants to support a group of a junior or senior principal investigator and the first priority is the development of an initial, promising idea. 2. The “Materials” (NMBP) programme is under the LEIT pillar (leading and enabling industrial technology) and is aimed at funding projects between TRL3-7. These are typically collaborative projects with a consortium with a mixture of academic and industrial partners to ensure that the goals have specific and realistic industrial relevance. In material modelling projects, the industrial partners could be either software companies or manufacturers or finished product sellers. 3. TRL7-8 is taken care of by companies who will customise the results and use them in commercial operations.

In this chapter all phases in materials modelling software engineering are briefly addressed and then the text concentrates on the software development done in the LEIT programme. This guidance is meant to help guide H2020 projects and discuss how physics and chemistry PhD students can become ready to do the work in H2020 LEIT NMBP. The transfer of software developed in many universities to industry remains insufficient. Academic institutions do not target to provide fully developed software or materials models services. For this a lot of effort is to be invested (corresponding to some 70% of the total software development) and for this spin-off companies are created or the software is transferred to existing commercial companies.

To stimulate this transfer to industry an inquiry is done into the requirements of commercial companies on the quality of software. Quality of the model is the ability of the software to solve the initially defined problem. Quality of the software is defined by:  Code design.  Stability and resilience.  Modularity.  Performance (CPU, memory, …) and the software quality should lead to software which is easy to maintain, understand, improve and adapt, and deploy to the target users.

Cooperation forms

Most software houses do not adopt software in which they have not been involved. The continuum model vendors tend to develop the software themselves, while in the discrete world models are adopted by the commercial vendor. Most companies have standing relations with a university group where the PhD students change but the relation continues. And this allows the software to be adapted to later customer needs. Access to the original developers over the course of the software life time is important. EU projects are thus just a stage in this long-lasting relation.

As the investment is large academics and companies agree licenses with their co-developers and customers that allow the return of profits.

Consideration of the advantages and drawbacks and pitfalls of different licensing schemes is important. Many commercial companies feel open licenses and viral licensing schemes like GPL are a blocking point when transferring or using software from academia to industry as they do not allow commercial exploitation. However other companies support Open Source code – like the many Linux support companies. Trends in main licensing schemes were mentioned during the discussion: o One-to-one licensing. Service License Agreement/Contract can be limited in time (and thus cheaper) and allow "software (solutions provided) as service and/or on demand". o LGPL is better than the “viral” GPL scheme, but poses a commercial constraint as only “dynamic linking” into commercial software is commercially viable – and dynamic linking has a performance disadvantage. o BSD or Apache licensing schemes are most permissive in allowing to link technology building blocks of non-commercial R&D partners into commercial software in a performant manner.

o Dual licensing: Many academic institutions go for dual licensing which keeps the software free to academia but allows commercial protection and there is some ROI.

Commercial SWO recommend to use a permissive licensing scheme (as BSD or Apache) already for the R&D and prototyping phase of new methods and software tools, as the resulting technology blocks will be acceptable to commercial tool vendors downstream, which smoothens the procedure to get new software modules into industrial deployment (by leveraging on the installed base of commercial software at manufacturing industry).

In the current situation, three phases of software development can be identified.

PHASE I Exploratory phase (modelling)

In this phase new models2 are elaborated with new physics/chemistry, and the models are applied to one or two specific test cases. Exploratory model development takes place mostly in academia. Software developed in this stage is typically developed to test a scientific idea. ERC funding could be requested for this Phase. In this phase the science is important and the software is considered to be a side product. The ideas are often the basis for literature articles.

The software is not user-friendly and is often shared freely among specialists (mostly academics) through PhD and postdoc collaborations. IP protection is usually only covered by the academic code of conduct.

If a SWO becomes interested, this interest of the SWO is often based for 80% on the functionality and for 20% on the software quality. Huge amounts of money and time are wasted on maintaining and developing a bad piece of software. (The PhD student is spending all their time on making a code converge or to restart the code when it crashes). If the commercial company rewrites the code then they either lose the benefit of future academic developments or have to spend their time re-implementing the ideas in their code.

PHASE II Bridging Phase: new material modelling software and software prototyping

New material modelling software has been validated on some test cases and has thus proven wider applicability and the software has the ability to solve new problem(s) of value for industry. The software is in a prototype phase and the software has to become validated trusted code during this phase. In this document we do not address the quality of the model nor the influence of boundary conditions nor solver technologies nor coupling to other models. This phase can be subdivided further:

 Phase II a: Proof-of-concept phase. Techies from industrial R&D departments become interested in academic results or new models. Their drive is to find something new. In this phase they may work with software developers/ companies to develop software for proof of concept.

 Phase IIb: Visionaries in industrial context get involved. They are concerned in finding better solutions within a broader business context. Projects in this phase typically last 2-3 years and are used also in collaboration with software developers to solve particular useful problems, including validation and metrology.

2 Materials are complex systems and the equations that describe the physical and chemical behaviour of real systems are often too complicated to be solved easily. In order to save computer time, which is a precious and limited resource, the description of phenomena has to be simplified. Fortunately, often not all details need be taken into account in order to reproduce and predict experimental results. Key assumptions about reality can be made ignoring the complexity that is not necessary to describe the given situation. These approximations are called "models" (see "Review of Materials Modelling What makes a material function? Let me compute the ways…", 3rd edition, 2014, http://ec.europa.eu/research/industrial_technologies/pdf/modelling-brochure_en.pdf)

Often, scientific/academic modellers work together with commercial software owners and follow their software habits. The academics will need to understand and respect standards, formatting, protocols etc. with regard to the existing software data structures and architectures. Licensing: Academics often use open source licences like GPL. Alternative models are used like L- GPL and small commercial companies (spin-offs) may be involved at this stage to support the commercial development and exploitation. Alternatively, dual licensing models are used so that academics can continue to develop the code and commercial companies can explore those cases where potential industrial users/consumers are not yet clearly identified or the value of the results in the industrial setting is not yet established. In the later stages of this phase, the software is used by a wider community and applied to a wider range of systems. Versioning: Software versioning supporting tools are sometimes used but it’s too often considered too cumbersome. Additional software writing may also happen in this Phase, e.g. scripting, may be at the level of a material scientist (depending on the language and individual skills) automating and packaging (not usually in their expertise…) Good software engineering practices will help in overcoming the so-called "CHASM"3, where many new models fail to be introduced to the mainstream market.

PHASE III Commercial modelling software.

The main target is the commercial scale-up of software for more than a small community of end- users. In this phase "pragmatists" will need to become convinced that a new technology is worth their time, effort and money to get it deployed into their organisations. These pragmatists are managers which are primarily interested in the economics behind a new approach, they are reluctant to change, and will only decide on a change if they’re convinced that it’s worth it for their operational / ROI targets. Improvement in performance is only one factor in this phase, several other aspects are considered: investments already done, ‘cost of change’ (in training and process changes), ability to cope with potential demand for new products. It may be preferred to buy out the software in this phase.

The effort needed to rewrite the code for exploitation purposes is large as software developing skills by material scientist are often not sufficient (even when they can write codes for themselves that calculate useful things) and professional expertise might be necessary. Today this deployment step unfortunately often involves a complete rewrite of the code by software engineers and this phase amounts often to 70% of the total development effort and this is to be reduced.

Quality control is performed using multiple quality targets that must be monitored and considered simultaneously for every software release. This allows avoiding ‘waterbed effects’: focusing intensively on improving 1 quality target will risk to reduce the performance of another quality target. For example, reducing the level of details provided to the user reduces the ‘content’ quality and accuracy, but increases the speed of calculation and result evaluation. Formal software quality management metrics are used e.g. CFURPS4.

3 "Crossing the Chasm" by G.A. Moore (1991)

4 Compatibility, Functionality Usability Reliability Performance Supportability (CFURPS)

Commercial companies put a large effort into ensuring full validation, documentation, user- friendly interface, testing suites, durability long term support systems are developed since the life span of the successful models is many decades.

In order to get the software into an industrial framework the code need to be portable, well defined and documented APIs and product packaging on the one hand, and communication between developers on both sides on the other. In general, for commercial exploitation, a piece of software must be robust and relatively easy to use, with a good user interface. This can require a great deal of development in the:

1. Installer and licensing system, 2. Graphical User Interface, 3. Help system and manuals, 4. Updating system.

The software company will consider data and exchange standards. In case wrappers and homogenisation tools are needed also these need to be developed if they do not yet exist.

There could be a range of tasks required to be undertaken to get the software/data in a form ready for exploitation. Maintenance (adaptation to new IT) is an important issue as software is on the market for many years/decades and both the solution and the framework are not static in time, nor are the underlying hardware architectures. This development involves constant updating to changing environments (like Apple dropping the active support for Java on Mac).The company has to think about possibilities for service provision and training that can accompany the software.

Catalysts to facilitate the flow of innovation from model developers to mainstream end users use are:  Bi-directional communication: awareness upstream at academia w.r.t. downstream industry needs, and vice-versa awareness downstream at industry w.r.t. promising academic methods.  Availability of information: store material models/data, document best practice methods/tools, and demonstrate their impact on the basis of industrial use cases.  Standardisation of data and interfaces to enable and facilitate the take-up of information by other actors in the industrial value chain, and with other tools that cover parts of this value chain. Note that multi-scale modelling in itself can, in simple cases, also be seen as an interface between different tools available at different simulation levels, which must be integrated to be able to deal with applications at a higher scale.

For making and selling new tools that operate within a standard “mainstream” process at the industrial end user, a shortcut may be found when the innovative component is implemented as a new “feature” (an integrated module) into the “mainstream software” that is deployed at the end user. This allows the design engineers at the end user company to use the new “content block” directly, without making any (disruptive) changes to the software tool chain, nor to the in-house process to use the tools, nor requiring too extensive training of the staff involved, nor requiring changes to the teaming and organisation. The “new content block” simply acts as a new / improved feature within a well-known process and tool chain, familiar to the users, hence there’s a smaller chasm: there are less hurdles in the organisation to be overcome before deployment of the new feature within the tool chain that’s already well known and broadly used.

Proposed guidelines on how material modelling software should be developed in EU-LEIT funded projects

The purpose of these guidelines is to make it more likely that models developed in LEIT projects are used in industry. The purpose of these guidelines is thus to ensure that the models/software are transferred to professional software owners (academic and commercial) who licence the code

to third parties and maintain the code. After the code is fully developed we enter phase III and the code can be sold by (commercial) SWO who sell the codes to an end-user, or academic software SWO who transfer the code to other users , but also by new translator actors (e.g. spin- offs) who use the code themselves in R&D services done for industrial end users. In this document we only focus on Phase II, the completion of the software development up to TRL 7. The target of EU H2020 –LEIT research and innovation funding will be to support Phase II in the projects since it will bridge the gap over the software valley of death. Phase III is considered commercial and thus not part of EU funding.

The cost of developing code after the initial research on the functionality of the model can be substantial. It is certainly so when software funding is starting to demand small proof-of-concept or emerging technology software components to be developed. To optimize these investments, the following recommendations have been gathered:

Proposed recommendations for phase II software development

- Prove wider applicability via validation on a set of fully documented test cases. (benchmark test and literature references, proof of some sort)- Documented results obtained in collaboration with industrial users solving specific industrial problems. - Document accuracy/ functionality proven in high profile academic publications (especially important in some markets, e.g. Japan) - Demostrate good numerical implementation, proven numerical stability (performance, boundaries on values of parameters for numerical stability), pragmatic approach to software engineering including the use of software metrics (e.g. Halstead (1977), Watson & McCabe (1996) (Kan, 2003). - Provide good documentation of underlying equations and (justification of choice of) algorithms, validation cases, boundaries of validity, clear mapping of raw formula to code variables, manuals/tutorials explaining what the code can do. - Include appropriate testing procedures and document the results in deliverables. - Provide clear documentation of which version of the code was used to obtain what result and content of the next upgrades (not necessarily professional versioning). - Provide documentation about IT requirements (operating system, compilers, MPI distribution, …) and how to compile the code. - Adopt a licence allowing commercial industrial use -Demonstrate interest of potential customer, and traction with potential future users -Collaborate with SWO to drive the direction (mentor for software writing)

In H2020 programmes under the "Leadership in Enabling Industrial Technologies" pillar, it is of crucial importance that proposals are led by industrial needs.

When the new model addresses a new and previously unaddressed problem in a “niche” market, reference cases are of paramount importance to generate new business, research grants should show the potential of the new method on an application case that is familiar to the target end user (at least in terms of having similar complexity and comparable workflow)

Developers in phase II should consider if the new model can be implemented as an innovative integrated component of the “mainstream software” that is deployed at the end user; this approach has a high ROI (return on investment) as a more effective industrialization can be achieved.

Licences

It is recommended that the guiding principle should be “Have an organized system of sequential licensing options, which would allow for commercialization under specific terms” and not only “Don't put any obstacles for future commercialization”.

Licences should be chosen together with the mentoring SWO in the project who is likely to exploit the software. Although in the “prototype" phase II in principle any tool (and licensing scheme) can be used for the purpose of validating a methodology, we believe that it’s wise to keep in mind future re-usability of code blocks in case an innovation moves downstream the innovation chain, as this reduces the hurdles to bring the innovation in position to provide value to the end users by solving their application challenges.

Education

It is of utmost importance that academic software developers receive better information on alternative licensing models that do not preclude commercial exploitation.

Workshops on basic software writing schemes may be useful at this stage as well as workshops on versioning, software repositories and testing suites that can guide the development. Several existing activities are running in Europe and some documentation is available online. Academics should be informed about best software writing practises before starting to write any code – not just at the exploitation stage.

The course should deal with issues like  Code design. - This depends on the problem solved and on the parallelisation/load balancing concepts employed in the code - memory distribution, structures and communication patterns. There are multiple ways to achieve this. Best practices are about code neatness (file, modularisation, dependences, architectural design), cleanliness, testing, comments, keeping track of changes (repositories), test case to demonstrate performance and functionality, and documentation.  Modularity. - Mentioned in code design as code neatness (file, modularisation, dependences architectural design), cleanliness  Performance (CPU, memory, …). - also mentioned above  Portability  Numerical stability deviations from standard models with controlled termination when entering ill-defined problem input (rarely). There may be much more depending on the hardware architecture too.

Annex I Annotated template for MODA

Purpose of the MODA document

The MODA contain a data element organisation that is applicable to ALL materials modelling simulations. The MODA should contain all elements that are needed to describe a simulation. This information spans from end-user (manufacturer) information to the computational modelling details. Each simulation will have its own MODA fiche. Metadata for these elements are to be elaborated over time.

MODA for simulated in project

OVERVIEW of the SIMULATION

General description of the User Case.

Please give the properties and behaviour of the particular material, 1 USER CASE manufacturing process and/or in-service-behaviour to be simulated. No information on the modelling should appear here. The idea is that this user-case can also be simulated by others with other models and that the results can then be compared.

The MODA do not serve to demonstrate the wide applicability of your code. In case you do a series of independent simulations with the same model (like in high-throughput approaches to find the best material), you can list this set of user cases here.

Please identify the first model.Note these are assumed to be physics-based models unless it is specified differently. MODEL 1 CHAIN OF Most modelling projects consist of a chain of models, 2 MODELS (workflow). Here only the Physics Equations should be given and only names appearing in the content list of the Review of Materials Modelling IV should be entered. This review is available on http://ec.europa.eu/research/industrial_technologies/e- library.cfm).All models should be identified as electronic, atomistic, mesoscopic or continuum.

MODEL 2 Please identify the second model. DATA-BASED If data-based models are used, please specify. MODEL PUBLICATION Please give the publication which documents the data of this ONE simulation. PEER- 3 REVIEWING THE This article should ensure the quality of this data set (and not only the DATA quality of the models).

ACCESS Please list whether the model and/or data are free, commercial or open 4 CONDITIONS source.Please list the owner and the name of the software or database (including web link if available).

Please give a textual rationale of why you as a modeller have chosen these WORKFLOW AND 5 models and this workflow. ITS RATIONALE This should include the reason why a particular aspect of the user case is to be simulated with a particular model.

Workflow picture

Each physics-based model used in this simulation is to be documented in four chapters:

1. Aspect of the User Case or system simulated with this model 2. The Mode is to be identified by its Physics Equation and Materials Relation.  Tightly coupled models can be written up collectively in one set of four tables. To solve tightly coupled equations one matrix is set up and solved in one go.  For continuum models the PE is often only the conservation equations coded up in bought software packages. Often the MR is established by the modeller. 3. Computational aspects document how the simulation specifications are translated into computer language. 4. Post processing documents how the raw output of one simulation is processed into input for the next simulation. This will information given under 4.1 in the first model will be the same as the "simulated input" information under 2.4 for the next model. This is the essence of model inter-operability!

Each data-based model in this simulation is to be documentd in three chapters:

1. Aspect of the User Case or system simulated with this data-based model 2. Data-based Model 3. Computational detail of the datamining operation

MODA

Physics-based Model

Model X

Please give the number

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

Describe the aspects of the user case textually.

No modelling information should appear in this box. This case could ASPECT OF THE also be simulated by other models in a benchmarking operation! The information in this chapter can be end-user information, USER CASE TO BE measured data, library data etc. It will appear in the pink circle of 1.1 SIMULATED your workflow picture. Simulated input which would have been calculated by another model should not be included (but in chapter 2.4)

Also the result of pre-processing necessary to translate the user case specifications to values for the physics variables of the entities van be documented here.

1.2 MATERIAL Describe the chemical composition, …

Size, form, picture of the system (if applicable) 1.3 GEOMETRY

Note that computational choices like simulation boxes are to be documented in chapter 3.

Duration of the case to be simulated. 1.4 TIME LAPSE This is the duration of the situation to be simulated. This is not the same as the computational times to be given in chapter 3.

If relevant, please list the conditions to be simulated (if applicable) This can be manufacturing process conditions or in-service conditions, physics (kinematic) constraints.

E.g. physics boundary conditions like heated walls, external CONDITIONS TO pressures and bending forces. 1.5 BE SIMULATED Please note that these might appear as terms in the PE or as boundary conditions, and this will be documented in the relevant chapters. Also kinematic constraints express the properties of the user case and as they are physics and not computational they need to be documented here and not in chapter 3.

PUBLICATION ON Publication documenting the simulation with this single model (if 1.6 THIS DATA available and if not already included in the overall publication).

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE AND NAME Model type and name chosen from RoMM content list (the PE).

2.0 This and only this will appear in the blue circle of your workflow picture. Please do not insert any other text although an indication of the MR is allowed.

MODEL ENTITY The entity in this materials model is

Equation Name, description and mathematical form of the PE

In case of tightly coupled PEs set up as one matrix which MODEL is solved in one go, more than one PE can appear. PHYSICS/

2.2 CHEMISTRY Physical EQUATION quantities Please name the physics quantities in PE, these are PE parameters (constants, matrices) and variables that appear in the PE, like wave function, Hamiltonian, spin, velocity, external force.

Relation Please give the name of the material relation and which PE it completes.

MATERIALS Physical 2.3 RELATIONS quantities/ Please give the name of the physics quantities, descriptors parameters (constants, matrices) and variables that for each appear in the MR(s) MR

SIMULATED INPUT Please document the simulated input and with which model it is calculated.

This box documents the interoperability of the models in case of sequential or iterative model workflows. Simulated output of the one 2.4 model is input for the next model. Thus what you enter here in 2.4 will also appear in 4.1 of the model that calculated this input.

If you do simulations in isolation, then this box will remain empty.

Note that all measured input is documented in chapter 1.

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS

NUMERICAL Please give name andtype of the solver 3.1 SOLVER e.g. Monte Carlo, SPH, FE, …iterative, multi-grid, adaptive,…

Please give the name and if this is your own code, please specify if it 3.2 SOFTWARE TOOL can be shared with an evt link to website/publication.

If applicable, please give the timestep used in the solving operations. 3.3 TIME STEP This is the numerical time step and this is not the same as the time lapse of the case to be simulated (see 1.4)

PHYSICS EQUATION, Computational representation of the physics equation, MATERIAL materials relation and material. RELATIONS, COMPUTATIONAL MATERIAL There is no need to repeat user case info. REPRESENTATIO 3.4 N “Computational” means that this only needs to be filled in when your computational solver represents the material, properties, equation variables, in a specific way.

If applicable. COMPUTATIONAL

3.5 BOUNDARY Please note hat these can be translations of the physical boundary CONDITIONS conditions set in the user case or they can be pure computational.

Please specify pure internal numerical solver details (if applicable), ADDITIONAL like 3.6 SOLVER  Specific tolerances PARAMETERS  Cut-offs, convergence criteria  Integrator options

Post processing

The “raw output” calculated by the model is per definition values for the physics variable in the PE(s). This variable is already specified in2.2 and will appear in your dark green circle in the workflow picture.

This raw output is often processed  to calculate values for physics variables for different entities that can be input to the next model. the output is homogenised for larger volumes  the output is processed in the form of a MR for the next model  the output are processed into a Descriptor Rule that is the final output of the total simulation. This processed output will appear in your light green circle in the workflow picture and also in 2.4 of the next model.

The methodology (often including physics) used to do this calculation is to be documented in 4.2

4 POST PROCESSING

THE PROCESSED Please specify the post processed output. OUTPUT If applicable then specify the entity in the next model in the chain for which this is calculated: electrons, atoms, grains, larger/smaller finite volumes. 4.1 In case of homogenisation, please specify the averaging volumes.

Output can be calculated values for parameters, new MR and descriptor rules (data-based models)

METHODOLOGIES Please describe the mathematics and/or physics used in this post- processing calculation.

4.2 In homogenisation this is volume averaging. But also physics equations can be used to derive e.g.,thermodynamics quantities or optical quantities from Quantum Mechanic raw output.

MARGIN OF ERROR Please specify the margin of error (accuracy in percentages) of the 4.3 property calculated and explain the reasons to an industrial end-user.

MODA Data-based Model

1 USER CASE:

ASPECT OF THE USER CASE 1.1 TO BE CALCULATED

1.2 MATERIAL

1.3 GEOMETRY

1.4 TIME LAPSE

MANUFACTURING PROCESS 1.5 OR IN-SERVICE CONDITIONS

PUBLICATION ON THIS ONE 1.6 DATAMINING OPERATION

2 THE DATA-BASED MODEL

EQUATION e.g. energy minimizer 2.0 TYPE AND NAME

DATABASE e.g. thermodynamic database CALPHAD 2.1 AND TYPE e.g. simulated data with DFT model and experimental data from AFM

HYPOTHESIS The hypothetical relation assumed

EQUATION 2.2

PHYSICAL QUANTITIES

3 COMPUTATIONAL DETAIL OF DATAMINING OPERATION

NUMERICAL 3.1 OPERATIONS

SOFTWARE 3.2 TOOL

MARGIN OF 3.3 ERROR

Annex II H2020 project MODA

Multi-parametric optimization of car material

ALLIANCE (723893)

Summary of the project

Higher fuel/energy efficiency in both conventional and electric vehicles needs advanced materials and production technologies which have a high potential in reducing weight and environmental impact at low cost for high volume production. A range of innovative solutions based on steel, aluminium, composites and hybrid materials will be developed and validated in 8 high-reality demonstrator modules.

Crash-worthiness of car wheel-house

Project Acronym and Number: ALLIANCE 723893 Project Title: AffordabLe LIghtweight Automobiles AlliaNCE Start and End Dates: from 1/10/2016 till 30/09/2019 EU Contribution: 7,981,772.50 € Coordinator: Sama MBANG, [email protected] Modeller(s): Thilo BEIN, [email protected]

MODA

Crash-worthiness of car wheel-house

in ALLIANCE

OVERVIEW of the SIMULATION Crash worthiness of a joint, lightweight optimised wheel house with strut tower and rails (one component) of a passenger car (C-segment) according current Euro NCAP standards 1 USER CASE Properties to be simulated are fatigue, noise, vibration and harshness (NVH) properties and crash performance.

Continuum macro-mechanic: solid mechanics CHAIN OF MODEL 1 (conservation eqs) to calculate fatigue/damage, plasticity, 2 MODELS structural dynamics (eigenfrequencies, mode shapes)

Continuum macro-mechanic: solid mechanics CHAIN OF MODEL 2 (conservation equations and eqs of motion)to calculate 2 MODELS crash behaviour

PUBLICATION 3 ON THIS ONE None available so far SIMULATION

Input data: proprietary CAD/FE-models from the modules (OPEL)

ACCESS Model 1: Multi-parametric optimization (commercial code (IPEK, IKA, 4 CONDITIONS LBF); implementation using commercial software Matlab/Simulink (mathworks.com) and commercial FE-software ANSYS (ansys.com), Abaqus (3ds.com))

The refinement and multi-parametric optimization of functional concepts is performed. The optimization is an iterative process, consisting of the following subtasks WORKFLOW  Detailing of CAD models 5 AND ITS  Structural optimization (model 1) to optimize fatigue and NVH RATIONALE properties  Multidisciplinary design optimization (MDO) using parametric model order reduction (pMOR) methods  Crash behavior (model 2) and consequent optimization. 

Model 1 for Structural Optimisation

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF Simulation of the fatigue and NVH behavior of a joint, lightweight THE USER optimized wheel house with strut tower and rails (one component) of a 1.1 CASE TO BE passenger car (C-segment) according allowable stresses and SIMULATED requirements for NVH defined by OPEL SotA material data for steel and aluminum will be used; once material 1.2 MATERIAL data measured within ALLIANCE become available those will be implemented joint wheel house with strut tower and rails (one component) of a C- segment vehicle 1.3 GEOMETRY Inputs are the CAD data provided by OPEL and/or derived within the project

1.4 TIME LAPSE Unknown

MANUFACTUR Operational loads defined by OPEL (accelerations, forces, displacements) ING PROCESS 1.5 OR IN- SERVICE CONDITIONS

PUBLICATION None available so far

1.6 ON THIS ONE SIMULATION

2 GENERIC PHYSICS OF THE MODEL EQUATION MODEL TYPE Solid mechanics (macro-mechanics) 2.0 AND NAME

MODEL finite volumes 2.1 ENTITY

MODEL Equation conservation of energy PHYSICS/ Physical Masses and mass moments of inertia, damping, stiffness, 2.2 CHEMISTRY EQUATION quantities displacement, internal and external forces PE

Relation Only constant values are entered, no constitutive equations are used

MATERIALS Physical 1. Masses and mass moments of inertia (M; matrix) RELATIONS 2.3 quantities/ 2. Damping (B; matrix) 3. Stiffness (C; matrix) descriptors 4. Displacement for each 5. Stresses MR 6. Internal and external forces (F; matrix) SIMULATED none 2.4 INPUT

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS NUMERICAL Implicit finite element solvers 3.1 SOLVER

3.2 SOFTWARE TOOL ANSYS, Abaqus

3.3 TIME STEP variable

PHYSICS Written up for the entity in the model EQUATION COMPUTATIONAL , 3.4 REPRESENTATION MATERIAL , RELATION S, MATERIAL

COMPUTATIONAL  Degrees of Freedom of the entire model 3.5 BOUNDARY  run-time of simulation CONDITIONS

ADDITIONAL SOLVER 3.6 PARAMETERS

4 POST PROCESSING

THE PROCESSED Allowable stresses and required eigenfrequencies which are used to 4.1 OUTPUT optimize the concept for a module. For this concept a crash test is done with model 2.

4.2 METHODOLOGIES n/a

4.3 MARGIN OF ERROR within 10% of measured mechanical properties

Model 2 for crash analysis

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE Simulation of the crash worthiness of a joint, lightweight optimised USER CASE TO BE wheel house with strut tower and rails (one component) of a 1.1 SIMULATED passenger car (C-segment) according current Euro NCAP standards; accelerations, displacements, forces and stresses will be iteratively optimized to meet weight targets and Euro NCAP standards

SotA material data for steel and aluminum will be used; once material 1.2 MATERIAL data measured within ALLIANCE become available those will be implemented

Optimised (with model 1) joint wheel house with strut tower and rails 1.3 GEOMETRY (one component) of a C-segment vehicle

1.4 TIME LAPSE about 100 milliseconds

MANUFACTURING crash conditions according current EURO NCAP standards; external PROCESS OR IN- forces and displacements (crash analysis) 1.5 SERVICE CONDITIONS

1.6 PUBLICATIONON None available so far

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE Solid mechanics (macro-mechanics) 2.0 AND NAME

MODEL finite volumes 2.1 ENTITY

MODEL Equation Tightly coupled time dependent equations of motion and PHYSICS/ conservation of energy CHEMISTRY 2.2 EQUATION Physical Masses and mass moments of inertia, damping, stiffness, quantities displacement, velocity, and acceleration, internal and PE external forces, time

Relation Only constant values are entered, no constitutive equations are used

MATERIALS Physical 1. Masses and mass moments of inertia (M; matrix) RELATIONS 2.3 quantities/ 2. Damping (B; matrix) 3. Stiffness (C; matrix) descriptors 4. Displacement, velocity, and acceleration (u, v, a; for each vectors) 5. Internal and external forces (F; matrix) MR 6. Stresses 7. Time (t; vector) SIMULATED  none 2.4 INPUT

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS

NUMERICAL 3.1 Implicit finite element solvers and explicit finite difference solver SOLVER

3.2 SOFTWARE TOOL ANSYS, Abaqus

3.3 TIME STEP variable

PHYSICS COMPUTATIONAL EQUATION, REPRESENTATION 3.4 MATERIAL Written up for the entity in the model RELATIONS,

MATERIAL

COMPUTATIONAL 3.5 BOUNDARY  Degrees of Freedom of the entire model CONDITIONS  run-time of simulation

ADDITIONAL 3.6 SOLVER PARAMETERS

4 POST PROCESSING

THE PROCESSED Crash worthiness is used to further optimize the concept for a 4.1 OUTPUT module.

4.2 METHODOLOGIES n/a

4.3 MARGIN OF ERROR within 10% of measured mechanical properties

ALMA (645776)

Summary of the project

ALMA will address the predictive design of heat management in materials and structures. In the current worldwide competition to develop better technologies, heat management poses a grand challenge that blocks further development in disciplines as varied as nano-electronics, power devices, random access memories, high temperature turbines, or thermoelectric energy conversion, to cite a few. In all these technologies, the right combination of novel compositions and structures can make the difference between a working device and one that will be disabled by thermal dissipation problems.

Heat in an electronic device

Project Acronym and Number: ALMA 645776 Project Title: ALL-SCALE PREDICTIVE DESIGN OF HEAT MANAGEMENT MATERIAL STRUCTURES WITH APPLICATIONS IN POWER ELECTRONICS Start and End Dates: from 01/06/2015 till 31/05/2018 EU Contribution: 3,264,664 € Coordinator: Natalio MINGO, [email protected] Modeller(s): Jesús Carrete Montaña, [email protected] Natalio Mingo, [email protected]

MODA Heat management in electronic devices in ALMA

OVERVIEW of the SIMULATION

The user wants to analyse the time and space evolution of the temperature distribution in a device, including effects beyond the reach of Fourier’s law, 1 USER CASE such as ballistic and sub-ballistic transport, and frequency-dependent boundary effects. MODEL 1 Electronic model: Electronic Density Functional Theory CHAIN OF 2 Atomistic phonon model: Monte Carlo solution of the Boltzmann MODELS MODEL 2 Transport Equation in the relaxation time approximation  W. Li, J. Carrete, N. A. Katcho & N. Mingo, Comp. Phys. Comm. 185 (2014) 1747 3 PUBLICATION  J.-P. M. Péraud, C. D. Landon & N.G. Hadjiconstantinou, Annual Rev. Heat Transfer, 17 (2014) 205 A variety of DFT packages are available under either commercial or open- source licenses. ACCESS The BTE part is implemented in AlmaBTE, an Apache-licensed (open-source) 4 CONDITIONS software package developed and owned by the ALMA development team (J. Carrete, G. Madsen, N. Mingo, B. Vermeersch & T. Wang). Web site: http://www.almabte.eu

Model 1

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED ASPECT OF THE Forces on each atom in a part of a semiconductor device consisting of USER CASE TO atoms whose species and positions are known. BE SIMULATED 1.1 AND ITS ROLE IN THE WORKFLOW 1.2 MATERIAL A crystalline semiconductor 1.3 GEOMETRY Bravais lattice + atomic motif 1.4 TIME LAPSE Zero: static setting MANUFACTURIN Zero pressure, zero temperature G PROCESS OR 1.5 IN-SERVICE CONDITIONS R. Martin, Electronic Structure: Basic Theory and Practical Methods 1.6 PUBLICATION (Cambridge University Press, 2004), ISBN 0521782856

2 GENERIC PHYSICS OF THE MODEL EQUATION MODEL Electronic model: Quantum Density Functional Theory 2.0 TYPE AND NAME MODEL Electrons 2.1 ENTITY MODEL Equations Kohn – Sham DFT 2.2 PHYSICS/

CHEMISTRY Physical Spatial coordinates, Bloch wave vector, Kohn – Sham EQUATION quantities wave functions, Hamiltonian, electronic charge density PE’S for each equation

Equations 1. Exchange and correlation functional 2. Projected-augmented wave dataset MATERIALS Physical 1. Exchange energy, correlation energy, electronic charge RELATIONS quantities/ density descriptors 2. Kinetic energy, all-electron charge densities, pseudo for each electron core densities, all-electron partial waves, MR pseudo partial waves, projector functions, matching radii PUBLICATION 2.3 ON THIS SIMULATION

3 SPECIFIC COMPUTATIONAL MODELLING METADATA NUMERICAL Self-Consistent Field (SCF) procedure 3.1 SOLVER 3.2 SOFTWARE TOOL VASP, https://www.vasp.at/ 3.4 TIME STEP Stationary state solution The DFT equations are applied to the set of valence COMPUTATIONAL electrons defined by the constituent atoms in the REPRESENTATION semiconductor. Nuclei are represented by points. The Refers to how PHYSICS wave functions of electrons are defined over a your EQUATION parallelepipedic unit cell. One-electron orbitals, the computational electronic charge density, and the local potential are 3.5 solver expressed in plane wave basis sets. represents the MATERIAL The exchange and correlation functionals are material, RELATIONS hardcoded. properties, MATERIAL The PAW datasets characterizing each kind of atom are equation expressed in terms of spherical harmonics and radial variables, grids BOUNDARY The calculations are done on a representative CONDITIONS parallelepipedic unit cell with periodic boundary conditions ADDITIONAL 1. Plane wave energy cutoff SOLVER 2. Number of Bloch wave vectors

PARAMETERS 3. Tolerance for the convergence of the SCF method

3.6 PUBLICATION

4 POST PROCESSING

THE PROCESSED Forces on atoms, Quantum mechanical phonon Hamiltonian (yielding 4.1 OUTPUT scattering amplitudes, group velocities, …) for atoms

METHODOLOGIES The Hellmann-Feynman theorem is used to compute the forces on 4.2 atoms in a set of configurations. A quantum mechanical phonon Hamiltonian is built from finite differences between these forces.

MARGIN OF ERROR Margin of error: typically within 10%, mostly due to the error in the 4.3 material relations (exchange and correlation functionals).

Model 2

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE Distribution of temperature vs. space and time, the thermal USER CASE TO BE conductivities, and so on in a system made up of crystalline 1.1 SIMULATED materials with or without explicit defects AND ITS ROLE IN THE WORKFLOW Crystalline semiconductors with various distributions of defects 1.2 MATERIAL (vacancies, dislocations…) Arbitrary geometries in scales ranging from nm to mm. The geometry 1.3 GEOMETRY is defined by an external boundary plus a set of atomistically described interfaces.

1.4 TIME LAPSE From ps to ms

MANUFACTURIN Isothermal or diffusive walls (interfaces between parts of the system) G PROCESS OR 1.5 IN-SERVICE CONDITIONS

1.6 PUBLICATION Unpublished work

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE Atomistic phonon model: Boltzmann Transport Equation and atomistic 2.0 AND NAME quantum-mechanics for phonon scattering

MODEL Atoms 2.1 ENTITY Equations 1. Peierls-Boltzmann transport equation

MODEL 2. Lippmann–Schwinger equation PHYSICS/ Physical 1. Time, spatial coordinates, phonon frequencies, phonon CHEMISTRY 2.2 quantities group velocities, phonon occupation numbers, EQUATION for each scattering rates PE’S equation 2. Green’s function, phonon wave functions, perturbation matrix, t matrix Equations 1. Phonon dispersion relations 2. Anharmonic force constants 3. Perturbation matrix MATERIALS Physical 1. Phonon wave vectors, phonon frequencies, phonon RELATIONS quantities/ group velocities

descriptors for 2. Phonon wave vectors, phonon branch indices, each MR anharmonic force constants 3. Perturbation to the phonon Hamiltonian in real or mixed real / reciprocal space Simulated A quantum mechanical phonon Hamiltonian calculated with DFT to 2.3 Input simulate phonon dynamics.

2.4 PUBLICATION

3 SPECIFIC COMPUTATIONAL MODELLING METADATA

NUMERICAL Monte Carlo 3.1 SOLVER

3.2 SOFTWARE TOOL AlmaBTE, http://www.almabte.eu, Apache license

3.4 TIME STEP Time is not discretized

COMPUTATIONAL PHYSICS Phonon-related quantities are defined over phonon REPRESENTATION EQUATION wave vectors and over phonon branches. Real space dependences are explicitly considered Refers to how MATERIAL your Anharmonic force constants are defined over atoms computational RELATIONS in real space. General perturbation matrices are 3.5 solver defined in N real space dimensions and M reciprocal represents the space dimensions, with N+M=3. material, MATERIAL Materials are characterized by properties, by an computationally described geometry of the equation atoms and the properties for each type of atoms variables, stored in HDF5 files

BOUNDARY Isothermal walls (phonon reservoirs in thermal CONDITIONS equilibrium), periodic boundaries, diffusive walls

(with elastic but otherwise random scattering of phonons) and atomistically described internal interfaces.

ADDITIONAL 1. Density of the wave vector grid SOLVER 2. Broadening of the phonon modes PARAMETERS

3.6 PUBLICATION

4 POST PROCESSING

THE PROCESSED Finite volumes 4.1 OUTPUT IS CALCULATED FOR

METHODOLOGIES Temperatures, thermal currents and thermal conductivities and 4.2 functions of space and time are computed by integrating the results of the BTE solver over wave vectors and frequencies

MARGIN OF For most semiconductors, errors within 10% are achievable, and ERROR come mostly from imprecisions inherited from DFT. For some high- 4.3 conductivity materials, systematic errors of 20-30% come from the relaxation time approximation.

AMPHIBIAN (720853)

Summary of the project

The main goal of the project is to develop up-scalable and cost-efficient methods for the fabrication of ferrite-based hybrid magnets with enhanced magnetic performance. These are to substitute rare-earth permanent magnets currently used in energy storage applications.

Magnets for a flywheel

Project Acronym and Number: AMPHIBIAN 720853 Project Title: Anisometric permanent hybrid magnets based on inexpensive and non-critical materials Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution: 4,948,707.50 € Coordinator: Adrian QUESADA, [email protected] Modeller(s): Adrián QUESADA, [email protected] Dmitry Berkov, [email protected]

ARGICS-M

ARGIGS-M (720887)

Summary of the project

ARCIGS-M aims to further develop the Copper Indium Gallium Selenide thin film solar cell technology towards higher efficienc, by using novel approaches in passivation, patterning and optical design. These advances of the technology enable the use of ultra-thin CIGS layers and the use of steel as substrate materials along with glass. They target the building integrated photovoltaic market.

Optical and electrical behaviour of solar cell

Project Acronym and Number: ARGIGS-M 720887 Project Title: Advanced aRchitectures for ultra-thin high-efficiency CIGS solar cells with high Manufacturability Start and End Dates: from 1/12/2016 till 30/11/2019 EU Contribution: 4,498,700.88 € Coordinator: Marika Edoff, [email protected] Modeller(s): Janez Krc, [email protected] Marko Topic, [email protected] Joop van Deelen, [email protected]

ARGICS-M

MODA

Optical and electrical device simulation

Project ARCIGS-M

OVERVIEW of the SIMULATION The user wants to simulate (ultra-thin) CIGS solar cells with different contacting schemes. Concepts such as additional passivation layers, highly reflective back reflector, local back contacting are included. The 1 USER CASE purpose of simulation is to understand and analyse opto-electronic behaviour of the device and to optimize it with respect of optical (light management) and electrical (layer and interface quality, contacting scheme) point of view. Continuum model: electromagnetic wave propagation in the MODEL 1 device, propagation of light in (semi) absorbing material, interface reflection, transmission, scattering included. Electronic model: statistical drift-diffusion transport model used in continuum material, transport of charge carriers CHAIN OF MODEL 2 (electron and holes) in semiconductor and contacting layers, 2 MODELS optical and thermal carrier generations and recombinations, interface recombinations, Continuum model: simple one- or two-diode electrical model, MODEL 3 describing relationship between electrical voltage and current of the device, theory behind is the drift-diffusion model ,

PUBLICATION ON THIS 3 ONE SIMULATION The specified models are widely used in opto-electronic simulations of ACCESS 4 semiconductor devices and are implemented in commercial software such CONDITIONS as COMSOL, Sentaurus T-CAD and others. Thicknesses of the CIGS absorber is in the range of a few hundred nanometers, thus, no special quantum effects need to be included in the simulations. First, optical simulation is performed to determine charge-generation WORKFLO distribution in layers as input parameter for the electrical simulation. 5 W AND ITS These two models are linked. Additionally, well known one- and two- RATIONALE diode model of a solar cell is then linked further to get additional information about the quality of the solar cell device. (input J(V) characteristics)

ARGICS-M

MODEL 1

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE To perform detailed optical simulation of (ultra-thin) CIGS solar cell. To USER CASE TO BE analyse and understand optical behaviour, to generate input for linked 1.1 SIMULATED electrical simulation, to optimize device optically (proposed light management strategies). Simulated device consists of the following basic layers: front transparent contact: ZnO:Al + ZnO window layer: CdS (n-type) 1.2 MATERIAL absorber layer: (ultra-thin) Cu(In, Ga)Se2 (p-type) passivation layer: Al2O and MgF2 back contact: Mo substrate: thin steel foil / soda lime glass vertical dimensions of device (W/o substrate): ~ m, lateral 1.3 GEOMETRY dimensions: mm to several cm

1.4 TIME LAPSE not applicable

MANUFACTURING PROCESS OR IN- 1.5 incoming light SERVICE CONDITIONS

PUBLICATION 1.6 ON THIS ONE SIMULATION

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE Continuum model - Electromagnetism - Optics 2.0 AND NAME

MODEL finite volumes 2.1 ENTITY Equation PE: Maxwell’s equations  E   B  0 B E   t MODEL E PHYSICS/ BJ    2.2 CHEMISTRY t EQUATION which present the basis for wave equation, describing the PE propagation of electromagnetic waves. Physical  – space charge density quantities E – electric field B – magnetic flux density J – electrical current density Relation 2.3 MATERIALS MR: DE  , BH 

ARGICS-M

RELATIONS  and  describe material properties and directly determine complex refractive indices of layers Physical D – electric flux density quantities / E – electric field descriptor B – magnetic flux density s for each MR H – magnetic field  - permittivity (material property)  - permeability (material property)

SIMULATED 2.4 INPUT

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS

NUMERICAL Finite element method (FEM) 3.1 SOLVER

3.2 SOFTWARE TOOL COMSOL Multiphysics

3.3 TIME STEP not applicable, frequency domain

PHYSICS PE: Maxwell’s equations (see above) applied to each EQUATION, discrete element in the mash-grid. COMPUTATIONAL MATERIAL 3.4 REPRESENTATION MR: connections between E and H and D and B via RELATIONS, permittivity and permeability, permittivity is linked to , MATERIAL complex refractive indexes which are actual input parameters of simulation top and bottom side of the device: Perfectly matched layers (PML), COMPUTATIONAL Absorbing boundary condition (ABC), 3.5 BOUNDARY other sides of the device: CONDITIONS Periodic boundary condition (PBC), Symmetry boundary condition (SBC)

ADDITIONAL mesh-grid: > 5 discrete elements per effective wavelength 3.6 SOLVER PARAMETERS

Post processing

4 POST PROCESSING

THE PROCESSED charge carrier generation distribution, optical reflection, transmission 4.1 OUTPUT and absorption in individual layers for Model 2

METHODOLOGIE Volume averaging; applying Poynting vector to electric and magnetic 4.2 S field

MARGIN OF 4.3 numerical error < 1 % in post-processing ERROR

ARGICS-M

MODEL 2

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE To perform detailed electrical simulation of (ultra-thin) CIGS solar cell. To 1.1 USER CASE TO analyse and understand electrical behaviour, to optimize device BE SIMULATED electrically (layers, interfaces, contacting schemes). Device consists of the following basic layers: front transparent contact: ZnO:Al + ZnO window layer: CdS (n-type) absorber layer: (ultra-thin) Cu(In, Ga)Se2 (p-type) 1.2 MATERIAL passivation layer: Al2O and MgF2 back contact: Mo substrate: thin steel foil / soda lime glass energy bandgaps, electron affinities, doping, tails states, mobilities, interface recomb.,

1.3 GEOMETRY several cm

1.4 TIME LAPSE steady state analysis

MANUFACTURIN voltage bias, temperature G PROCESS OR 1.5 IN-SERVICE CONDITIONS

PUBLICATION 1.6 ON THIS ONE SIMULATION

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE Electronic model, Statistical charge transport model – Drift-diffusion 2.0 AND NAME applied to continuum material

MODEL finite volumes 2.1 ENTITY Equation PE: basic semiconductor equations (represented for 1D, can be extended to 2D and 3D): dn J q n E q D n n n dx dp J q p E q D p p p dx p 11JJpp GR  pp  0  MODEL t q  x p q  x PHYSICS/ n 11J n  n  J 2.2 CHEMISTRY GR  nn  0  EQUATION t q  x n q  x PE Eq  ()p  n  N  N x  DA

Physical J – electrical current density (n- of electrons and p - holes) quantities n – electron concentration p – hole concentration E – electric field  – space charge density

ARGICS-M

G – charge generation rate R – charge recombination rate

ND – donor concentration

NA – acceptor concentration  – mobility coefficient of carriers D – diffusion coefficient of carriers q – elementary charge Relation 푞퐷푛(푝) Einstein relation: 휇푛(푝) = 푘퐵푇 MATERIALS Physical relation between mobility n(p) and diffusion coefficient Dn(p) 2.3 RELATIONS quantities to each other; T = temperature /descript ors for each MR

2.4 SIMULATED INPUT charge carrier generation distribution from Model 1

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS

NUMERICAL Finite difference / Finite element method 3.1 SOLVER SCAPS (1D) / ASPIN3 (2D) / ATLAS / SENTAURUS T-CAD (3D) 3.2 SOFTWARE TOOL decision made upon specifics of the problem

3.3 TIME STEP not applicable, steady state simulation

PHYSICS Above mentioned semiconductor equations are applied COMPUTATIONAL EQUATION, to discrete elements of the device structure 3.4 REPRESENTATION MATERIAL RELATIONS, MATERIAL

COMPUTATIONAL ohmic contact, selective, schottky, perfect isolation surface, periodic 3.5 BOUNDARY CONDITIONS

ADDITIONAL SOLVER mesh-grid: order of diffusion length 3.6 PARAMETERS

Post processing

4 POST PROCESSING

THE PROCESSED current density – voltage (J(V)) curve, external quantum efficiency (EQE) 4.1 OUTPUT and any internal parameter distribution upon user request

METHODOLOGIE applying different voltages to device in simulation and calculate current 4.2 S densities, separate application of charge generation by light to obtain spectral responses such as EQE

MARGIN OF 4.3 numerical error < 2 % in post-processing ERROR

ARGICS-M

MODEL 3

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE To extract basic parameters of the one- and two-diode model of (ultra- 1.1 USER CASE TO thin) CIGS solar cell and to generally evaluate the quality of the solar cell BE SIMULATED CIGS solar cell represented by equivalent electrical circuit with two 1.2 MATERIAL electrical connection ports

1.3 GEOMETRY complete solar cell area

1.4 TIME LAPSE steady state analysis

MANUFACTURIN temperature G PROCESS OR 1.5 IN-SERVICE CONDITIONS

PUBLICATION 1.6 ON THIS ONE SIMULATION

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL Continuum model – Electromagnetism - electrical 2.0 TYPE AND NAME

MODEL complete device volume 2.1 ENTITY Equation PE1: one-diode equation

Physical I – device electrical current quantities IL – photocurrent V– device voltage

RS – series resistance

RSH – shunt resistance MODEL

PHYSICS/ I0 – diode saturation current CHEMISTRY 2.2 n – diode ideality factor EQUATION

PE Equation PE2: two-diode equation

ARGICS-M

Physical I – device electrical current quantities IL – photocurrent V– device voltage

RS – series resistance

RSH – shunt resistance

I0 – diode saturation current (of first and second diode) n – diode idelaity factor (of first and second diode) Relation   2 p n I0  AkTni () LNLNp D n A

Physical S – diode saturation current quantities/ A – area MATERIALS descriptors 2.3 RELATIONS k – Boltzmann constant for each MR ni – intrinsic concentration of electrons  – mobility coefficient of carriers (e-electrons, p-holes) L – diffusion length of carriers

ND – donor concentration

NA – acceptor concentration

SIMULATED current density – voltage (J(V)) curve 2.4 INPUT .

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS

NUMERICAL method for solving the system of non-linear equations (e.g. Newton) 3.1 SOLVER

3.2 SOFTWARE TOOL Matlab

3.3 TIME STEP not applicable, steady state simulation

COMPUTATIONAL PHYSICS EQUATION, depending on the selected method of solving 3.4 REPRESENTATION MATERIAL RELATIONS, the system of non-linear equations , MATERIAL

COMPUTATIONAL none 3.5 BOUNDARY CONDITIONS

ADDITIONAL SOLVER accuracy tolerance 3.6 PARAMETERS

Post processing

4 POST PROCESSING

THE PROCESSED There is no post-processing related to this model. I0 and n values as well 4.1 OUTPUT as the values for parallel (shunt) and series resistances of realistic diodes are already the raw output data of Model 3.

4.2 METHODOLOGIES

MARGIN OF 4.3 ERROR

CRITCAT(686053)

Summary of the project

CRITCAT will provide solutions for the substitution of critical metals, especially rare platinum group metals , used in heterogeneous and electrochemical catalysis. CRITCAT will explore the properties of ultra-small transition metal alloy, phosphide, sulphide, oxide, and carbide nanoparticles in order to achieve optimal catalytic performance with sustainable, earth-abundant materials.

Catalist performance of ultra-small metal alloys

Continue

Project Acronym and Number: CRITCAT 686053 Project Title: Towards Replacement of Critical Catalyst Materials by Improved Nanoparticle Control and Rational Design Start and End Dates: from 01/06/2016 till 31/05/2019 EU Contribution: 4,369,292.5 € Coordinator: Jaakko AKOLA, [email protected] Modeller(s): Adam Foster, [email protected] David Gao, [email protected] Jaakko Akola, [email protected] Kari Laasonen, [email protected]

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DEEPEN (604416)

Summary of the project

DEEPEN focuses on new energy-efficient nanoscale electronic and photonic devices. Nanowires, nanoparticle arrays and quantum wells are just some of the large ensemble of new structures proposed for future device applications. This project aims at the development of an integrated multi-scale modelling environment, particularly suited for studying electronic, transport and optical properties of novel nanoscale devices.

Behaviour of LED structures

Project Acronym and Number: DEEPEN 604416 Project Title: From atom-to-Device Explicit simulation Environment for Photonics and Electronics Nanostructures Start and End Dates: from 01/01/2014 till 31/12/2016 EU Contribution: 2,686,000 € Coordinator: Eoin O'Reilly, [email protected] Modeller(s): Eoin O' Reilly, [email protected] Fabio Enrico Sacconi, [email protected] James Greer, [email protected] Mathieu Luisier, [email protected]

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MODA

Characteristics of nano-electronic devices

DEEPEN

OVERVIEW of the SIMULATION

Current-voltage characteristics of an InGaAs-based nanoelectronic device, or 1 USER CASE current-voltage-luminescence characteristics of III-N light-emitting-diode (LED) structures. Semi-empirical tight binding potential (TB) model (electronic MODEL 1 model) CHAIN OF 2 MODELS Non-Equilibrium Green’s Function Model for Transport of MODEL 2 Electrons (electronic model)

MODEL 3 Semi-classical Drift-Diffusion model (continuum model) 3 PUBLICATION

Within DEEPEN, two commercial tools are used for drift-diffusion model: ACCESS Sentaurus Device (from Synopsys) and TiberCAD (from TiberLab) (both 4 CONDITIONS available for purchase). Two in-house tools are used for NEGF model: OMEN (from ETHZ) and TiMeS (from Tyndall) (neither currently supported for external users, but other NEGF codes also available). WORKFLO Quantum mechanical treatment of the device core region, while treating the 5 W AND ITS materials surrounding the core using continuum models. RATIONALE

Schematic of a typical device structure simulated in DEEPEN

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MODEL 1 Semi-empirical tight binding potential model (TB)

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

Calculation of interactions (expressed by Hamiltonian) in the core ASPECT OF THE region, taking account of factors such as nanodevice composition and USER CASE TO 1.1 geometry, including local atomic configurations, as well as influence of BE SIMULATED externally applied perturbations such as electric fields. The calculated AND ITS USE IN Hamiltonian is to be used in the next model for calculation of THE WORKFLOW electronic structure of semiconductor nanoelectronic devices. Nano-scale transistor with InGaAs channel. Non simulated input to describe this material will be tight-binding on-site and interatomic 1.2 MATERIAL matrix elements, including their dependence on bond length and bond angle distortions. Atomic coordinates and atom type at each position in region are calculated in a pre-processing operation 1.3 GEOMETRY See device schematic at front of document 1.4 TIME LAPSE Not applicable

MANUFACTURIN Not applicable 1.5 G PROCESS OR IN-SERVICE CONDITIONS 1.6 PUBLICATION

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE Semi-empirical tight binding potential (TB) 2.0 AND NAME

MODEL The entity in this materials model is electrons 2.1 ENTITY

Equation Time-independent Schrödinger Equation (TISE) for electron states MODEL PHYSICS/ Hψ = Eψ 2.2 CHEMISTRY EQUATION Physical H Hamiltonian PE1 quantities  Wavefunctiion E Energy

Equation TISE expressed in matrix form, with individual

diagonal matrix elements Hii and off-diagonal matrix

elements Hij and with overlap between different basis MATERIALS states given by Sij; RELATION 1 2.2.1 MR1 TO det|Hij − ESij| = 0 PE1 Physical On-diagonal elements Hii giving basis state self-energy quantities/ (may include external potential or may be added in

next step of workflow), off-diagonal elements Hij giving

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descriptors energy interaction between basis states and Sij describing overlap between states, with overlap

generally given by Sij = δij in TB model. The quantities

that contribute to the values of Hii and Hij include atomic orbital self-energies, interatomic matrix elements, spin-orbit coupling energies, crystal field splitting energies, band structure deformation potentials, strain tensor, polarization fields; number of treated conduction and valence bands. 2. SIMULATED None 4 INPUT

2. PUBLICATIO 5 N

3 COMPUTATIONAL MODELLING METADATA

NUMERICAL Matrix Algebra 3.1 SOLVER

Tight-binding Hamiltonian matrix can be generated as part of OMEN suite of codes for input into OMEN NEGF calculations. TB matrix can also be generated using other codes, but may then need post- 3.2 SOFTWARE TOOL processing to ensure matrix appropriately formatted for input to OMEN. [OMEN not currently supported for external users, but other NEGF codes also available].

Matrix size determined by number of atoms included in calculation 3.3 GRID SIZE times number of basis states used per atom.

3.4 TIME STEP None

COMPUTATIONAL PHYSICS TISE is expressed in a matrix format. REPRESENTATION EQUATION

refers to how MATERIAL Value of individual matrix elements determined by your RELATIONS atom type and neighbouring atom types, as well as by computational relative positions of a given atom and its neighbours. 3.5 solver represents the MATERIAL Atomic coordinates and parameters are stored as material, floating point values. NEGF codes undertake matrix properties, manipulations in double precision. equation variables,…..

3.6 PUBLICATION

4 POST PROCESSING

4. THE Hamiltonian calculated for finite volumes representing the core

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1 PROCESSED region of the device to be used in next model NEGF, OUTPUT IS Band structure may be calculated at selected k points CALCULATED FOR

METHODOLOGI  The order of storing the Hamiltonian matrix elements generated, H , may need to be re-arranged in order to 4. ES ij be in format suitable for input into NEGF code used in 2 workflow.  band structure [E(n,k)] calculated directly from single particle energies MARGIN OF  Main sources of error: 1) accuracy in materials parameters used; 2) size of supercell used RROR E  error due to choice of materials parameters from ~1 4. meV (best case) to ~100 meV (extreme case); 3  error due to size of supercell also varies with materials; for materials where properties vary smoothly with supercell size (such as InGaAs devices), error in band- edge energy can be converged to < 1% for moderate size supercells (~103 atoms).

MODEL 2 NEGF for quantum transport

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED

ASPECT OF THE Calculation of quantum transport of electrons and holes in USER CASE TO BE semiconductor devices based on nanostructure. Electrical properties such as current density and charge densities are to be 1.1 SIMULATED calculated taking into account applied bias and material and AND HOW IT FORMS geometrical properties of the device. These properties will be used A PART OF THE to calculate the flow of electrons through the device. TOTAL USER CASE

1.2 MATERIAL Nano-scale transistor with InGaAs channel.

1.3 GEOMETRY See device schematic at front of document

1.4 TIME LAPSE Not applicable

B MANUFACTURING f (E, EfB) Fermi-Dirac distribution function of the electrons in PROCESS OR IN- contact B with the Fermi level E . The applied bias determines the 1.5 fB SERVICE shift of the contact Fermi levels with respect to their equilibrium CONDITIONS position.

1.6 PUBLICATION

2 GENERIC PHYSICS OF THE MODEL EQUATION

MODEL TYPE AND Non-Equilibrium Green’s Function Model for Transport of Electrons 2.0 NAME

2.1 MODEL ENTITY The entity in this materials model is electrons expressed by Green's

105

functions.

Green’s function equations (SE-H)G(E)=I

MODEL Equation This equation applied for quantum transport is often PHYSICS/ combined with the MR given below. But here we give 2.2 CHEMISTRY the most generic form of the PE. EQUATION E Electron energy PE1 Physical quantities H Hamiltonian matrix representing the device S Overlap matrix between all involved atomic orbitals

Physical Hamiltonian in NEGF described using localised basis quantities/ states in a matrix equation; with on-diagonal elements Hii giving basis state on-site energy (interaction descriptors between one atomic-like orbital and itself), including external potential, off-diagonal elements Hij (interactions with neighbours) giving energy interaction between basis states and Sij describing overlap between states; Hij = ⟨ϕi|H|ϕj⟩; Sij = ⟨ϕi|ϕj⟩where I are localised basis states over which H defined.

The generic PE is often combined with the MR given below and then reads

Retarded Green function: [ES − H − ΣRB(E) − ΣRS(E)]GR(E) = I Lesser/Greater Green’s Functions: MATERIALS G≷(E) = GR(E). (Σ≷B(E) + Σ≷S(E)) . GA(E) 2.2.1 RELATION 1

MR1 TO PE1 ΣRB(E) Boundary retarded self-energy ΣRS(E) Scattering retarded self-energy Σ≷B(E) Boundary lesser/greater self-energy Σ≷S(E) Scattering lesser/greater self-energy GR(E) Retarded Green’s Function GA(E) Advanced Green’s Function G<(E) Lesser Green’s Function G>(E) Greater Green’s Function Here the advanced Green's function is defined as : GA(E) = (GR(E))† Note that retarded and advanced solutions correspond to outgoing and incoming waves in contacts.

The Green’s functions dependencies are: GR(E) − GA(E) = G>(E) − G<(E) Difference between the retarded and advanced Green’s functions is equal to the difference between the greater and lesser Green’s functions

106

From the definition of the self-energies, the following relations that ensure current conservation are derived

First relation between the boundary self- energies

ΣRB(E) − ΣAB(E) = Σ>B(E) − Σ

Difference between the boundary retarded and advanced self-energies is equal to the difference between the boundary greater and lesser self-energies

Advanced boundary self-energy:

ΣAB(E) = (ΣRB(E) )†

Conjugate of boundary retarded self-energy ΣRB(E) is boundary advanced self-energy ΣRA(E)

Second relation between the boundary self- energies:

>B RB AB Σ (E) = − (Σ (E) − Σ (E)) ∙ (fC(E)-1) fc(E) Fermi distribution function of the electrons in the contact C. It requires the knowledge of the corresponding Fermi level EFc.

Scattering self-energies (description of alloy disorder, roughness, impurity, electron-phonon, and carrier-carrier scattering)

RS Σ (E) = ℒR(scattering mechanisms)

~~>S Σ (E) = ℒ>(scattering mechanisms)~~

~~ℒR Function relating any scattering mechanism to the retarded self-energy ΣRS(E)~~

~~ℒ< Function relating any scattering mechanism to the lesser self-energy Σ~~

~~ℒ> Function relating any scattering mechanism to the greater self-energy Σ>S(E)~~

~~First relation between the scattering self- energies~~

~~ΣRS(E) − ΣAS(E) = Σ>S(E) − Σ~~

~~Difference between the scattering retarded and advanced self-energies is equal to the difference~~

~~107~~

~~between the scattering greater and lesser self-energies~~

~~Advanced scattering self-energy:~~

~~† ΣAS(E) = (ΣRS(E) )~~

~~Conjugate of boundary retarded self-energy ΣRB(E) is boundary advanced self-energy ΣRA(E)~~

~~Second relation between the scattering self- energies:~~

~~Γ(E) dE′ Γ(E′) ΣRS(E) = −i + ℘ ∫ 2 2π E − E′~~

~~Γ(E) = i(Σ>S(E) − Σ~~

~~℘ Cauchy principal integral value~~

~~Boundary self-energies (coupling of device with its contacts)~~

~~RB Σ (E) = ℱR(HDC)~~

~~>B B Σ (E) = ℱ>(HDC)(f (E, EfB) − 1)~~

~~where:~~

~~HDC Hamiltonian matrix describing the coupling between the device (D) and its contacts (C)~~

~~ℱR Function relating HDC and the boundary retarded self- energy. Several models exist.~~

~~ℱ< Function relating HDC and the boundary lesser self- energy. Several models exist.~~

~~ℱ> Function relating HDC and the boundary greater self- energy. Several models exist.~~

~~SIMULATED HAMILTONIAN matrix from model 1, including details of open 2.4 INPUT contacts~~

~~PUBLICATION 2.6 ON THIS ONE SIMULATION~~

~~3 COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Matrix Algebra 3.1 SOLVER~~

~~Within DEEPEN, two in-house tools are used: OMEN (from ETHZ) and 3.2 SOFTWARE TOOL TiMeS (from Tyndall) (neither currently supported for external users, but other NEGF codes also available)~~

~~108~~

~~Matrix size determined by number of atoms included in calculation 3.3 GRID SIZE times number of basis states used per atom.~~

~~3.4 TIME STEP None~~

~~COMPUTATIONAL PHYSICS TISE, Green’s function and self-energy equations all REPRESENTATION EQUATION expressed in a matrix format.~~

refers to how MATERIAL Green’s function, self-energy and Hamiltonian matrix your RELATIONS elements calculated by iterative solution of coupled computational equations. 3.5 solver represents the MATERIAL Hamiltonian, Green’s function and self-energy data all material, stored as floating point values. NEGF codes undertake properties, matrix manipulations in double precision. equation variables,…..

The approach taken in OMEN is overviewed in M. Luisier, "Atomistic simulation of transport phenomena in nanoelectronic devices", Chem. Soc. Rev., 2014,43, 4357-4367. The approach taken in TiMeS is overviewed in D. Sharma, L. Ansari, B. Feldman, 3.6 PUBLICATION M. Iakovidis, J. C. Greer and G. Fagas “Transport properties and electrical device characteristics with the TiMeS computational platform: Application in silicon nanowires”, J. Appl. Phys. 113, 203708 (2013)

~~4 POST PROCESSING~~

THE PROCESSED  Distribution of electron states with respect to energy with open OUTPUT IS boundary conditions CALCULATED FOR  Spatially- and energetically-resolved density-of-states (DOS)  Energy-resolved transmission probability 4.1  Carrier density  Current flow Electrostatic potential all of these are calculated for finite volumes to be used in the continuum model 3.

~~109~~

METHODOLOGIES  Electrostatic potential from the carrier density through the Poisson equation ∇. ε∇V = −q(p − n + ∑i[δ(퐫Di − 퐫)] − ∑j[δ(퐫Aj − 퐫)]) with  Dielectric constant th rDi Position of i donor atom th rAj Position of j acceptor atom

Spatially- and energetically-resolved density-of-states (DOS) i calculated through energy integration, n = − ∫ dE G<(E) ; p = 4.2 2π i ∫ dE G>(E); with carrier densities n (p) and potential V 2π

~~The electrostatic potential is determined from the carrier density through the Poisson equation~~

~~ Energy-resolved transmission probability from Green’s or Wave Function  Current flow from the transmission probability, through energy integration~~

MARGIN OF  Generation of energy grid that captures the DOS features, can lead to significant error in the carrier density. 4.3 ERROR  Convergence of Poisson equation, needed: <0.1% variations in the electrostatic potential. If not, possible changes in the current by >10%.

~~MODEL 3 Semi-classical Drift-Diffusion model~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Device characteristics of nano-scale InGaAs transistors. Electrical ASPECT OF THE properties such as current density and charge densities are obtained 1.1 USER CASE TO taking into account applied bias and material and geometrical properties BE SIMULATED of the device.

~~1.2 MATERIAL Nano-scale transistor with InGaAs channel.~~

~~1.3 GEOMETRY See device schematic at front of document~~

~~1.4 TIME LAPSE Not applicable~~

~~MANUFACTURIN Voltage bias G PROCESS OR 1.5 IN-SERVICE CONDITIONS~~

~~PUBLICATION 1.6 OF THIS SIMULATION~~

~~110~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Semi-classical Drift-diffusion model (Chapter 4 in RoMM) 2.0 AND NAME This is a system of coupled current equations, Poisson equations and continuity equations~~

MODEL This is a materials model for concentration of electrons considered as a 2.1 ENTITY continuum and the equation is written up for finite volumes (the model entity) corresponding to the active layers in the device

~~Equation Current equations for electron current Jn and hole~~

~~current Jp~~

~~퐉n = qn(퐫)μn퐄 + qDn훁n~~

~~MODEL 퐉p = qn(퐫)μp퐄 + qDp훁p PHYSICS/ 2.2 CHEMISTRY Physical q Electron charge EQUATION quantities PE1 Jn(p) Electron (hole) current density~~

~~n(p) Electron (hole) mobility E Electric field, given by 퐄 = −훁V where V is potential~~

~~Dn(p) Electron (hole) diffusion coefficient~~

Equation Einstein relation qD MATERIALS n(p) μn(p) = RELATION 1 kBT MR1 TO Physical Einstein relation often (not always) used to relate PE1 quantities/ values of mobilityn(p) and diffusion coefficient Dn(p) descriptors to each other; T = temperature

Equation Mobility models – wide range of models in use MATERIALS RELATION 2 Physical Models for mobility can include many factors, MR2 TO quantities/ including phonon scattering, charged impurity 2.2.1 PE1 descriptors scattering alloy scattering, each with different specified T dependence

MATERIALS Equation Relation between carrier densities n, p and potential RELATION 3 V MR3 TO Physical Range of different approaches used; all include a PE1 quantities/ dependence on intrinsic carrier density, ni, potential descriptors V and electron (hole) quasi-Fermi energies, n(p), e.g. in Boltzmann approximation

~~q(V − ϕn) n = niexp ( ) kBT~~

~~Equation Poisson equation, describing how the potential varies with position MODEL PHYSICS ∇. ε∇V = −q(p − n + ND − NA)~~

~~EQUATION Physical  Dielectric constant PE 2 quantities ND Donor doping density~~

~~NA Acceptor doping density~~

~~111~~

~~Equation Relation between carrier densities n, p and potential V~~

MATERIALS Physical Range of different approaches used; all include a RELATION 1 quantities/ dependence on intrinsic carrier density, n , potential i MR1 TO descriptors V and electron (hole) quasi-Fermi energies, n(p), PE2 e.g. in Boltzmann approximation

~~q(V − ϕn) n = niexp ( ) kBT~~

Equation Continuity equations, to ensure conservation of charge: MODEL ∂n 1 = 훁. J + U PHYSICS/ ∂t q n n CHEMISTRY ∂p 1 = − 훁. J + U EQUATION ∂t q p p PE 3 Physical Un Net electron generation rate quantities Up Net hole generation rate

~~Equation Many different expressions available for Un, Up, most common of which is Shockley-Read-Hall recombination expression:~~

~~MATERIALS RELATION 1~~

MR1 TO PE3 Physical ni,eff intrinsic carrier concentration quantities/ n(p) electron (hole) lifetime parameters descriptors n(p)1 parameters that introduce the dependency of the recombination rate on the trapping energy

~~level Eτ~~

Material composition as function of position in device, with composition SIMULATED 2.4 also determining energy gap, density of states and intrinsic band offsets. INPUT Doping, carrier mobilities and recombination rates as function of position.

~~2.6 PUBLICATION~~

~~3 COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Finite element model 3.1 SOLVER~~

~~Within DEEPEN, two commercial tools are used: Sentaurus Device 3.2 SOFTWARE TOOL (from Synopsys) and TiberCAD (from TiberLAB) (both available for purchase)~~

Nm scale grid size. See http://www.tiberlab.com/en/documentation.html for TiberCAD details. 3.3 GRID SIZE Sentaurus Device application examples can be requested from http://www.synopsys.com/cgi-bin/tcad/appex/req1.cgi.

~~3.4 TIME STEP N/A~~

~~3.5 COMPUTATIONAL PHYSICS Finite element discretisation of equations given in part 2~~

~~112~~

REPRESENTATION EQUATION where variable e.g. charge density defined for each refers to how finite element. See your http://www.tiberlab.com/en/documentation.html for computational TiberCAD details. Sentaurus Device application solver examples can be requested from represents the http://www.synopsys.com/cgi-bin/tcad/appex/req1.cgi.

material, MATERIAL Finite element discretisation of relations given in part 2 properties, RELATIONS where equation defined for each finite element and its equation neighbours. See variables,….. http://www.tiberlab.com/en/documentation.html for TiberCAD details. Sentaurus Device application examples can be requested from http://www.synopsys.com/cgi-bin/tcad/appex/req1.cgi.

MATERIAL Material determines which input parameter set is selected. See http://www.tiberlab.com/en/documentation.html for TiberCAD details. Sentaurus Device application examples can be requested from http://www.synopsys.com/cgi-bin/tcad/appex/req1.cgi.

Sentaurus Device newsletters and further information can be requested from http://www.synopsys.com/cgi- 3.6 PUBLICATION bin/tcad/appex/req1.cgi. See http://www.tiberlab.com/en/documentation.html for TiberCAD details.

~~4 POST PROCESSING~~

THE PROCESSED  a finite volume, representing the active layers and contacts OUTPUT IS and is the current-voltage curves. [Current-voltage-luminance CALCULATED FOR data can also be obtained in simulation of III-N devices.] 4.1  Data can also be processed to give:  Electric field (from voltage profile)  Heat source (from current and voltage profile)  Quasi Fermi level (electro-chemical potential)

METHODOLOGIES  Run the DD model for a series of voltages to obtain 4.2 current-voltage curves, or for time following a stimulus to analyse device high-speed characteristics MARGIN OF ERROR  Due to exponential dependence of charge density on electrostatic potential, variations <0.1% in the electrostatic potential are needed in solving Poisson 4.3 equation; otherwise possible changes in the current by >10%.  The error is sensitive to the accuracy of the input parameters, and to the extent to which these parameters represent real devices. An error of 10% is attainable.

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~~EENSULATE (723868)~~

~~Summary of the project~~

EENSULATE works in the domain of energy friendly construction. The project will develop a highly insulating mono-component and environmentally friendly spray foam for the opaque components of curtain walls which will also reduce thermal bridges thus increasing the thermal resistance of the whole façade. The project will also develop a lightweight and thin double pane vacuum glass manufactured through an innovative low temperature process using polymeric flexible adhesives and distributed getter technology. A multifunctional thermos-tuneable coating will allow for dynamic solar gain control as well as anti-fogging and self-cleaning.

~~Sorption and permeation in insulating material for windows~~

~~continue~~

~~114~~

~~Thermal and mechanical behaviour of window with the new material~~

Project Acronym and Number: EENSULATE 723868 Project Title: Development of innovative lightweight and highly insulating energy efficient components and associated enabling materials for cost-effective retrofitting and new construction of curtain wall facades Start and End Dates: from 1/8/2016 till 31/01/2020 EU Contribution: 5,201,843.13 € Coordinator: Daniela RECCARDO, [email protected] Modeller(s): Daniela Reccardo, [email protected]

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~~EIROS (685842)~~

~~Summary of the project~~

The EIROS project will develop self-renewing, self-healing, erosion resistant and anti-icing composite materials for use in extreme environments (high erosion and very low temperature). Potential end user applications include on wind turbine blades, aircraft and rotorcraft leading edges, automotive components and cryogenic storage tanks for space applications. Multiple-functionalised nanoparticles added to the bulk resin of fibre-reinforced composites.

~~Materials for extreme environments~~

~~continue~~

~~116~~

Project Acronym and Number: EIROS 685842 Project Title: Erosion and Ice Resistant cOmposite for Severe operating conditions Start and End Dates: from 08/03/2016 till 07/03/2019 EU Contribution: 7,993,173.75 € Coordinator: Simona SCHRAMMEL, [email protected] Modeller(s): Peter Schiffels, [email protected]

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~~EXTMOS (646176)~~

~~Summary of the project~~

EXTMOS’ objective is to pioneer development of a chain of models that enables application specific optimization of doped organic semiconductors, organic semi-conductor materials, devices and circuits. Two case studies for two selected devices are small molecule organic light emitting diodes, organic light emitting diodes, for use in displays and lighting and polymer based organic thin film transistors for use in display drivers, image pixels, logic inverters, ring oscillators and sensors.

~~New models for organic electronics~~

~~For legend see next page~~

~~Continue~~

~~118~~

Project Acronym and Number: EXTMOS 646176 Project Title: EXTended Model of Organic Semiconductors Start and End Dates: from 01/107/2015 till 30/06/2019 EU Contribution: 4,998,000 € Coordinator: Alison Walker, [email protected] Modeller(s): Alison Walker (Bridget Jensen), [email protected] David Beljonne, [email protected] Thierry Deutsch , [email protected] Timo Strunk, [email protected] Wolfgang Wenzel, [email protected]

~~119~~

~~MODA Behaviour of organic light emitting diodes EXTMOS~~

OVERVIEW of the SIMULATION Device characteristics for organic light emitting diodes made with small 1 USER CASE molecule films MODEL 1 QC- Higher level ab-initio models (electronic model) ABINITIO MODEL 2 Molecular Dynamics (MD) methods to grow atomistic MC/MD morphologies (atomistic model)

Coarse Grained Molecular Dynamics, CGMD, (mesoscopic MODEL 3 model) finds packing arrangements of entities which are CGMD ellipsoids representing groups of atoms Time-independent Schrödinger Equation TISE, (linear scaling, MODEL 4 constrained DFT, electrostatic embedding) finds charge and QC- CHAIN OF energy transfer rates and on site energies (thousand atoms) 2 POLARON MODELS (electronic model) MODEL 5 QC- Electronic model (effective Hamiltonian) EXCITON Semi-classical Boltzmann transport equation BTE (statistical MODEL 6 mechanics electronic model) predicts charge and energy BTE transport with as post processor an optical model, OPT, model 8 Drift diffusion model, DD, (continuum model) predicts charge MODEL 7 and energy transport with as post process or an optical DD model, OPT, model 8.

3 PUBLICATION Models 1,3,5. Fiesta, BigDFT, Mescal resp.are open source. DEPOSIT model x and QuantumPatch model Y will be made available as open source code. ACCESS 4 The complete EXTMOS package will be covered by a restrictive licence CONDITIONS enabling commercialisation by the firm Nanomatch to pay for staff to support and update the model after Extmos has finished.

~~Model 1~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED: QC-ABINITIO~~

ASPECT OF Quantitative understanding of the doping mechanism and of the excited THE USER states 1.1 CASE TO BE responsible for light emission in doped organic semiconductors/Validation SIMULATED of lower-level techniques (e.g. DFT) Validation system: F4TCNQ doped pentacene atomic geometries partitioned into a subsystem (a few hundred atoms) 1.2 MATERIAL treated at the GW/BSE level and a surrounding subsystem (a few thousand atoms with their atomic polarizability) treated at the microelectrostatic level Embedded cluster (a dopant surrounded by nearest-neighbour shell + 1.3 GEOMETRY microelectrostatic embedding) 1.4 TIME LAPSE

~~120~~

~~MANUFACTUR 1.5 ING PROCESS~~

~~I. Duchemin, D. Jacquemin, X. Blase, J. Chem. Phys. (2016), 144, 1.6 PUBLICATION 164106.~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION: QC-ABINITIO~~

MODEL TYPE Higher level ab-initio models 2.0 AND NAME MODEL Polarons and excitons: quasiparticles in the form of electrons or holes or 2.1 ENTITY electron-hole pairs coupled to lattice modes Equation Time-independent Schrödinger Equation (TISE): 퐻휓 = 퐸휓 MODEL where 휓 is either an electronic (GW) or electron-hole PHYSICS/ 2.2 (excitonic, BSE) state. CHEMISTRY Physical Wavefunctions, energies and Hamiltonian EQUATION quantities MR GW correction to DFT Kohn-Sham electronic energy levels: Equations

~~Bethe-Salpeter Hamiltonian (with electron-hole interaction)~~

~~MATERIALS 2.3 RELATIONS~~

Physical GW: the DFT electron-electron interaction potential (VXC) is quantities replaced by the higher-level self-energy =iGW to produce or accurate electronic energy levels; BSE: the screened (W; descriptors 2nd term) and exchange (VC;3rd term) electron-hole for each interactions are added to the GW electron and hole MR energies (1st term) to generate excitonic energies and wavefunctions. SIMULATED 2.4 INPUT

3 COMPUTATIONAL MODELLING METADATA QC-ABINITIO NUMERICAL Gaussian-basis implementation of the GW and Bethe-Salpeter formalisms 3.1 SOLVER with microelectrostatic (ME) semi-empirical embedding. SOFTWARE 3.2 FIESTA combined with MESCAL for microelectrostatic embedding TOOL 3.3 GRID SIZE Atomic-like Gaussian basis (typically 30 orbitals/atom). 3.4 TIME STEP PHYSICS Electronic wavefunction expressed in an atomic-like basis EQUATION => GW equation recast into a linear-algebra eigenvalue problem; the BSE hamiltonian is expressed in the electron-hole wavefunction-product basis => excitonic COMPUTATIONAL eigenstates expressed in terms of weighted transitions 3.5 REPRESENTATION between occupied and unoccupied electronic energy levels. MATERIAL The eigenvalues of the GW problem provides the energy RELATIONS levels and wavefunction for the electron and holes in the system; the Bethe-Salpeter excitonic Hamiltonian provides the energies, oscillator strengths and electron-

~~121~~

hole wavefunctions associated with optical transitions, providing information on the electron and hole localization and the nature of the excitation (localized/charge- transfer, associated dipole, bright/dark, etc.) MATERIAL Atom-scale model comprising a number of atomic nuclei with defined relative positions both for the QM subsystem treated at the GW/BSE level and the environment treated at the ME level.

4 POST PROCESSING QC-ABINITIO THE PROCESSED Parameters (q, ) and optimized starting atom coordinates r for the OUTPUT IS force fields for model 2 and 3 4.1 CALCULATED FOR Output is also used in the post processor OPT to calculate the global optical device characteristics METHODOLOGIE Force field parameters associated with lower-level methods (exchange- S correlation functional in DFT, onsite/hopping parameters in tight- 4.2 binding models, etc.) will be adjusted so as to reproduce the GW/BSE interatomic potentials (force fields) on representative systems (e.g. F4TCNQ-doped pentacene, etc.) MARGIN OF 4.3 0.1-0.2 eV for force fields ERROR

~~Model 2 MOLECULAR DYNAMICS SOLVED BY MC~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED:~~

ASPECT OF Simulation of thin-film morphologies of small organic molecules. THE USER A user wants to have an atomic representation of an organic thin-film, 1.1 CASE TO BE which was either solution processed or processed using physical vapour SIMULATED deposition. Organic small molecules (<200 atoms), specifically HTL, Hole transport layer host Alpha-NPD N, N'-di- (alpha-naphthyl) -N, N'-diphenyl-1,1'- biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'-(perfluoronaphthalene- 2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl-1,10-phenanthroline, n-dopant Tetrakis 1.2 MATERIAL (1,3,4,6,7,8-Hexahydro-2H-pyrimido[1,2-a]pyrimidinato)–di- tungsten(II). EL, Emissive layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’-di(naphthalen-2-yl)-N,N-diphenyl-benzidine and :Ir(MDQ)2(acac) is iridium(III)bis(2-methyl-dibenzo- [f,h]quinoxaline)(acetylacetonate in an all-atom representation. Thin films of size < 20x20x20nm3, xyz periodicity for MD, xy periodicity 1.3 GEOMETRY for MC 1.4 TIME LAPSE none MANUFACTUR MD: simulation in multiple thermodynamic ensembles, such as NPT or ING PROCESS NVT 1.5 OR IN- SERVICE CONDITIONS

~~1.6 PUBLICATION~~

~~122~~

2 Generic Physics Of The Model Equation MD SOLVED BY MC Model type MOLECULAR DYNAMICS 2.0 and name Model Atoms 2.1 entity Equation Newton’s equations of motion. Model Detailed Balance Physics/ 2.2 Chemistry equation Physical atom coordinates, atom velocities. PE quantities Equation Parameterized force fields and energies, such as the OPLS and GAFF force fields, general vacuum electrostatics (Coulomb equation), VdW interactions and Pauli repulsion (Lennard Jones equations) F(r,q,), E(r,q,) Materials physical F is the force acting on the atoms. 2.3 relation quantities/ E is the energy of the system MR to PE

descriptors r are the coordinates of all atoms coupled equations coupled to be repeated in case of of case in repeated to be q are all charges of all atoms  are the Lennard-Jones parameters (radii, interactions strength) of all atoms Simulated Input parameters (q, ) and optimized starting atom coordinates r for 2.4 Input the force fields can be obtained via ab-initio models Publication 2.5

~~3 Computational Modelling Metadata MD Metropolis Monte Carlo Numerical 3.1 Verlet Integrator Solver~~

~~GROMACS, LAMMPS 3.2 Software tool DEPOSIT, available at Nanomatch (www.nanomatch.com) Optional, 0.1nm 3.3 grid size~~

MD: 1 fs, total simulation time 40-60 ns 3.4 Time step MC: N/A Physics Newton’s equations are discretized, e.g. in a Verlet Equation scheme. VdW and Electrostatic interaction can be discretized in a uniform grid format. Material MD: Integration of the timestep using an integrator Relations provides the coordinates of the next timestep based on Computational previous coordinates. 3.5 Representation MC: A random displacement of the coordinates

provides the coordinates at the next step, if accepted according to the detailed balance criterion. Material Atomic coordinates and parameters, energies, forces are stored as floating point values. Both single and double precision are supported. COMPUTATIO optionally periodic boundary conditions. NAL The atom positions are concatenated and optionally

~~BOUNDARY periodically extended. CONDITIONS 3.6 Publication~~

~~123~~

4 POST PROCESSING MC/MD THE PROCESSED The raw output is positions of atoms in a finite volume (atomistic OUTPUT IS morphology), and is mapped to beads in model 3, CGMD. CALCULATED FOR Back-mapping from bead to atomic coordinates for model 4 is used 4.1 in which a correspondence between models 3 and 4; i.e. identifying which atoms make up which bead METHODOLOGIES The radial distribution function yields the distribution of centre of 4.2 mass pair distances between molecules. The back-mapping procedure is addressed in the CGMD description 4.3 MARGIN OF ERROR Atomic densities typically have <20% margin of error

~~Model 3 COARSE GRAINED MOLECULAR DYNAMICS, CGMD~~

~~1 ASPECT OF THE USER CASE/SYSTEM~~

ASPECT OF THE Coarse Grained Molecular Dynamics, CGMD, finds packing 1.1 USER CASE TO BE arrangements of entities which are ellipsoids representing groups of SIMULATED atoms HTL, Hole transport layer host Alpha-NPD N, N'-di- (alpha-naphthyl) - N, N'-diphenyl-1,1'-biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'- (perfluoronaphthalene-2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl-1,10- phenanthroline, n-dopant Tetrakis (1,3,4,6,7,8-Hexahydro-2H- pyrimido[1,2-a]pyrimidinato)–di-tungsten(II). EL, Emissive layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’- di(naphthalen-2-yl)-N,N-diphenyl-benzidine and :Ir(MDQ)2(acac) is 1.2 MATERIAL iridium(III)bis(2-methyl-dibenzo-[f,h]quinoxaline)(acetylacetonate) The organic molecules are represented by one or more entities referred to as beads. A bead represents a group of atoms, typically a functional organic group. The size of the group depends on the extent of coarse graining of the simulation, that in turn depends on the system size. A bead is often chosen to represent a whole molecule in the case of small and/or rigid molecules.

~~1.3 GEOMETRY Vertical device consisting of cathode: Ag, 100 nm, ETL: 40-265 nm,~~

~~1.4 TIME LAPSE 0.9 ns/day for 5.25 million beads (without charges) on 256 cores Manufacturing 1.5 process or in- service conditions 1.6 PUBLICATION~~

2 Generic Physics Of The Model Equation CGMD Model type COARSE GRAINED MOLECULAR DYNAMICS, CGMD (mesoscopic model) 2.0 and name Model Coarse grained (CG) representation of grouped atoms called beads (each 2.1 entity bead corresponds to a group of atoms, typically a functional organic group)

~~124~~

~~Equation Newton’s equations of motion. Model Physics/ 2.2 Chemistry Physical Positions, orientations, and velocities of CG-entity equation quantities PE~~

~~Equation Force fields appropriate to beads 12 휎푐 푈(풖푖, 풖푗, 풓) = 4휀0휀휇휈(풖푖, 풖푗, 풓) [( ) 푟 − 휎(풖푖, 풖푗, 풓) + 휎푐 휎 6~~

− ( 푐 ) ] coupled equations coupled to be repeated in case of of case in repeated to be 푟 − 휎(풖푖, 풖푗, 풓) + 휎푐 Materials Here U is the biaxial Gay-Berne (GB) potential, parameters 2.3 relation σ(u ,u ,r) and ε (u ,u ,r) are the contact distances and well MR to PE i j μν i j depths, and ε0 , σc scaling energies and lengths. physical U is the Gay-Berne potential of a given pair of CG-entities. quantities/  is the effective radius, S is contact distance,  is descriptors interaction energy, r is the distance between the CG-entity (bead) centres of mass. The parameters of the GB potential are fitted to reproduce energy profiles of interaction for the corresponding full-atom model. Additional terms are added to U to allow for electrostatic contributions. Simulated 2.4 Input Publication 2.5

3 Computational Modelling Metadata CGMD Velocity Verlet, predictor-corrector Verlet algorithm or predictor- Numerical corrector 3.1 Solver equations combined with appropriate thermostat and barostat to control temperature and pressure respectively. SIMONA, GBMAP, LAMMPS, DL-POLY SIMONA and GBMAP convert between atomistic and coarse grained, 3.2 Software tool CG, representations LAMMPS and DL-POLY solve the equations of motion in the CG representation. 3.3 grid size 0.1 nm 20 fs, total simulation time 40-60 ns 3.4 Time step Physics To be determined Computational Equation 3.5 Representation Material

~~Relations Material 3.6 Publication~~

~~125~~

POST PROCESSING CGMD THE PROCESSED OUTPUT IS These quantities will be used to validate the model. CALCULATED FOR CG-entity positions (raw output) are processed into electron positions required by the DFT-SE QC-POLARON and QC EXCITON model 4 and 5 . For the latter, the morphology determines the sites 4.1 on which electrons, holes, excitons are localised between hops. Molecule coordinates output for beads in model 6 BTE. The internal energy, number density profiles and radial distribution function for the modelled material will be used in the global post processing with OPT into optical device characteristics.

METHODOLOGIES Averaged ellipsoid trajectories over around 1000 timesteps once 4.2 equilibrium achieved identified from total energy vs time are required for the BTE model. MARGIN OF ERROR Typically 1%, depends on simulated cell size, accuracy of force 4.3 fields, simulation time.

~~Model 4~~

1 Aspect of the User Case/System to be Simulated: QC-POLARON Aspect of the Electronic and atomistic structure of films of ~104 molecules of 1.1 User Case to be doped and pristine organic semiconductors. simulated HTL, Hole transport layer host -NPD N, N'-di- (alpha-naphthyl) - N, N'-diphenyl-1,1'-biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'-(perfluoronaphthalene-2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl- 1,10-phenanthroline, n-dopant Tetrakis (1,3,4,6,7,8-Hexahydro- 2H-pyrimido[1,2-a]pyrimidinato)–di-tungsten(II). EL, Emissive 1.2 Material layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’- di(naphthalen-2-yl)-N,N-diphenyl-benzidine and :Ir(MDQ)2(acac) is iridium(III)bis(2-methyl-dibenzo- [f,h]quinoxaline)(acetylacetonate) described by atomic positions, grid spacing, radius around each atom, exchange-correlation functional, net charge Vertical device consisting of cathode: Ag, 100 nm, ETL: 40-265 1.3 Geometry nm, 1.4 Time Lapse N/A Manufacturing process or in- 1.5 service conditions 1.6 Publication

2 Generic Physics Of The Model Equation QC-POLARON Model type Electronic model (effective Hamiltonian) combined with polarisable 2.0 and name continuum model Model Polarons: quasiparticles in the form of electrons or holes coupled to 2.1 entity lattice modes Model Equation Schrödinger Equation (SE) for electron states, Kohn-Sham Physics/ equations. 2.2 2 Chemistry ℏ 2 퐻Ψ푖 = [− ∇ + 푉퐾푆(풓 )] Ψ푖 = E푖Ψ푖 , equation 2푚푒

~~126~~

~~to be repeated in case of of case in repeated to be equations coupled~~

푁푎푡표푚푠 PE 푒2푛 (풓′) 푉 (풓) = ∑ 푉 (풓 − 푹 ) + ∫ 푠 d풓′ + 푉 [푛 (푟)] 퐾푆 푝푠 풊 |풓 − 풓′| 푋퐶 푠 푖=1 Physical Ψ푖 are the Kohn-Sham electronic orbitals, H is the mean- quantities field Kohn-Sham Hamiltonian, E I the Kohn-Sham eigenvalues, VKS the effective Kohn-Sham one-electron potential, Vps( 풓 − 푹풊) the pseudopotential energy from the external field due to the nuclei located at 푹풊 and corresponding inner electrons . Equation Kohn-Sham formulation of the Hamiltonian using all- Materials electron (Turbomole, Gaussian) or pseudopotential 2.3 relation MR (BigDFT) to PE physical quantities Exchange-correlation functional, pseudopotentials

Positions of atomic and electronic sites from the back mapped CGMD model 2.4 Input Orbitals and their energies from GW-BSE model 1 that are linked to charge transfer states close to dopants and to excited states. 2.5 Publication

3 Computational Modelling Metadata QC-POLARON BigDFT calculates electronic structure in systems of more than 10,000 atoms going beyond DFT. It uses Constrained DFT methods. localized support functions expressed in an underlying Daubechies wavelet basis which offers ideal properties for accurate linear scaling calculations. Atom positions are determined by conjugate gradients or molecular dynamics implemented self consistently within the code. QuantumPatch computes environmental effects on polarons and excitons in systems of more than 1000 atoms. It partitions the total charge density into charge densities of single molecules. For each molecule, the charge densities of the other molecules are replaced by a set of point charges. Intermolecular electrostatic interactions are Numerical allowed for by partial charges. Initial partial charges use vacuum partial 3.1 Solver charges for each molecule, and then solve the SE for each molecule. Partial charges are updated from the new electron densities for a molecule with Kohn–Sham orbitals. MESCal coupled with BigDFT finds the self-consistent polarization state of a system of atoms. It implements a polarizable points description of electronic polarization to compute the polarization energy of a localized charge carrier and dielectric tensor. Constrained DFT, where a Lagrange multiplier term is added to the Kohn Sham energy functional, is used to evaluate on-site energies and charge-transfer integrals. The electron density is self consistently calculated for clusters of nearest neighbours and then on-site energies and charge-transfer integrals obtained. Software BigDFT, QuantumPatch, MESCal and Deposit are being used to create 3.2 Tools MESO-EL Grid Size, 0.05 nm, 4 fs per step for molecular dynamics simulations 3.3 Time Step Computational Physics Equation As for QC-ABINITIO 3.4 Representation Refers To Material Relations As for QC-ABINITIO Your Computational Solver Material As for QC-ABINITIO

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4 POST PROCESSING QC-POLARON THE PROCESSED In principle, any experimentally observable quantity, e.g. optical OUTPUT IS spectra and optical constants, may be computed as a function of 4.1 CALCULATED FOR the energies. This is done with OPT in the global post processing. Charge transfer rates and recombination rates are provided to the BTE model 6. METHODOLOGIES Charge transfer rates are determined by Marcus theory and require charge transfer and overlap integrals obtained from the 4.2 orbitals using time dependent perturbation theory. HOMO and LUMO offsets at interfaces are deduced in the same way as for the GW-BSE model. -4 MARGIN OF ERROR Bond lengths 10 nm, on-site energies 10 meV, transfer integrals 4.3 10 meV

~~Model 5~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED: QC-EXCITON~~

ASPECT OF Quantitative understanding of the doping mechanism and of the THE USER excited states responsible for light emission in doped organic 1.1 CASE TO BE semiconductors. SIMULATED HTL, Hole transport layer host Alpha-NPD N, N'-di- (alpha-naphthyl) - N, N'-diphenyl-1,1'-biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'- (perfluoronaphthalene-2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl-1,10- 1.2 MATERIAL phenanthroline, n-dopant Tetrakis (1,3,4,6,7,8-Hexahydro-2H- pyrimido[1,2-a]pyrimidinato)–di-tungsten(II). EL, Emissive layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’-di(naphthalen-2- yl)-N,N-diphenyl-benzidine and :Ir(MDQ)2(acac) is iridium(III)bis(2- methyl-dibenzo-[f,h]quinoxaline)(acetylacetonate) 1.3 GEOMETRY Vertical device consisting of cathode: Ag, 100 nm, ETL: 40-265 nm, 1.4 TIME LAPSE N/A

~~MANUFACTUR 1.5 ING PROCESS~~

~~1.6 PUBLICATION~~

2 Generic Physics Of The Model Equation QC-EXCITON Model type Electronic model (effective Hamiltonian) 2.0 and name Model entity Excitons: quasiparticles in the form of electron-hole pairs coupled to 2.1 lattice modes Equation Schrödinger Equation (SE) for exciton states. 푁 Model ( ) Physics/ 퐻|푛 >= [ℏ휔0−0 + ℏ퐷 + ∑ 퐽0 |푛 >< 푛 + 1| + |푛 + 1 >< 푛| 2.2 푛=1 Chemistry 푁 equation PE + ∑ Λ푛(|푛 >< 푛|)] |푛 >

~~푛=1~~

~~128~~

~~to be repeated in case of of case in repeated to be equations coupled~~

Physical |n> represents a pure (S1) electronic excitation at quantities site n with all other molecules electronically unexcited in state S0, H is the Hamiltonian, J0 the nearest neighbour coupling, ℏ휔0−0 is the energy corresponding to the S0 S1 transition, typically dipole allowed in the UV-Vis spectral region, D is a non-resonant gas-to-crystal (red) shift which is due to the greater stabilization of S1 compared to S0 upon aggregation and n is the transition energy offset for the nth chromophore. Equation 푁 푁 푁 푁 † 퐻 = ∑ 퐻푚 + ∑ ∑ 푉̂푚푛 + ℏ휔푣푖푏 ∑ 푏푛푏푛 + ℏ휆휔푣푖푏 ∑ |푛 푚=1 푚=1 푛<푚 푛<푚 푛 † 2 >< 푛|(푏푛 + 푏푛) + ℏ휆 휔푣푖푏 physical Hm describes the intramolecular Hamiltonian for site Materials m and 푉̂ is an operator representing the relation MR to quantities/ 푚푛 2.3 intermolecular interactions between sites m and n. PE descriptors The third term represents the vibrational energy, † with 푏푛 (bn) creating (annihilating) a vibrational quantum on the nth chromophore. The local, linear exciton-vibrational coupling term is represented by the third term. Orbitals and their energies from GW-BSE that are linked to excitons. The positions of the atoms and quasi-particle sites are deduced 2.4 Input from/based on the centres of mass of the ellipsoids obtained from the CGMD model. 2.5 Publication

3. COMPUTATIONAL MODELLING METADATA QC-EXCITON NUMERICAL Gaussian-basis implementation with microelectrostatic (ME) semi-empirical SOLVER embedding SOFTWARE TOOL FIESTA combined with MESCAL for microelectrostatic embedding GRID SIZE N/A TIME STEP N/A PHYSICS ∑ < 휙(푎}|퐻| 휙(푏} > = 퐸 < 휙(푎}| 휙(푏} > EQUATION {푏} The exciton Hamiltonian is written in terms of the adiabatic electronic states, m,a, of the single chromophores m. MATERIAL 푁 1 푝 RELATIONS |휙( } ≥ ∑(−1) 푃[∏ |휑 > COMPUTATIONAL 푛 푚,푛 √푁푝! REPRESENTATION 푚푛 푚=1 refers to how your ∗ 푥 휌푚,푔푒(푟푚) = 휑푚,푒(푟푚) 휑푚,푔(푟푚), 휇푚 = ∫ 푑푥 휇̂푚 휌푚,푔푒(푟푚) computational solver P generates a permutation over electronic coordinates of the represents the molecules in the aggregate and Np is the number of such material, permutations. The aggregate electronic states |휓 >= properties, ∑{푎} 퐶({푎})|휙{푎} > with variational coefficients C({a}) are equation solutions of the Schrödinger equation. The transition density variables,…..  for ground, g, to excited, e, states is obtained from frontier molecular orbitals  and is used to find the x,y,z components of the transition dipole moment m and the Coulomb term in the Hamiltonian. MATERIAL Atom-scale model comprising a number of atomic nuclei with defined relative positions and the same number of electrons to ensure overall charge neutrality.

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~~4 POST PROCESSING QC-EXCITON~~

THE PROCESSED 퐴(휔) 푆(휔) 0−휐푙 ⁄ = ∑훼 푓푘=0,훼 Γ(휔 − 휔푘=0,훼), ⁄ = ∑휐 퐼 Γ(휔 − 휔푒푚 + 휐푙휔푣푖푏) OUTPUT IS 푁 푁 푙 푃퐿 CALCULATED FOR A() is the absorption spectrum required for validation, fk=0, the oscillator strength,  represents the multitude of eigenstates which all have a centre of mass (quasi) momentum k equal to zero but with varying amounts of vibrational dressing. () is a line shape function usually taken to be Gaussian for the case of 4.1 inhomogeneous broadening and Lorentzian for homogeneous broadening. 푆(휔) is the reduced photoluminescence, PL spectrum. These will be used in the global post processor OPT for optical device characteristics.

~~Exciton transfer rates and sSite energies and recombination rates are provided for BTE model 6.~~

METHODOLOGIES Optical spectra and optical constants are obtained from excited 4.2 state energies by calculating the time dependent dipole moment output by the solver. MARGIN OF 4.3 On-site energies 10 meV, transfer integrals 10 meV ERROR

~~Model 6 Boltzmann Transport Equation, BTE~~

~~1 ASPECT OF THE USER CASE~~

ASPECT OF THE Transfer of electrons and excitons between point representations of 1.1 USER CASE TO BE molecules, leading to current density and electrical field profiles and SIMULATED colour and intensity of optical emission HTL, Hole transport layer host Alpha-NPD N, N'-di- (alpha-naphthyl) -N, N'-diphenyl-1,1'-biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'- (perfluoronaphthalene-2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl-1,10- phenanthroline, n-dopant Tetrakis (1,3,4,6,7,8-Hexahydro-2H- 1.2 MATERIAL pyrimido[1,2-a]pyrimidinato)–di-tungsten(II). EL, Emissive layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’- di(naphthalen-2-yl)-N,N-diphenyl-benzidine and :Ir(MDQ)2(acac) is iridium(III)bis(2-methyl-dibenzo-[f,h]quinoxaline)(acetylacetonate) represented by electrons and excitons on ellipsoids (molecules) 1.3 GEOMETRY Vertical device consisting of cathode: Ag, 100 nm, ETL: 40-265 nm, 1.4 TIME LAPSE 50 ps to ms MANUFACTURING PROCESS OR IN- 1.5 SERVICE CONDITIONS

~~1.6 PUBLICATION~~

2 Generic Physics Of The Model Equation BTE Model Semi-classical Boltzmann transport equation, BTE (statistical mechanics 2.0 type and electronic). name Model Electron polarons, hole polarons, singlet and triplet excitons 2.1 entity Model Equation Boltzmann transport equation Waiting time before a reaction 2.2 Physics/ with reaction rate k for a uniformly distributed random number Chemistr R between 0 and 1

~~130~~

~~to be repeated in case of of case in repeated to be equations coupled~~

y ln (푅) 휏 = − equation 푘 PE Physical Charge, exciton, current density and field profiles quantities Hopping rates and generation and recombination rates that are taken from 2.3 MR DFT-SE Energy barrier between neighbouring sites Exciton and charge transfer rates and recombination rates from DFT-SE. Simulate 2.4 The positions of the sites on which electrons, holes, excitons are localised d Input between hops from CGMD. Publicati 2.5 on

3 Computational Modelling Metadata BTE Numerical Kinetic Monte Carlo, KMC 3.1 Solver Software Merged Bath KMC and KIT KMC codes 3.2 tool 3.3 grid size N/A ps to ms 3.4 Time step Computational Physics

~~Representation Equation refers to how Material~~

your Relations computational 3.5 Material Each site has a label determining which material it is solver represents and which particle species occupies it that varies with the material, elapsed time properties, equation variables,….. 3.6 Publication

4 POST PROCESSING BTE THE PROCESSED Material/layer characteristic scalars/parameters for continuum OUTPUT IS model 7: CALCULATED FOR Carrier mobilities, doping efficiencies, recombination rates , exciton 4.1 diffusion lengths and coefficients. For the global post processing into device electrical characteristics the following is calculated : fFinite volume resolved current densities, emitted light intensity and spectrum. METHODOLOGIES Current densities found from particle fluxes, charge mobilities from net drift velocity d of ensemble of electron trajectories deduced 4.2 from net distance travelled over a fixed time period at a given external field. The optical model is needed to find the emitted light intensity and spectrum. MARGIN OF ERROR Typically 1% for all quantities, depending on number of trajectories 4.3 calculated

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~~Model 7~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED DD ASPECT OF THE Device characteristics for doped organic semiconductor organic 1.1 USER CASE TO BE light emitting devices SIMULATED HTL, Hole transport layer host Alpha-NPD N, N'-di- (alpha- naphthyl) -N, N'-diphenyl-1,1'-biphenyl- 4,4'-diamine, p dopant F6TCNNQ 2,2'-(perfluoronaphthalene-2,6-diylidene) dimalononitrile. HBL ETL, Electron transport layer host TPPhen 2,4,7,9-tetraphenyl-1,10-phenanthroline, n-dopant Tetrakis (1,3,4,6,7,8-Hexahydro-2H-pyrimido[1,2-a]pyrimidinato)–di- 1.2 MATERIAL tungsten(II). EL, Emissive layerB Alq3 doped with NPB:Ir(MDQ)2(acac) where NPB is N,N’-di(naphthalen-2-yl)-N,N- diphenyl-benzidine and :Ir(MDQ)2(acac) is iridium(III)bis(2- methyl-dibenzo-[f,h]quinoxaline)(acetylacetonate) described as continuum with specific values fo part s of the device (describe which pls) Vertical device consisting of cathode: Ag, 100 nm, ETL: 40-265 1.3 GEOMETRY nm, described as continuum with specific values for the parts of the device nl…… 1.4 TIME LAPSE Not applicable MANUFACTURING PROCESS OR IN- Voltage bias 1.5 SERVICE CONDITIONS

~~1.6 PUBLICATION~~

2 GENERIC PHYSICS OF THE MODEL EQUATION DD MODEL Semi-classical Drift-diffusion model ( continuum CFD with electric circuit TYPE equations) 2.0 AND NAME MODEL This is a materials model for concentration of electrons or excitons and the 2.1 ENTITY equation is written up for finite volumes (the model entity) corresponding to the active layers in the device

Equation Current equations for electron current Jn and hole current Jp 푱푛 = 푞푛(풓)휇푛푬 + 푞퐷푛훁푛 MODEL 푱푝 = 푞푛(풓)휇푝푬 + 푞퐷푝훁푝 PHYSICS/ 2.2. Physical q Electron charge CHEMISTRY a quantities J Electron (hole) current density EQUATION n(p)  Electron (hole) mobility PE1 n(p) E Electric field, given by 퐄 = −훁V where V is potential Dn(p) Electron (hole) diffusion coefficient Equation Einstein relation 푞퐷푛(푝) MATERIALS 휇푛(푝) = 푘퐵푇 RELATION 1 Physical Einstein relation used to relate values of mobility MR1 TO PE1 n(p) 2.3. quantities/ and diffusion coefficient Dn(p) to each other; T = a descriptors temperature MATERIALS Equation Relation between carrier densities n, p and potential V RELATION 3

~~MR3 TO PE1 Physical dependence on intrinsic carrier density, ni, potential V quantities/ and electron (hole) quasi-Fermi energies, n(p)~~

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~~descriptors~~

Equation Poisson equation, describing how the potential varies MODEL with position 2.2. PHYSICS ∇. 휀∇푉 = −푞(푝 − 푛 + 푁퐷 − 푁퐴) b EQUATION Physical  Dielectric constant PE 2 quantities ND Donor doping density NA Acceptor doping density Equation Relation between carrier densities n, p and potential V

MATERIALS Physical Dependence on intrinsic carrier density, ni, potential V 2.3. RELATION 1 quantities/ and electron (hole) quasi-Fermi energies, n(p), from b MR1 TO PE2 descriptors Boltzmann approximation 푞(푉 − 휙푛) 푛 = 푛푖exp ( ) 푘퐵푇

Equation Continuity equations, to ensure conservation of MODEL charge: 휕푛 1 휕푝 1 2.2 PHYSICS = 훁. 퐽푛 − 푟푛푝 , = − 훁. 퐽푝 − 푟푛푝 c EQUATION 휕푡 푞 휕푡 푞 PE 3 Physical r is the electron-hole recombination rate quantities

EQUATION 휕푆 2 푄 푆 = 퐷푆∇ 푆 + 휂푠푡푟푛푝 − − PE 4 휕푡 ℎ휈 휏푆 Physical S is exciton concentration quantities 휂푠푡 singlet-triplet ratio Q is the generated photon flux Eopt is field arising from photons  is absorption coefficient From Model 1 GW-BSE Interface energy offsets, Optical constants 2.4 INPUT From Model 4 BTE: Carrier mobilities, doping efficiencies, Exciton diffusion lengths and coefficients, Recombination rates, Densities of states

~~2.5 PUBLICATION~~

3 COMPUTATIONAL MODELLING METADATA DD NUMERICA Finite element model 3.1 L SOLVER SOFTWARE SIlvaco Atlas code 3.2 TOOL 3.3 GRID SIZE nm 3.4 TIME STEP N/A PHYSICS Finite element discretisation of equations given in part 2 EQUATION where variable e.g. charge density defined for each finite COMPUTAT element. IONAL 3.5 MATERIAL Finite element discretisation of relations given in part 2 REPRESEN RELATIONS where equation defined for each finite element and its TATION neighbours. MATERIAL Material determines which input parameter set is selected http://www.silvaco.com/examples/tcad/section38/example1/index.h 3.6 PUBLICATION tml

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4 POST PROCESSING DD THE For the global post processing into electrical device characteristics the PROCESSED following is calculated for a finite volume, representing the active OUTPUT IS layers and contacts:current-voltage curves. Outputs are current- 4.1 CALCULATED voltage-Luminance characteristics, the emitted light spectrum, Cole- FOR Cole plots giving impedance variation with frequency of a time varying external bias, circuit characteristics. METHODOLOG Run the DD model for a series of voltages to obtain current-voltage IES curves, or for time following a stimulus, e.g. change in applied bias in 4.2 the dark for dark injection transients, equivalent circuit models provide impedance of device in a circuit. The optical model produces the luminance and emitted light spectrum. MARGIN OF The error is sensitive to the accuracy of the input parameters, and to 4.3 ERROR the extent to which these parameters represent real devices. An error of 10% is attainable.

1 Global Post processor OPTICAL MODEL Calculation of intensity variations for visible light produced by Case to be 1.1 OLEDs and for absorption of incident light and of emitted simulated photons Raw output to be Exciton density profiles

~~processed of BTE Raw output to be Exciton and electron density profiles~~

~~processed of DD 1.6 Publication~~

2 GENERIC PHYSICS OF THE MODEL EQUATION OPT MODEL TYPE Maxwell’s equations in a microcavity (Continuum model, 4.6 in 2.0 AND NAME ROMM) MODEL ENTITY This is a materials model for electric and magnetic field and intensity 2.1 variations and the equation is for finite volumes (the model entity) Equation ∇. 퐷 = 휌 , ∇. 퐵 = 0 , ∇ × 퐸 = − 휕퐵⁄ , ∇ × 퐻 = 휕퐷⁄ + 퐽 MODEL 휕푡 휕푡 PHYSICS/ Physical D Displacement, B magnetic flux density, J Current 2.2 CHEMISTRY quantities density,  charge density EQUATION E Electric field, given by 퐸 = −∇푉 where V is potential t PE1 time Equation 푫 = 휖푬 MATERIALS RELATION 1 MR1 TO PE1 Physical quantities/ 휖 dielectric constant descriptors 2.2. Equation Γ푐푎푣 = Γ푛푟 + 퐹Γ푟 1 MATERIALS RELATION 2 Physical Γ excited state decay rate, subscripts cav for cavity MR2 TO PE1 quantities/ formed by device contacts, nr nonradiative, r descriptors radiative ∞ MATERIALS Equation F = ∫ Κ(κ)dκ2 RELATION 3 0

~~134~~

MR3 TO PE1 Physical total power 퐹 supplied by the dipole antenna quantities/ (including dissipation in absorbing media and descriptors radiation into the far field) Optical constants from GW-BSE. Positions of excitons undergoing radiative decay from BTE or exciton 2.3 Input recombination profile from DD. Here radiating excitons are modelled as radiating dipoles, device geometry including the contacts and their compositions, luminosity function for photopic vision

~~3 COMPUTATIONAL MODELLING METADATA OPT~~

~~NUMERICAL Transfer matrix 3.1 SOLVER~~

3.2 SOFTWARE TOOL Code in MESO-TRANS or ATLAS 3.3 GRID SIZE nm width 3.4 TIME STEP N/A PHYSICS Reflection and transmission matrices for each layer EQUATION MATERIAL COMPUTATIONAL As given in part 2 3.5 RELATIONS REPRESENTATION MATERIAL Material determines which complex dielectric constant and radiative and nonradiative decay rate obtained from TISE is selected

~~3.6 PUBLICATION~~

4 POST PROCESSING OPT THE PROCESSED Luminance, angular dependence of emission, colour coordinates, 4.1 OUTPUT IS reflection transmittance and absorbance spectra of device CALCULATED FOR METHODOLOGIES Luminance obtained from emission spectrum obtained from energy of radiating exciton, out-coupling efficiency, i.e. probability of a 4.2 photon generated in the device being emitted into free space calculated by averaging over finite elements MARGIN OF Typically 5%, main sources of error are from the BTE or DD models 4.3 ERROR where the morphologies and defect concentrations, energies and types which are hard to establish

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~~FASTGRID (721019)~~

~~Summary of the project~~

Energy systems suffer from fault currents and this problem aggravates now that renewable energy with huge volumes of electricity are transmitted over long distances. The project aims at improving existing conductor material and architecture to make superconducting fault current limiters economically attractive for high voltage direct current super-grids.

They aim to enhance the electric field and so the economical SCFCL attractiveness and the tape should reach a higher critical current and enhanced homogeneity as compared to today’s standards. The shunt surface will also be functionalized to boost the thermal exchanges with coolant.

~~In parallel to this main line of work, developments will be carried out on ultra high electric field tapes based on sapphire substrates.~~

~~Superconducting fault current limiters~~

Project Acronym and Number: FASTGRID 721019 Project Title: Cost effective FCL using advanced superconducting tapes for future HVDC grids Start and End Dates: from 1/01/2017 till 30/06/2020 EU Contribution: 7,248,236 € Coordinator: Frédéric Sirois, [email protected] Modeller(s): Frédéric Sirois, [email protected]

~~136~~

~~MODA-1 Quench simulations in 2G HTS CCs FASTGRID~~

~~OVERVIEW of the SIMULATION~~

A figure of merit must be calculated to compare the performances of various high temperature superconductor (HTS) coated conductor (CC) tape 1 USER CASE architectures (different materials properties and geometric configurations) in which there are weaker regions where hot spots will nucleate, thus initiating a quench propagation Fully coupled electro-thermal model. CHAIN OF MODEL 1 2 MODELS

~~3 PUBLICATION~~

The model was developed by C. Lacroix and F. Sirois, from Ecole Polytechnique de Montreal (EPM) in the COMSOL Multiphysics commercial code. The model files are not yet publicly available. However, since EPM is one of the partners of the FASTGRID European project, there is no issue to 4 ACCESS access the model files. The participation of EPM in this project also ensures CONDITIONS that the know-how to parameterize and execute these simulations is present in the project right from the beginning. Materials data required for this project are available from public literature. For the classical tape architectures, these materials properties are already included in the COMSOL model files that EPM will provide. All desired outputs will be obtained with one simulation model, so our methodology involves a single one-step procedure (see picture below: Workflow of a “Quench” simulation). WORKFLOW The problem is highly nonlinear (especially the material properties), so it is 5 AND ITS simulated in the time domain. It is not possible to linearize the simulation in RATIONALE any way to speed it up. The 3-D nature of the model is also unavoidable since patterns in thin films need to be modelled and are known to have a substantial impact on the overall performance of the tape in its final application.

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~~MODEL 1~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

The typical user case is to fix the choice of materials and geometric parameters of an HTS tape, then submit this tape to a transport current and evaluate how it responds upon the appearance of a hot spot. In output, three quantities need to be provided: ASPECT OF i) the maximum temperature achieved at the hot spot (Tmax), THE USER 1.1 ii) the total voltage developed at the terminals of the simulated tape CASE TO BE (Vtape), SIMULATED iii) the normal zone propagated velocity (NZPV)

These outputs are the best figures of merit that allow comparing the performances of various tapes architectures, and will guide the manufacturers towards efficient solutions without losing time on approaches with little benefits. The materials entering in the fabrication of HTS tapes are listed in 1.3. More specifically, we have: silver and/or other metals (for the stabilizer layer), various oxides, such as CeO2 or others (for the interfacial resistance and also for the buffer layers), (RE)BCO (for the superconducting layer) 1.2 and stainless steel or nickel alloys (for the substrate). Knowing the exact MATERIALS chemical compositions of these materials are not so important for the continuum-type simulations that we are performing within this project: as long as we know the electrical and thermal properties of our materials, as characterized experimentally or taken from literature, this is sufficient, but their temperature dependence must be accurate. The typical geometry of an HTS tape is illustrated below. Note that the silver layer (also called stabilizer) can also be present on the side edges of the tape.

~~1.3 GEOMETRY~~

The typical dimensions of a tape are: -Length: 5-100 mm (sufficient for most cases) -Width: 4-12 mm -Thickness of layers: -Silver: 0.1-3 um -Interfacial resistance: 10-100 nm -(RE)BCO: 1-3 um -Buffer layers: 0.2-1 um -Substrate: 50-100 um 1.4 TIME LAPSE The quench process to be simulated lasts typically from 10 ms to 1 s.

MANUFACTURING An HTS tape used as fault current limiter is cooled down in a liquid 1.5 PROCESS OR IN- nitrogen environment at 77 K or slightly below that (but not less SERVICE than 65 K) if we work in sub-cooled conditions. CONDITIONS

~~1.6 PUBLICATION ON THIS ONE SIMULATION~~

~~138~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION 2.0 MODEL TYPE Continuum electro-thermal model AND NAME 2.1 MODEL ENTITY 3-D volume corresponding to an HTS tape (see picture above)~~

~~Equation Laplace equation for the electric potential:~~

~~(1) Heat equation:~~

(2) MODEL Coupling equation (Joule losses): PHYSICS/ 2.2 CHEMISTRY (3) EQUATION Equations (1) and (2) are very tightly coupled through (3). PE The only option to achieve good convergence is to solve them simultaneously. Physical The model solves for 2 states variables, i.e.: quantities i) Electric potential: V (scalar field) ii) Temperature: T (scalar field) Since the problem is 3-D, the raw output is a map of V(x,y,z,t) and T(x,y,z,t) everywhere in the simulated volume. Relation 1. Electrical conductivity of all materials EXCEPT (RE)BCO  sigma(T): (1,3)  Interpolation table from literature 2. Electrical conductivity of (RE)BCO  sigma_SC(T,E): (1,3)

~~MATERIALS 2.3 RELATIONS~~

3. Thermal conductivity of all materials  kappa(T): (2)  Interpolation table from literature 4. Specific heat capacity of all materials  C_p(T): (2)  Interpolation table from literature Physical 1. Electrical conductivity of all materials EXCEPT (RE)BCO quantities/  No specific parameter since interpolation table descriptors 2. Electrical conductivity of (RE)BCO  sigma_SC(T,E): for each (1,3) MR Jc0: critical current density in self-field (constant)

~~n0: power-law exponent at temperature T0~~

~~Tc: Critical temperature~~

~~Jc(T): Critical current density as function of~~

~~139~~

~~temperature n(T): Power law exponent as function of temperature~~

E0: Constant (1E-4 V/m) E: Electric field ( E = – grad(V) ) 3. Thermal conductivity of all materials  kappa(T): (2)  No specific parameter since interpolation table 4. Specific heat capacity of all materials  rho_m(T): (2)  No specific parameter since interpolation table SIMULATED Not applicable: all inputs are specified by the user (geometry and 2.4 INPUT materials parameters)

~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

NUMERICAL Finite element method (nonlinear time transient simulation) 3.1 SOLVER COMSOL Multiphysics, available commercially, and already accessible 3.2 SOFTWARE TOOL to many of the consortium members Adaptive time steps using the built-in solver of COMSOL Multiphysics 3.3 TIME STEP (customized version of the widespread DASSL solver – used in particular in the Matlab ODE solvers suite)

PHYSICS a) Physics equations are defined at high level in their EQUATION, strong form, and a finite element weak form is MATERIAL internally handled by COMSOL Multiphysics RELATIONS, b) Materials equations are treated according to the MATERIAL two following cases i) Interpolation tables are entered directly in the front-end of the program COMPUTATIONAL ii) Analytical functions are entered as such and are 3.4 REPRESENTATION evaluated as required by the low-level matrix assembly engine The equations apply to the entire 3-D domain being simulated, with material properties being different from domain to domain. Note that since we use a commercial code, we do not know exactly all the internal details, so it is difficult to describe with extreme details the numerical implementation. Boundary conditions for V are mostly Neumann boundary conditions, meaning that the current must flow within the simulated domain. A current constraint is added to force a precise electrical current to flow in the tape (and thus one of the faces of the tape is associated to an COMPUTATIONAL unknown electric potential, which turns out to be a Langrage multiplier 3.5 BOUNDARY in the final system of equations. CONDITIONS Boundary conditions for T are also Neumann everywhere where the tape is thermally insulated (adiabatic condition), except on the faces where cooling is present. In this case, the Newton law of Cooling can be used, with an effective convection coefficient between liquid nitrogen and the conductor face. Relative tolerance of 0.1-1% on all state variables is usually sufficient ADDITIONAL to achieve convergence. 3.6 SOLVER

~~PARAMETERS~~

~~140~~

~~4 POST PROCESSING~~

THE PROCESSED Both raw state variables V and T are post-processed to extract the OUTPUT desired outputs: i) the maximum temperature achieved at the hot spot 4.1 (Tmax), ii) the total voltage developed at the terminals of the simulated tape (Vtape), iii) the normal zone propagated velocity (NZPV)

~~METHODOLOGIES In the case of Tmax, one only need to probe the evolution of temperature at the hot spot location, and find the maximum value of the field in that part of the geometry.~~

In the case of Vtape, one just needs to take to potential difference between the surface of the tape at the tape end terminal and at the hot spot location. 4.2 Finally, the NZPV requires more work: one must compute the speed at which the temperature Tc progress over time. Alternatively, one can also fix a voltage criterion, and see how fast this voltage propagates over time. Both approaches give the same result within 1% of accuracy. No output is re-used in successive simulation since our model is a single-step one. MARGIN OF The results are accurate within an interval of confidence that does not 4.3 ERROR exceed that of the accuracy of the material models themselves. If we assume the material models as perfect, the numerical simulations agree within a few percent with the mathematical solution.

~~141~~

~~FEMTOSPIN (281043)~~

~~Summary of project~~

The project addresses spin dynamics for magnetic information storage technology, which is based on nanostructured magnetic materials, and for spin electronics in which the manipulation of the spin forms the basis of the device operation. Magnetic spins can be manipulated on the femtosecond timescale, while the actual switching by precessional motion lasts hundreds of picoseconds. The project investigates the physics of these multi-scale processes.

~~Spin dynamics for storage of information~~

Project Acronym and Number: FEMTOSPIN 281043 Project Title: Multiscale Modelling of Femtosecond Spin Dynamics Start and End Dates: from 1/06/2012 till 31/05/2015 EU Contribution: 3,999,600 € Coordinator: Roy Chantrell, [email protected] Modeller(s): Roy Chantrell, [email protected]

~~142~~

~~GO FAST (280555)~~

~~Summary of the project~~

The aim of this research project is to develop femtoscale-modelling schemes to study electronic, optical and structural properties of correlated materials driven out of equilibrium. The possibility to optically switch on and off the metallic phase in a model Mott insulator (vanadium sesquioxide) and the superconducting phase in model high-temperature superconductors (cuprates) will be investigated and tested. The photo-excited phases are investigated experimentally by different time-resolved spectroscopic tools, like reflectivity or photoemission.

~~Correlated materials in insulators and superconductors~~

Project Acronym and Number: GO FAST 280555 Project Title: Governing ultrafast the conductivity of correlated materials Start and End Dates: from 01/04/2012 till 31/03/2015 EU Contribution: 1,673,200 € Coordinator: Michele Fabrizio, [email protected] Modeller(s): Michele Fabrizio, [email protected]

~~143~~

~~ICMEg (606711)~~

~~Summary of the project~~

The project established a network of stakeholders in the field Integrated Computational Materials Engineering. The project proposed an open, global standard for materials descriptions that can underpin the information exchange between all materials simulation tools of the electronic, atomistic, mesoscopic and continuum model type. Sandbox scenarios were elaborated to demonstrate the applicability of the proposed material description standards.

~~Elastic properties of polycrystalline polypropylenes~~

~~144~~

~~High Throughput Discovery of Single Crystal Ferroelectrics Film~~

Project Acronym and Number: ICMEg 606711 Project Title: Integrative Computational Materials Engineering Expert Group Start and End Dates: from 1/10/2013 till 30/09/2016 EU Contribution: 800,000 € Coordinator: Georg Schmitz, [email protected] Modeller(s): Albertus Wilhelmus Antonius Konter, [email protected] Georg J. Schmitz, [email protected] Javier Llorca, [email protected] John Agren, [email protected] Laurent Adam, [email protected] Michele Chiumenti, [email protected] Ralph Bernhardt, [email protected] Roger Assaker, [email protected] Ulrich Prahl, [email protected] Yuwen Cui, [email protected]

~~145~~

~~MODA~~

~~Multiscale simulation to predict microstructure dependent effective properties of an injection moulded polypropylene component~~

~~Project ICMEG~~

~~OVERVIEW of the simulation~~

~~Predict microstructure dependent effective properties of an injection 1 USER CASE moulded polypropylene (PP) plate over different sections of the plate.~~

Continuum multi-phase flow model consisting of tightly coupled CFD, heat and flow front equations: Simulation of MODEL 1 the injection moulding process at the macroscale. The flow, the cooling, and the solidification of the melt are calculated.

~~CHAIN OF Continuum Thermodynamics model describing the 2 MODELS MODEL 2 nucleation and the growth of individual polypropylene spherulites.~~

~~Atomistic Molecular Dynamic simulation of the helicoidal MODEL 3 chain of -isotactic polypropylene to derive the theoretical Young modulus in the chain direction.~~

G. Laschet, M. Spekowius, R. Spina, Ch. Hopmann: “Multiscale PUBLICATIONS simulation to predict microstructure dependent effective elastic AA ON THIS properties of an injection molded polypropylene component”, SIMULATION Mechanics of Materials, under peer review, 2016

1.The 1st model is build up via several user subroutines which are linked to the commercial COMSOL multiphysics solver. 2. The 2nd model (for 3D microstructure evolution ) is developed as a ACCESS non-commercial program, named SphaeroSim. This program is not 4 CONDITIONS free available and is the property of the Institute of Plastics Processing of the RWTH Aachen University 3. The commercial code MaterialStudio from Biovia has been used to perform the molecular dynamics simulations.

The workflow of the multiscale simulation of the injection moulding process of PP components is outlined in the figures 1 & 2. WORKFLOW The continuum model gives the boundary conditions for the 5 AND ITS RATIONALE thermodynamics model applied at a finer scale. The results of the thermodynamics model is combined with the results of the MD simulation.

~~146~~

~~Fig. 1: Graphics Workflow of the multiscale simulation of injection moulding of a PP part~~

~~MODEL 1~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE Simulation of the injection moulding process at the USER CASE TO BE macroscale to describe the polymer crystallization 1.1 SIMULATED~~

~~isotactic polypropylene (-iPP) type 505P from Sabic AG 1.2 MATERIAL (Netherlands)~~

~~Geometrical configuration of the -iPP staggered plate produced by injection moulding~~

~~1.3 GEOMETRY~~

~~1.4 TIME LAPSE A pressure time of 20 sec and a cooling time of 40 sec are simulated~~

An inlet flow of 25cm3/sec a pressure level of 70% of the maximum MANUFACTURING injection pressure of 120 MPa, a pressure time of 20 sec followed by PROCESS OR IN- 1.5 a cooling time of 40 sec. The mould wall temperature was set to SERVICE 40°C, whereas a melt temperature of 220°C has been adopted. CONDITIONS

~~1.6 PUBLICATION R. Spina, M. Spekowius, C. Hopmann: “Analysis of polymer~~

~~147~~

~~ON THIS ONE crystallization with a multiscale modelling approach”, Key Engng. SIMULATION Materials, vol. 611—612, 2014, pp. 928-936.~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

MODEL TYPE Continuum model: Tightly coupled Navier-Stokes / Heat transfer /flow 2.0 AND NAME front evolution equations with Crystallisation MR to predict mould filling, heat transfer and solidification

~~MODEL Finite elements 2.1 ENTITY~~

~~Equation Incompressible viscous flow of melt described by the conservation of mass, momentum and energy.~~

~~Continuity:  u  0~~

~~Momentum:  u    uu  p   τ  Fext  t ~~

~~Heat transfer:~~

~~MODEL  T  abs   cp   uT   kT  τ : u  max Hc PHYSICS/  t  t 2.2 CHEMISTRY~~

EQUATION Flow front evolution: PE      u    S    1    t  |  | where  is the phase variable,  describes the thickness of the transition region between the two

~~fluids, and  S denotes a stabilization term.~~

~~Physical The velocity field u, the pressure field p, the quantities temperature field T are the unknowns as well as the relative crystallization degree  and the phase variable .~~

~~Relation Materials relations for following physical quantities are involved in these equations: the density , the viscous~~

~~stress tensor , the external forces Fext, the thermal~~

~~conductivity k, the heat capacity cp, the latent heat of~~

crystallization HC. Each thermophysical property f, MATERIALS like e.g. the conductivity k, is function of the degree 2.3 RELATIONS of crystallization via following expression: abs abs f  fcryst  max  famorph  1    (1  max )

~~푎푏푠 where 휉푚푎푥 is the maximum degree of crystallization, set to 0.51 here~~

~~Crystallization model of Nakamura et al (1973):~~

~~148~~

~~and~~

~~where the degree of crystallization ξ is a function of the Avrami exponent n and of the overall non- isothermal kinetic rate constant K(T).~~

~~The density is not expressed via a simple mixture rule, but via a cooling rate dependent, modified 2-domain Tait model. The melt viscosity is given by:~~

~~B abs sph         1  max  amorph     sph ~~

Physical 1.  : melt viscosity and amorph, is the viscosity of quantities/ the amorpheous state given by a simple cross-WLF approach descriptors 2. B : the Einstein coefficient for each MR 3. sph : the volume fraction of spherulites

~~SIMULATED Not applicable 2.4 INPUT~~

~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

To compute accurately the filling progress P2-P1 Taylor-Hood finite NUMERICAL elements with quadratic shape functions for the velocity and the free 3.1 SOLVER surface fields u and , and linear shape functions for the pressure and temperature fields are used.

~~3.2 SOFTWARE TOOL COMSOL Multiphysics version 5.1 please see https://www.comsol.de~~

~~3.3 TIME STEP Variable time step is used in the simulation (increasing from the start)~~

~~PHYSICS Please see §3.1 where the finite element COMPUTATIONAL EQUATION, discretization of the mould cavity is outlined for the 3.4 REPRESENTATION MATERIAL unknown fields. RELATIONS, MATERIAL~~

~~COMPUTATIONAL Symmetry plane defined parallel to the melt inflow is used in the 3D 3.5 BOUNDARY model CONDITIONS~~

~~ADDITIONAL 3.6 SOLVER~~

~~149~~

~~PARAMETERS~~

~~Post processing~~

~~4 POST PROCESSING~~

THE PROCESSED Melt velocity, temperature and pressure and the filling front position OUTPUT resp. the phase fractions are forwarded as time dependant boundary conditions to the microstructure evolution model (Model 2). Each 4.1 finite element on the macroscale will be discretized by fine grid with 150 cells per direction.

METHODOLOGIES The nodal temperatures of each macro-element are interpolated linearly to generate the boundary conditions for the microstructure evolution simulation. For the velocity, a linear interpolation is not 4.2 sufficient because the free energy induced by the flow is mainly defined by the spatial gradient of the velocity field. Therefore, a more accurate interpolation based on Bezier curves is performed for the velocity field.

~~MARGIN OF 4.3 ERROR~~

~~150~~

~~MODEL 2~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE 3D microstructure evolution during the crystallization process SIMULATED USER of PP 1.1 CASE~~

~~1.2 MATERIAL isotactic polypropylene (-iPP) type 505P from Sabic AG (Netherlands)~~

The outer geometry of the RVE for model 2 corresponds to the dimension of one finite element of the macroscopic model 1. For both 1.3 GEOMETRY investigated sections S3 and S2 (see fig. 2) 10 and 7 elements of 300 m3 are specified over the cross section respectively. Each RVE contains 150 cells per direction with a grid spacing of 2 m.

~~Depending on the location of RVE in the staggered plate, the 1.4 TIME LAPSE simulation time varies from 20 sec up to 40 sec.~~

MANUFACTURING The temperature and velocity values are derived from the nodal PROCESS OR IN- values of the mould filling simulation, as outlined in the post- 1.5 SERVICE processing step of model 1. CONDITIONS

PUBLICATION M. Spekowius, R. Spina, C. Hopmann: „Mesoscale simulation of the solidification process in injection molded parts”; Journal of Polymer 1.6 ON THIS ONE Engineering, 2016, vol 36 (6), 563-574. SIMULATION

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Thermodynamic model: nucleation and radial spherulite growth 2.0 AND NAME~~

~~MODEL ENTITY Continuum in cells of a representative volume element RVE whose 2.1 extension is defined by the element size of the finite element at the macroscale~~

~~Equation Nucleation model of Lauritzen & Hoffman (1960): Q K  n N  CkBTG exp( ) exp( n ) kT TG~~

MODEL The crystal growth is described by the Hoffman, PHYSICS/ Davis and Lauritzen model (1976): 2.2 CHEMISTRY * 2 EQUATION U  T (T  T ) G m,0 m,0 (14) vG  v0 exp( ) exp( ) PE R(T  T ) 2  2T (Tm,0  T ) U * Here, the term exp( ) describes the R(T  T ) temperature dependence of the rate at which new polymer chain segments solidifies.

~~151~~

Physical Nucleation model: quantities T = temperature ; 푁̇ is the nucleation rate G = the Gibbs free energy per unit volume is calculated via microscopic material models Q = the activation energy for the formation of the nucleus,

~~kB= Boltzmann constant~~

Kn is a material parameter describing the geometry of the nucleus Exponent n takes either value 1 or 2, depending on the temperature regime where nucleation occurs. The model parameters C, Q, n and Kn are calibrated by means of isothermal experiments.

~~Growth model:~~

~~G = crystallization growth speed~~

~~0 = volume of a periodic region accompanied by a chain segment~~

~~KG is a constant material parameter U* = activation energy of the growth model~~

~~T is a hypothetical temperature at which no movement of the molecular chains occurs (assumed~~

~~as T ≈ TG – 60K)~~

~~Tm,0 = equilibrium melting temperature R = universal gas constant~~

~~Relation Gibbs free energy: G  Gq  Gf (i) Temperature dependent term: T~~

~~Gq  Hc (1 ) Tm,0 (ii) Flow induced term, based on the reptation model of Doi & Edwards (1988):~~

~~t 3ck BT G f  dt(t,t) duln (| E(t,t) u |) MATERIALS   4  2.3 RELATIONS where~~

~~The nonlinear viscoelastic behaviour of the melt is given by the memory function: 8 1  i2t  (t)  exp  , where the disengagement 2  2    i i   d ~~

~~time d describes the relaxation behavior of the polymer. This time is linked to the molecular weight~~

~~of the entanglement Me and to the zero shear~~

~~viscosity 0(T) by:~~

~~152~~

~~20 M   e  T d 2 0   RTmelt~~

~~Physical 1. Me: molecular weight of the entanglement~~

~~quantities/ 2. 0 : zero shear viscosity descriptors 3. T: temperature~~

~~for each MR 4. melt: density of the PP melt~~

5. ∆Hc= enthalpy of crystallisation 6. (t,t) is the memory function of Doi and Edwards 7. c : the entanglement 8. E t,t' defines the deformation tensor of the chain between the times t and t 9. u is a unit vector.

~~10. d : disengagement time~~

~~SIMULATED The interpolated temperature and velocity fields simulated in the 2.4 INPUT Continuum CFD-applied to macroscale simulation for the considered RVE~~

~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

~~1. Numerical integration of the nucleation rate evaluates the number of active nuclei per unit volume at any time. 2. Two crystal growth algorithms are implemented in the in-house code SphaeroSim:~~

NUMERICAL - Monte Carlo method: for each cell a probability is calculated 3.1 and converted in a phase change in a further Monte-Carlo SOLVER step - Ray tracing method: a time is calculated for each cell at the growth front by integrating the growth along a path staring in the spherulite center. Phase change happens when the front reaches the far side intersection point of the cell. SphaeroSim is an in-house code of the Department of Plastics SOFTWARE TOOL Processing of the RWTH Aachen University.

~~-4 3.3 TIME STEP The time step is small: 10 sec~~

~~COMPUTATIONAL PHYSICS EQUATION, 3.4 REPRESENTATION MATERIAL RELATIONS, MATERIAL~~

~~COMPUTATIONAL Interpolated temperature and velocity fields, coming from the macro- 3.5 BOUNDARY simulation. CONDITIONS~~

~~ADDITIONAL 3.6 SOLVER PARAMETERS~~

~~153~~

~~Post processing~~

~~4 POST PROCESSING~~

~~THE PROCESSED The output of the present model (model 2) is the microstructure OUTPUT consisting of an arrangement of spherulites with varying crystallisation degree.~~

Before the solidified spherulite microstructure is stored in a VTK file, the boundaries between two spherulites are marked as an interface layer having one cell thickness. These interface layers are considered as individual phase in the subsequent homogenization processing step (see methodology below). Moreover, a special file 4.1 containing the spherulite centres is built for these simulations.

This information on microstructure is then combined with the elastic properties of isotactic PP (as determined by post processing the output of model 3) and with an experimentally motivated design of nanoscopic bilamella (which is an additional input to the homogenisation processor). This information is jointly processed into the effective properties of the injection moulded PP component by a two level homogenisation scheme.

~~METHODOLOGIES Homogenization of heterogeneous materials based on the asymptotic expansion method - Two-level homogenization scheme~~

~~Nanoscale: effective properties of bilamella designs of amorphous and crystalline phases using chain Young modulus of model 3 and experimental data to specify lamella arrangement (see fig. 4).~~

~~Figure 3: RVE definition of the bilamella depending if secondary branches exist or not~~

~~4.2 a) RVE without branches~~

~~b) RVE with secondary branches~~

~~154~~

Microscale: a dedicate spherulite model is developed. It describes a radial distribution of effective bilamella around the spherulite centre (nucleus). Each discretized spherulite of the solidified microstructure is described by this model. Moreover, in order to derive the effective properties of a polyspherulite microstructure, the interface between spherulites (output of model 2) are considered as separate phase in the homogenisation runs.

In the asymptotic homogenization method the effective Hooke matrix of the heterogeneous material is given by: hom 0 1 0 0 kl H (T )   H (T , y)  H (T , y).ers (ζ )dy ijkl Y Y ijkl ijrs

where T0 is the mean temperature on the RVE, |Y| the volume of the rs RVE and ers (ζ ) the microscopic total strains of the microscopic rs rs rs rs displacement fields where ζ [ζx ,ζy ,ζz ] with rs = xx, yy, zz, xy, 0 xz, yz, induced by the initial macrostrains Ers (x) , which are taken unitary in elasticity.

Using a 3D finite element discretization of the RVE, the nodal values Zrs of the unknown displacement fields are solution from the following 0 rs im,H ΔH discretized RVE problems: K (T )* Z g  g (24) where:  K(T0) is the elastic stiffness matrix of the RVE;  gim,H are implicit surface tractions, which are induced by the jump of the Hooke matrix at the phase boundaries;  gH are implicit body forces, which are induced by the variation of the Hooke matrix within each material phase of the RVE.

The post-processing has been performed using HOMAT version 5.3. This version will be commercialized by ACCESS e.V in combination with MICRESS. The radial distribution of the effective amorphous- crystalline bi-lamellae within a spherulite is described by a specific model, developed on the finite discretization of each spherulite. This model takes into account that the bilamella is twisted. Linear or quadratic volume elements can be used for the RVE discretization.

Final output of the post processing step are: - thermoelastic homogenization:: Hooke and flexibility matrix, eigenstrain, thermal expansion tensor - thermal homogenization: thermal conductivity tensor

~~MARGIN OF 4.3 ERROR~~

~~155~~

~~156~~

~~MODEL 3~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE Behaviour of the helicoidal chain of isotactic polypropylene SIMULATED USER under tensile loading 1.1 CASE~~

~~1.2 MATERIAL isotactic polypropylene (-iPP) type 505P from Sabic AG (Netherlands)~~

The helicoidal crystal structure of Hikosaka and Seto (1973) was used 1.3 GEOMETRY to define the atomistic RVE, whose extension is a= 6.65 A, b = 20.73 A and c (chain) = 6.5 A and  = 98°40 within an RVE comprising 6 H and 2 C atoms in a P2/c group configuration.

~~1.4 TIME LAPSE~~

~~MANUFACTURING Room temperature is adopted as the effective properties of the PROCESS OR IN- injection moulded stepped plate are evaluated at room temperature. 1.5 SERVICE CONDITIONS~~

~~PUBLICATION Not applicable~~

~~1.6 ON THIS ONE SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Molecular Dynamics: Calculation of normal mode frequencies and of 2.0 AND NAME elastic constants~~

~~2.1 MODEL ENTITY Mesoscopic helicoidal molecule consisting of 8 atoms in an RVE~~

Equation Dynamical equation for normal mode frequencies: −1/2 푇 −1/2 |푀 퐵 퐹푅퐵푀 − 휆퐸| = 0 MODEL PHYSICS/ 2.2 CHEMISTRY EQUATION Physical FR, B, and M are matrices related to the force PE quantities constants, geometry and atomic masses. E is the identity matrix and  is an eigenvalue.

~~Relation The elastic constant tensor C is given by: 1 MATERIALS 퐶 = [퐹 − 퐹푇 퐹 −1퐹 ] 푉     2.3 RELATIONS~~

~~Mass of the atoms, intramolecular force constants of Urey-Bradley type~~

~~157~~

~~Physical V is the volume of the asymmetric RVE and F, F~~

quantities/ and F are matrices constructed by the atomic descriptors coordinates, the B matrix and the force constants. for each MR The intramolecular force constants of Urey-Bradley type are taken from literature and the atom mass from standard data tables.

~~SIMULATED 2.4 INPUT~~

~~. 3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

~~3.1 NUMERICAL SOLVER as implemented in Materials Studio, details unknown.~~

~~Materials Studio from BIOVIA, SOFTWARE TOOL accelrys.com/products/collaborative-science/biovia-materials- studio~~

~~3.3 TIME STEP~~

~~COMPUTATIONAL PE, MR 3.4 REPRESENTATION~~

~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~

~~ADDITIONAL SOLVER 3.6 PARAMETERS~~

~~Post processing~~

~~4 POST PROCESSING~~

THE PROCESSED The molecular dynamic simulation of model 3 provides a theoretical OUTPUT Hooke matrix of the crystalline phase of the isotactic PP. It neglects the adjacent tied amorphous interface and also the crimping of the molecular chain. Therefore, by simple model assumptions and analytical formula the elastic constant in the chain axis is reduced in a post processing step. Moreover, as the packing of the folded chain is

~~4.1 higher in the growth direction E1 than in the perpendicular direction E2 due to larger molecular forces, Young modulus in E1 > Young~~

modulus in E2. Result of this post-processing operation is a modified, more realistic Hooke matrix of the crystalline phase for the subsequent homogenization analysis ( see post processing of model 2).

~~METHODOLOGIES Combined with post processing of model 2. Please see respective 4.2 chapter 4.2 for model 2 for full details.~~

~~4.3 ERROR MARGIN~~

~~158~~

~~MODA~~

~~High Throughput Discovery of Single Crystal Ferroelectrics Film~~

~~Project ICMEg~~

~~OVERVIEW of the simulation~~

~~Search for the candidates of novel single crystal ferroelectric 1 USER CASE film.~~

~~MODEL 1 DFT based First Principles Calculations~~

~~DATA- CHAIN OF MINING Computational Thermodynamics MODELS BASED MODEL~~

~~MODEL 2 Phase Field/Ginzburg-Landau~~

1. Zi-Kui Liu, Long-Qing Chen, Integration of first-principles calculations, calphad modeling, and phase-field simulations, in Applied Computational 3 PUBLICATION Materials Modeling, eds G. Bozzolo, R. D. Noebe, P. B. Abel, D.R. Vij, pp 171-213.

~~Software/ Models copyright owner links Database~~

~~First Universität http://www.va VASP commercial Principles Wien sp.at/~~

~~http://www.th Thermo- Computati ermocalc.com/ onal Thermo-Calc Commercial/ Calc AB/ ACCESS http://www.co 4 Thermody & Pandat Commercial Computher CONDITIONS mputherm.com namics m LLC /~~

~~Phase field- based Dr. Yuwen GLsim In-house n/a Ginzburg- Cui Landau Model~~

~~159~~

The DFT based First Principle Calculations serves as the starting points of the high throughput screening for the candidates of novel single crystal ferroelectric film. It is capable of predicting such material properties as crystal structure, atomic structure imperfection, phase stability, and dielectric of ferroelectrics over the composition space (arrays) of low order system. The predicted energetics, phase stability, and phonon spectra, etc. can be served as inputs to computational thermodynamics and kinetics (CALPHAD) for extrapolating the descriptions of energy and relevant physical properties of systems WORKFLOW multinary ferroelectrics from lower order systems. Meanwhile, the 5 AND ITS predicted elastic stiffness, phonons and static dielectric constants from RATIONALE first principle calculations will be also adopted as inputs for Ginzburg- Landau modelling for simulating the domain pattern formation and hysteresis in ferroelectrics. By combining DFT based First Principle calculations, computational thermodynamics and Phase Field (Ginzburg- Landau) modeling at mesoscale with intelligent data mining and database construction (for quantitative descriptions of energies, mobilities, and materials parameters, etc. toward the multicomponent systems ), the task of searching novel transition metal oxides for desirable ferroelectric candidates can be achieved.

~~MODEL 1~~

~~1 FIRST PRINCIPLES CALCULATION OF PHYSICAL PROPERTIES~~

Predict both the crystalline structures and physical properties (esp including elastic stiffness, phonon and static dielectric constants, etc.) ASPECT OF THE and to explore the microscopic mechanisms of the phase transition 1.1 USER CASE TO BE through the DFT-based First \principles calculations. The key material SIMULATED properties crystal structure, atomic structure imperfection, phase stability, and static permittivity of ferroelectrics are to be simulated over the composition space (arrays) of low order system.

~~Perovskite (Ba,Sr)TiO3 ferroelectrics 1.2 MATERIAL Crystallographic structure and lattice parameters.~~

~~1.3 GEOMETRY homogeneous~~

~~1.4 TIME LAPSE ~ps~~

~~MANUFACTURING 0 Kelvin, 1 atm PROCESS OR IN- 1.5 SERVICE CONDITIONS~~

PUBLICATION S. Curtarolo, G. L. W. Hart, M. B.Nardelli, N. Mingo, S. Sanvito and O. 1.6 ON THIS ONE Levy, The high-throughput highway to computational materials SIMULATION design, Nature Materials, 12(2013) 191-201

~~160~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Density Functional Theory 2.0 AND NAME~~

~~MODEL Ion core and electrons 2.1 ENTITY~~

Equation E ()() r V r dr F  V   ext HK   1 (rr ) ( ') F  T   drdr'  E   HK2' rr xc 1 (rr ) ( ') MODEL E Eion  drdr'()()  E xc  r V xc r dr PHYSICS/ 2'rr  2.2 CHEMISTRY EQUATION PE Physical Exc[]- exchange-correlation potential quantities - electron density

~~Eion is the energy of ion T() is the kinetic energy~~

~~Vext is the external potential~~

~~Vxc is the exchange-correction potential E is the total energy~~

~~Relation 1. △Hf(BaTiO3)=E (BaTiO3)- E(Ba)- E(Ti)- 3/2E(O2)~~

~~2. △Hf (SrTiO3)=E (SrTiO3)- E(Sr)- E(Ti)- 3/2E(O2) ∆H is the formation enthalpy~~

MATERIALS 2.3 Physical 1. △Hf(BaTiO3)-formation energy (i.e. also enthalpy here) RELATIONS quantities/ 2. E(Ba/SrTiO3)-total bulk energy descriptors 3. E(Ba/Ti)-total atomic energy of element for each MR 4. E(O2)-total molecular energy

~~SIMULATED NA 2.4 INPUT~~

~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

~~NUMERICAL iterative 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL VASP~~

~~3.3 TIME STEP static~~

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PHYSICS △E=EAFM-EFM COMPUTATIONAL EQUATION, △E-Total energy difference 3.4 REPRESENTATION MATERIAL E -Total energy with ferromagnetic ordering , RELATIONS, AFM MATERIAL EFM- Total energy with anti-ferromagnetic ordering

~~COMPUTATIONAL Periodic boundary condition 3.5 BOUNDARY CONDITIONS~~

~~ Exchange interactions of electrons: GGA-PBE ADDITIONAL  Energy cutoff = 400 eV 3.6 SOLVER  Total energy difference < 10-6 eV PARAMETERS  Maximum Hellman-Feynman force < 10-2 eV/Å~~

~~4 POST PROCESSING~~

THE PROCESSED 1.The formation enthalpy of ferroelectric phase with different OUTPUT concentration of doping elements 2. Temperature dependence of elastic stiffness of ferroelectric phase. 3. Static dielectric matrix. 4.1 4. Lattice vibration dependence of dielectric matrix 5. Computation of molar volumes

~~All to be used in the computational thermodynamics data mining based model and stored in its database.~~

METHODOLOGIES 1. This is related to the energetics above described. Characterize the effect of doping elements by comparing to atomic energies and/or projecting the system properties into specific atoms. 2. Temperature dependence qualitative studies can be obtained from either high temperature phase structures or by considering how thermal energy modifies atomic distances, phonon vibrations... 3. The expressions for both born effective charges and ion-clumped static dielectric matrix are:

~~Ω 휕푃푖 1 휕퐹푖 푍푖푗 = = 4.2 푒 휕푢푗 푒 휕퐸푗~~

~~∞ 4휋 휕푃푖 휀푖푗 = 훿푖푗 + 휀0 휕퐸푗 This is calculated by using the following equation:~~

~~4. The frequency dependence of the dielectric matrix is expressed as the imaginary part:~~

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2 2 (2) 4휋 푒 1 휀 (휔) = lim ∑ 2휛퐾훿(휖푐퐾 − 휖휈퐾 − 휔) 훼훽 Ω 푞→0 푞2 푐,푣,퐾 ∗ × ⟨휇푐퐾 + 푒훼푞|휇푐퐾⟩⟨휇푐퐾 + 푒훽푞|휇푐퐾⟩ and the real part:

~~∞ (2) ′ ′ ( ) 2 휀훼훽 (휔 )휔 휀 1 (휔) = 1 + 푃 ∫ 푑휔′ 훼훽 휋 휔′2 − 휔2 + 푖휂 0~~

Molar volumes of (Ba,Sr)TiO3 can be calculated either regarding to a repetition cell or to a group of atoms by defining the specific radius related to the atomic interaction (ionic, convalent, van der Waals…).

MARGIN OF ERROR 1. Enthalpies are calculated through total energies which are typically reliable within 1 meV/atom. 2. DFT can only provide qualitative insights about the temperature dependence of structural parameters. 4.3 3. Born effective charges and ion-clumper static dielectric matrices typically converge within 5 and 10% (from measurement) respectively. 5. Molar volumes are overestimated around 15% using GGA functionals.

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~~Data-based Model~~

~~1 DATA-SET FOR SELECTING~~

The first goal is to establish a dataset and functions for ASPECT OF THE Gibbs/Helmholtz energy and chemical potential. 1.1 USER CASE TO The second goal is to find the composition and temperature BE CALCULATED dependence of elastic stiffness and static permittivity in continuous functional to be used in model 2 Phase Field

~~1.2 MATERIAL Perovskite (Ba,Sr)TiO3 ferroelectrics~~

~~3 1.3 GEOMETRY 1 mole for thermodynamic functions and cm for elastic properties~~

~~1.4 TIME LAPSE n/a (static thermodynamic properties are time irrelevant)~~

~~MANUFACTURIN Temperature: 298K-3000K G PROCESS OR 1.5 Pressure: 1 atm IN-SERVICE Entire composition range CONDITIONS~~

S. Lee, C. A. Randall, Zi-Kui Liu, Comprehensive Linkage of Defect PUBLICATION and Phase Equilibria through Ferroelectric Transition Behavior in 1.6 ON THIS ONE BaTiO3-Based Dielectrics: Part 1. Defect Energies Under Ambient Air DATAMINING Conditions, 91(2008) 1748–1752 OPERATION

~~2 THE DATA BASED MODEL~~

~~EQUATION TYPE  2.0 Energy minimizer Gm  0 AND NAME~~

Database and In the frame of CALPHAD, thermodynamic database and elastic type modulus database are described in compound energy formalism. The thermodynamic database includes Gibbs energy whose 2.1 derivatives should be equal to the values of simulated data by DFT model and experimental data from AFM. The elastic modulus database includes values of bulk, shear, Young’s modulus, and stiffness.

Equati on I II,  I I II II ex  Gm yyG i j i: j  RTayybyy(  i ln i   j ln j )  G m i j i j ex II I I v,,,,  I I I v I II II v  II II II v Gm yyyLyy m  ijijij ,,()()    y i  yyLyy mn  mnmn  m i,, j i v i m n m v EQUATION 2.1 I I II II rec yi y j y m y n L i,, j m n

~~xi x i y j ~~

~~L -adjustable parameters to describe interaction effect among atoms~~

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Physic al 1. Molar Gibbs energy of individual phases: quanti 2. xi-composition, yj-site fraction ties 3. fi-phase fraction 4. T -temperature, R -gas constant 5. L -adjustable parameters to describe interaction effect among atoms 6. Formation enthalpy, vibrational entropy, molar volume, activity, etc.

~~3 COMPUTATIONAL DETAIL OF DATAMINING OPERATION~~

By evaluating the discrete physical properties from experiments and atomistic simulations, the phenomenological expressions of NUMERICAL energy, elastic stiffness and permittivity of paraelectric and 3.1 OPERATIONS ferroelectric phases are extrapolated to entire composition and temperature in the spirit of CALPHAD. Least-squares optimization

~~3.2 SOFTWARE TOOL Thermo-Calc PARROT module~~

The predicted value of energy has an error in 0.1-10 kJ/mole. It is MARGIN OF generated from the compromise among the different errors from 3.3 ERROR measured thermal chemical properties and DFT based calculations.

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~~MODEL 2~~

~~1 PHASE FIELD (GINZBURG-LANDAU) MODELING~~

Simulate the temporal and spatial imhomogeneity of single ASPECT OF THE crystal ferroelectrics in variant and twinning of product phase, as 1.1 USER CASE TO BE well as such materials properties as polarization and dielectric SIMULATED constant, breakdown voltage, etc.

~~1.2 MATERIAL Perovskite (Ba,Sr)TiO3 ferroelectrics~~

~~3 3 1.3 GEOMETRY ~10 nm~~

~~1.4 TIME LAPSE ps ~microsecond~~

~~MANUFACTURING Arbitrary temperature, w/wo external stress PROCESS OR IN- 1.5 SERVICE CONDITIONS~~

P. Marton, I. Rychetsky, J. Hlinka, Domain walls of PUBLICATION ferroelectric BaTiO3 within the Ginzburg-Landau- 1.6 ON THIS ONE Devonshire phenomenological model, Phys. Rev. B SIMULATION 81(2010) 144125

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Phase field/ Ginzburg-Landau 2.0 AND NAME~~

~~2.1 MODEL ENTITY Compound in finite volumes~~

~~Equation~~

~~MODELPHYSIC S/ CHEMISTRY 2.2 EQUATION Physical 1. ϕ order parameter, i.e. polarization P or strain e. PE quantities 2. t time 3. F Helmholtz energy 4. L mobility~~

~~Relation~~

~~MATERIALS 2.3 RELATIONS~~

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~~Physical Fbulk -bulk energy~~

~~quantities/ Eelastic -elastic energy~~

~~descriptors Eele -electric energy~~

~~for each MR Echem -chemical energy (from CALPHAD)~~

~~λijkl -elastic stiffness ε -strain component σ - applied stress P -polarization εo -vacuum permittivity~~

SIMULATED With the properties from the atomistic models (vibrational entropy and INPUT molar volume, etc) and the energy functional from computational 2.4 thermodynamics (formation enthalpy and activity, etc), the Landau and phase field models are applied to mesoscale.

~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~

~~NUMERICAL Finite difference in Fourier Space 3.1 SOLVER~~

~~GLsim an in-house software for microstructure simulation. It keeps 3.2 SOFTWARE TOOL the physical inherency and ensures the data-passing and integration of the model physical and deterministic.~~

~~3.3 TIME STEP 1ps-1ns adjustable~~

PHYSICS EQUATION, (n 1) ( n ) ( n ) 2 ( n ) pk   p k   t F  p  k  p  k COMPUTATIONAL MATERIAL  k RELATIONS, 3.4 REPRESENTATION MATERIAL k -wave vector, wave hat – Fourier Transformation

~~COMPUTATIONAL Periodic/ Neumann/ Fixed in spatial space 3.5 BOUNDARY Fixed/continuous cooling temperature. CONDITIONS~~

~~-3 ADDITIONAL  Cutoff 10 in P 3.6 SOLVER PARAMETERS~~

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~~4 POST PROCESSING~~

~~THE PROCESSED The simulated microstructure pattern and hysteresis curves 4.1 OUTPUT All to be used for fast high throughput discovery and evaluation of ferroelectrics.~~

~~METHODOLOGIES Image processing for pattern visualization Evolution algorithm (like genetic algorithm). 4.2 Data mining and regression for the plot of hysteresis.~~

~~MARGIN OF ERROR The error will be controlled to be compared with experimental 4.3 data by adjusting the kinetic parameters in Allen-Cahn Equation~~

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~~INNOVIP (723441)~~

~~Summary of the project~~

INNOVIP will work on insulation solutions to reach the energy efficiency of the opaque parts of the building envelope. They will improve insulating material for vacuum-insulation-panels by improving their thermal performance and making them adjustable, mountable and machineable. They will reduce the density of the core material with less expensive envelopes as gas barrier. Besides, the new product will have a reduced embodied energy and, attaching different cover layers, the panels can fulfil also other functions like photo-catalytic volatile organic compound removal from indoor- and outdoor air, moisture buffering or cutting off summer heat by latent heat activated in phase change materials or prevent moulding.

~~Insulation of buildings~~

Project Acronym and Number: INNOVIP 723441 Project Title: Innovative multi-functional Vacuum-Insulation-Panels (VIPs) for use in the building sector Start and End Dates: from 1/10/2016 till 30/09/2019 EU Contribution: 4,982,505 € Coordinator: Christoph SPRENGARD, [email protected] Modeller(s): Christoph SPRENGARD, [email protected]

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~~MODA~~

~~Insulation of buildings~~

~~INNOVIP~~

~~OVERVIEW of the simulation~~

~~MODA 1: Determine heat-transfer through material, building components and systems~~

~~MODA 2: Determine dynamic building behavior and the energy savings~~

1 USER CASE associated with the technical solutions and to transfer the INNOVIP idea to other climatic zones and different buildings. Check for moisture accumulation and drying of the components. VIPs are a total barrier for water vapour in building constructions – except at their panel to panel joints. Moisture accumulation in the component or drying out of water used for mortar and plaster can only occur at these joints.

~~MODEL 1 Continuum model Heat flow equation used on the three aspects MODA 1 of the user case~~

Dynamic building simulation modelling using the heat flow equation with radiative term for solar heat gain (RoMM Ch 4.3) but also CFD (Chapter 4.2) for the mass (moisture) transfer CHAIN OF 2 MODELS through the building components as MODEL 2 Extra terms are added to the heat flow equation used in MODA MODA 2 1 to model hygrothermal effect like phase change etc (see below). The simulations will be done with different material relations (MR).

~~PUBLICATION 3 ON THE SIMULATION~~

All MR will be treated as “confidential” The software-tools for the PE are all commercial – except “Therm” for 2-dim ACCESS 4 CONDITIONS Heat Transfer. Therm is available for free at LBNL (Lawrence Berkeley National Laboratory) https://windows.lbl.gov/software/therm/therm.html

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~~MODA 1: Heat-transfer through material, building components and systems~~

~~MODEL 1: Continuum Model for Heat-flow and thermo-mechanics~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

Application 1: Determine the thermal bridging effects “psi-value” and total heat flux caused by the metallized layers of the foil-envelopes of the VIP and the additional materials placed at the edges to form the new “edge design” of the INNOVIP product.

Application 2: Determine the thermal bridging effects if additional cover layers on the panels are used. Depending on the thermal conductivity of the cover ASPECT OF THE layer material, these layers can function as a remarkable additional USER CASE TO BE thermal resistance reducing the thermal bridging effect at the panel SIMULATED 1.1 edge or in an opposite way as a collector for heat from the AND HOW IT FORMS A PART OF THE undisturbed part of the panel towards the edge. We will determine a TOTAL USER CASE range for the total heat flux that is optimized for the desired function and for thermal performance of the insulation construction.

Application 3: Determine the additional effect of penetrating fasteners and fixing solutions on the heat transfer (point thermal transmittance of fasteners). Some of the optimized combinations of Application 1 and Application 2 will be simulated to determine the additional thermal bridging effect that is caused by fasteners and penetrating fixing solutions (point thermal transmittance: “chi-value”)

A wide range of materials for which thermal performance values can be found with tabulated values in international standards, such as ISO 10456 and ISO 10077-2. For stationary heat-transfer modelling, only thermal conductivity values (ideally: temperature dependent) are needed. Relevant temperature dependent properties are taken into account (e.g. temperature dependent thermal conductivity, temperature dependent heat capacity, moisture content etc.). 1.2 MATERIAL Properties taken from databases or measured values. Temperature dependent properties will be used if necessary. Isotropic material properties will be used mostly. Anisotropic properties only if needed for the correct definition of the heat transfer of the simulated component (e.g. equivalent thermal conductivity of air-gaps or anisotropic thermal conductivity behavior of some building materials (baked clay)).

~~1.3 GEOMETRY The size of the model will be “real” size, measured in m or mm.~~

~~1.4 TIME LAPSE Stationary situation~~

Simulations for thermal performance can be carried out for standard MANUFACTURING conditions given in CEN or ISO standards (e.g. 20°C inside the PROCESS OR IN- 1.5 building and -5°C or -10°C for the exterior climate). SERVICE CONDITIONS The warm side surface Resistance is (due to slow air speed from natural convection): Rsi = 0.13 m²*K/W and the cold side resistance

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usually 0.04 m²*K/W (higher wind-speeds on the outside surface). Heat-transfer simulations are carried out on non-deformed systems, omitting bending forces, external pressure or dilatation as a result of temperature increase or decrease.

~~PUBLICATION~~

~~1.6 ON THIS ONE SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum Model: 2.0 AND NAME 4.3 Heat flow and thermo mechanics~~

~~2.1 MODEL ENTITY Flat (2d) elements and volumetric (3d) elements.~~

~~Equations When modelling heat-transfer in (and through) building~~

parts and components, the PE has three terms of heat o t transfer: - Heat-Conduction in the solid material and conduction in liquids and gases (Fourier’s law) - Convection (various descriptions bases on Newton’s law of cooling) - Radiation (Stephan-Boltzmann’s law)

MODEL PHYSICS/ CHEMISTRY 2.2 EQUATION PE’S Physical 푞̇ heat-flux density in W/m² quantities for each equation K (in building systems usually called thermal transmittance “U-value”) in W/(m²*K) Delta T is the temperature difference at the system’s boundaries in K k Thermal conductivity (usually λ is used for building materials) in W/(m*K) T absolute Temperature in K ∇T: Temperature Gradient/ Temperature Difference on a specific layer in K h (convective) heat transfer coefficient ε emissivity of surfaces σ Stephan-Boltzmann constant

~~MR Equations~~

~~MATERIALS RELATIONS~~

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~~ = L3D – U*A~~

~~U = 1/(Rsi+Σdi/λi+Rse)~~

~~Physical quantities/ descriptors for each MR~~

~~L3d thermal coupling coefficient from three-dimensional calculation U U-value A Area Rsi internal surface resistance d thickness of layer  thermal conductivity Rse external surface resisstance~~

~~ point thermal transmittance in W/K~~

~~SIMULATED 2.4 No simulated input used. INPUT~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

Finite-Difference (FD) or Finite-Element (FE) in 2-dim and 3-dim will be used. The solver is part of the software tool used. Iterative Solvers can NUMERICAL 3.1 be used if the dimensions of neighboring elements don’t differ too SOLVER much. FD is strongly recommended for the very thin layers of the foils at the edges of VIPs.

~~3.2 SOFTWARE TOOL Therm; Heat 2d; Heat 3d; Nastran; COMSOL~~

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~~3.3 TIME STEP Not applicable for stationary heat transfer~~

COMPUTATIONAL PHYSICS Material properties and all other physics variables are REPRESENTATION EQUATION, written up for the entity in the model. Refers to how MATERIAL your RELATIONS, MATERIAL computational 3.4 solver represents the material, properties, equation variables,

~~COMPUTATIO NAL~~

~~BOUNDARY CONDITIONS~~

ADDITIONAL Stop criteria on convergence: SOLVER PARAMETERS Heat-flux density: 0.001 to 0.0001 W/m² from simulation step to simulation step. Temperature: Usually around 0.00001 to 0.000001 K from step to step. A finer mesh will be used at specific areas. Symmetric planes will be used to limit the number of nodes and elements and to increase the speed of the solver.

For stationary heat-transfer modelling (until equilibrium is reached for constant boundary conditions on the warm and the cold side of the model) the time lapse is not relevant, as the simulation will be carried out until a stop criterion is reached. As stop criterion the deviation of temperature or total-heat flux from one simulation step to the next step is limited to a certain value. The simulation is faster if it is carried out without heat-capacity properties of the materials.

~~Post processing~~

~~4 POST PROCESSING~~

~~THE PROCESSED Simulated output is usually the total heat flux for the given model or OUTPUT IS the heat-flux density or temperature. CALCULATED FOR~~

~~4.1 The processed output is not used as input for model 2. INNOVIP will use the ouput to optimise the design.~~

METHODOLOGIES The total heat flux or the heat flux density is calculated by volume averaging. (by calculating the effective R- or U-value of the simulated 4.2 system with all influencing factors). This is used to derive the thermal performance of the construction directly

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~~The total heat flux or the heat flux density is further used to define the linear thermal transmittance (Psi-value) for the optimized edge and for the optimized edge when using cover layers:~~

~~The processed output from the 3-dim Simulation of the fasteners will be used to derive the point thermal transmittance (Chi-value) for fasteners.~~

~~ = L3D – U*A~~

MARGIN OF ERROR For the heat flow from the simulation the program validation procedure in ISO 10211 is carried out and all programs should be within 1 % of the total heat flow. The total margin of Error is strongly depending on the quality of the model and on some limitations of the program in comparison to the real building component (e.g. cracks in wall constructions influencing the thermal conduction in the material; measurement tolerances in the building sector usually exceed some mm). In addition to that 4.3 thermal modelling of building components strongly depend on the quality of the input data – especially for thermal conductivity of the material. Therefore the total margin of error (based on the heat flux) can only be estimated to be in between ±1% (for the programs with fixed input values) and ±10 % (for program plus dimensions plus measured values of thermal conductivity plus insufficient drying etc….). For heat transport simulation in wet materials the margin of error is estimated even higher around ±15%).

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~~MODA 2: Dynamic building behavior~~

~~MODEL 2: Dynamic building simulation with Continuum Model for Heat-flow and thermo-mechanics~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

ASPECT OF THE Dynamic building behaviour. USER CASE TO BE Determination of thermal performance in use SIMULATED 1.1 Energy savings in different climates AND HOW IT FORMS A PART OF THE Building physical aspects of the use of the INNOVIP elements in TOTAL USER CASE constructions.

Thermal: see Model 1 For simulating the combined heat and mass transfer, additional 1.2 MATERIAL properties are needed, such as capillary effects in the material, water absorption, water intake, pore sizes, temperature and moisture dependent sorption isotherms etc.

~~1.3 GEOMETRY Simulation on real size building components (m).~~

For instationary heat-transfer (e.g. for non-constant boundary conditions on the warm and on the cold side of the model) the time 1.4 TIME LAPSE lapse is usually set by the given climatic data. For short time simulations, minute or 5-minute values are used – for long term simulations usually hourly, daily or monthly-values are used.

~~Hygrothermic simulations are carried out on non-deformed systems, omitting bending forces, external pressure or dilatation as a result of temperature increase or decrease.~~

MANUFACTURING PROCESS OR IN- 1.5 SERVICE Standard Conditions given by climatic data for various climatic regions CONDITIONS of the world. Hygrothermal: Typical Meteorological Data is used (standard reference years with additional data on the amount and the duration of rain). This is processed climatic data, but not a simulated input.

~~PUBLICATION Publication documenting the simulation with this single model (if available and if not~~

~~t o 1.6 ON THIS ONE included in the overall publication). SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Dynamic simulation with combined heat and mass transfer - making use of 2.0 AND NAME a Continuum Model: Heat flow and CFD~~

~~MODEL 2.1 1-dim and 2-dim Elements, 3-dim Volumes ENTITY~~

Equations When modelling heat-transfer in (and through) building parts MODEL and components, the PE has three terms of heat transfer: PHYSICS/ 2.2 CHEMISTRY - Heat-Conduction in the solid material and EQUATION conduction in liquids and gases (Fourier’s PE’S law)

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~~- Convection (various descriptions bases on Newton’s law of cooling) - Radiation (Stephan-Boltzmann’s law)~~

In this simulation of hygrothermal behavior, many additional effects are taken into account nl phase change of water (ice – water – water vapour), latent heat transported by warm water moving through the component, additional effects on solid conduction (reduced coupling resistances and higher conductivity due to absorbed water):

~~Phase change between liquid and vapour, i.e. the release of latent heat, is considered as part of the convective heat flow through the structure.~~

~~Conservation of mass can be used to determine the air flow rate. If buoyancy can be neglected the air flow rate is calculated from the total pressure difference over the construction.~~

The increase of the moisture content of a control volume is determined by the net inflow of moisture. The moisture flow rate equals the sum of the vapour flow rate and the flow rate of liquid water.

The liquid phase of water inside a building material can be described by the moisture content mass by volume. Due to the capillary forces the pressure inside the water is different from the pressure of the surrounding air. The difference is called suction.

~~The suction of the pore water is related to the relative humidity of the surrounding air by the Kelvin equation:~~

The heat transport through heat conduction is calculated with Fourier’s law and includes all processes where the transport of heat is closely correlated to the temperature gradient. The second heat flow term accounts for the effects of both air flow and moisture flow, including sensible and latent heat:

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~~Air (and liquid moisture) flow into the construction:~~

Physical 푞̇ heat-flux density in W/m² quantities for each K (in building systems usually called thermal transmittance equation “U-value”) in W/(m²*K) Delta T is the temperature difference at the system’s boundaries in K k Thermal conductivity (usually λ is used for building materials) in W/(m*K) T absolute Temperature in K ∇T: Temperature Gradient/ Temperature Difference on a specific layer in K h (convective) heat transfer coefficient ε emissivity of surfaces σ Stephan-Boltzmann constant

~~Symbol Quantity Unit – hygrothermal simulations~~

~~C flow coefficient per unit area m³/(m² s Pan)~~

~~Dl liquid diffusivity m²/s~~

~~Isol total flux of incident solar radiation W/m2~~

~~Pa pressure of the surrounding air Pa~~

~~Pa total air pressure difference Pa~~

~~Pl water pressure inside pores Pa~~

~~RH2O gas constant of water vapour J/(kg K)~~

~~Rl liquid moisture flow resistance of interface, m/s T thermodynamic temperature K~~

~~Ta air temperature of the surrounding environment K~~

~~Teq equivalent temperature of the surrounding environment K~~

~~Tr mean radiation temperature of the surrounding environment K~~

~~Tref arbitrary reference temperature K~~

~~Ts surface temperature K~~

~~cp,a specific heat capacity at constant pressure of air J/(kg K)~~

~~cp,l specific heat capacity at constant pressure of liquid water J/(kg K)~~

~~cp,s specific heat capacity at constant pressure of solid matrix J/(kg K)~~

~~dI thickness of the layer I m g density of moisture flow rate kg/(m² s)~~

~~gr density of air mass flow rate kg/(m² s)~~

~~gl density of liquid moisture flow rate kg/(m² s)~~

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~~gp available water due from to precipitation kg/(m² s)~~

~~gv density of vapour flow rate kg/(m² s)~~

~~hc convective heat transfer coefficient W/(m2⋅K)~~

~~he specific enthalpy of liquid-vapour phase change J/kg~~

~~heff effective heat transfer coefficient W/(m2⋅K)~~

~~hr radiative heat transfer coefficient W/(m2⋅K) n flow exponent -~~

~~pv partial vapour pressure, Pa~~

~~pv,sat saturated vapour pressure Pa~~

~~q density of heat flow rate W/m2~~

~~qcond density of conduction heat flow rate W/m2~~

~~qconv density of convection heat flow rate W/m2 s suction Pa s suction difference across interface Pa s mean suction at interface Pa~~

~~sd equivalent vapour diffusion thickness m v wind speed m/s~~

~~w moisture content kg/m3~~

~~wl water content kg/m3~~

~~sol solar absorptance –~~

~~0 permeability of vapour in air kg/m s Pa  long-wave emissivity of the external surface -  thermal conductivity W/(m⋅K)~~

~~m,l moisture conductivity for capillary water transport s  relative humidity -  diffusion resistance factor –~~

~~l liquid water density kg/m³~~

~~a density of air kg/m³~~

~~s density of solid matrix kg/m³~~

~~MR Equations Effective heat transfer coefficient and the equivalent temperature:~~

~~MATERIALS RELATIONS~~

~~Physical quantities/ See List above… descriptors for each MR~~

~~SIMULATED 2.4 NA INPUT~~

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~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

Finite volume based solver Coupled Heat and Mass transfer equations on components: implicite, iterative finite-volume solver with adaptive time steps - with iterative NUMERICAL 3.1 coupling of heat and mass transfer. SOLVER Building simulation between zones: energy balance equations with implicit and iterative solver with adaptive time steps or explicit solver with short time steps (auto-adjusted) depending on the sub-models used

~~WUFI + (combined hygrothermal simulation and dynamic building 3.2 SOFTWARE TOOL simulation program)~~

~~Hygrothermal: Time step dependent on climatic data (real time – 5 min 3.3 TIME STEP or hourly values)~~

~~COMPUTATIONAL PHYSICS All physical vlaues are written up for finite volumes REPRESENTATION EQUATION,~~

~~Refers to how MATERIAL your RELATIONS, computational MATERIAL 3.4 solver represents the material, properties, equation variables,~~

~~COMPUTATIONAL The physics b.c. are written up for the faces of theouter BOUNDARY finite volumes. CONDITIONS~~

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~~4 POST PROCESSING~~

THE PROCESSED Hygrothermal: simulated output is the temperature, the heat-flux OUTPUT IS and the local water content. From these, the risk for mould growth CALCULATED FOR or the moisture accumulation within the component will be derived.

~~Dynamic building simulation: the output is the performance of the building in the specific climatic zone.~~

The output is calculated to provide building data and building component data directly to the End-User. The user needs 4.1 information about the safety in use (regarding to moisture problems) and about the overall thermal performance in relation to the original state before refurbishment with the INNOVIP solution (energy savings).

Safety in use: Moisture content of the material in a certain position over time and the equivalent temperature. Energy Savings compared to the state before refurbishment: Effective heat transfer coefficient

~~METHODOLOGIES~~

~~4.2~~

~~MARGIN OF ERROR For heat transport simulation in wet materials the margin of error is 4.3 estimated around ±15%).~~

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~~IN-POWER (720749)~~

~~Summary of the project~~

IN POWER project will develop concentrated solar power architectures. Such thermoelectric plants concentrate sun heating power into a receptor. The receptor is designed to optimize the heat transfer to a Heat Transfer Fluid that circulates inside tubes allowing the heat transport to the power storage block, while minimizing thermal losses. This heat is used to power the conventional thermal cycle and produce electricity. The project will develop smart light mirrors consisting of a polymeric substrate with multi-layered coatings with reflective, self-healing and anti-soiling functionalities. They will also develop a high working temperature absorber in vacuum free receiver designed for high temperature operation and an optimized reduced mass support structure. Furthermore they will develop thermal storage materials for medium and high temperature thermal storage systems.

~~Mirror support design for thermoelectric plant~~

~~GFRP is glass fibre reinforced polyester~~

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~~continue~~

Project Acronym and Number: IN-POWER 720749 Project Title: Advanced Materials technologies to QUADRUPLE the Concentrated Solar Thermal current POWER GENERATION Start and End Dates: from 1/1/2017 till 31/12/2020 EU Contribution: 4,998,928.13 € Coordinator: Emilie Mespoulhes, [email protected] Modeller(s): Mónica Della, [email protected]

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~~MODA Design and simulation of advanced materials for mirrors in CSP plants~~

~~In Power~~

~~THE SIMULATION GENERAL DESCRIPTION~~

Design and simulation of advanced materials for innovative mirrors suitable for use in different type of CSP plant. The materials include 1 USER CASE polymeric substrate, metallic reflective coating, self-healing coating, antidust coating and composite for support. This includes also the manufacturing process and the operational conditions.

Continuum model for industrial application. Solid mechanics. (model 4.1 in ROMM) The model 1 is dedicated to find the MODEL 1 optimal processes in order to avoid deformation in the final customizable CSP mirror substrate; the validation will be done using planar geometry.

Continuum models:. Tightly coupled Heat flow and thermomechanics. (model 4.3 in ROMM) and Electromagnetism (optics) (model 4.6 in ROMM) MODEL 2 Define the optimal non planar mirror geometry in order to find a solution in which there is a four times increase of the power CHAIN OF generation considering performance of materials in service 2 MODELS #1 Continuum model for industrial application. Solid mechanics. (model 4.1 in ROMM)

~~MODEL 3 Continuum model. Heat flow and thermo-mechanics. (model 4.3 in ROMM) Definition of new composite for mirror support~~

~~Continuum model for industrial application. Solid mechanics. (model 4.1 in ROMM) MODEL 4 Definition of support geometry considering performance of materials in service.~~

~~3 PUBLICATION Not available~~

~~ACCESS Restrictive licence: Autodesk Moldflow, Altair HyperWorks, Altair Partner 4 CONDITIONS Alliance softwares, TracePro and Matlab, ABAQUS from SIMULIA Platform~~

Each model used in a simulation is documented in four chapters: 1-Aspect of the User Case/ system simulated with the model 2-Model 3-Computation 4-Post-Processing. In some cases between two simulations the post/preprocessing takes place. This processes the output (or part of the output) of one simulation into input for next simulation.

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~~1. MODEL 1 for Design of injection mold for mirror substrate for CSP.~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF The model 1 is dedicated to find the optimal injection mold THE USER process in order to avoid deformation on customizable CSP 1.1 CASE TO BE mirror substrate. SIMULATED~~

~~1.2 MATERIAL Polycarbonate based material.~~

~~Planar geometry, from 10cm x 10cm to 0.7m x 1m, multilayer material system. 1.3 GEOMETRY Customizable to other geometries. Design of mirror’s substrate by CATIA from task 3.1.~~

~~1.4 TIME LAPSE Static setting.~~

~~MANUFACTURI Manufacturing process: temperature and pressure of injection process NG PROCESS 1.5 OR IN- SERVICE CONDITIONS~~

~~1.6 PUBLICATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum Solid mechanics. (model 4.1 in ROMM) 2.0 AND NAME~~

~~MODEL The entity in this materials model is finite volumes corresponding to 2.1 ENTITY polymeric substrate injected with different process parameters.~~

Equations Hooke law relating forces and displacement MODEL PHYSICS/ Physical 2.2 CHEMISTRY quantities Lagrangian deformation and strain tensor. Shear EQUATION for each strain equation PE’S Position of material point, deformation due to external forces

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~~Equations~~

~~MATERIALS RELATIONS~~

Physical Variables: shear () and strain () due to external quantities/ loads during injection process. descriptors for Parameters: (1) external forces applied during the each MR injection process (ex. P in previous scheme) (2) dimension of polymeric sample (ex. a, h in previous scheme) (3) material density, etc.

~~SIMULATED 2.4 INPUT~~

~~2.5 PUBLICATION Publication documenting the model.~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL FEM ( Finite Element Method) and CFD (Computacional Fluid Dynamic) 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL Autodesk Moldflow~~

~~3.3 TIME STEP If applicable~~

PHYSICS At this stage, a first approximation of the original geometry is EQUATION, done by a set of points (nodes) connected via elements. MATERIAL Modelling of the deformation of geometry, meshing, and RELATIONS, element definition (shells or solids, linear or quadratic function, COMPUTATIONAL MATERIAL fully or reduced integration, etc.). REPRESENTATION Refers to how your computational 3.4 solver represents the material, properties, equation variables,

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~~BOUNDARY Visual representation into the geometry. Ex. pressure CONDITION injection profile. S~~

~~ADDITIONAL They will be defined during the project, when facing the SOLVER simulation analysis of the mirror’ substrate mold. PARAMETER S~~

~~3.5 PUBLICATION Publication documenting the simulation or web link~~

~~4 POST PROCESSING~~

THE PROCESSED The optimal parameters, such as OUTPUT IS temperature at flow front, CALCULATED FOR pressure at injection location, flow rate, for injection process and mold geometry in order to avoid deformation in bulk and in surface of mirror’s substrate. The outputs of the modelling 4.1 give the following values regarding injection process. Optimal design and process will define the final geometry of injection mold for manufacture the samples. In particular, planar samples will be empirically validated. This will be used in model 2.

METHODOLOGIES Uneven compaction piece volumetric contractions leading to very large deformation are determined by visual representation of internal deformation of the pieces The deformation 4.2 can be visualized in bulk and in surface. Then, if deformations exist in simulated piece, change in parameter of injection process (such as type of injection process, injection points, etc,) will be done in order to avoid them.

~~MARGIN OF 4.3 To be defined. ERROR~~

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~~MODEL 2 for simulated new solar collector with non planar mirrors for CSP.~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

ASPECT OF Define the optimal non planar mirror geometry in order to find a THE USER solution in which there is a four times increase of the power generation 1.1 CASE TO BE considering performance of materials in service SIMULATED

~~Mirror’s materials~~

~~1.2 MATERIAL Heat Transfer Fluids properties. Heater composed material~~

~~Non planar geometry for mirror 1.3 GEOMETRY Heater container geometry~~

~~1.4 TIME LAPSE Static state~~

~~MANUFACTURI In service conditions: incident solar radiation NG PROCESS Different incident angle and incident power radiation will be used. 1.5 OR IN- SERVICE CONDITIONS~~

~~1.6 PUBLICATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Tightly couples system of AND NAME Continuum model. Heat flow and thermo-mechanics. (model 4.3 in 2.0 ROMM) Continuum model. Electromagnetism (optics) (model 4.6 in ROMM)~~

~~MODEL The entity in this materials model is finite volumes. 2.1 ENTITY~~

~~Equations Head transfer balance equation of:~~

~~Advection: Q = vρcpΔT~~

~~Conduction: Q = vρcp~~

~~Convection: Q̇ = hA(Ta − Tb)~~

~~4 4 MODEL Radiation: Q = ϵσ(Ta − Tb ) PHYSICS/~~

~~2.2 CHEMISTRY Incompressible Navier-Stokes equations EQUATION ∂퐮 PE’S + (퐮 · ∇)퐮 − ν∇2퐮 = −∇w + 퐠 ∂t~~

~~Snell’s equations sin θ v λ n 1 = 1 = 1 = 2 sin θ2 v2 λ2 n1~~

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Physical For CFD models: quantities Ri is the equation residual at an element vertex i, for each W is the weight factor, equation i Q is the heat flux conservation equation expressed on an element basis and Ve is the volume of the element. h is the heat transfer coefficient, A is the area of the object, σ is the Stefan-Boltzmann constant

~~For Ray-tracing models:~~

~~Lo is the outgoing light,~~

~~Le is the emitted light and ω is the reflected light.~~

~~θi angle measured from the normal of the boundary,~~

~~vi velocity of light in the respective medium,~~

~~λi wavelength of light in the respective medium MR Equations Thermal expansion 1 ∂V αV = ( ) V ∂T p~~

~~Physical Where quantities/ V is the volume, MATERIALS descriptors for T is the temperature, RELATIONS each MR subscript p indicates that the pressure is held constant, ρ is density~~

~~cp heat capacity at constant pressure ϵ is the emissivity~~

~~ni refractive index of the respective medium .~~

~~SIMULATED Optimized mirror materials and the final quality of the surface’s piece, 2.4 INPUT from model 1, in order to be use as interface between mirror and air in Ray Trace model.~~

~~2.5 PUBLICATION~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL MonteCarlo, Ray Trace Model, C Finite Element Method. Each model 3.1 SOLVER is independent and it is used as an input for the next model.~~

~~Altair HyperWorks, Altair Partner Alliance softwares, TracePro and 3.2 SOFTWARE TOOL Matlab~~

~~3.3 TIME STEP . It will be determined during the creation of the model, depend on~~

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~~itsconvergency.~~

~~PHYSICS Finite element-based Computational Fluid Dynamics EQUATION, (CFD) MATERIAL R = ∭ W Q dVe RELATIONS, i i MATERIAL Where~~

~~Ri is the equation residual at an element vertex i,~~

COMPUTATIONAL Wi is the weight factor, REPRESENTATION Q is the heat flux conservation equation expressed Refers to how on an element basis and your Ve is the volume of the element. computational 3.4 solver BOUNDARY Solar irradiation profile CONDITIONS represents the as function of θi , λi and ni refractive index of the material, respective medium (interface air/mirror) properties, Heater container profile equation variables,

~~ADDITIONAL They will be defined during the project, when facing SOLVER the simulation analysis of the heater and the heat PARAMETERS transfer fluid.~~

~~3.5 PUBLICATION~~

~~4 POST PROCESSING~~

THE PROCESSED The out of process: Qcap : heat captured on the heater due to solar OUTPUT IS radiation and QHTF: heat transferred by the Heat Transfer Fluid is CALCULATED FOR used to calculate the solar-thermal conversion (ST). We define ST 4.1 as the ratio between both outputs: Q ST = HTF Qcap

METHODOLOGIES Solar radiation profile is used as incident spectra radiation. Using (at first step) a parabolic mirror shape, Snell equation is used in order to know the amount of radiation arrives to the heater. Then this radiation is converted into heat trough the heater’s container. The

heat capture by the heater (Qcap) will depend on material of the heater and its geometry (both fixed). The heat then is transfer to the 4.2 heat transfer fluid (QHTF) into the heater and piping system.

Knowing Qcap and QHTF, ST is calculated. It is expected to have higher ST conversion respect to PTC solar field using a fixed land size. Then the optimization of the geometry of non planar mirror will be evaluated in order to achieve high values of ST.

~~MARGIN OF 4.3 To be defined. ERROR~~

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~~2. MODEL 3 for optimization of composite for mirror structure. 3.~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE USER Definition of new composite for mirror support 1.1 CASE TO BE SIMULATED~~

~~1.2 MATERIAL Glass Fibre Reinforced Polymer (GFRP)~~

~~Planar geometry of mirrors but support geometry will be 1.3 GEOMETRY defined. Standards profile will be used as starting point.~~

~~1.4 TIME LAPSE Quasi-static~~

~~MANUFACTURING . 1.5 PROCESS OR IN- In service conditions: bending forces. SERVICE CONDITIONS~~

~~1.6 PUBLICATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

MODEL TYPE Tightly coupled system of AND NAME Continuum model for industrial application. Solid mechanics. (model 4.1 2.0 in ROMM) Continuum model. Heat flow and thermo-mechanics. (model 4.3 in ROMM)

~~MODEL The entity in this materials model is finite volumes of GFRP with different 2.1 ENTITY ratio of glass fibre.~~

Equations Hooke Law MODEL {푓} = [퐾] ∙ {푢} PHYSICS/ Physical Where 2.2 CHEMISTRY quantities for EQUATION {푓} is the force vector, each equation PE’S [퐾] is the stiffness matrix and {푢} is the displacement vector.

~~MR Equations Stiffness matrix for a transversely isotropic material~~

~~퐾11 퐾12 퐾12 0 0 0 퐾 퐾 퐾 0 0 0 21 22 23 퐾31 퐾32 퐾33 0 0 0 MATERIALS [퐾] = 0 0 0 퐾44 0 0 RELATIONS 0 0 0 0 퐾55 0 [ 0 0 0 0 0 퐾66]~~

Physical Where 퐾푖푗 are different physic properties depending quantities/ on the analysed case and the position into the descriptors for matrix (e.g. they are computed from Young’s each MR modulus, shear modulus, Poisson’s ratio and

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~~thermal conductivity among others).~~

~~SIMULATED 2.4 INPUT~~

~~2.5 PUBLICATION~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Finite Element Method 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL Altair HyperWorks and Altair Partner Alliance softwares.~~

~~3.3 TIME STEP If applicable~~

PHYSICS Hooke law, defining the external loads taking into EQUATION, account thermo-mechanical properties of the MATERIAL composite such as Young modulus, inertia moment, RELATIONS, etc. The modelling of the geometry will be done MATERIAL through meshing, and element definition (shells or

COMPUTATIONAL solids, linear or quadratic function, fully or reduced REPRESENTATION integration, etc.). Refers to how your computational 3.4 solver represents the material, properties, equation BOUNDARY Visual representation into the geometry through variables, CONDITIONS HyperMesh and HyperView.

~~ADDITIONAL They will be defined during the project, when facing SOLVER the simulation analysis of the GFRP composite PARAMETERS structure.~~

~~3.5 PUBLICATION Publication documenting the simulation or web link~~

~~4 POST PROCESSING~~

THE PROCESSED The Optimal composition of GFRP for light and robust supports will OUTPUT IS be calculated. The density and then the ratio of component are CALCULATED FOR selected in terms of robustness of defined pieces under external loads. The density will be selected following the in service 4.1 requirements (tension, impacts, etc) depend on solar field specification of the CSP pilot plant. Among this, This output will be used for design of planar mirror support as input of next model 4

~~4.2 METHODOLOGIES Standard tests of GFRP samples will be performed in order to~~

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obtain empiric results. The same tests will be modelled using FEM. Correlation of model vs. empiric will be carried out in order to adjust simulation model. GFRP structure designs will be computed via FEM. Optimisation and validation of the GFRP structure. Variables calculated: - Stress field of the GFRP structure below yield strength - Strain field of the GFRP structure to accomplish service conditions - Displacements of the GFRP structure below maximum deflections permitted - Weight of GFRP structure optimised for minimum weight without compromising integrity of the structure.

~~MARGIN OF ERROR Preliminary results will be correlated with standard tests to validate 4.3 the model and ensure the minimum error (expected error will be below 5-10%).~~

~~1. MODEL 4 Solid mechanics for 3D design for mirror structure.~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF Calculation ion of robustness in front of external loads and minimizing THE USER its weight of support geometry considering performance of materials in 1.1 CASE TO BE service. SIMULATED~~

~~1.2 MATERIAL Mirror’s support: material comes from model 3.~~

~~1.3 GEOMETRY To be defined but restricted to planar mirror.~~

~~1.4 TIME LAPSE Quasi-static~~

~~MANUFACTURI In service conditions: external loads and own weight. NG PROCESS 1.5 OR IN- SERVICE CONDITIONS~~

~~1.6 PUBLICATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model for industrial application. Solid mechanics. (model 2.0 AND NAME 4.1 in ROMM)~~

~~MODEL ENTITY The entity in this materials model is finite volumes of optimal GRFP 2.1 composite from model 4.~~

~~휕휔 푀 MODEL Equations 휏 = [ − (푧 − 푧 )] · 푥 푥푦 휕푦 퐶 퐽 HYSICS P / 휕휔 푀푥 2.2 휏푥푧 = [ − (푦 − 푦퐶)] · CHEMISTRY 휕푧 퐽 EQUATION~~

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~~PE’S~~

~~Physical Where, quantities 휏: strain for each yc, zc: coordinates of the cutting center section equation 휔: warpage of the structure. Mx: torque. J: torsor module.~~

~~Equations For rectangular section: ∞ 1 192푏 푘ℎ휋 퐽 = 푏3ℎ [1 − ∑ tanh ( )] 3 ℎ휋5 2푏 푘=1,3,…~~

~~For any other section (circular, elliptical):~~

~~MATERIALS 2 2 휕휔 RELATIONS 퐽 = ∫ [(푦 − 푦푐) + (푧 − 푧푐) − (푦 − 푦푐) + (푧 − 푧푐) + (푧 퐴 휕푧 휕휔 − 푧 ) ] 푑푦푑푧 푐 휕푦~~

~~Physical Where, quantities/ b, h: section of the structure where b is higher descriptors for than h. each MR~~

~~SIMULATED Optimal GFRP composite properties from previous model 3 2.4 INPUT~~

~~2.5 PUBLICATION~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Finite element method 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL ABAQUS from SIMULIA Platform~~

During a static step a time period to the analysis can be assigned. This is necessary for cross-references to the amplitude options, which can be used to determine the variation of loads and other externally prescribed parameters during a step. In some cases this 3.3 TIME STEP time scale is quite real. If a time period is not specified, Abaqus defaults to a time period in which “time” varies from 0.0 to 1.0 over the step. The “time” increments are then simply fractions of the total period of the step.

COMPUTATIONAL PHYSICS Static analysis is used for stable problems and REPRESENTATION EQUATION, can include linear or nonlinear response. The 3.4 Refers to how MATERIAL total stress is defined from the total elastic 푒푙 푒푙 your RELATIONS, strain as 휎 = 퐷 휀 , where 휎 is the total stress, 푒푙 푒푙 computational MATERIAL 퐷 is the foruth-order elasticity tensor, and 휀 is

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solver the total elastic strain. represents the material, For this model different elements can be properties, selected according to the problem requirements equation in order to minimize the calculation error: variables,

~~Material relations (for anisotropic characteristics). The stress-strain relations are as follows:~~

~~Where the material stiffness parameters (퐷푖푗푘푙) are giver directly, Abaqus imposes the constraint~~

~~휎33 = 0 for the plane stress case to reduce the material’s stiffness matrix as required.- Each~~

퐷푖푗푘푙 is function of Young’s modulus and Poisson’s ratio for each direction. In Abaqus spatially varying anisotropic elastic behaviour can be defined for homogeneous solid continuum elements by using a distribution. The distribution must include default values for the elastic moduli. If a distribution is used, no dependences on temperature and/or field variables for the elastic constants can be defined.

~~Computational representation of the physics equation, materials relation and material ( e.g. “written up for the entity in the model” or in the~~

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~~case of statistical approached “written up for finite volumes”)~~

BOUNDARY The previous system of equations is furthermore CONDITIONS subject to essential boundary conditions, e.g. prescribed displacements or velocities along a surface, mechanical conditions, etc. In this software boundary conditions are represented into the simulated geometry.

훼 ADDITIONAL 1. Residual control (푅푛 ) is the convergence SOLVER criterion for the ratio of the largest residual PARAMETERS to the corresponding average flux norm. 훼 The default value is 푅푛 = 5x10-3, which is rather strict by engineering standards but in all but exceptional cases will guarantee an accurate solution to complex nonlinear problems. The value for this ratio can be increased to a larger number if some accuracy can be sacrificed for computational speed. 2. The torque each 0.01 meters structure is evaluated.

~~3.5 PUBLICATION Not publication~~

~~4 POST PROCESSING~~

THE PROCESSED The optimal design for mirror support will be defined in this activity OUTPUT IS with high robustness in front of external loads and minimizing its 4.1 CALCULATED weight. Also, its design will be used for define planar mirror in model FOR 1, for empirical validation in pilot CSP plant.

~~METHODOLOGIE The postprocessing calculator performs the following calculations on S data written to the output database:~~

. Extrapolation of integration point quantities to the nodes or interpolation of integration point quantities to the centroid of an element, according to the user-specified position for element output.

4.2 . Calculation of history output at tracer particles By default, the postprocessing calculator will run automatically upon the completion of an analysis. During the execution of the analysis, Abaqus will determine if there are keywords in the input file that require the use of the calculator and will initiate the calculator upon completion if it is required. Additionally, the postprocessing calculator can be run manually.

MARGIN OF The ability of a finite element analysis to make useful predictions of ERROR physical behavior depends on many factors, including: - representation of geometry, material behavior, load history, and various other modeling aspects associated with describing the 4.3 problem posed; - spatial and temporal discretization (mesh refinement and incrementation); and - convergence tolerances.

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The finite element discretization of a model domain results in an approximation to the exact solution for all but trivial analyses. For aiding in understanding the extent and spatial distribution of the discretization error in a finite element solution, Abaqus provides a set of error indicator output variables. Ideally, error indicator output variables should be supplemented by other techniques, such as a mesh refinement study, to gain confidence that discretization error is not significantly degrading the ability of the finite element analysis to make useful predictions. In fact, error indicators can help automate a mesh refinement study through the adaptive remeshing functionality of Abaqus/CAE. Abaqus error indicator variables provide a measure of the local error resulting from mesh discretization. Each error indicator, provides an indication of error in a particular base solution variable. Following table shows the available error indicator variables and the corresponding base solution variables. The algorithms used by Abaqus/CAE to modify mesh seed sizes for the adaptive remeshing capability consider error indicator values and corresponding base solution values together. When a remeshing rule is created and requested a particular error indicator, Abaqus automatically writes the error indicator and corresponding base solution variable to the output database. The error indicators are approximate measures of the local error in the base solution and are, themselves, subject to discretization error. The accuracy of the error estimates tends to improve as the mesh is refined. Each error indicator variable has the same units has the corresponding base solution variable, which facilitates comparison of local estimates of the error magnitude with local estimates of the base solution.

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~~MODA 2 Thermal storage systems in different type of power block in CSP plant. In Power~~

~~THE SIMULATION GENERAL DESCRIPTION~~

Design and simulation of thermal storage materials for innovative Thermal storage (TES) systems in different type of power block in CSP 1 USER CASE plant. The materials eutectic mixtures and Phase Change Material are selected.

Continuum model. Continuum thermodynamic and phase field model (model 4.4 from ROMM). The model 1 is dedicated to MODEL 1 find the optimal TES eutectic mixture material in order to have high thermal capacity, three times respect state of the art.

Continuum model. Fluid mechanics, heat flow and thermomechanics (4.2 and 4.3 models from ROMM). The CHAIN OF MODEL 2 model 2 is related to simulate performance of new thermocline 2 MODELS #2 TES system geometry, for high temperature storage systems with oil or salts as HTF.

Continuum model. Fluid mechanics, heat flow and thermomechanics (4.2 and 4.3 models from ROMM). The MODEL 3 model 3 is related to simulate performance of new multitank TES system, for Direct Steam Generation power plants.

~~3 PUBLICATION Not available~~

Scilab: free software from Scilab Enterprises Dymola: commercial modeling and simulation environment based on the ACCESS 4 open Modelica modeling language from Dassault Systèmes AB. CONDITIONS FactSage Version 6.4. FACT Pure Substances Database, FACT Solutions Database. Licensed.

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

Evaluation of eutectic point from simulated phase diagram and the ASPECT OF THE liquidus surface of quaternary X-Y-NO3 (X = K, Na, Li and Y=Sr) 1.1 USER CASE TO BE system. Definition of new eutectic mixture with high thermal SIMULATED capacity, looking for three times thermal capacity respect to state of the art.

~~1.2 MATERIAL Eutectic X-Y-NO3 (X = K, Na, Li and Y=Sr) mixtures~~

~~1.3 GEOMETRY atoms~~

~~1.4 TIME LAPSE static~~

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~~MANUFACTURING Melting behaviour of selected compositions used in different TES PROCESS OR IN- systems. 1.5 SERVICE CONDITIONS~~

~~H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics – The Calphad method. Cambridge University PUBLICATION Press (2007).~~

1.6 ON THIS ONE Christian Robelin, Patrice Chartrand, Arthur D. Pelton, SIMULATION “Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system”, Chem.Thermodynamics 83 (2015) 12–26.

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model. Continuum thermodynamic and phase field model 2.0 AND NAME (model 4.4 from ROMM)~~

~~2.1 MODEL ENTITY Thermodynamic description of condensed phases Equation Gibbs equation 0 0 config G = (nAg A + nBg B ) - TΔS + (nAB /2) MODEL ΔgAB PHYSICS/~~

2.2 CHEMISTRY EQUATION Physical A and B system components, G is Gibbs free energy, PE quantities g0A and g0B are molar Gibbs energies of the pure components, ΔSconfig is the configurational entropy of mixing.

~~Relation 푖푗 푖 푗 ∆푔퐴퐵 = ∑ 푔퐴퐵푌퐴 푌퐵 , 푖 ≥ 0, 푗 ≥ 0, 푖+푗≥0~~

~~푘 = ∑ 푔푘 푌푏 MATERIALS 푘≥0 2.3 RELATIONS Physical gk and Ykb are free parameters to be quantities/ determined from experimental data. descriptors for each MR~~

~~SIMULATED Not applicable 2.4 INPUT~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Included in FactSage Software. 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL FactSage Version 6.4. FACT Pure Substances Database, FACT~~

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~~Solutions Database.~~

~~3.3 TIME STEP Not aplicable~~

PHYSICS Gibbs free energy of the phases of the system EQUATION, (example of visual representation of phase MATERIAL RELATIONS, MATERIAL COMPUTATIONAL REPRESENTATION Refers to how your computational 3.4 solver represents the material, diagram). properties, equation Written up for the entity in the model.

~~variables, BOUNDARY Not applicable. CONDITIONS~~

~~ADDITIONAL To be defined. SOLVER PARAMETERS~~

~~3.5 PUBLICATION http://www.IPSEpro.com~~

~~4 POST PROCESSING~~

THE PROCESSED The Phase equilibrium diagram will let to decide the best liquid TES 4.1 OUTPUT IS materials to be applied in the TES systems. The TES material with CALCULATED FOR highest thermal capacity will be used for model 2 and 3.

METHODOLOGIES Simulation/calculation of phase diagram and liquidus surface from calculated Gibbs free energy functions of the phases will let to establish the invariant points of system (eutectic, peritectic…) as well as heat capacity of the liquid phase. Formulation of new compositions and optimal working conditions are done in terms of the simulated phase diagrams and liquidus surfaces. For this, phase diagram, thermodynamic properties of the liquid 4.2 phase and finally invariant (eutectic, peritectic…) points of binary to multicomponent system are established. The invariant points will be evaluated from minimization of the Gibbs free energy of condensed phases in multicomponent systems. Molten salt phase: Modified quasichemical model. Solid solution phases: Compound Energy Formalism. Multicomponent properties: Generalized Kohler-Toop technique.

~~4.3 MARGIN OF ERROR Temperature 5%. Composition 10%~~

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~~1. Model 2: Thermocline TES system for high temperature storage. [WP5: Task 5.3].~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

ASPECT OF THE The model will be used to design and size high temperature USER CASE TO thermocline storage for commercial scale CSP plants with oil or molten 1.1 BE SIMULATED salts as heat transfer fluid (HTF).

~~HTF: a eutectic molten salt mixture coming from model 1; and 1.2 MATERIAL encapsulated PCM (aluminium alloys).~~

~~Geometry will take into account a unique tank in connexion with (boundary conditions) the solar field and the power block.~~

~~1.3 GEOMETRY~~

~~1.4 TIME LAPSE One charge-discharge cycle (approximately 24 hours)~~

MANUFACTURIN In service conditions: Several operating strategies will be simulated G PROCESS OR (selection of the optimum operating temperature range, best 1.5 IN-SERVICE combination of HTF and filler material to meet a specific storage CONDITIONS requirement, etc.)

~~PUBLICATION The corresponding model will be developed during the project, thus~~

~~1.6 ON THIS ONE there are no publications yet documenting this ONE simulation. SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model. Fluid mechanics, heat flow and thermomechanics 2.0 AND NAME (4.2 and 4.3 models from ROMM).~~

~~MODEL ENTITY Continuum model of dual-media thermocline systems with the 2.1 additional use of top and/or bottom PCM layers, with heat flow~~

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~~calculations.~~

Equation Mass and energy conservation in storage fluid, PCM and filler material. Conservation of mass 휕휌 = 훻. (휌 푢⃗ ) 휕푡 Conservation of momentum, 휕(휌푢⃗ ) ∫ ( + 훻 ∙ (휌푢⃗ 푢⃗ )) 푑푣 = ∮ 푛⃗ ∙ 휎 푑푠 + ∫ 휌푓 푑푣 푉 휕푡 푆 푉

~~Conservation of energy~~

~~MODEL PHYSICS/ CHEMISTRY 2.2 EQUATION Heat flow is derived from the energy conservation PE law. Heat due to conduction or convection will be modelled.~~

~~Physical u: velocity vector quantities : stress matrix F:external forces (like gravity) : energy density P: pressure~~

~~Fk: conductive flux Also: Temperatures / enthalpies and mass flows of storage fluid.Temperatures / enthalpies and masses of PCM and filler material.~~

Relation Closure relations or materials relations will take into account, giving thermal and physical properties of the materials, such as densisty (), viscosity, thermal conductivity, density, specific heat,etc. All these relations, as functions of the temperature (for solid and monophasic fluids) or of pressure and enthalpy (for PCM and diphasic fluids).Materials are considered MATERIALS isotropic and at macroscopic scale. Constitutive 2.3 RELATIONS equations are the Fourier's law for conductive heat flow, and Newton's law of cooling for convective heat flow.

~~Physical Thermal and physical properties of the materials. quantities/ descriptors for each MR~~

~~SIMULATED Mass and energy flows of the HTF, from model 1, at the inlet of the 2.4 INPUT storage system.~~

~~202~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL To be defined 3.1 SOLVER~~

~~Two simulation software tools are considered at this point: either 3.2 SOFTWARE TOOL Scilab or Dymola~~

~~3.3 TIME STEP From 1 s to 5 min.~~

~~PHYSICS Written up for elementary volumes with 1D EQUATION, discretization. MATERIAL RELATIONS, MATERIAL~~

~~COMPUTATIONAL REPRESENTATION Refers to how your computational 3.4 solver represents the material, properties,~~

~~equation variables, BOUNDARY To be defined CONDITION S~~

~~ADDITIONAL To be defined. SOLVER PARAMETER S~~

~~3.5 PUBLICATION~~

~~4 POST PROCESSING~~

THE PROCESSED The evaluation of thermal capacity of the system and cost- OUTPUT IS performance model to determine the unit cost of storage capacity 4.1 CALCULATED FOR (€/KWh) for a given operating temperature range and storage materials combination will be done..

METHODOLOGIES Thermocline storages are using a combination of HTF and filler material to meet a specific storage requirement. Optimal HTF, coming from model 1, is a eutectic molten salt mixture with optimized low melting point, stable, affordable and non-toxic salt 4.2 formulation. To increase the utilization rate of the storage system, the use of encapsulated PCM (aluminium alloys) layer at the top of the tank is considered. Thermal capacity will be evaluated, under the boundary conditions (solar field and power block inputs). Mass, energy and momentum

~~203~~

balances, in differential form and at any direction where gradients are expected (along and across the flow) will be considered using ordinary differential equations (ODEs) or partial differential equations (PDEs), under the hypotheses of Newtonian fluids and incompressible flow. Two phases (solid and liquid) will be considered for PCM. Changes in mechanical properties will be considered as a function of the temperature. Then, energy balances will be assessed through integration of heat flows. Cost performance: Mass of storage fluid, filler materials, and containers will be deduced from the TES optimized design in order to calculate the global cost of the system (in €); This cost will be compared to the simulated storage capacity (in kWh) to determine the unit cost in €/kWh. Material costs will be found in the literature. All the methodology will follow definition of storage key features following standards from SolarPaces and IEC.

~~4.3 MARGIN OF ERROR To be determined~~

~~2. Model 3: Two tanks TES system for Direct Steam Generation CSP plants. (WP5: Task 5.4)~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE The model will be used to design and size high temperature multi- USER CASE TO BE stage storage for commercial scale DSG CSP plants. 1.1 SIMULATED~~

~~Eutectic mixture from model 1, as high temperature sensible 1.2 MATERIAL storage; and sodium nitrate PCM for latent heat storage.~~

~~Geometry will take into account two tanks (cold and hot) in connexion with (boundary conditions) the solar field and the power block.~~

~~1.3 GEOMETRY~~

~~204~~

~~1.4 TIME LAPSE One charge-discharge cycle (approximately 24 hours)~~

MANUFACTURING In service conditions. Several operating strategies will be simulated PROCESS OR IN- (selection of the optimum operating temperature and pressure 1.5 SERVICE range, water level control, etc.) CONDITIONS

~~PUBLICATION The corresponding model will be developed during the project, thus~~

~~1.6 ON THIS ONE there are no publications yet documenting this ONE simulation. SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model. Fluid mechanics, heat flow and thermomechanics (4.2 2.0 AND NAME and 4.3 models from ROMM)~~

~~MODEL ENTITY Continuum thermodynamics and phase field model, with heat flow 2.1 calculations.~~

Equation Mass and energy conservation in HTF (water-steam) and storage media (eutectic molten salts and PCM). Conservation of mass 휕휌 = 훻. (휌 푢⃗ ) 휕푡 Conservation of momentum, 휕(휌푢⃗ ) ∫ ( + 훻 ∙ (휌푢⃗ 푢⃗ )) 푑푣 = ∮ 푛⃗ ∙ 휎 푑푠 + ∫ 휌푓 푑푣 푉 휕푡 푆 푉

~~Conservation of energy~~

~~MODEL PHYSICS/~~

2.2 CHEMISTRY EQUATION Heat flow is derived from the energy conservation law. Heat due to conduction or convection will be modelled. PE Physical ; density quantities u: velocity vector : stress matrix F:external forces (like gravity) : energy density P: pressure

~~Fk: conductive flux Also: (1) enthalpies, pressures and mass flows of HTF (water-steam). (2) Temperatures / enthalpies and masses of storage media (eutectic molten salts and PCM).~~

~~2.3 MATERIALS Relation Closure relations or materials relations are the formulas~~

~~205~~

RELATIONS giving thermal and physical properties of the materials (viscosity, thermal conductivity, density, specific heat,…) as functions of the temperature (for solid and monophasic fluids) or of pressure and enthalpy (for water / steam). Materials are considered isotropic and at macroscopic scale. Constitutive equations are the Fourier's law for conductive heat flow, and Newton's law of cooling for convective heat flow.

~~Physical Thermal and physical properties of the materials. quantities/ descriptors for each MR~~

~~SIMULATED Mass and energy flows of the HTF at the inlet of the storage system. 2.4 INPUT~~

~~3 Solver and Computational translation of the specifications~~

~~NUMERICAL To be defined. 3.1 SOLVER~~

~~Two simulation software tools are considered at this point: either Scilab 3.2 SOFTWARE TOOL or Dymola~~

~~3.3 TIME STEP From 1 s to 5 min.~~

~~PHYSICS Written up for elementary volumes with 1D EQUATION, discretization. MATERIAL RELATIONS, MATERIAL~~

~~COMPUTATIONAL 3.4 REPRESENTATION ,~~

~~3.5 COMPUTATIONAL To be defined.~~

~~206~~

~~BOUNDARY CONDITIONS~~

~~ADDITIONAL SOLVER To be defined. 3.6 PARAMETERS~~

~~4 POST PROCESSING~~

THE PROCESSED The modelling let predict the optimal, in terms of thermal storage OUTPUT capacity and costs, of multitank system design. The evaluation of Thermal capacity of the system and cost-performance model to determine the unit cost of storage capacity (€/KWh) for a given operating temperature range and storage materials combination will be done. 4.1 Thermodynamic variables of the storage material and heat transfer fuid (HTF) as temperature, pressure, mass flow, specific enthalpy. Mass of storage fluid, filler materials, and containers will be deduced from the TES optimized design in order to calculate the global cost of the system (in €); This cost will be compared to the simulated storage capacity (in kWh) to determine the unit cost in €/kWh.

METHODOLOGIES Parametric studies will be performed to optimize geometry (for example the tank shape will be adjusted to minimize the thermal gradient across the height of the tank, and the insulation thickness will also be determined to minimize the heat loss to the surroundings) and the operating strategies through performance predictions and experimental validation.

Thermal storage capacity: Mass, energy and momentum balances, in differential form and at any direction where gradients are expected (along and across the flow) will be considered using ordinary differential equations (ODEs) or partial differential equations (PDEs), under the hypotheses of Newtonian fluids. Two phases (solid and liquid) will be considered for PCM. Changes in 4.2 mechanical properties will be considered as a function of the temperature. A two-phase flow (liquid and vapour) is also considered for the HTF (water / steam). Energy balances, storage levels, and storage efficiencies will be evaluated.

Cost performance: Energy balances will be assessed through integration of heat flows. Mass of storage fluid, filler materials, and containers will be deduced from the TES optimized design in order to calculate the global cost of the system (in €); This cost will be compared to the simulated storage capacity (in kWh) to determine the unit cost in €/kWh. Material costs will be found in the literature. All the modelling will follow definition of storage key features following standards from SolarPaces and IEC.

~~4.3 MARGIN OF ERROR To be defined.~~

~~207~~

~~INSPIRED (646155)~~

~~Summary of the project~~

The project will develop and demonstrate cost-effective, high throughput synthesis and functionalization of nanomaterials for printed electronic systems using high volume printing techniques. Targeted demonstrators are CIGs photovoltaic cells, capacitive touch screens and LC displays.

~~Reactor design for functionalised nanomaterials~~

Project Acronym and Number: INSPIRED 646155 Project Title: INdustrial Scale Production of Innovative nanomateRials for printEd Devices Start and End Dates: from 1/1/2015 till 31/12/2018 EU Contribution: 6,414,871.80 € Coordinator: Dr. Martina Trinkel, [email protected] Modeller(s): Marco Boselli, [email protected] Matteo Gherardi, [email protected]

~~208~~

~~MODA~~

~~Reactor design for functionlaised nanomaterials~~

~~INSPIRED~~

THE SIMULATION GENERAL DESCRIPTION Synthesis of copper nanopowders in Inductively Coupled 1 USER CASE Plasma (ICP) systems Continuum modelling of materials- 4.2 Fluid MODEL 1 CHAIN OF Mechanics and EM 2 MODELS Continuum modelling of materials - 4.2 Fluid MODEL 2 Mechanics V Colombo, E Ghedini, M Gherardi and P Sanibondi, Evaluation of precursor evaporation in Si nano-particle synthesis by radio- 3 PUBLICATION frequency induction thermal plasmas, (2013) Plasma Sources Science and Technology 22 (3), 035010

~~ACCESS Self-developed model based on commercial software 4 CONDITIONS Based on ANSYS (Fluent)~~

~~Model 1~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE Evaporation of copper microsized solid precursors in a RF ICP 1.1 USER CASE TO BE torch SIMULATED~~

~~Copper, Argon Plasma thermodynamic and transport properties have been 1.2 MATERIAL obtained by atomistic statistical mechanics Boltzmann kinetic gas equation.~~

~~209~~

~~1.3 GEOMETRY~~

~~B-G Hong et al., THERMAL PLASMA SYNTHESIS OF NANO-SIZED POWDERS, Nuclear Engineering and Technology (2012), 44(1) 9-20~~

~~None (the system operates in continuous mode, 1.4 TIME LAPSE thus in a steady state condition)~~

MANUFACTURING Precursor and plasma gases mass flow rates. PROCESS OR IN- 1.5 Coupled power to the plasma torch. SERVICE Quenching gases flow rates CONDITIONS Colombo V, Ghedini E and Sanibondi P “Three- dimensional investigation of particle treatment in a 1.6 PUBLICATION RF thermal plasma with reaction chamber” 2010 Plasma Sci. Technol 19 065024

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Fluid mechanics 2.0 AND NAME Computational Fluid-Dynamics (CFD) for plasma physics and precursor evaporation~~

~~2.1 MODEL ENTITY Finite volumes~~

~~Equations PE 1. Mass conservation MODEL 2.2 PHYSICS/ 훻 ∙ 휌풖 = 0 CHEMISTRY PE 2. Momentum conservation~~

~~210~~

~~EQUATION 훻 ∙ (휌풖풖) = −훻푝 + 훻 ∙ 흉 + 휌품 + 푭푳 PE’S PE 3. Energy conservation~~

푘푒푓푓 훻 ∙ (휌풖ℎ) = 훻 ∙ ( 훻ℎ) + 푃퐽 − 푄푟 푐푝 PE 4. Electromagnetic vector potential equation 2 훻 푨 − 푖 휇0휎2휋푓푨 + 휇0 푱풄풐풊풍 = 0 PE 5. k-ε model equations

~~휇푇 훻 ∙ (휌풖푘) = 훻 ∙ ((휇 + ) 훻푘) + 퐺푘 − 휌 휀 휎푘~~

~~휇푇 휀 훻 ∙ (휌풖휀) = 훻 ∙ ((휇 + ) 훻휀) + 퐶1휀 퐺푘 휎휀 푘 휀2 − 퐶 휌 2휀 푘 PE 6. Precursor trajectories equation~~

휕풖푷 3 휌 퐶퐷 = ( ) (풖 − 풖푷)|풖 − 풖푷| + 품 휕푡 4 푑푃 휌푃 PE 7. Precursor thermal history 푑푇 푞 푃 = 푑푡 푚푃푐푃 PE 8. Precursor liquid fraction equation 푑푥 6 푞 푃 = 푑푡 푑푃 휌푃 휆푚 PE 9. Precursor heat and mass balance equation 푑 푑 2 푞 푃 = − 푑푡 휌푃 휆푣 PE 10. Vapor conservation equation 휇 + 휇 푃 훻 ∙ [푢 푁] = 훻 ∙ [ 푇 훻푁] + 퐶3 휌푃 푣

Physical PE 1: ρ plasma gas density; u gas velocity. quantities PE 2: ρ plasma gas density; u gas velocity; p gas for each pressure; τ viscous stress tensor; g gravitational equation acceleration; FL Lorentz force. PE 3: ρ plasma gas density; u gas velocity; h

~~enthalpy of the fluid; keff effective thermal~~

~~conductivity; cp plasma specific heat; PJ Joule~~

~~dissipation; Qr plasma volumetric radiative loss. PE 4: A vector potential complex phasor; i~~

~~imaginary unit; Jcoil complex phasor for the~~

~~211~~

~~current flowing in the coil; 휇0 magnetic permeability of free space; σ plasma electrical conductivity; f frequency of the electromagnetic field. PE 5: ρ plasma gas density; u gas velocity; k~~

~~turbulence kinetic energy; 휇 laminar viscosity; 휇푇~~

~~turbulent viscosity; ε turbulent dissipation; Gk generation of turbulence kinetic energy due to~~

~~mean velocity gradients; C1ε, C2ε, σε and σk constants (set respectively to 1.44, 1.92, 0.25 and 1.0).~~

~~PE 6: up precursor particle velocity; t time; ρ~~

~~plasma gas density; CD drag coefficient; u gas~~

~~velocity; dP precursor particle diameter; ρP precursor particle density; g gravitational acceleration.~~

~~PE 7: TP temperature of the precursor; t time; q~~

~~heat flux to the precursor; mP mass of the~~

~~particle; cP precursor specific heat.~~

~~PE 8: xP precursor liquid fraction; t time; q heat~~

~~flux to the precursor; dP precursor particle~~

~~diameter; ρP precursor particle density; λm latent heat of particle melting.~~

~~PE 9: dP precursor particle diameter; t time; q~~

~~heat flux to the precursor; ρP precursor particle~~

~~density; λv latent heat of particle vaporization. PE 10: u gas velocity; N vapour concentration; 휇~~

~~laminar viscosity; 휇푇 turbulent viscosity; C3 constant (set to 0.9); v monomer volume, P~~

~~vapour mass evaporation source term; ρP precursor particle density.~~

Equations MR 1. Lorentz force (PE 2) 1 푭 = ℜ( 푱 × 푩∗) 푳 2 MR 2. Joule dissipation (PE 3) 1 푃 = ℜ( 푱 ∙ 푬∗) 퐽 2 MR 3. Electric field (PE 3) MATERIALS 푬 = −푖2휋푓푨 RELATIONS MR 4. Magnetic field (PE 3)

~~푩 = ∇ × 푨 MR 5. Plasma electric current (PE 3) 푱 = 휎푬 MR 6. Turbulent viscosity (PE 5) 푘2 휇 = 휌 퐶 푇 휇 휀 MR 7. Drag coefficient (PE 6)~~

~~212~~

24 푓표푟 푅푒 < 0.2 푅푒 24 ( ) (1 + 0.1875푅푒) 푓표푟 0.2 < 푅푒 < 2 퐶 = 푅푒 퐷 24 ( ) (1 + 0.11푅푒0.81) 푓표푟 2 < 푅푒 < 21 푅푒 24 ( ) (1 + 0.189푅푒0.632) 푓표푟 21 < 푅푒 < 200 { 푅푒 MR 8. Reynolds number (PE 6) |풖| 푅푒 = 휌 푑 푃 휇 MR 9. Precursor heat flux (PE 7,9) 4 4 푞 = 퐴푃 ℎ퐶 (푇 − 푇푃) − 퐴푃 휀푃 휎푆퐵 (푇푃 − 푇a )

~~Physical MR1: FL Lorentz force; J current induced in the quantities/ plasma; B magnetic field.~~

descriptors for MR2: PJ Joule dissipation; J current induced in the each MR plasma; E electric field. MR3: E electric field; i imaginary unit; f frequency of the electromagnetic field; A vector potential complex phasor. MR4: B magnetic field; A vector potential complex phasor. MR5: J current induced in the plasma; σ plasma electrical conductivity; E electric field.

~~MR6: 휇푇 turbulent viscosity; ρ plasma gas~~

~~density; Cμ constant (set to 0.09); k turbulence kinetic energy; ε turbulent dissipation.~~

~~MR7: CD drag coefficient; Re Reynolds number.~~

~~MR8: Re Reynolds number; ρ plasma gas density;~~

~~dP precursor particle diameter; u gas velocity; 휇 laminar viscosity.~~

~~MR9: q heat flux to the precursor; AP particle~~

~~surface; hc local convective coefficient; T plasma~~

~~gas temperature; TP temperature of the~~

~~precursor; εP emissivity of the particle; σSB~~

~~Stefan-Boltzmann coefficient; Ta temperature of the walls of the reaction chamber.~~

~~SIMULATED N/A 2.4 INPUT~~

~~PUBLICATION Colombo V, Ghedini E and Sanibondi P “Three-dimensional 2.5 investigation of particle treatment in a RF thermal plasma with reaction chamber” 2010 Plasma Sci. Technol 19 065024~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~3.1 NUMERICAL Finite volume~~

~~213~~

~~SOLVER~~

~~3.2 SOFTWARE TOOL ANSYS(FLUENT)~~

~~3.3 TIME STEP Implicit solver, stationary~~

~~PHYSICS Standard Fluent equations with additional~~

~~COMPUTATIONAL EQUATION, source terms MATERIAL 3.4 REPRESENTATION User defined scalar equations RELATIONS, User defined memory MATERIAL Written up for finite volumes~~

~~BOUNDARY Mass flow rate of the process gas flow CONDITIONS Inlet gas and reaction chamber walls temperature~~

~~ADDITIONAL SOLVER PARAMETERS~~

~~Colombo V, Ghedini E and Sanibondi P “Three-dimensional 3.5 PUBLICATION investigation of particle treatment in a RF thermal plasma with reaction chamber” 2010 Plasma Sci. Technol 19 065024~~

~~4 POST PROCESSING~~

~~THE PROCESSED No post processing 4.1 OUTPUT IS CALCULATED FOR~~

~~4.2 METHODOLOGIES N/A~~

~~MARGIN OF 4.3 N/A ERROR~~

~~214~~

~~Model 2~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE Synthesis of copper nanopowders in a RF ICP torch and 1.1 USER CASE TO BE nucleation, condensation and agglomeration in a reaction SIMULATED chamber~~

~~1.2 MATERIAL Copper, Argon~~

~~1.3 GEOMETRY~~

~~B-G Hong et al., THERMAL PLASMA SYNTHESIS OF NANO-SIZED POWDERS, Nuclear Engineering and Technology (2012), 44(1) 9-20~~

~~1.4 TIME LAPSE None (steady state)~~

~~MANUFACTURING Precursor and plasma gases mass flow rates. PROCESS OR IN- 1.5 Coupled power to the plasma torch. SERVICE Quenching gases flow rates CONDITIONS~~

Colombo V, Ghedini E, Gherardi M and Sanibondi P, Modelling for the optimization of the reaction chamber in silicon nanoparticle 1.6 PUBLICATION synthesis by radio-frequency induction thermal plasma, (2012) Plasma Sources Science and Technology 21 (5),055007

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE AND Fluid mechanics GDE moment equations for nanopowder 2.0 NAME synthesis, transport and growth~~

~~2.1 MODEL ENTITY Finite volumes~~

~~2.2 MODEL Equations PE 1. Moment equations~~

~~215~~

PHYSICS/ 훻 ∙ [풖 푀 ] = 훻 ∙ [퐷푡표푡 ∇푀 ] + [푀̇ ] 푘 푃 푘 푘 푛푢푐푙푒푎푡푖표푛 CHEMISTRY + [푀̇ ] EQUATION 푘 푐표푛푑푒푛푠푎푡푖표푛 + [푀̇ ] 푘 PE’S 푘 푐표푎푔푢푙푎푡푖표푛 = 0, 1, 2

Physical PE 1: u gas velocity; Mk kth-order quantities 푡표푡 moment; 퐷푃 total diffusion coefficient; for each equation [Ṁk]nucleation nucleation net production rate; [Ṁk]condensation condensation net

~~production rate; [Ṁk]coagulation coagulation net production rate.~~

~~Equations MR 1. Kth-order moment ∞ 푘 푀푘 = ∫ 푣푃 푛(푣푃)푑푣푃 푘 = 0, 1, 2 0 MR 2. Geometric standard deviation~~

2 1 푀0 푀2 ln 휎푔 = ln ( ) 9 푀1 MR 3. Geometric mean volume 2 푀1 푣푔 = 3 1 ⁄2 ⁄2 푀0 푀2 MR 4. Relation between moments 9 푀 = 푀 푣푘 exp ( 푘2 ln 휎 ) 푘 0 푔 2 푔 MATERIALS MR 5. Total diffusion coefficient RELATIONS 푘 푇 −2퐴3 휇 푡표푡 퐵 퐾푛 푇 퐷푃 = {1 + 퐾푛푛 [퐴1 + 퐴2푒 푛 ]} + 3휋휇푑푃 휌푆푐

~~Physical MR1: Mk kth-order moment; vP particle quantities/ volume; k kth-order; n(vP) particle size descriptors for distribution function. each MR MR2: σg geometric standard deviation;~~

~~M0 zeroth order moment; M1 first order~~

~~moment; M2 second order moment.~~

~~MR3: vg geometric mean volume; M0~~

~~zeroth order moment; M1 first order~~

~~moment; M2 second order moment.~~

~~MR4: Mk kth-order moment; M0 zeroth~~

~~order moment; vg geometric mean~~

~~volume; σg geometric standard deviation.~~

~~216~~

~~푡표푡 MR5: 퐷푃 total vapour diffusion~~

~~coefficient; kB Boltzmann constant; T plasma gas temperature; 휇 laminar~~

~~viscosity; dP precursor particle diameter;~~

~~Knn particle Knudsen number; A1, A2 and~~

~~A3 constants (set respectively to 1.257,~~

~~0.4 and 0.55); 휇푇 turbulent viscosity ; ρ~~

~~plasma gas density; Sc Schmidt number.~~

~~SIMULATED Temperature, pressure, velocity and copper vapour 2.4 INPUT distribution from previous model~~

PUBLICATION Mendoza-Gonzalez N Y, Morsli M E and Proulx P, Production of Nanoparticles in Thermal Plasmas: A Model Including Evaporation, Nucleation, Condensation, and Fractal Aggregation (2008) J. Therm. Spray Technol. 17 533-550 2.5 Colombo V, Ghedini E, Gherardi M and Sanibondi P, Modelling for the optimization of the reaction chamber in silicon nanoparticle synthesis by radio-frequency induction thermal plasma, (2012) Plasma Sources Science and Technology 21 (5),055007

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL 3.1 Finite volume SOLVER~~

~~3.2 SOFTWARE TOOL ANSYS(FLUENT)~~

~~3.3 TIME STEP Implicit solver, stationary~~

~~PHYSICS User defined scalar equations COMPUTATIONAL EQUATION, User defined memory 3.4 REPRESENTATION MATERIAL RELATIONS, Written up for finite volumes MATERIAL~~

~~BOUNDARY Zero value for all the three CONDITIONS moments at the inner walls~~

~~ADDITIONAL SOLVER PARAMETERS~~

Colombo V, Ghedini E, Gherardi M and Sanibondi P, Modelling for the optimization of the reaction chamber in silicon 3.5 PUBLICATION nanoparticle synthesis by radio-frequency induction thermal plasma, (2012) Plasma Sources Science and Technology 21 (5),055007

~~217~~

~~4 POST PROCESSING~~

~~THE PROCESSED Yield, particle size distribution and vapour consumption for the 4.1 OUTPUT IS same FV used in model 1. CALCULATED FOR~~

METHODOLOGIES Nanoparticle production yield and deposition on reaction chamber walls, obtained by mass flow rate spatial integration 4.2 Particle size distribution, obtained by moments calculations

MARGIN OF ERROR Experimental validation of the model has been performed in the environment of SIMBA FP7 project. Good agreement has been found with experimental deposition rate on reaction chamber walls. Good agreement on nanoparticle mean particle size obtained with selected operating conditions without recirculating gas flow conditions in the chamber. 4.3 M. Boselli, V. Colombo, N. Daniëls, C. Delval, E. Ghedini, M. Gherardi, C. Jaeggi, M. Leparoux, S. Put, P. Sanibondi "Influence of processing parameters on the properties of silicon nanoparticles synthesized by radio-frequency induction thermal plasma," Plasma Science (ICOPS), 2012 Abstracts IEEE International Conference on, Edinburgh, 2012, pp. 7D-2-7D-2.

~~218~~

~~LOCOMATECH (723517)~~

~~Summary of the project~~

The project is to reduce the cost and environmental impact of the vehicle components/structures manufactured with a solution heat treatment, cold die forming and quenching aluminium manufacturing technology. The low-cost manufacturing technology developed would allow it to be used for mass production (popular) car body and chassis structures, vehicles in general, and hence, full aluminium body and chassis become possible for low-end vehicles. LoCoMaTech will construct world first low-cost HFQ® aluminium production line (prototype).

~~Forming process for aluminium production~~

Project Acronym and Number: LOCOMATECH 723517 Project Title: Low Cost Materials Processing Technologies for Mass Production of Lightweight Vehicles Start and End Dates: from 1/9/2016 till 31/08/2019 EU Contribution: 7,997,725 € Coordinator: Jianguo LIN, [email protected] Modeller(s): Jianguo Lin, [email protected]

~~219~~

~~MODA~~

~~Low Cost Materials Processing Technologies for Mass Production of Lightweight Vehicles~~

~~LoCoMaTech~~

~~OVERVIEW of the simulation~~

The automotive industry users want to optimize the design of structure, subsystem, components and manufacturing processes for complex shaped, 1 USER CASE lightweight panel components by optimizing the material selection, structural properties/performance.

~~The structural mechanics model for forming which describes the MODEL 1 onset of failure/necking is part of Chapter 4 Continuum modelling of materials in the Review of Materials Modelling V.~~

The structural mechanics model for tool life which describes CHAIN OF MODEL 2 wear and the life time is part of Chapter 4 Continuum modelling 2 MODELS of materials in the Review of Materials Modelling V.

The structural mechanics model for tool maker which describes interfacial heat transfer in the forming process is part of Chapter MODEL 3 4 Continuum modelling of materials in the Review of Materials Modelling V.

~~PUBLICATION 3 ON THE N/A SIMULATION~~

The Forming Limit model, Tool Life model and Tool Maker model are ACCESS developed by the researchers at Imperial College London. The published 4 CONDITIONS model and data for the LoCoMaTech project are open to share. The software can be found on http://smartforming.com/ .

~~Model 1~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

~~ASPECT OF THE USER The prediction of the necking/failure conditions in a sheet 1.1 CASE TO BE SIMULATED forming process in which temperature, strain path and strain rate changes occur.~~

~~1.2 MATERIAL Aluminium alloys (mainly consists of Al, Mg, Si, Zn, etc.)~~

~~The geometry of vehicle components such as the door inner with 1.3 GEOMETRY approximation of dimension of 1.5 m by 1 m by 0.02 m.~~

~~1.4 TIME LAPSE The Forming Limit model runs from minutes to hours.~~

The manufacturing condition is an anisothermal process with high MANUFACTURING forming speed which can influence the strain change rate. For hot PROCESS OR IN- forming and quenching (HFQ) process, the temperature of sheet 1.5 SERVICE metal material is up to 500 degree Celsius and that of forming tool is CONDITIONS approximately 50 degree Celsius. The forming speed is up to 400 mm/s.

~~220~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum solid mechanics model (fracture) 2.0 AND NAME~~

~~MODEL Finite elements 2.1 ENTITY~~

~~Equations Conservation equation of mass and energy t~~

MODEL 퐸푘푖푛푒푡푖푐 + 퐸푝표푡푒푛푡푖푎푙 = 퐸푡표푡푎푙 PHYSICS/ Physical Kinetic energy within a system, 퐸 2.2 CHEMISTRY 푘푖푛푒푡푖푐 quantities EQUATION Pontential energy within a system, 퐸푝표푡푒푛푡푖푎푙 for each PE’S equation Total energy within a system, 퐸푡표푡푎푙

MR The unified viscoplastic-Hosford-MK constitutive equations Equations are established by data mining on experimental data for high temperature forming limit diagram prediction. It is assumed that there exists an initial imperfection in the material, denoted zone B, where the thickness is slightly lower than the rest of the material, denoted zone A.

~~σ̅ −R −푘 n1 1. ε̅̇ = ( (퐴,퐵) (A,B) ) P(A,B) K 0.5 2. R(A,B) = Bρ̅(A,B) ̇ ̇ 푛2 3. 휌̅(퐴,퐵) = 퐴(1 − 휌̅(퐴,퐵))휀푃̅ (퐴,퐵) − 퐶휌̅(퐴,퐵)~~

4. 휎̅(퐴,퐵) = 퐸(휀(̅ 퐴,퐵) − 휀푃̅ (퐴,퐵)) 푎 푎 푎 푎 5. 푅2휎1 + 푅1휎2 + 푅1푅2(휎1 − 휎2) = 푅2(푅1 + 1)휎̅ 2.3 MATERIALS 6. 푓 = 푓 exp(휀 − 휀 ) RELATIONS 0 3퐵 3퐴 푑휀 푑휀 7. 1퐵 ≥ 10, 표푟 3퐵 ≥ 10 , condition for the onset of necking 푑휀1퐴 푑휀3퐴

~~Physical 1. Temperature-dependent material constants, 푘, 퐾, 푛1, 퐵, 퐴, quantities/ 퐶 푎푛푑 퐸 descriptors 2. Constants, 푎, 푛2 for each 3. Dislocation density, 휌̅(퐴,퐵)~~

~~MR 4. Longitudinal or transvers r-values, 푅1, 푅2~~

~~5. Isotropic hardening, 푅(퐴,퐵) 6. Imperfect factor, 푓~~

~~7. Initial imperfect factor, 푓0,~~

~~8. Strain, 휀푛(퐴,퐵), 푛 = 1,2 표푟 3 (orientation in x, y and z axis)~~

~~9. Stress, 휎푛(퐴,퐵),, 푛 = 1,2 표푟 3 (orientation in x, y and z axis)~~

~~10. Plastic strain, 휀푃̅ (퐴,퐵), the subscript ‘P’ stands for plastic~~

~~2.4 SIMULATED INPUT N/A~~

~~221~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Solver developed at Imperial College London 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL The functional modules are shared on http://smartforming.com/~~

~~The typical time step is 1e-4 seconds for providing sufficient 3.3 TIME STEP accuracy and good computation speed.~~

PHYSICS The explicit Euler solver for differential equations is EQUATION, used. At each time step, the strain is incremented MATERIAL and the corresponding variables are updated to COMPUTATIONAL RELATIONS, calculate the stress and also used to check the failure 3.4 REPRESENTATION MATERIAL condition. The computation is completed when either the forming process is finished or the onset of necking occurs beforehand based on the condition 푑휀 푑휀 being met: 1퐵 ≥ 10, 표푟 3퐵 ≥ 10. 푑휀1퐴 푑휀3퐴

~~BOUNDARY N/A~~

~~CONDITIONS~~

~~ADDITIONAL N/A SOLVER PARAMETERS~~

~~4 POST PROCESSING~~

~~THE PROCESSED The calculated results from the Forming Limit model are imported for 4.1 OUTPUT IS visualising the onset of necking (part of the same software as the CALCULATED FOR solver).~~

METHODOLOGIES The failure condition values at each computed element are sampled 4.2 using a self-developed data format, and then the distribution map of onset of necking for a component is plotted.

~~MARGIN OF Based on the data obtained from the forming of a door inner of a 4.3 ERROR vehicle, the error of calculation is controlled at about 5-10%.~~

~~222~~

~~Model 2~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

ASPECT OF THE USER The prediction of service life of tools, such as punch, blank holder CASE TO BE and die in industrial environment. Reduction of coating in SIMULATED operation cycles due to stamping/pressure. The improvement of 1.1 AND HOW IT FORMS A tool design will enhance the operation life of the manufacturing PART OF THE TOTAL facility. USER CASE

~~1.2 MATERIAL TiN coating on a component of a forming tool.~~

~~A typical lab forming test component, such as a dome with 1.3 GEOMETRY diameter of 0.2 m.~~

~~1.4 TIME LAPSE The tool life model operates within 2 minutes.~~

The manufacturing process to be simulated includes stamping MANUFACTURING speed, initial friction coefficient, high temperature and external PROCESS OR IN- 1.5 pressure that can influence the coating thickness and relative SERVICE wear distance in the industrial operation, such as the hot CONDITIONS stamping process.

~~PUBLICATION 1.6 ON THIS ONE N/A SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model – Solid Mechanics 2.0 AND NAME~~

~~MODEL Finite elements 2.1 ENTITY~~

Equations Conservation equation of energy t MODEL 퐸푘푖푛푒푡푖푐 + 퐸푝표푡푒푛푡푖푎푙 = 퐸푡표푡푎푙 HYSICS P / 2.2 CHEMISTRY Physical Kinetic energy within a system, 퐸푘푖푛푒푡푖푐 EQUATION quantities for Pontential energy within a system, 퐸푝표푡푒푛푡푖푎푙 PE’S each equation Total energy within a system, 퐸푡표푡푎푙

~~MR Equations Friction model~~

~~1. 휇 = 휇훼 + 휇푃푐, friction~~

~~휆2 2. 휇푃푐 = 휇푃푠푒푥푝 [−(휆1ℎ) ]~~

~~3. ℎ = ℎ0 − ℎ̇푑푡 ATERIALS 2.3 M 퐾푃푣 4. ℎ̇ = RELATIONS 퐻푐 훼2+ℎ훽2 5. 퐻 = 퐻 ( ) 푐 푠 훼+ℎ훽2~~

~~푁휆1 6. 휆1 = 푘휆1푃~~

~~푁퐾 7. 퐾 = 푘퐾푃 Archard equation:~~

~~223~~

~~퐾푊퐿 8. 푄 = 퐻~~

Physical 1. Load independent parameters, μ(Ps ) and λ1 quantities/ 2. Hardness ratio between coating and substrate, α descriptors for 3. Coefficient of thickness, β each MR 4. Constants, 푘휆1 , 푘퐾, 푁퐾 and 푁휆1 5. Volume of wear, Q 6. Constant, K 7. Load, W 8. Sliding distance, L 9. Hardness, H

~~SIMULATED N/A 2.4 INPUT~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICA Solver (code) developed at Imperial College London 3.1 L SOLVER~~

~~SOFTWARE The FE model can be shared on http://smartforming.com/ 3.2 TOOL~~

~~3.3 TIME STEP Unclear~~

PHYSICS The explicit Euler solver for differential equations is used. At COMPUTAT EQUATION, given time step, the thickness of coating is reduced and the IONAL MATERIAL corresponding variables are updated to calculate the 3.4 REPRESEN RELATIONS, remaining thickness and are used to quantify the coating TATION MATERIAL failure condition. The computation stops when either the coating failure occurs or a certain number of operation cycles for the coated component is achieved.

~~BOUNDARY N/A~~

~~CONDITIONS~~

~~ADDITIONAL N/A SOLVER PARAMETERS~~

~~4 POST PROCESSING~~

THE PROCESSED The calculated results from the Tool Life model are imported for OUTPUT IS visualising the friction distribution of coating and the profile of 4.1 CALCULATED FOR thickness variation of coating (part of the same software as the solver).

METHODOLOGIES The coefficient of friction and remaining coating thickness for each 4.2 computed element are collected using a self-developed data format, and then a single distribution map of friction of coating is plotted.

~~4.3 MARGIN OF ERROR N/A~~

~~224~~

~~Model 3~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

ASPECT OF THE USER CASE TO BE The prediction of temperature evolution and hence quenching rate of SIMULATED 1.1 blank material in the forming process. AND HOW IT FORMS A PART OF THE TOTAL USER CASE

~~1.2 MATERIAL Aluminium alloys (mainly consists of Al, Mg, Si, Zn, etc.)~~

~~A typical lab forming testing sample, e.g. a dome with diameter of 0.2 1.3 GEOMETRY m.~~

~~1.4 TIME LAPSE The forming process is completed within half an hour.~~

MANUFACTURING The manufacturing condition to be simulated includes die quenching PROCESS OR IN- pressure, lubricant thickness, die material, surface roughness, cooling 1.5 SERVICE rate and forming speed etc. For example, a blank material is CONDITIONS quenched to room temperature during the forming process.

~~PUBLICATION N/A~~

~~1.6 ON THIS ONE SIMULATION~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

~~MODEL TYPE Continuum model – Heat flow and thermal-mechanical 2.0 AND NAME~~

~~MODEL Finite elements 2.1 ENTITY~~

Equations The conservation equation of energy t 퐸푖푛 + 퐸푐표푛푣푒푟푠푖표푛 − 퐸표푢푡 = ∆퐸푠푡표푟푒 MODEL PHYSICS/ Physical Thermal energy transferred into a system, 퐸 2.2 CHEMISTRY 푖푛 quantities EQUATION Thermal energy transferred out of a system, 퐸표푢푡 for each PE’S equation Thermal energy generated due to another energy source, 퐸푐표푛푣푒푟푠푖표푛

Stored energy in the system, ∆퐸푠푡표푟푒 MR Equations Interfacial heat transfer coefficient (IHTC) ℎ = 푎(1 − exp (−푏 푃)) 2.3 MATERIALS RELATIONS Physical 1. IHTC, ℎ quantities/ 2. Contact pressure, 푃 descriptors for 3. Constants, 푎 and 푏 each MR

~~SIMULATED N/A 2.4 INPUT~~

~~225~~

~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL FE 3.1 SOLVER~~

~~3.2 SOFTWARE TOOL The FE model can be shared on http://smartforming.com/~~

~~3.3 TIME STEP Unclear~~

PHYSICS The explicit Euler solver for differential equations is used. COMPUTATIONAL EQUATION, At each time step, the time value is incremented and the 3.4 REPRESENTATION MATERIAL temperature field is updated. The computation is RELATIONS, completed when the target time is reached. MATERIAL

~~BOUNDARY N/A~~

~~CONDITIONS~~

~~ADDITIONAL N/A SOLVER PARAMETERS~~

~~4 POST PROCESSING~~

THE PROCESSED The calculated results from the Tool Maker model are imported for OUTPUT IS visualisation which helps the user to select blank holding force, material, 4.1 CALCULATED FOR lubricant and coating for forming process (part of the same software as the solver).

METHODOLOGIES The calculated quenching rate is compared with the pre-defined critical 4.2 quenching rate until the agreement is achieving by varying the holding force, lubricant thickness and surface roughness in the calculation.

~~4.3 MARGIN OF ERROR N/A~~

~~226~~

~~LORCENIS (685445)~~

~~Summary of the project~~

The project is to develop long lasting reinforced concrete for energy infrastructures used under extreme operating conditions. Novel technologies involve customized protection, repairing and self- diagnosis methodologies. Integration of multi-functional nano-additives in concrete structures are to meet a wide range of requirements for extreme conditions like: low temperature, including artic (offshore wind parks, gravity-based structures, harbours or shelf areas with drift ice), high temperature constructions (Concentrated Solar Power, coal-fired and nuclear power plants, drilling oil well), structures subjected to high mechanical fatigue (concrete tower, slabs and grouts in windmills and maritime structures) and highly corrosive environments (acid attack in biogas plants and cooling towers; chlorides ingress in deep sea and offshore structures) depending on the location of the energy infrastructures.

~~Reinforced concrete~~

~~continue~~

~~227~~

Project Acronym and Number: LORCENIS 685445 Project Title: Long Lasting Reinforced Concrete for Energy Infrastructure under Severe Operating Conditions Start and End Dates: from 1/4/2016 till 31/3/2020 EU Contribution: 7653530 € Coordinator: Christian SIMON, [email protected] Modeller(s): Daniel Hoeche, [email protected] Philippe Maincon, [email protected] Kamyab Zandi, [email protected]

~~228~~

~~MODA Reinforced concrete LORCENIS~~

~~THE SIMULATION~~

The purpose is ageing control due to concrete additives and service- life prediction of energy infrastructures exposed to accelerated salt corrosive environment. The final purpose of multiscale modeling action is the extrapolation of timescale of macroscopic continuum models based on “corrosive” SVE/RVE. The newly developed elements contain information (MRs) gained from multiscale models and also include the additive effect. The MRs will be achieved by linking atomistic effects (chemical 1 USER CASE reaction engineering), continuum models of corrosion at microscale, continuum models of concrete at mesoscopic and continuum models of reinforced concrete at macroscale for damage initiation and progress. Each model does not include a full extrapolation of timescale but it delivers MRs based on respective PEs which allow to extrapolate the final continuum (SVE/RVE) simulation (initially via Abaqus) add improved forecasting accuracy. The main advantage is that the model can be applied without extensive (expensive) infrastructure which makes it attractive even for SME’s.

~~MODEL 1 Electronic DFT model~~

~~CHAIN OF MODEL 2 Continuum model at microscale 2 MODELS MODEL 3 Continuum model at mesoscale~~

~~MODEL 4 Continuum model at macroscale~~

~~3 PUBLICATION -~~

~~ACCESS Open access publication – yes; Open access to data – partially 4 CONDITIONS (restricted by project contract)~~

~~Model 1: Electronic DFT modelling~~

~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~

An atom-scale model for hydrated, hardened cement paste must be designed and evaluated. Volume changes of the cement as a function of water content may be calculated directly through a series of energy minimizations of atomistic/electronic models containing different amounts of water. kinetics of chemical changes occurring over time ASPECT OF THE (oxide/hydroxide equilibria; others) may be determined by calculating 1.1 USER CASE TO BE activation energies of the relevant reactions, using the activation SIMULATED energies as input to calculation of kinetics through transition state theory; hence giving relevant insight into phenomena of importance for long-term changes (swelling, creep, changes in material properties). The energy profile for water/chloride as a function of its position in the material will be computed, resulting in activation energies for the diffusion process. From these, diffusion coefficients

~~229~~

~~may be calculated using transition state theory like the kinetic parameters above.~~

~~Calcium silicates; more generally oxides of calcium, aluminium, and 1.2 MATERIAL silicon. Water.~~

~~Semi-amorphous, at the atomic scale, designed taking experimental 1.3 GEOMETRY characterization results as a starting point.~~

~~1.4 TIME LAPSE~~

~~MANUFACTURING Water content. Concentration gradients of water and/or chloride. PROCESS OR IN- 1.5 SERVICE CONDITIONS~~

~~1.6 PUBLICATION -~~

~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~

MODEL TYPE DFT: Energies of atomic scale systems as a function of relative AND NAME positions of atomic nuclei, computed by approximate solutions of the 2.0 Schrödinger equation. In principle, any experimentally observable quantity may be computed as a function of the energies.

~~MODEL Atoms, electrons. 2.1 ENTITY~~

2.2 Equation Schrödinger equation. Kohn-Sham equations. MODEL PHYSICS/ Physical wave function, Hamiltonian, electronic energies, bonding CHEMISTRY quantitie energies, spectroscopic parameters. EQUATION s PE

~~Equation chemical kinetics, diffusion, transition state theory~~

~~MATERIALS coupled equations coupled to be repeated in case of of case in repeated to be RELATION physical Chemical reaction rate constants, diffusion MR TO PE quantities/ coefficients descriptors~~

~~“REDUNDANT N/A 2.3 ” PHYSICS QUANTITIES~~

PUBLICATION Arstad, Bjørnar, Richard Blom, and Ole Swang. "CO2 absorption in aqueous solutions of alkanolamines: mechanistic insight from 2.4 quantum chemical calculations." The Journal of Physical Chemistry A 111.7 (2007): 1222-1228.

~~230~~

~~3 COMPUTATIONAL MODELLING METADATA~~

~~NUMERICAL Kohn-Sham equation solver, 3.1 SOLVER~~

~~The necessary software is available in the public domain (Quantum- 3.2 SOFTWARE TOOL Espresso; LAMMPS; others)~~

~~3.3 GRID SIZE N/A~~

~~3.4 TIME STEP~~

~~~~PHYSICS DFT: Plane-wave basis combined with pseudopotentials. EQUATION~~~~

~~~~COMPUTATIONAL MATERIAL e. g. oxide/hydroxide equilibria ( MO +H2O = M(OH)2 ), 3.5 REPRESENTATION RELATIONS chloride binding~~~~

~~~~MATERIAL Atom-scale model comprising a number of atomic nuclei with defined relative positions. Number of electrons to ensure overall charge neutrality. Pseudopotentials.~~~~

~~~~R.G. Parr, Weitao Yang, "Density-functional theory of atoms and 3.6 PUBLICATION molecules", Oxford University Press 1994, ISBN 0-19-504279-4~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Activation energies of diffusion from which diffusion coefficients may be 4.1 OUTPUT IS computed. CALCULATED FOR Swelling of cement as a function of water content.~~~~

~~~~4.2 METHODOLOGIES Transition state theory.~~~~

~~~~MARGIN OF DFT/diffusion: Absolute activation energies to 30 kJ/mol. Relative 4.3 ERROR activation energies to 20 kJ/mol.~~~~

~~~~Model 2: Continuum model at the microscale (corrosion)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF Model 2 will compute the variation of local conditions (chemical, THE USER electrochemical) within reinforced concrete and deliver information like pH 1.1 CASE TO BE change, concentration changes of active species, etc. for mesoscale SIMULATED models but partially also for the macroscale model

~~~~Oxides of calcium, aluminium, silicon (cement paste ), chloride, steel, 1.2 MATERIAL water~~~~

~~~~1.3 GEOMETRY Idealized cavities (tubes), 3 layer domain~~~~

~~~~1.4 TIME LAPSE s-d~~~~

~~~~1.5 MANUFACTURI Corrosive exposure of scenario 1 geometry to salt environment (aging) as~~~~

~~~~231~~~~

~~~~NG PROCESS in-service condition OR IN- SERVICE CONDITIONS t~~~~

Daniela Zander, Daniel Höche, Johan Deconinck, Theo Hack., Corrosion 1.6 PUBLICATION and its Context in Service-Life, Chapter 2.10 in Handbook for Software Solutions for ICME, eds. G. Schmitz, U. Prahl, 2016, in print.

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum modelling of chemical and electrochemical reactions and 2.0 AND NAME related species transport~~~~

~~~~MODEL FE 2.1 ENTITY~~~~

~~~~2.2 Equation PE1: Chemical and electrochemical reactions according to diluted solutions / electrolyte (aqueous) exposure MODEL PE2: Dissolved species transport equation (mass balance) PHYSICS/~~~~

incl. , Gauss law, Nernst equation, and at the rebar CHEMISTRY boundary modified Butler-Volmer, Tafel EQUATION PE Physical Concentrations, local potential, pH, current density, quantities porosity, deposit rates, surface conversion, rebar surface

chemistry coupled equations coupled to be repeated in case of of case in repeated to be Equation Expressions for chemical kinetics, diffusion, electrochemical kinetics partially derived from model 1 MATERIALS e.g. spatially resolved stability constants under severe RELATION exposure conditions MR TO PE Physical forward/ -backward reaction coefficients, anodic/ - quantities/ cathodic coefficients at re-bars, surface coverage via descriptors corrosion products

~~~~“REDUNDANT - 2.3 ” PHYSICS QUANTITIES~~~~

~~PUBLICATION Höche, D., Simulation of Corrosion Product Deposit Layer Growth on 2.4 Bare Magnesium Galvanically Coupled to Aluminium. Journal of The Electrochemical Society, 2015. 162(1): p. C1-C11.~~

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL FEM 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL COMSOL~~~~

~~~~3.3 GRID SIZE adapted~~~~

~~~~3.4 TIME STEP adapted~~~~

~~~~3.5 COMPUTATIONAL PHYSICS Written up for finite volumes~~~~

~~~~232~~~~

~~~~REPRESENTATION EQUATION~~~~

~~~~MATERIAL Functionals (as matrix) of time dependent e.g. RELATIONS concentration profiles, and constants (as numbers) like chemical and electrochemical coefficients~~~~

~~~~MATERIAL calcium, aluminium, silicon (cement paste ), chloride, steel, water~~~~

~~~~3.6 PUBLICATION -~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Raw output for fine volumes is averaged for finite volumes of (100 nm 4.1 OUTPUT IS – 10 µm) CALCULATED FOR~~~~

~~~~METHODOLOGIES Computed via an coupled equation set via direct solver  Data - matrix 4.2 as input for model 3 and 4 (as averaged finite micro volume)~~~~

~~~~MARGIN OF Based on experience the accuracy remains high until the driving 4.3 ERROR mechanism changes (e.g. from diffusion driven process to convection driven process)~~~~

~~~~Model 3: Continuum model applied at mesoscale~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

Material properties pertaining to the physical phenomena of mass transport in concrete are ultimately derived from material heterogeneities found at different subscales. At the mesoscale level, these heterogeneities are mainly ASPECT OF characterized by the presence of embedded aggregates in the cement paste, THE USER 1.1 together with cracks. Model 3 will compute moisture and chloride transport CASE TO BE in concrete and deliver information regarding deformational characteristics, SIMULATED where the mesoscale heterogeneities are explicitly accounted for by means of geometrical and constitutive descriptions along with computational homogenization.

~~~~Mesoscale constituents cement paste, aggregates and the highly porous 1.2 MATERIAL interface material~~~~

Aggregate representation and FE discretization In 2D, the aggregate representation will be based on octagons and the randomness in shape of the aggregate will be rendered by adding a random variation to each corner point in the octagon. The finite element discretization will be carried out using a Delaunay triangulation algorithm. 1.3 GEOMETRY In 3D, the aggregates will be modelled as spheres. In contrast to the 2D representation, no random variation in shape will be applied. The spatial discretization technique will be based on voxelization to create a structured grid of identically sized voxels (cubes). The concept is to subdivide the continuous SVE into a discrete set of voxels which are considered solid finite elements.

~~~~1.4 TIME LAPSE h-d~~~~

~~~~MANUFACTURING Homogeneous transport properties at macroscale 1.5 PROCESS OR IN-~~~~

~~~~233~~~~

~~~~SERVICE CONDITIONS~~~~

Zandi, K., (2015). Corrosion-Induced Cover Spalling and Anchorage Capacity, Structure and Infrastructure Engineering. Vol. 11 (2015), 12, p. 1547-1564. Zandi, K., et al. (2013). Three-dimensional modelling of structural effects of corroding steel reinforcement in concrete, Structure and Infrastructure Engineering, Vol. 9, No. 7, pp 702–718. 1.6 PUBLICATION F. Nilenius et al. (2013). Macroscopic diffusivity in concrete determined by computationalhomogenization, International Journal for Numerical and Analytical Methods in Geomechanics. Vol. 37, 11, p. 1535-1551. F. Nilenius et al. (2014), FE2 Method for Coupled Transient Diffusion Phenomena in Concrete, Journal of engineering mechanics. Vol. 141, No. 2.

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum modelling of moisture and chloride transport 2.0 AND NAME~~~~

~~~~MODEL Finite elements – two- and three-dimensional Statistical Volume Elements 2.1 ENTITY (SVEs) of mesoscale concrete~~~~

Equation Moisture transport  For saturated conditions, pressure gradients are the main driving forces for moisture transport.  For unsaturated conditions, moisture exists simultaneously in two phases as liquid and as vapour. The driving forces for the liquid phase are pressure gradients in addition to capillary forces. For the vapour phase, diffusion and convection are the two main transport mechanisms.

2.2 Chloride transport Chlorides are solved only in the liquid phase of moisture, not MODEL in the vapour phase. This phenomenon makes the transport PHYSICS/ of chloride ions intrinsically coupled to the transport of CHEMISTRY moisture. The three main transport processes are diffusion, EQUATION convection and migration. PE

Coupled chloride ions and moisture transport coupled equations coupled to be repeated in case of of case in repeated to be The constitutive model will be a modified expression of Fick’s law by Ababneh and Xi et al. for the cement paste, which cross-couples the fluxes of chloride ions and moisture in the following way:

~~~~J∅ = −D∅∇∅ − εcDc∇c~~~~

~~~~Jc = −ε∅D∅∇∅ − Dc∇c~~~~

~~~~Physical Relative pore humidity (φ), free chloride ion concentration~~~~

~~~~quantities (c), Flux (J•) and diffusion coefficient (D•)~~~~

~~~~Equation relation between pore chemistry and to be repeated MATERIALS composition and crack initiation~~~~

~~~~234~~~~

~~~~if necessary RELATION parameters~~~~

~~~~MR TO PE Physical micro convection, humidity quantities/ descriptors~~~~

~~~~“REDUNDANT” PHYSICS N/A 2.3 QUANTITIES~~~~

PUBLICA Zandi, K., (2010). Structural Behaviour of Deteriorated Concrete Structures. TION Göteborg: Chalmers University of Technology. Doctoral thesis, ISBN/ISSN: 978-91-7385-461-0. A. Ababneh and Y. Xi. “An experimental study on the effect of chloride penetration on moisture diffusion in concrete”. In: Materials and Structures 35.10 (Dec. 2002), pp. 659–663.- 2.4 F. Nilenius et al., Computational homogenization of diffusion in three-phase mesoscale concrete, Computational Mechanics (0178-7675). Vol. 54 (2014), 2, p. 461-472. F. Nilenius (2014), Moisture and Chloride Transport in Concrete, Göteborg : Chalmers University of Technology, Doctoral thesis. ISBN: 978-91-7385-977- 6, 166 pp.

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

Finite Element Method (FEM) NUMERICAL The SVEs will be employed numerically using the finite element method 3.1 SOLVER (FEM) to simulate mass transport—for both stationary and transient conditions—in order to compute macroscale diffusivities.

~~~~3.2 SOFTWARE TOOL MATLAB; access to source codes are restricted by project contract~~~~

~~~~3.3 GRID SIZE Adapted~~~~

~~~~3.4 TIME STEP Adapted~~~~

PHYSICS The computation is done according to standard FEM. EQUATION Dirichlet boundary conditions will be used in the numerical implementations and all numerical results will be — as a consequence — upper bound solutions. COMPUTATIONAL MATERIAL Constitutive models for cement paste and aggregate in 3.5 REPRESENTATION RELATIONS compression and tension. Constitutive model for ITZ

~~~~governing normal and tangential traction and displacement.~~~~

~~~~MATERIAL Cement paste, aggregates and the highly porous interface material~~~~

Zandi, K., et al. (2011). Bond capacity of severely corroded bars with corroded stirrups, Magazine of Concrete Research, Vol. 63, No.12, pp 953–968. 3.6 PUBLICATION F. Nilenius et al., Computational homogenization of diffusion in three- phase mesoscale concrete, Computational Mechanics (0178-7675). Vol. 54 (2014), 2, p. 461-472.

~~~~235~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE (Finite volumes) Homogeneous transport properties on the macroscale, PROCESSED chloride ingress in cracks 4.1 OUTPUT IS CALCULATED FOR~~~~

METHODOLOG Matrix-based computation of: Normalized effective diffusivities as a IES function of aggregate contents for varying diffusivities in the ITZ, time 4.2 evolution of macroscale relative humidity, and Effective diffusivities as functions of SVE size and ITZ diffusivities and volume aggregate contents.

MARGIN OF The accuracy remains reasonably high until at least one of the following ERROR assumptions is violated: (1) The mass transfer of chloride ions and moisture are concentration gradient-driven processes, allowing for Fick’s 4.3 law to be used, (2) the macroscale fields of moisture and chloride ions vary linearly within the SVE, and (3) the mesoscale constituents are assumed to be homogeneous, and the laws of continuum physics are assumed to apply at the mesoscale level.

~~~~Model 4: Continuum model at the macroscale~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~Structural integrity and aging behaviour of concrete structure (Scenario ASPECT OF THE 1) 1.1 USER CASE TO BE~~~~

~~~~SIMULATED~~~~

~~~~1.2 MATERIAL Oxides of calcium, aluminium, silicon (cement paste ), chloride, steel~~~~

~~~~1.3 GEOMETRY Structure/structural component. (test beam Scenario 1)~~~~

~~~~1.4 TIME LAPSE Years~~~~

~~~~MANUFACTURING Corrosive exposure to salt environment (aging) under steady PROCESS OR IN- mechanical loads 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION -~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Coupled multiphysics, macroscale, continuum model: "Engineering 2.0 AND NAME model"~~~~

~~~~MODEL FE (finite elements) 2.1 ENTITY~~~~

~~~~236~~~~

~~~~Equation Continuum mechanics Strain definition Stress as dual of strain Equilibrium/virtual work principle~~~~

~~~~Re-bar expansion~~~~

Mass transport (from model 3) 2.2 Conservation of mass Chemical equilibrium or kinetics MODEL PHYSICS/ Corrosion (from model 2) CHEMISTRY EQUATION Conservation of mass (oxygen) in the corrosion process PE Physical Continuum mechanics quantities Displacement, stress, strains, surface forces

~~~~to be repeated in case of coupled equations coupled of case in repeated to be Mass transport Solute concentrations/partial pressures~~~~

~~~~Corrosion Loss of cross section Increase in effective diameter~~~~

~~~~Equation Bulk Strain is related to the smeared cracking, itself related to stress, mass transport (from model 3)~~~~

Re-bar Oxygen absorption is related to loss of cross MATERIALS to be section and increase in volume (from model 2) repeated if RELATION Physical Bulk necessary MR TO PE quantities/ Strain, stresses, mass-diffusivity, smeared-crack descriptors tensor.

~~~~Re-Bar Remaining cross section, mass-absorption, diameter~~~~

~~~~“REDUNDANT” - 2.3 PHYSICS QUANTITIES~~~~

PUBLICATION Kane, Alexandre, and Erling Østby. "Crystal Plasticity Modeling of the Local Crack Tip Stress Field." The Twenty-first International 2.4 Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers, 2011.

~~~~237~~~~

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL FEM 3.1 SOLVER~~~~

~~~~SOFTWARE Abaqus, user defined elements for a) re-bars and b) bulk 3.2 TOOL~~~~

The model is to be "light" enough for engineering purposes. To this effect, specialised elements must be developed: – a beam element (re-bars) with additional mass diffusion and expansion 3.3 GRID SIZE degree of freedom - A volume element (bulk) with additional degrees of freedom for radial expansion around a re-bar, and degrees of freedom for mass diffusion

~~~~3.4 TIME STEP Of the order of weeks or months~~~~

~~~~PHYSICS Coupled differential equations to be discretized using EQUATION Galerkin finite element method.~~~~

COMPUTATIO MATERIAL To be determined from models 2 and 3. NAL RELATIONS Phenomenological models will probably be introduced. 3.5 REPRESENTAT ION MATERIAL Bulk Internal variables for smeared cracking Re-bar No internal variables foreseen

~~~~Alvaro Antonio, Mainçon Philippe Osen Vidar, FEM formulation for mass 3.6 PUBLICATION diffusion through UMATHT subroutine, SINTEF reports 2014~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Finite volumes OUTPUT IS Bulk CALCULATED FOR Coalescence of micro-cracks into macro-cracks (cracking, spalling), 4.1 which can be defined as an engineering limit state. Re-bars Stresses in the re-bars in excess of yield or ultimate stresses, again an engineering limit state

~~~~4.2 METHODOLOGIES -~~~~

~~~~4.3 MARGIN OF ERROR -~~~~

~~~~238~~~~

~~~~MODCOMP (685844)~~~~

~~~~Summary of the project~~~~

The project aims to develop novel engineered fibre-based materials for technical, high value, high performance products for non-clothing applications at realistic cost. These materials can be used in a wide range of industrial sectors (transport, construction, leisure and electronics). The project focuses on two types of materials: carbon-fibre-based structures with increased functionality (enhanced mechanical, electrical and thermal properties) and carbon nanofibre-based structures for flexible electronics applications.

~~~~Electrical properties of fibre-based materials~~~~

~~~~continue~~~~

~~~~239~~~~

~~~~Thermal properties of fibre-based materials~~~~

Project Acronym and Number: MODCOMP 685844 Project Title: Modified cost effective fibre based structures with improved multi-functionality and performance Start and End Dates: from 4/1/2016 till 3/31/2020 EU Contribution: 7.980.036 € Coordinator: Constantinos CHARITIDIS, [email protected] Modeller(s): Agustin Chiminelli, [email protected] Pietro Asinari, [email protected] Mohammad Rouhi, [email protected] Cristian Lira, [email protected]

~~~~240~~~~

~~~~MODA ELECTRICAL PROPERTIES MODCOMP~~~~

~~~~OVERVIEW of the simulation~~~~

Simulation of the electrical conductivity of the composites with a 1 USER CASE reinforcement fabric structure. The fabric structure is made of carbon fibres (CFs) and the resin is enriched by carbon nanotubes (CNTs).

~~~~MESOSCOPIC MODEL with Ohm’s law to find the mesoscale MODEL 1 - percolation threshold based on the shortest path finding. MESO CHAIN OF~~~~

~~~~2 MODELS~~~~

~~~~MODEL 2 - CONTINUUM MODEL. Conservation law for charge. CONT~~~~

~~~~PUBLICATION 3 ON THIS  SIMULATION~~~~

~~~~ACCESS 4 Open source. CONDITIONS~~~~

We simulate composites with carbon fibres and resin enhanced by carbon nanotubes. The mesoscopic model (Model 1) is used for characterizing the percolation electrical network due to carbon nanotubes (CNTs) only. Hence Model 1 is used for computing the effective electrical conductivity of the resin enriched by the CNTs. The continuum model (Model 2) is used for WORKFLOW characterizing the percolation electrical network due to fabrics made by 5 AND ITS carbon fibres (CFs). Hence Model 1 and Model 2 together are used for RATIONALE computing the effective electrical conductivity of composites made by carbon fibres and by a resin with carbon nanotubes. Models 1 and 2 perform a direct numerical simulation of the electrical conduction for a representative portion of material (CNTs/CFs distribution, orientation, weight percent,...).

~~~~241~~~~

~~~~Model 1 – Electrical properties~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Modelling electrical conductivity of CNTs-resin composites 1.1 USER CASE TO BE SIMULATED~~~~

Carbon nanotubes (CNTs) are described in terms of discrete beads, namely electrically conductive rods, and the internal structure of the 1.2 MATERIAL CNTs is neglected. The surrounding resin is described by a continuum model with an average electrical conductivity.

~~~~1.3 GEOMETRY Tens of microns, cubic periodic box.~~~~

~~~~1.4 TIME LAPSE Static~~~~

~~~~MANUFACTURIN N/A. G PROCESS OR 1.5 IN-SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A.~~~~

~~~~1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE MESOSCOPIC MODEL. Ohm’s law for standard transport of electrons 2.0 AND NAME and phenomenological correlations for describing the tunnelling (quantum) effect.~~~~

~~~~MODEL ENTITY Beads, namely carbon nanotubes (CNTs) described as conducting path 2.1 sections di.~~~~

MODEL Equation  Ohm’s law for standard transport of electrons PHYSICS/ CHEMISTRY 2.2 Physical  Positions of the conducting path sections EQUATION quantities  di.is the length of the i-th conducting path PE sections Relation  Exponentially decaying electronic conductivity due to tunnelling (quantum) effect.  The electrical conductivity is computed by the following formula

~~~~MATERIALS 2.3 RELATIONS~~~~

~~~~where conducting path sections are randomly distributed in the domain~~~~

~~~~ Conductivity pre-exponential factor, 0, is assumed as a constant  Tunnelling length, , is assumed as a~~~~

~~~~242~~~~

~~~~constant~~~~

~~~~Physical N/A quantities /descriptor s for each MR~~~~

~~~~SIMULATED N/A 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Dijkstra algorithm. 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL In-house.~~~~

~~~~3.3 TIME STEP N/A.~~~~

~~~~PHYSICS Written up for the entity in the model. COMPUTATIONAL EQUATION, 3.4 REPRESENTATION MATERIAL RELATIONS, MATERIAL~~~~

~~~~COMPUTATIONAL Dirichlet boundary conditions. (electrical potential). 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL N/A 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED The effective electrical conductivity for a random distribution of 4.1 OUTPUT beads (CNTs) can be computed.~~~~

~~~~METHODOLOGIES Averaging over the computational box containing all the beads 4.2 (CNTs)..~~~~

~~~~4.3 MARGIN OF ERROR +/-20%.~~~~

~~~~243~~~~

~~~~Model 2 – Electrical properties~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE USER Electrical conductivity of composites made of resin enriched by CASE TO BE carbon nanotubes (CNTs) and fabrics made of carbon fibres SIMULATED (CFs). 1.1 AND HOW IT FORMS A PART OF THE TOTAL USER CASE

Carbon fibre / polymer resin composites. Specific systems to be analysed: 1) Fabrics made of carbon fibres. 2) Epoxy resins filled with CNTs. 1.2 MATERIAL Carbon fibres (CFs) are described by control volumes (sub- domain) with the electrical properties of the CFs. The surrounding resin, eventually enriched by CNTs, is described by continuum control volumes with the effective electrical properties, for taking into account the enhancement due to enrichment.

~~~~1.3 GEOMETRY Yarns woven according to the desired fabric structure.~~~~

~~~~1.4 TIME LAPSE Seconds (quasi-static analysis)~~~~

~~~~MANUFACTURING N/A PROCESS OR IN- 1.5 SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE CONTINUUM MODEL. Conservation laws. 2.0 AND NAME~~~~

~~~~MODEL Finite volumes 2.1 ENTITY~~~~

~~~~Equations PE Conservation laws 1. PE1. Mass conservation equation (continuity equation):~~~~

~~~~MODEL PHYSICS/ CHEMISTRY 2.2 2. PE2: Momentum conservation equation (mechanical EQUATION stresses) PE’S~~~~

~~~~3. PE3: Energy conservation equation (heat transfer)~~~~

~~~~244~~~~

~~~~4. PE4: Charge conservation equation~~~~

Physical Physics quantities of the system of equations PE1 + PE2 + quantities PE3: 흆 is the mass density, 풗 is the velocity, 풆 is the total for each energy per unit mass, 풒 is the heat flux vector. The total equation energy reduces to the internal energy and the latter can be expressed as a function of the temperature T . The thermal flux 풒 depends on α which is the thermal conductivity. In PE4, 흆 is the charge density, J electric current density.

~~~~MR Equations 1. Electric conductivity of the yarns (function)~~~~

~~~~MATERIALS RELATIONS Physical 1. Electric conductivity depends on the considered uantities/ material (fibre or resin) provided by model 1~~~~

~~~~descriptors for each MR~~~~

~~~~SIMULATED Effective electrical conductivities for resin/CNTs in the form of constitutive 2.4 INPUT equations (see Model 1)~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Implicit Finite Element Method 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Abaqus (http://www.3ds.com/es/productos-y-servicios/simulia)~~~~

~~~~3.3 TIME STEP Seconds~~~~

~~~~PHYSICS EQUATION, Discretization - variational statement of the COMPUTATIONAL MATERIAL energy balance and the Maxwell equations. 3.4 REPRESENTATION RELATIONS,~~~~

~~~~MATERIAL~~~~

~~~~BOUNDARY Periodic boundary conditions.~~~~

~~~~CONDITIONS~~~~

~~~~ADDITIONAL SOLVER N/A~~~~

~~~~PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED The effective electrical conductivity can be computed by averaging 4.1 OUTPUT IS over all control volumes. CALCULATED FOR~~~~

~~~~4.2 METHODOLOGIES volume averages~~~~

~~~~4.3 MARGIN OF ERROR +/-20%~~~~

~~~~245~~~~

~~~~MODA Thermal properties MODCOMP~~~~

~~~~OVERVIEW of the simulation~~~~

Simulation of the thermal conductivity of the composites with a 1 USER CASE reinforcement fabric structure. The fabric structure is made of carbon fibres (CFs) and the resin is enriched by carbon nanotubes (CNTs).

~~~~MODEL 1 - ATOMISTIC MODEL. Classical molecular dynamics (MD) MD with empirical force fields (material relations).~~~~

~~~~CHAIN OF MODEL 2 - CONTINUUM MODEL. Heat transfer equation (Fourier 2 MODELS CONT conduction equation).~~~~

~~~~MODEL 3 - CONTINUUM MODEL. Conservation laws for mass, CONT momentum and energy.~~~~

~~~~3 PUBLICATION -~~~~

~~~~4 ACCESS Open source.~~~~

The atomistic model (Model 1) is used for characterizing the thermal interface between resin and carbon nanotubes. The first continuum model (Model 2) for characterizing the percolation thermal network in case of using carbon nanotubes only. The second continuum model (Model 3) for characterizing the percolation thermal network and its impact on the mechanical properties, in case of using also fabrics made by carbon fibres. In case of composites with carbon fibres and resin enhanced by carbon nanotubes, all three models are used: Model 1 for computing the Kapitza resistance; Model 2 for the effective thermal conductivity of the resin with carbon nanotubes; Model 3 for WORKFLOW effective thermal conductivity of composites made by carbon fibres 5 AND ITS and by a resin with carbon nanotubes. RATIONALE Model 1 is used to determine the thermal (Kapitza) resistance between carbon nanotubes/fibres and resin contacts. For that, a small portion of the CNTs/CFs will be virtually immersed in a solvent as a simple way to mimic the soft matter around the fibre, i.e. the matrix. The order of magnitude of the thermal Kapitza resistance will be determined in this simplified setup and then the results will be properly scaled for the realistic setup to the polymer resin by a representative portion of material. Models 2 and 3 will perform a direct numerical simulation of the thermal conduction for a representative portion of material (CNTs/CFs distribution, orientation, weight percent,...).

~~~~246~~~~

~~~~Model 1 – Thermal properties~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF Thermal conductivity of nanotubes-resin interfaces. THE USER 1.1 CASE TO BE SIMULATED~~~~

~~~~Carbon nanotubes made of carbon atoms with different hybridization. 1.2 MATERIAL Resins are simulated by analogy with small hydrocarbons, e.g. octane.~~~~

~~~~1.3 GEOMETRY Tens of nanometers, cubic periodic box.~~~~

~~~~1.4 TIME LAPSE Static~~~~

~~~~1.5 CONDITIONS N/A.~~~~

~~~~1.6 PUBLICATION N/A.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION #1~~~~

~~~~MODEL ATOMISTIC MODEL. Classical molecular dynamics (MD). Classical 2.0 Newton laws.~~~~

~~~~2.1 MODEL ENTITY Atoms.~~~~

~~~~Equation~~~~

~~~~MODEL~~~~

~~~~PHYSICS/ 2.2 CHEMISTRY Physical  ri is the atom position.~~~~

~~~~EQUATION quantities  Fi is the force acting on the atom. PE~~~~

~~~~Relation  Parameterized force fields (table).~~~~

~~~~MATERIALS Physical  Force fields depend on Lennard-Jones .3 RELATIONS quantities size and interaction energies of every /descriptors atom and partial charges of every atom. for each MR~~~~

~~~~SIMULATED NA 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL VERLET solver, finite difference method for Ordinary Differential 3.1 SOLVER Equations (ODEs).~~~~

~~~~3.2 SOFTWARE TOOL GROMACS.~~~~

~~~~3.3 TIME STEP Picoseconds.~~~~

~~~~COMPUTATIONAL PE, MR Written up for the entity in the model. 3.4 REPRESENTATION~~~~

~~~~247~~~~

~~~~COMPUTATIONAL Periodic. 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Interaction potential cut-offs. 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The atom positions and velocities are post processed in order to OUTPUT derive the information about heat transfer by dividing the effective heat transfer by the imposed temperature difference, the Kapitza 4.1 transmittance (G) can be computed. The Kaptiza resistance R, which is a good estimate of the interfacial thermal property, is R=1/G.

~~~~4.2 METHODOLOGIES Statistical mechanics.~~~~

~~~~MARGIN OF Typically large, namely +/-50%, due to statistical representability 4.3 ERROR of the samples.~~~~

~~~~248~~~~

~~~~Model 2 – Thermal properties~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Thermal conductivity of composites made of resin and carbon 1.1 USER CASE TO BE nanotubes. SIMULATED~~~~

~~~~CNTs which are described as filaments. Industrially relevant resins 1.2 MATERIAL are used.~~~~

~~~~1.3 GEOMETRY Tens of microns, cubic periodic box.~~~~

~~~~1.4 TIME LAPSE Static~~~~

~~~~1.5 CONDITIONS N/A.~~~~

~~~~1.6 PUBLICATION N/A.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION #2~~~~

~~~~MODEL TYPE CONTINUUM MODEL. Energy conservation equation + Fourier 2.0 AND NAME phenomenological equation.~~~~

~~~~MODEL Finite volumes. 2.1 ENTITY~~~~

~~~~Equation~~~~

~~~~MODEL~~~~

~~~~PHYSICS/ 2.2 CHEMISTRY Physical  T is the local sample temperature. EQUATION quantities PE~~~~

Relation  Thermal conductivity,  (function).  Kapitza thermal resistance between fibres and resin, R (table), taken from the previous MATERIALS model (linking). 2.3 RELATIONS Physical  Thermal conductivity () depends on the quantities considered material (fibres or resin). /descript  Kapitza thermal resistance (R) depends on the ors for relative orientation between the fibre and the each MR resin (see previous atomistic model).

~~~~SIMULATED The Kaptiza resistance R is taken from the previous model about 2.4 INPUT interfacial properties (see section 4.1 of the previous atomistic model).~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Finite Element Method (FEM). 3.1 SOLVER~~~~

~~~~249~~~~

~~~~SOFTWARE COMSOL. 3.2 TOOL~~~~

~~~~3.3 TIME STEP Static. Iterative solving procedure.~~~~

~~~~COMPUTATIONA PHYSICS Written up for finite elements which are used to L EQUATION, discretize the finite volumes. 3.4 REPRESENTATI MATERIAL ON RELATIONS, , MATERIAL~~~~

~~~~COMPUTATIONA Dirichlet boundary conditions (temperature). 3.5 L BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL N/A. 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The temperature as a function of time are post-processed into heat OUTPUT transfer Dividing the effective heat transfer by the imposed 4.1 temperature difference, the effective thermal conductivity can be computed and a new constitutive equation can be derived.

~~~~4.2 METHODOLOGIES Application of the definition of heat transfer~~~~

~~~~MARGIN OF 4.3 +/-20%. ERROR~~~~

~~~~250~~~~

~~~~Model 3 -Thermal properties~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Thermal conductivity of composites made of resin enriched by 1.1 USER CASE TO BE carbon nanotubes and fabrics made of carbon fibres. SIMULATED~~~~

~~~~Carbon fibre / polymer resin composites. Specific systems to be analysed: 1.2 MATERIAL 1) Fabrics made of carbon fibres functionalized with CNTs. 2) Epoxy resins filled with CNTs.~~~~

~~~~1.3 GEOMETRY Yarns woven according to the desired fabric structure.~~~~

~~~~1.4 TIME LAPSE Seconds (quasi-static analysis)~~~~

~~~~1.5 CONDITIONS N/A~~~~

~~~~1.6 PUBLICATION N/A~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE CONTINUUM MODEL. Conservation laws. 2.0 AND NAME~~~~

~~~~2.1 MODEL ENTITY Finite volumes.~~~~

~~~~Equations PE Conservation laws 1. PE1. Mass conservation equation (continuity equation):~~~~

~~~~2. PE2: Momentum conservation equation (mechanical stresses)~~~~

~~~~MODEL~~~~

~~~~PHYSICS/ 3. PE3: Energy conservation equation (heat 2.2 CHEMISTRY transfer) EQUATION~~~~

~~~~PE’S~~~~

Physical Physics quantities of the system of equations PE1 + quantities PE2 + PE3: 흆 is the mass density, 풗 is the velocity, 풆 for each is the total energy per unit mass, 풒 is the heat flux equation vector. The total energy reduces to the internal energy and the latter can be expressed as a function of the temperature T . The thermal flux 풒 depends on α which is the thermal conductivity.

~~~~MATERIALS MR 1. Thermal conductivity of the yarns, α (function) RELATIONS Equations provided by model 2~~~~

~~~~251~~~~

~~~~Physical 1. Thermal conductivity depends on the considered quantities material (fibres or resin) provided by model 2 for each MR~~~~

~~~~SIMULA Effective thermal conductivities for resin/fibre (Thermal properties – Model 2.4 TED 2) in the form of constitutive equations INPUT~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Implicit Finite Element Method 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Abaqus (http://www.3ds.com/es/productos-y-servicios/simulia)~~~~

~~~~3.3 TIME STEP Seconds~~~~

PHYSICS Discretization - variational statement of the COMPUTATIONAL EQUATION, energy balance and the Fourier equations. 3.4 REPRESENTATION MATERIAL Time integration through the backward RELATIONS, difference algorithm. MATERIAL

~~~~BOUNDARY Periodic boundary conditions.~~~~

~~~~CONDITIONS~~~~

~~~~ADDITIONAL N/A SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The .. is post processed into heat transfer Dividing the OUTPUT IS effective heat transfer by the imposed temperature 4.1 CALCULATED FOR difference, the effective thermal conductivity can be computed.

~~~~4.2 METHODOLOGIES Continuum mechanics~~~~

~~~~4.3 MARGIN OF ERROR +/-20%~~~~

~~~~252~~~~

~~~~MODENA (680793)~~~~

~~~~Summary of the project~~~~

The project developed a multi-scale software-modelling framework. An open-source software-suite is constructed that interlinks scale and problem specific software spanning from quantum scale to macroscale, using a software orchestrator that communicates information. As an application the behaviour of polyurethane foams was modelled on all scales.

~~~~Behaviour of polyurethane foams~~~~

Project Acronym and Number: MODENA 604271 Project Title: Modelling of morphology Development of micro- and Nano Structures Start and End Dates: from 1/1/2014 till 31/12/2016 EU Contribution: 3,555,975.00 € Coordinator: NTNU- NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET - Heinz Preisig, [email protected] Modeller(s): Erik Laurini, [email protected] Sabrina Pricl, [email protected]

~~~~253~~~~

~~~~MODA Thermo-Physical Properties Simulations MODENA~~~~

OVERVIEW of the SIMULATION 1 Thermophysical properties of thermoplastic polyurethanes (TPU)-based USER CASE nanocomposites (TNCs) MODEL 1 Atomistic MD 2 MODEL 2 Mesoscopic DPD CHAIN OF MODELS MODEL 3 Continuum Solid Mechanics 3 PUBLICATION No publication yet. Models are implemented in commercial software from BIOVIA 4 ACCESS (http://accelrys.com/products/collaborative-science/biovia-materials- CONDITIONS studio/).

~~~~Model 1 (Molecular Dynamics)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE To extract coarse grained Interaction parameters from Molecular 1.1 USER CASE TO Dynamics. BE SIMULATED Thermoplastic polyurethane (TPU) composed by poly(tetramethylene glycol) as soft segment, 4,4’-methyldiphenyldiisocyanate (MDI)/1,4- butandiol (BDO) as the hard segment and different nanofillers. Optimized molecular geometry obtained from Molecular Mechanics 1.2 MATERIAL Pre-processor using the so –called “SMART” algorithm, which is a cascade of the Steepest Descent, Adopted Basis Newton–Raphson (ABNR), and Quasi-Newton methods, see http://accelrys.com/products/datasheets/forcite.pdf A PU formulation assumed to be in a large container (large pot of 1.3 GEOMETRY liquid), no influence of the walls (i.e. a bulk system). NA (in the actual physical process this represents a process that lasts 1.4 TIME LAPSE up to milliseconds, but in the simulation no time is explicitly included).

~~~~MANUFACTURIN NA, preparation of the initial mixture (formulation) components. No G PROCESS OR specific service conditions are needed. 1.5 IN-SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION Unpublished yet.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~2.0 MODEL TYPE AND NAME Atomistic Model: Molecular Dynamics.~~~~

~~~~2.1 MODEL ENTITY atoms~~~~

~~~~254~~~~

~~~~EQUATIONS Newton’s mechanics~~~~

~~~~Newton equations of motion for a set of N interacting particles (atoms)~~~~

~~~~푚푖푟̈푖=푓푖, for i=1,2,…N and 푓푖=훻 푟푖푉(푟1,푟2,…).~~~~

MODEL PHYSICAL Force, mass, potential energy. 2.2 QUANTITIES FOR EACH EQUATION 푚푖: mass of an atom, 풓푖: position of an atom, 풇푖: the force on an atom, which in principle is a result of the interaction with all other atoms and external forces which is given by the potential energy at (푟푖).

~~~~The independent variables are time 푡, and position 풓.~~~~

EQUATIONS COMPASS Force field as published by H. Sun (J. Phys. Chem. B 1998, 102, 7338-7364) The functions can be divided into two categories valence terms including diagonal and off-diagonal cross-coupling terms and nonbond interaction terms. The valence terms represent internal coordinates of bond (b), angle (Θ), torsion angle (φ), and out of- plane angle (χ), and the cross-coupling terms include combinations of two or three internal coordinates. The cross-coupling terms are important for predicting vibration frequencies and structural variations associated with conformational changes. The nonbond interactions, which include a Lennard Jones-9-6 function for the van der Waals term and a Coulombic function for an electrostatic interaction, are used for interactions between pairs of atoms that are separated by two or more intervening atoms or those that belong to different molecules.

~~~~MATERIALS RELATIONS~~~~

The motions of the atoms are coupled to a thermostat and barostat based on the Berendsen scheme (NPT ensemble). PHYSICAL Equilibrium bond lengths, angles, torsion, and dihedrals QUANTITIES/ and relevant constants; van der Waals parameters, partial

~~~~255~~~~

~~~~DESCRIPTORS FOR charges; crossed interactions energy terms. Relate to the EACH MR symbols in the equations:~~~~

~~~~ ki are force field proportionality constants;~~~~

 bi, I, b’i and ’i are bond and angle force field equilibrium values (i.e., reference values of the internal coordinates)  b, ,  and  are the internal coordinates of bond, angle, torsion angle and out-of-plane angle, respectively

~~~~ qi are atomic partial charges 0  ij and r ij are the Lennard-Jones 9-6 parameters for like atom pairs~~~~

~~~~ rij is the distance between two atom pairs.~~~~

~~~~The independent variables are the internal coordinates (b,~~~~

~~~~,  and ), and the interatomic distances rij. 2.4 SIMULATED INPUT~~~~

~~~~2.5 PUBLICATION ON THIS DATA~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~3.1 NUMERICAL Classical molecular dynamics. SOLVER 3.2 Forcite (http://accelrys.com/products/collaborative-science/biovia- SOFTWARE TOOL materials-studio/) 3.3 1 fs TIME STEP~~~~

PHYSICS Atoms are treated as spherical entities in space EQUATION, with the radius and mass determined by the COMPUTATIONAL 3.4 MATERIAL element type. They are moved in each time step REPRESENTATION RELATIONS, according to the forces acting upon them (see 2.2).

~~~~MATERIAL The time step integration is carried out by a Verlet integration. BOUNDARY 3D periodic boundary conditions.~~~~

~~~~CONDITIONS ADDITIONAL Cut-off: half of the simulation box. SOLVER Non-bonded interactions via Particle Mesh Ewald, PARAMETERS accuracy 0.001 kcal/mol.~~~~

Integrator: Verlet. Thermostat/Barostat: Berendsen, coupling time constant 0.1 ps for temperature and 0.5 ps for pressure. Scocchi G, Posocco P, Fermeglia M, Pricl S, Polymer-Clay Nanocomposites: A Multiscale Molecular Modeling Approach, Journal of Physical Chemistry B, 111: 2143-2151 (2007); Fermeglia M, Pricl S, Multiscale modeling for polymer systems of industrial interest, Progress in Organic Coatings, 58:187-199 (2007); Toth R, Voorn D- 3.5 J, Handgraaf J-W, Fraaije JGEM, Fermeglia M, Pricl S, Posocco P, PUBLICATION Multiscale computer simulation studies of water-based montmorillonite/poly(ethylene oxide) nanocomposites, Macromolecules, 42:8260-8270 (2009); Scocchi G, Posocco P, Handgraaf JW, Fraaije JGEM, Fermeglia M, Pricl S, A complete multiscale modelling approach for polymer-clay nanocomposites Chemistry - A European Journal, 7586-7592:61 (2009); Toth R,

~~~~256~~~~

~~Santese F, Pereira SP, Nieto DR, Pricl S, Fermeglia M, Posocco P Size and shape matter! A multiscale molecular simulation approach to polymer nanocomposites, J. Mater. Chem. , 5398-5409:22 (2012)~~

4 POST PROCESSING THE PROCESSED Destination entity (coarse-grained bead) in Dissipative Particle 4.1 OUTPUT IS Dynamic (DPD) model:DPD bead size CALCULATED FOR DPD Conservative Force interaction parameters aij

METHODOLOGIES The interaction parameters needed as input for the mesoscopic DPD 4.2 calculations have been obtained by a mapping procedure of the binding energy values between different species as described in the above publications.

~~~~257~~~~

~~~~Model 2 (DPD)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE 3D density distribution and morphology. 1.1 USER CASE TO BE SIMULATED Thermoplastic polyurethane (TPU) composed of poly(tetramethylene 1.2 glycol) as soft segment, 4,4’-methyldiphenyldiisocyanate MATERIAL (MDI)/1,4-butandiol (BDO) as the hard segment and different nanofillers. Represented by beads calculated with the MD model. 1.3 NA GEOMETRY 1.4 N/A TIME LAPSE

~~~~MANUFACTURING PROCESS NA OR IN-SERVICE CONDITIONS 1.6 Unpublished yet. PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~2.0 MODEL TYPE AND NAME Mesoscopic model: Dissipative Particle Dynamics (DPD).~~~~

~~~~2.1 MODEL ENTITY beads~~~~

~~~~EQUATIONS Newton’s equations for the beads:~~~~

~~~~2.2 MODEL Forces are given by a sum of conservative Fc, dissipative FD, and random FR:~~~~

~~~~푭 = 푭퐶 + 푭퐷 + 푭푅~~~~

~~~~PHYSICAL Velocity, bead coordinates, temperature. QUANTITIES FOR EACH EQUATION~~~~

~~~~EQUATIONS Conservative force: 푎 (1 − 푟 /푟 )풓 (푟 ≤ 푟 ) 푭퐶 = { 푖푗 푖푗 푐 푖푗 푖푗 푐 0 ( 푟푖푗 ≥ 푟푐) Dissipative force:~~~~

~~~~æ ö D D rij rij F = -gijw (rij )ç × vij ÷ ç r ÷ r MATERIALS RELATIONS è ij ø ij~~~~

~~~~Random force:~~~~

~~~~z r F R = s w R r ij ij ij ( ij ) Dt rij~~~~

~~~~ aij and rij = ri – rj are the maximum repulsion and the separation vector~~~~

~~~~258~~~~

~~~~between beads i and j;~~~~

~~~~ rc is the cut-off distance at which the influence of FC vanishes; D R  ω (rij) and ω (rij) are weight functions that vanish for rij ≥ rc;  ij is the friction coefficient;~~~~

~~~~ ij is the noise amplitude;~~~~

~~~~ ij = i - j is the velocity vector;~~~~

~~~~ ij = ji is a Gaussian random number with zero mean and unit variance that is chosen independently for each pair of interacting particles;  Δt is the time step.~~~~

~~~~Typically (and here) only the pairwise off- diagonal interaction parameters are used to describe the material.~~~~

~~~~Cut-off distance rc = 6.7 Å; DPD system density ρ = 3.~~~~

PHYSICAL Conservative interactions, dissipative QUANTITIES/ forces, random forces, spring constant, DESCRIPTORS FOR unstretched length, bond and angle EACH MR parameters for the beads, pairwise interaction parameters. 2.4 SIMULATED INPUT Bead size, system dimension and bead numbers, pairwise interaction parameters from the MD model PUBLICATION Scocchi G, Posocco P, Fermeglia M, Pricl S, Polymer-Clay Nanocomposites: A Multiscale Molecular Modeling Approach, Journal of Physical Chemistry B, 111: 2143-2151 (2007); Fermeglia M, Pricl S, Multiscale modeling for polymer systems of industrial interest, Progress in Organic Coatings, 58:187-199 (2007); Toth R, Voorn D-J, Handgraaf J-W, Fraaije JGEM, Fermeglia M, Pricl S, Posocco P, Multiscale computer simulation 2.5 studies of water-based montmorillonite/poly(ethylene oxide) nanocomposites, Macromolecules, 42:8260-8270 (2009); Scocchi G, Posocco P, Handgraaf JW, Fraaije JGEM, Fermeglia M, Pricl S, A complete multiscale modelling approach for polymer-clay nanocomposites Chemistry - A European Journal, 7586-7592:61 (2009); Toth R, Santese F, Pereira SP, Nieto DR, Pricl S, Fermeglia M, Posocco P Size and shape matter! A multiscale molecular simulation approach to polymer nanocomposites, J. Mater. Chem. , 5398-5409:22 (2012).

~~~~3 Specific Computational Modelling Metadata~~~~

~~~~3.1 NUMERICAL Dissipative Particle Dynamics (DPD). SOLVER 3.2 SOFTWARE DPD module (http://accelrys.com/products/collaborative- TOOL science/biovia-materials-studio/). 3.3 TIME STEP 0.04~~~~

~~~~COMPUTATIONAL PHYSICS Beads are treated as points in space and 3.4 REPRESENTATION EQUATION, moved in each time step according to the MATERIAL forces acting upon them (see 2.2).~~~~

~~~~259~~~~

~~~~RELATIONS, MATERIAL BOUNDARY 3D periodic boundary conditions.~~~~

~~~~CONDITIONS ADDITIONAL SOLVER~~~~

PARAMETERS Scocchi G, Posocco P, Fermeglia M, Pricl S, Polymer-Clay Nanocomposites: A Multiscale Molecular Modeling Approach, Journal of Physical Chemistry B, 111: 2143-2151 (2007); Fermeglia M, Pricl S, Multiscale modeling for polymer systems of industrial interest, Progress in Organic Coatings, 58:187-199 (2007); Toth R, Voorn D-J, Handgraaf J-W, Fraaije JGEM, Fermeglia M, Pricl S, Posocco P, Multiscale computer simulation studies of water-based montmorillonite/poly(ethylene oxide) 3.5 PUBLICATION nanocomposites, Macromolecules, 42:8260-8270 (2009); Scocchi G, Posocco P, Handgraaf JW, Fraaije JGEM, Fermeglia M, Pricl S, A complete multiscale modelling approach for polymer-clay nanocomposites Chemistry - A European Journal, 7586-7592:61 (2009); Toth R, Santese F, Pereira SP, Nieto DR, Pricl S, Fermeglia M, Posocco P Size and shape matter! A multiscale molecular simulation approach to polymer nanocomposites, J. Mater. Chem. , 5398-5409:22 (2012)

~~~~4 POST PROCESSING~~~~

THE PROCESSED Coordinates, and density distributions of the particles (bead), i.e. 4.1 OUTPUT IS morphologies CALCULATED FOR are processed into volume averages for the solid mechanics model. METHODOLOGIES The 3D density distribution of each bead is calculated from the 4.2 ratio between the mass distribution of each component in a specific volume and the corresponding volume.

~~~~260~~~~

~~~~Model 3 (Solid Mechanics)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE Macroscopic properties prediction (Young modulus, bulk modulus, 1.1 USER CASE TO shear modulus, Poisson ratio, thermal conductivity, gas permeability). BE SIMULATED Thermoplastic polyurethane (TPU) composed by poly(tetramethylene 1.2 glycol) as soft segment, 4,4’-methyldiphenyldiisocyanate MATERIAL (MDI)/1,4-butandiol (BDO) as the hard segment and different nanofillers. 1.3 Referred to a representative volume element, which statistically GEOMETRY represents nanocomposite macroscopic structure. 1.4 NA (time is not considered explicitly in the calculations since statics TIME LAPSE mechanics ignore inertial forces). 1.5 MANUFACTURING PROCESS NA OR IN-SERVICE CONDITIONS 1.6 Unpublished yet. PUBLICATION

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

2.0 MODEL TYPE AND Solid mechanics – Micromechanics (displacement-based finite NAME element route, linear elasticity theory) 2.1 MODEL ENTITY 3D elementary volume elements constituting the discretizing mesh EQUATIONS Algebraic equations for displacement {F} = [k]{d}

~~~~PHYSICAL Action {F} = force or heat 2.2 MODEL QUANTITIES FOR EACH EQUATION source~~~~

~~~~Material property [k] = stiffness or conductivity Behavior {d} = displacement or temperature~~~~

~~~~EQUATIONS Linear response relations, e.g. for thermo-elastic properties (mechanical properties)~~~~

~~~~ F= total strain energy  ft = elastic energy of MATERIALS RELATIONS tetrahedron t~~~~

~~~~ Vt = volume of tetrahedron t  Cik = elastic constants  ei = local strains (made up of mechanical and thermal parts)~~~~

~~~~For thermal conductivity λ (r) and gas permeability P(r)~~~~

~~~~261~~~~

~~~~div λ (r) grad (T) = 0 and div P (r) grad (μ) = 0 where T = temperature μ = chemical potential~~~~

PHYSICAL QUANTITIES/ Total strain energy, elastic DESCRIPTORS FOR EACH MR energy, elastic constants, strains, volume of tetrahedron, temperature, chemical potential. 2.4 SIMULATED INPUT Density profiles, material properties of nanocomposite components from DPD model PUBLICATION Scocchi G, Posocco P, Fermeglia M, Pricl S, Polymer-Clay Nanocomposites: A Multiscale Molecular Modeling Approach, Journal of Physical Chemistry B, 111: 2143-2151 (2007); Fermeglia M, Pricl S, Multiscale modeling for polymer systems of industrial interest, Progress in Organic Coatings, 58:187-199 (2007); Toth R, Voorn D-J, Handgraaf J-W, Fraaije JGEM, Fermeglia M, Pricl S, Posocco P, Multiscale computer simulation 2.5 studies of water-based montmorillonite/poly(ethylene oxide) nanocomposites, Macromolecules, 42:8260-8270 (2009); Scocchi G, Posocco P, Handgraaf JW, Fraaije JGEM, Fermeglia M, Pricl S, A complete multiscale modelling approach for polymer-clay nanocomposites Chemistry - A European Journal, 7586-7592:61 (2009); Toth R, Santese F, Pereira SP, Nieto DR, Pricl S, Fermeglia M, Posocco P Size and shape matter! A multiscale molecular simulation approach to polymer nanocomposites, J. Mater. Chem. , 5398-5409:22 (2012).

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~3.1 NUMERICAL Finite Element Method (FEM). SOLVER 3.2 SOFTWARE Palmyra (produced by MATSim, a spin-off company of ETH, Zurich, CH, TOOL website currently not available). 3.3 NA (see 1.4). TIME STEP~~

PHYSICS Continuous space discretized in three-dimensional COMPUTATIONAL EQUATION, elements connected by node upon which the 3.4 REPRESENTATION MATERIAL constitutive equations are solved and RELATIONS, thermal/mechanical loads are applied. MATERIAL BOUNDARY 3D periodic boundary conditions.

~~~~CONDITIONS ADDITIONAL FE parameter settings (e.g. mesh optimization)~~~~

SOLVER dependent on the specific system. PARAMETERS Scocchi G, Posocco P, Fermeglia M, Pricl S, Polymer-Clay Nanocomposites: A Multiscale Molecular Modeling Approach, Journal of Physical Chemistry B, 111: 2143-2151 (2007); Fermeglia M, Pricl S, Multiscale modeling for polymer systems of industrial interest, Progress in Organic Coatings, 58:187-199 (2007); Toth R, Voorn D-J, 3.5 PUBLICATION Handgraaf J-W, Fraaije JGEM, Fermeglia M, Pricl S, Posocco P, Multiscale computer simulation studies of water-based montmorillonite/poly(ethylene oxide) nanocomposites, Macromolecules, 42:8260-8270 (2009); Scocchi G, Posocco P, Handgraaf JW, Fraaije JGEM, Fermeglia M, Pricl S, A complete multiscale modelling approach for polymer-clay nanocomposites

~~~~262~~~~

Chemistry - A European Journal, 7586-7592:61 (2009); Toth R, Santese F, Pereira SP, Nieto DR, Pricl S, Fermeglia M, Posocco P Size and shape matter! A multiscale molecular simulation approach to polymer nanocomposites, J. Mater. Chem. , 5398-5409:22 (2012)

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Young modulus, Poisson ratio, bulk modulus, shear modulus, 4.1 OUTPUT IS thermal conductivity and gas permeability CALCULATED FOR~~~~

METHODOLOGIES Young modulus, bulk modulus, shear modulus, and Poisson ratio are obtaned by means of equations describing the fundamental relationships between elastic constant since Lamè constants are 4.2 calculated by solving the stiffness and the compliance matrices. Thermal conductivity is derived from the difference of the potential energies under temperature gradient by solving the Laplace equation.

~~~~263~~~~

~~~~MOSTOPHOS (646259)~~~~

~~~~Summary of the project~~~~

The project aims to increase lifetime, reliability, and efficiency of organic light emitting diodes by integrating various levels of theoretical materials characterization into a single software package. The project will develop efficient molecular dynamics schemes for mesoscale modelling of the vacuum deposition process of host-guest layers. Electronic modelling will compute the rates for charge/exciton transfer/recombination/injection. The physics included in this model will describe triplet-triplet annihilation and triplet-polaron quenching, which are often responsible for the efficiency roll-off and degradation. A mesoscopic stochastic off-lattice models, the BTE master equation, will yield charge and exciton dynamics in the stack, which will allow weighting the probabilities of degradation events by the occupation probabilities obtained from the excitonic and polaronic density profiles and hence describe the effect of spatial inhomogeneities on degradation. A continuum drift-diffusion model will complement the electronic/atomistic- and mesoscopic models with a description of the macroscopic electro-thermal effects as well as electromagnetic light out- coupling processes accounting for the role of heat dissipation and optical effects on degradation.

~~~~New models for stability of organic light emitting diodes~~~~

Project Acronym and Number: MOSTOPHOS 646259 Project Title: Modelling stability of organic phosphorescent light-emitting diodes Start and End Dates: from 6/1/2015 till 5/31/2018 EU Contribution: 3669436,75 € Coordinator: Denis ANDRIENKO, [email protected] Modeller(s): Aldo Di Carlo, [email protected] Denis Andrienko, [email protected] Francesco Mercuri, [email protected] Peter Bobbert, [email protected]

~~~~264~~~~

~~~~MODA Stability of organic phosphorescent light-emitting diodes MOSTOPHOS~~~~

OVERVIEW of the THE SIMULATION The user wants to model the functioning and the stability-limiting 1 USER CASE mechanisms under operational conditions of organic phosphorescent light-emitting diodes fabricated by vacuum deposition. Electronic model: Ab initio quantum-mechanical model for electron, hole, and exciton energies and wavefunctions; for transfer rates of electrons, holes and excitons, formation of MODEL 1 excitons, exciton quenching by charge-exciton and exciton- exciton interactions, radiative and non-radiative decay of excitons, and material degradation. Parameterization of polarizable force-fields for intra- and inter-molecular forces. Atomistic model: Molecular dynamics simulations of atomistic morphologies of vacuum deposited organic MODEL 2 semiconductor layers, using the force-fields from Model 1. Evaluation of the solid-state contribution to site energies (electrostatic and induction). CHAIN OF Statistical Electronic transport model (applied to 2 MODELS mesoscale): Discrete description of dynamics of quasiparticle densities: electrons, holes and excitons, formation of excitons, exciton quenching by charge-exciton MODEL 3 and exciton-exciton interactions, radiative and nonradiative decay of excitons, and material degradation, given the rates from Model 1 and morphologies from Model 2. Continuum model: Continuum description of dynamics of density of electrons, holes and excitons, formation of excitons, exciton quenching by charge-exciton and exciton- MODEL 4 exciton interactions, radiative and non-radiative decay of excitons, and material degradation, based on the output of Model 3.

3 PUBLICATION The programs VOTCA, GROMACS, Octopus, Abinit, Quantum Espresso, and Yambo used in MOSTOPHOS are open source codes. The programs ACCESS 4 Turbomole, Bumblebee and TiberCAD are commercially distributed by the CONDITIONS companies Cosmologic (www.cosmologic.com) Simbeyond (www.simbeyond.com) and tiberlab s.r.l. (www.tiberlab.com). Rationale for the choice of models in this workflow: we are aiming at materials pre-screening, hence the link of device properties to chemical structures must be retained. Complete ab initio description of the system is, however, computationally prohibitive, therefore we adopt a multiscale ansatz: classical atomistic models for morphologies (M2) and statistical 5 WORKFLOW quasiparticle description for drift-diffusion (M3), both parametrized using first-principles (M1). Phenomena which are difficult to describe with a mesoscopic model (M3) (heat balance, light in- and out-coupling) are then incorporated at a continuum model (M4).

~~~~265~~~~

~~~~Model 1~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE The user wants to calculate from first principles energies of neutral USER CASE TO BE and charged excitations of organic semiconducting molecules, the SIMULATED rates of transfer processes of these excitations between molecules, 1.1 AND HOW IT and the stability of the products of these processes. This information FORMS A PART OF is then used in Model 3. The user wants to develop parameterized THE TOTAL USER force-fields for intra- and inter-molecular forces, which are used as CASE input in Model 2. Organic semiconducting molecules, including phosphorescent dyes in the emission layers of organic light-emitting diodes. The organic 1.2 MATERIAL layers grown by vacuum deposition, leading to a disordered conformation and packing of the molecules. The ab initio model requires types of atoms as input.

~~~~1.3 GEOMETRY Single molecules and pairs of molecules.~~~~

~~~~1.4 TIME LAPSE Up to picoseconds.~~~~

~~~~MANUFACTURING PROCESS OR IN- 1.5 SERVICE~~~~

~~~~CONDITIONSt~~~~

~~~~PUBLICATION ON 1.6 THIS SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Electronic model: Higher-level ab initio models 2.0 AND NAME~~~~

MODEL Quasiparticles (electrons, holes, excitons). 2.1 ENTITY Equations 1. Dyson equation (in the GW approximation). MODEL 2. Bethe-Salpeter equation (BSE). PHYSICS/ 2.2 CHEMISTRY Physical 1. Quasiparticle wave functions. EQUATION quantities 2. Green function (G), self-energy (Σ), dynamically PE’S for each screened interaction (W). equation

Equations 1. Equation for dielectric function completes the Dyson equation and Bethe-Salpeter equations. MATERIALS 2. Electrons/holes are described via single- RELATIONS particle green functions, excitons by two- particle green functions. Physical quantities/ 1. Quasiparticle wave functions. descriptors for each MR 2. Coulomb interaction.

~~~~2.4 Simulated input None~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Eigensolver, propagator, GW and BSE solvers. 3.1 SOLVER Octopus (www.tddft.org/programs/octopus), Abinit 3.2 SOFTWARE TOOL (www.abinit.org), Quantum Espresso (www.quantum-~~~~

~~~~266~~~~

~~~~espresso.org), Yambo (www.yambo-code.org), VOTCA (www.votca.org)~~~~

~~~~3.4 TIME STEP~~~~

~~~~PHYSICS Abinit, Quantum Espresso, Turbomole (DFT), EQUATION Yambo (GW): wavefunctions and density are represented in plane-wave basis.~~~~

~~~~MATERIAL Pseudopotentials: representation on regular real- COMPUTATIONAL RELATIONS space grid (Octopus) and in plane-wave basis REPRESENTATION 3.5 (Quantum Espresso).~~~~

~~~~Dielectric functions: representation in plane-wave basis (Yambo).~~~~

~~~~MATERIAL The material is represented by the locations of its atoms.~~~~

~~~~BOUNDARY Absorbing boundary conditions or use of Coulomb cut-off CONDITIONS under periodic boundary conditions to prevent interaction of periodic images.~~~~

ADDITIONAL Eigensolver: SOLVER 1. Convergence of density. PARAMETERS 2. Convergence of eigenstates. 3. Convergence of forces. 4. Maximum number of iterations. Propagator: 1. Maximum number of iterations. 2. Method for approximation of the evolution operator.

~~~~PUBLICATI 3.6 ON~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Atoms in Model 2 and quasiparticles in Model 3 OUTPUT IS 4.1 CALCULATED FOR~~~~

METHODOLOGIE  The ab initio forces following from the calculations are S parameterized (calculation of values in a FF formula from the literature), leading to polarizable force-fields. This information is the input to Model 2.  The distribution of the energies of excitations leads to densities of states of quasiparticles (DOS) that are input to 4.2 Model 3.  The conformational dependent excitation energies lead to reorganization energies that are input to Model 3.  The charge and exciton transfer rates between two neighbouring organic molecules are calculated on the basis of the Fermi-golden rule for wave functions of the initial and final states. This information is input to Model 3.

~~~~MARGIN OF 4.3 30%. ERROR~~~~

~~~~267~~~~

~~~~Model 2~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE The user wants to calculate the amorphous morphology of a layer of USER CASE TO BE organic semiconducting molecules, possibly with phosphorescent dye SIMULATED molecules added. 1.1 and how it forms a part of the total user case Organic molecular semiconductors, including phosphorescent dyes in the emission layers of organic light-emitting diodes. The organic layers are grown by vacuum deposition, leading to a disordered conformation and packing of the molecules. MATERIAL AND The microscopic amorphous morphologies obtained from Model 2 are 1.2 ITS PROCESSING used as input for (i) pairs of molecules in Model 1 and (ii) the mesoscale morphologies, represented by the molecular centres of mass, in Model 3. If required, a stochastic expansion method is applied to expand the microscopic morphologies to mesoscale morphologies.

~~~~1.3 GEOMETRY Multilayered structure.~~~~

~~~~1.4 TIME LAPSE Picoseconds.~~~~

~~~~MANUFACTURING PROCESS OR IN- 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATIONt~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Atomistic model: Classical molecular dynamics (MD) (ROMM 2.3.1). 2.0 AND NAME~~~~

MODEL Atoms. 2.1 ENTITY Equations 1. Newton’s equation of motion. MODEL PHYSICS/ Physical 1. Spatial coordinates and velocities of all atoms. 2.2 CHEMISTRY quantities 2. Forces, partial multipoles, polarizabilities. EQUATION for each PE’S equation

Equations 1. Equation for intra- and intermolecular force-field for atoms. 2. Equation for the interaction cut-offs of the force MATERIALS field. RELATIONS Physical 1. Forces, positions of atoms, dihedral angles. quantities/ 2. Positions of atoms, dihedral angles. descriptors for each MR Simulated Ab-initio calculated values for forces fields from Model 1. 2.4 input

~~~~268~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Velocity-Verlet algorithm 3.1 SOLVER~~~~

~~~~SOFTWARE GROMACS (www.gromacs.org). 3.2 TOOL~~~~

~~~~3.4 TIME STEP 0.01fs~~~~

PHYSICS Newton’s equations of motion are applied to the set of EQUATION atomic coordinates and solved numerically by time discretization using a Verlet algorithm. An analogue of the Poisson equation is solved for polarizable force- fields by optimizing induced multipoles. COMPUTATIONAL MATERIAL The material-specific electrostatic potential and 3.5 REPRESENTATION RELATIONS interaction potential are represented as a sum over atomic-coordinate based force-field functions, making use of distributed multipoles, polarizabilities, and bonded constants.

~~~~MATERIAL The material is represented by the locations of its atoms.~~~~

~~~~BOUNDARY The calculations are done on a representative unit cell~~~~

~~~~CONDITIONS with periodic boundary conditions.~~~~

~~~~ADDITIONAL 1. Verlet list cutoff. SOLVER 2. Number of self-consistent iterations, tolerance. PARAMETERS 3. Ewald sum grid.~~~~

~~~~PUBLICATIO [1] B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, J. Chem. Theory 3.6 N Comput. 4, 435 (2008).~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED The amorphous morphology obtained in the present model is used as 4.1 OUTPUT IS input to Model 3. CALCULATED FOR~~~~

~~~~METHODOLOGIES The polarizable force-field is employed to calculate electrostatic and 4.2 polarization contributions to the site energies used in Model 3.~~~~

~~~~MARGIN OF ERROR Margin of error: typically within 10%, mostly due to the error in the 4.3 material relations (force-field parameters, basis set size).~~~~

~~~~269~~~~

~~~~Model 3~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE USER The user wants to analyse at the mesoscale all the electronic CASE TO BE processes under DC bias relevant for the functioning and material SIMULATED degradation of phosphorescent organic light-emitting diodes. 1.1 and its role in the Photons are generated in the device. and how it forms a part of the total user case Organic molecular semiconductors, including phosphorescent dyes in the emission layers of organic light-emitting diodes. 1.2 MATERIAL The microscopic morphologies of the used materials are obtained from Model 2 (Manufacturing has been done by vacuum deposition) Layers of several nanometres thick of (mixtures of) organic molecular semiconductors, each with a specific function: injection 1.3 GEOMETRY layers for electrons and holes, transport and blocking layers for electron and holes, emissive layers with dyes, exciton-blocking layers, etc.

~~~~1.4 TIME LAPSE Up to tens of microseconds.~~~~

~~~~MANUFACTURING A DC voltage is applied to the device. 1.5 PROCESS OR IN- SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Quasiparticle model: statistical semi-classical transport model 2.0 AND NAME~~~~

MODEL Quasiparticles. 2.1 ENTITY Equations 1. Boltzmann transport equation (BTE) describing how MODEL quasiparticles (charged and neutral excitations) hop PHYSICS/ between sites representing molecules. CHEMISTRY 2.2 Physical 1. Transfer rates of all hopping transfer processes; EQUATION quantities spatial profile of quasiparticles (charges, excitons), PE’S for each electric field and temperature. equation Equations Equations for the material-specific rates k of all hopping transfer process to complete BTE. MATERIALS RELATIONS Physical Material-specific energies and molecular quantities/ reorganization energies of charged and neutral

~~~~descriptors for excitations, exciton binding energies, intermolecular each MR electronic couplings, dielectric constant.~~~~

SIMULATED  Amorphous morphology calculated with Model 2. INPUT  Energies and molecular reorganization energies of charged and neutral excitations, exciton binding energies, intermolecular 2.4 electronic couplings, calculated with Model 1.  The microscopic information about DOS of charged and neutral excitations, the reorganization energies, and the rates of transfer processes of these excitations are obtained from Model 3.

~~~~270~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Kinetic Monte Carlo (kMC). 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Bumblebee (www.simbeyond.com).~~~~

~~~~3.4 TIME STEP Typically a nanosecond.~~~~

PHYSICS The BTE is solved by executing at each time step a EQUATION hopping transfer process from one site to another, chosen randomly with a probability proportional to its rate. Time is proceeded in each step by a time interval chosen from an exponential distribution with a decay time equal to the inverse of the sum of the rates of all possible hopping transfer processes.

MATERIAL Material- and excitation-specific transfer rates are used RELATIONS (Marcus transfer for electrons and holes, Förster transfer for singlet excitons, and Dexter transfer for triplet excitons). The material-specificity in these transfers comes in via the material-specific electronic energies and reorganisation energies for electrons, COMPUTATIONAL holes, and singlet and triplet excitons, exciton binding 3.5 REPRESENTATION energies, and intermolecular couplings.

MATERIAL The material is represented as a collection of molecular point sites at which charged (electrons and holes) and uncharged (singlet and triplet excitons) can reside. Each site has specific electronic energies and reorganisation energies for electrons, holes, and singlet and triplet excitons, and a specific exciton binding energy. Every pair of sites has specific intermolecular couplings for charge or exciton transfer. The dielectric properties of each material is represented by its dielectric constant. A specific material degradation scenario is chosen (example: an exciton-charge quenching event leads with a certain probability to disfunctioning of a molecule).

BOUNDARY In the direction of current flow the boundary conditions CONDITIONS are determined by the work functions of the electrode materials and the applied bias voltage. Periodic boundary conditions are used in the lateral directions perpendicular to the current flow.

~~~~ADDITIONAL 1. Maximum length of run. SOLVER 2. Criterion for reaching steady state. PARAMETERS 3. Criterion for reaching sufficient accuracy of physical quantity to be calculated.~~~~

~~~~3.6 PUBLICATION~~~~

~~~~4 POST PROCESSING~~~~

~~THE PROCESSED The output of the model is used to determine the form and values of OUTPUT IS parameters in the Material Relations in the continuum Model 4 (finite 4.1 CALCULATED differences) FOR~~

~~~~4.2 METHODOLOGIE - The raw output of the program is a time record of all charge hopping,~~~~

~~~~271~~~~

S exciton recombination, transfer, quenching, and radiative and nonradiative decay events. By spatial and temporal averaging, relations are determined for the following physical quantities: 1. Electron mobility. 2. Hole mobility. 3. Singlet exciton diffusion coefficient. 4. Triplet exciton diffusion coefficient. 5. Electron-hole recombination and generation rates. 6. Singlet exciton decay rate. 7. Triplet exciton decay rate. 8. Charge-exciton quenching rates. 9. Exciton-exciton quenching rates. The following relations and values found will be used as Material Relations of Model 4: 1. Current-voltage characteristics. 2. Luminescence-voltage characteristics. 3. Luminescence efficiency as a function of voltage. 4. Colour balance. 5. Efficiency roll-off (decrease of efficiency with increasing current). 6. Emission profile. 7. Degradation rate. These properties are used to benchmark the results of Model 4.

~~~~MARGIN OF 4.3 20-30%. ERROR~~~~

~~~~272~~~~

~~~~Model 4~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE The user wants to analyse at the macro scale all the processes USER CASE TO BE relevant for the functioning and material degradation of SIMULATED phosphorescent organic light-emitting diodes. Heat is generated in the 1.1 and how it device. forms a part of the total user case Organic molecular semiconductors, including phosphorescent dyes in 1.2 MATERIAL the emission layers of organic light-emitting diodes. Stacked OLED structure including electrons and holes transport layers, 1.3 GEOMETRY blocking layers and emission layers. Layers thickness ranges from a few nanometres up to tens of nanometres.

1.4 TIME LAPSE N/A: Reaching the steady state is simulated. The device in its in-service conditions is simulated: a voltage is MANUFACTURING applied and the transport of electrons, holes and excitons, as well as PROCESS OR IN- 1.5 exciton formation, exciton-charge quenching and exciton-exciton SERVICE quenching in the whole device are simulated. CONDITIONS

~~~~1.6 PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum model: semiclassical steady-state drift-diffusion (DD) model 2.0 AND NAME (ROMM 4.2~~~~

MODEL Density of quasiparticles in finite volumes 2.1 ENTITY Equations Tightly-Coupled PEs: 1. Poisson equation for the electrostatic potential. 2. Drift-diffusion equation for electrons. 3. Drift-diffusion equation for holes. 4. Diffusion equation for singlet excitons. MODEL PHYSICS/ 5. Diffusion equation for triplet excitons. 2.2 CHEMISTRY EQUATION Physical 1. Electrostatic potential, charge density. PE’S quantities 2. Current and charge density of electrons. for each 3. Current and charge density of holes. equation 4. Current and density of singlet excitons. 5. Current and density of triplet excitons. 6. Current and charge density of quasiparticles. Equations 1. Relation for dielectric constant, completes Poisson equation. 2. Relation for electron mobility, completes drift- MATERIALS diffusion equation electrons. RELATIONS 3. Relation for hole mobility, completes drift-

~~~~diffusion equation holes. 4. Relation for diffusion coefficient singlet excitons, completes diffusion equation for singlet excitons.~~~~

~~~~273~~~~

5. Relation for diffusion coefficient triplet excitons, completes diffusion equation for singlet excitons. 6. Relation for electron-hole recombination and generation rate, completes drift-diffusion equations electrons and holes and diffusion equations excitons. 7. Relation for singlet exciton decay rate, completes diffusion equation for singlet excitons. 8. Relation for triplet exciton decay rate, completes diffusion equation for singlet excitons. 9. Relations for charge-exciton quenching, complete diffusion equations for singlet and triplet excitons. 10. Relations for exciton-exciton quenching rates, complete diffusion equation for singlet and triplet excitons. Physical 1. Dielectric constant. quantities/ 2. Electron mobility. descriptors 3. Hole mobility. for each MR 4. Singlet exciton diffusion coefficient. 5. Triplet exciton diffusion coefficient. 6. Electron-hole recombination and generation rates. 7. Singlet exciton decay rate. 8. Triplet exciton decay rate. 9. Charge-exciton quenching rates. 10. Exciton-exciton quenching rates.

SIMULA Relations for the following quantities calculated with the mesoscopic Model 3 TED are the material input relations of the continuum Model 4: INPUT 1. Electron mobility. 2. Hole mobility. 3. Singlet exciton diffusion coefficient. 2.4 4. Triplet exciton diffusion coefficient. 5. Electron-hole recombination and generation rates. 6. Singlet exciton decay rate. 7. Triplet exciton decay rate. 8. Charge-exciton quenching rates. 9. Exciton-exciton quenching rates.

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Finite element discretization of the continuum problem (FEM) and 3.1 SOLVER Newton's method~~~~

~~~~3.2 SOFTWARE TOOL TiberCAD (www.tiberlab.com)~~~~

~~~~3.4 TIME STEP N/A: the steady state is simulated.~~~~

PHYSICS The full equations system (Poisson + drift-diffusion for EQUATION charges + diffusion for excitons) is written in matrix form using finite-element methods (FEM) and then COMPUTATIONAL 3.5 solved numerically using the Newton method REPRESENTATION (linearization of the system).

~~~~MATERIAL The relations for the electron and hole mobilities, the RELATIONS exciton diffusion coefficients, the electron-hole~~~~

~~~~274~~~~

~~~~recombination and generation rates, the exciton decay rates, the charge-exciton quenching rates, and the exciton-exciton quenching rates are parameterized.~~~~

MATERIAL Each layer of the device is defined by its material composition (host + dye). Also traps can be introduced, leading to Schottky-Read-Hall (RSH) recombination. Each material is defined by its dielectric constant, HOMO and LUMO levels, electron and holes density of states, and its relations for the electron and hole mobilities, the exciton diffusion coefficients, the electron-hole recombination and generation rates, the exciton decay rates, the charge-exciton quenching rates, and the exciton-exciton quenching rates.

COMPUTATIO Dirichlet boundary conditions are used to set the NAL applied electric potential and the Fermi level of the BOUNDARY metal contacts. Contacts are boundary models that CONDITIONS allow a nonzero normal electrical current. At Ohmic or Schottky contacts one defines surface recombination velocities for electrons and holes. This imposes Robin- type boundary conditions for the continuity equations.

~~~~ADDITIONAL N/A SOLVER PARAMETERS~~~~

~~~~3.6 PUBLICATION [~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Luminance and current for the device as a function of the applied 4.1 OUTPUT IS voltage and time (in case of degradation) CALCULATED FOR~~~~

METHODOLOGIES From the solution of the equations system (Poisson + drift-diffusion for charges + diffusion for excitons) the following OLED properties are extracted with volume averaging : 1. Current-voltage characteristics. 2. Luminescence-voltage characteristics. 3. Luminescence efficiency. 4. Colour balance. 4.2 5. Efficiency roll-off (decrease of efficiency with increasing current). 6. Emission profile. 7. Degradation rate (this process is faster than reaching the steady state). These are the same properties that can be extracted from the mesoscopic Model 3, but the numerical efficiency of the continuum Model 4 is much greater.

~~~~MARGIN OF 4.3 30% ERROR~~~~

~~~~275~~~~

~~~~N2B-patch (721098)~~~~

~~~~Summary of the project~~~~

The aim of N2B-patch is the development of a drug delivery technology for he chronic treatment of Multiple Sclerosis. This requires synthesis of a biomaterial-based galenic formulation and an applicator device delivering to the nasal olfactory region. The galenic formulation will consist of drug loaded biodegradable polymer embedded into a biodegradable hydrogel matrix to be deposited as a patch onto the olfactory region. A pH-sensitive, mucoadhesive particle coating will ensure an environment-specific adhesion to the olfactory epithelium.

~~~~Drug delivery fot multiple sclerosis~~~~

Project Acronym and Number: N2B-patch 721098 Project Title: Nose to Brain Delivery of NG-101 via the Olfactory Region for the RegenerativTreatment of Multiple Sclerosis Using Novel Multi-functional Biomaterials Combined with a Medical Device Start and End Dates: from 1/1/2017 till 12/31/2020 EU Contribution: 5.325.498 € Coordinator: Carmen GRUBER-TRAUB, [email protected] Modeller(s): Costas KIPARISSIDES, [email protected]

~~~~276~~~~

~~~~MODA Gel Attachment and Film Formation Drug Release and Penetration to the Mucosa N2B-PATCH~~~~

~~~~OVERVIEW of the SIMULATION~~~~

1 USER CASE Drug delivery to olfactory mucos. CFD and chemistry models for flow and mixing of a viscoelastic fluid in an applicator tube, or extrusion of a MODEL A1 viscoelastic fluid from an applicator tube and for film CHAIN OF formation of a viscoelastic fluid on a mucous layer 2 MODELS

Mass transfer and chemistry (mass balance and reaction MODEL B1 kinetics) models for hydrogel matrix biodegradation (4.2 & 4.5) Mass transfer and chemistry (mass balance and reaction MODEL B2 kinetics) models for drug release from biodegradable particles (4.2 & 4.5) CFD (mass transfer) for drug diffusion through a gel matrix MODEL B3 (4.2 & 4.5)

~~~~PUBLICATION ON 3 THIS ONE SIMULATION~~~~

~~~~ACCESS Model and data are not free 4 CONDITIONS Commercial (ANSYS) and in-house software (BEM)~~~~

The user case involves phenomena with different physics and the modellers choose to separate the case into two parts: A) Fast gelling hydrogel being extruded from an applicator tube. After extrusion the gel comes into contact with an overlying mucosal surface. The extruding gel expands and covers the mucosa. B) Release of drug from biodegrading microparticles - embedded in a hydrogel matrix attached to the olfactory mucosa – and diffusion to the Olfactory mucosa

~~~~WORKFLO Part A 5 W AND ITS RATIONALE~~~~

~~~~The diagram above presents the key processes underlying the gel application and film formation.~~~~

~~~~277~~~~

In A1 we have inertial constrained flow of a mostly viscous fluid In A2 we have extrusion and Stokes free-surface flow of a viscoelastic fluid In A3 we have free-surface Stokes flow of a mostly elastic fluid. The CFD and chemistry (Navier-Stokes, Laplace-Young equation and reaction kinetics + mass balances) model form a tightly coupled system. The models chosen (PE and MR) are the same for all three processes.

~~~~Part B~~~~

The materials have been selected to be biodegraded within the treatment window, e.g., one month. Consequently drug release and transfer to the mucosa must occur during this time. Therefore the time scales for drug release, transfer and particle degradation are similar and as these processes are also coupled (see workflow below) they must be modelled together. The geometry of the hydrogel film will be defined from the output of the N2B-patch applicator simulations (i.e., MODA-A).

~~~~In B1 we have hydrogel matrix biodegradation In B2 we have drug release from biodegradable particles In B3 we have drug diffusion through a gel matrix~~~~

~~~~ Degradation of hydrogel matrix affects diffusion of water and drug.  Degradation of particles influence drug release rate from particles.~~~~

~~~~The models chosen (mass transfer, mass balance, reaction kinetics) are the same for all three parts and are solved in a tightly coupled way.~~~~

~~~~The initial geometry input to Model B1 is obtained from the output of Model A3.~~~~

~~~~PART A Gel Attachment and Film Formation~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Fast gelling system, containing the drug loaded polymeric microparticles, ASPECT OF based on hyaluronic acid mixed with a gelling agent in an applicator tube THE USER and then extruded from the applicator tube into the olfactory cleft region 1.1 CASE TO BE adjacent to the olfactory mucosa. After extrusion the gel comes into SIMULATED contact with the overlying mucosal surface, expands and forms a film that covers the mucosa. Tyramine derivative of Hyaluronic acid, hydrogen peroxide as crosslinking agent, water and chitosan coated polymeric microparticles.

~~~~1.2 MATERIAL~~~~

~~~~1.3 GEOMETRY~~~~

~~~~278~~~~

~~~~A few seconds for the HA extrusion and minutes for the hydrogel film 1.4 TIME LAPSE formation~~~~

~~~~MANUFACTURING PROCESS OR IN- Body temperature, atmospheric pressure, 100% 1.5 SERVICE CONDITIONS humidity~~~~

~~~~PUBLICATION 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE CFD and chemistry applied to Gel Attachment and Film Formation 2.0 AND NAME~~~~

2.1 MODEL ENTITY Finite volumes/surfaces Equation PE1 - Navier-Stokes equations (NS) PE2 - Laplace-Young equation (LY) PE3 Chemistry model (reaction kinetics + mass MODEL balances) PHYSICS/ 2.2 These form a tightly coupled system CHEMISTRY EQUATION PE Physical Velocity quantities Pressure Interface and contact line positions Concentrations Reaction rate constants Relation MR1 - Linear-viscoelastic “materials relation” completes NS and LY models MATERIALS 2.3 MR2 - Mucoadhesion “materials relation” completes NS RELATIONS and LY models MR3 – Reaction rate coefficients

~~~~279~~~~

Physical MR1 - In general, viscosity and elasticity quantities. quantities/ Parameters number and values are dependent on descriptors the MR selected relation for each MR2 - Specific adhesion normal and tangential forces. MR Parameters number and values are dependent on the MR selected relation MR3 – Reaction rate coefficients.

~~~~SIMULATED As shown in the Workflow sub-models A2 and A3 employ as input 2.4 INPUT results from the preceding sub-models, A1 and A2, respectively.~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~3.1 NUMERICAL SOLVER Finite volumes and boundary element methods (BEM) ANSYS commercial fluid flow solver 3.2 SOFTWARE TOOL In-house BEM solver, cannot be shared, no website/publication.~~~~

~~~~3.3 TIME STEP 1ms< Dt <1s~~~~

PHYSICS NS (A1: inertial, A2 and A3: Stokes) and LY (A2 EQUATION, and A3) COMPUTATIONAL MATERIAL MR1 is time-dependent due to the crosslinking RELATIONS, 3.4 REPRESENTATION reaction. MATERIAL , MR2 is time-dependent due to the crosslinking reaction. Hyaluronic acid hydrogel Moving free-surface boundary between the extruded hydrogel and air. COMPUTATIONAL Hydrogel/mucous layer/air contact line follows a stick-slip boundary 3.5 BOUNDARY condition that is described by a mucoadhesion model CONDITIONS Stick boundary conditions for the applicator tube with parabolic inflow conditions A1: 3D tetrahedral grid, ~106 cells to describe static mixer, explicit ADDITIONAL solver, 10-4 residuals 3.6 SOLVER A2 & A3: 1D (curve in 2D) with 101 -103 adaptive elements or 2D PARAMETERS (surface in 3D) with 102 -106 adaptive elements, explicit solver.

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Final hydrogel film thickness over the mucosa 4.1 OUTPUT Percent mucosa coverage Mechanical stability to normal and shear forces.~~~~

METHODOLOGIES Local thickness and percent coverage are obtained from the final position of the gel and the geometry of the olfactory mucosa. Normal distances from the olfactory mucosa are employed to determine 4.2 thickness. Mechanical stability is determined based on minimal normal and shear forces necessary to displace the region of the gel in contact with the mucosa.

~~~~MARGIN OF Local thickness and Mechanical stability need to be determined as 4.3 ERROR accurately as possible, i.e., better than 10%.~~~~

~~~~280~~~~

~~~~Part B: Drug Release and Penetration to the Mucosa~~~~

OVERVIEW of the simulation Release of drug from biodegrading microparticles - embedded in a hydrogel 1 USER CASE matrix attached to the olfactory mucosa – and diffusion to the Olfactory mucosa. Mass transfer and chemistry (mass balance and reaction MODEL B1 kinetics) models for hydrogel matrix biodegradation Mass transfer and chemistry (mass balance and reaction CHAIN OF MODEL B2 kinetics) models for drug release from biodegradable 2 MODELS particles CFD (mass transfer) for drug diffusion through a gel MODEL B3 matrix

~~~~PUBLICATION ON THIS ONE 3 SIMULATION~~~~

4 ACCESS CONDITIONS Restricted The materials have been selected to be biodegraded within the treatment window, e.g., one month. Consequently drug release and transfer to the mucosa must occur during this time. Therefore the time scales for drug release, transfer and particle degradation are similar and as these processes are also coupled (see workflow below) they must be modelled together. The geometry of the hydrogel film will be defined from the output of the N2B-patch applicator simulations (i.e., MODA-A).

~~~~WORKFLOW 5 AND ITS RATIONALE~~~~

 Note: Degradation of hydrogel matrix affects diffusion of water and drug.  Degradation of particles influence drug release rate from particles.  Sub-models B1, B2, and B3 are coupled and must be solved simultaneously.  The initial geometry input to Model B1 is obtained from the output of Model A3.

~~~~281~~~~

~~~~MODEL B~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF Release of drug from biodegrading polymeric microparticles (embedded THE USER in a biodegrading hydrogel matrix based on hyaluronic acid attached to 1.1 CASE TO BE the olfactory mucosa) and diffusion to the Olfactory mucosa. SIMULATED Hydrogel based on tyramine-derivative of hyaluronic acid, coated chitosan polymeric microparticles, and water. Key assumption is a zero drug concentration at the hydrogel/mucosa 1.2 MATERIAL interface. This provides an upper limit to the drug mass flux. Alternatively finite constant values can be used based on experimental evidence.

~~~~1.3 GEOMETRY~~~~

~~~~1.4 TIME LAPSE One month~~~~

~~~~MANUFACTURING PROCESS Body temperature, atmospheric pressure, 100% humidity 1.5 OR IN-SERVICE CONDITIONS~~~~

~~~~UBLICATION Pt 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE CFD(Diffusion) and Chemistry applied to Drug Release and Transfer 2.0 AND NAME~~~~

2.1 MODEL ENTITY Finite volumes Equation PE1 – Mass-transfer equations (Diffusion) PE2 – Chemistry model (reaction kinetics + mass MODEL balances) PHYSICS/ These form a tightly coupled system 2.2 CHEMISTRY EQUATION Physical Drug concentration PE quantities Particle size, volume, mass, position Hydrogel matrix size, volume, mass Reaction rate constants

Relation 1. MR1 - Viscoelastic materials relation completes PE1 MATERIALS 2. MR2 - Drug diffusion coefficient MR affects PE1 2.3 RELATIONS 3. MR3 – Hydrogel swelling MR affects PE1 4. MR4 – Degradation kinetic rate constants MRs affect PE2

~~~~282~~~~

~~~~5. MR5 – Drug solubility and partitioning MR affects PE1~~~~

Physical MR1 - Viscosity and elasticity quantities. Parameters quantities/ number and values are dependent on the MR descriptors selected relation for each MR MR2 - Drug flux and drug release rate. Parameters number and values are dependent on the MR selected relation MR3 – Thermodynamic degree of swelling in terms of environmental conditions (e.g., water content, gel crosslinking density). Parameters number and values are dependent on the MR selected relation MR4 – Degradation kinetic rate constants in terms of materials properties (e.g., molecular weight) and environmental conditions (e.g., moisture, temperature). ). Parameters number and values are dependent on the MR selected relation MR5 – Drug concentrations in the hydrogel and particle phases in terms of the environmental conditions and materials properties

SIMULATED Key input is the geometry of the applied hydrogel matrix. This is 2.4 INPUT determined from the Applicator Model (MODA-A). As shown in the workflow figure, models B1, B2, B3 are tightly coupled.

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Finite Element Method (FEM), Finite Differences (FD), Collocation methods 3.1 SOLVER~~~~

~~~~SOFTWARE FEM, FD, Collocation solvers, sharing will be decided, website will be set up 3.2 TOOL later.~~~~

~~~~3.3 TIME STEP 1ms< Dt <1s~~~~

~~~~PHYSICS EQUATION COMPUTATIONAL , 3.4 REPRESENTATION , MATERIAL RELATION S, MATERIAL~~~~

~~~~COMPUTATI ONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Explicit solver 3.6 SOLVER Tolerance =10-6 PARAMETERS~~~~

~~~~283~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Drug flux as a function with time assuming a zero drug concentration OUTPUT at the mucosa. 4.1 Drug delivery effectiveness as a % of drug load. Particles and drug loss due to degradation of the gel matrix.

METHODOLOGIES Drug flux will vary with time but also position. A surface averaged flux will be obtained but also local averaged values, e.g., for the proximal olfactory region. 4.2 Total drug delivery will be determined as a percentage of the drug load. Particles and drug lost will depend on the matrix degradation mechanism.

~~~~MARGIN OF The total drug delivery will be calculated very accurately, i.e., <1%, 4.3 ERROR excluding the percentage of drug loss due to matrix degradation.~~~~

~~~~284~~~~

~~~~NANODOME (646121)~~~~

~~~~Summary of the project~~~~

The project is to develop a robust model-based design and engineering toolkit for the simulation of commercially-relevant generic bottom-up Gas-Phase synthesis processes and the detailed prediction of complex nanomaterial structures. The project will deliver a validated ready-to-use toolkit.

~~~~Gas-Phasesynthesis of complex nanomaterial structures~~~~

Project Acronym and Number: NANODOME 646121 Project Title: Nanomaterials via Gas-Phase Synthesis: A Design-Oriented Modelling and Engineering Approach Start and End Dates: from 15/09/2015 till 14/09/2018 EU Contribution: 3,999,110 € Coordinator: Emanuele GHEDINI, [email protected] Modeller(s): Amit Bhave, [email protected] Andreas Kempf, [email protected] Nicola Bianco, [email protected] Susanna Monti, [email protected] Vincenzo Carravetta, [email protected]

~~~~285~~~~

~~~~MODA Elements in materials modelling NANODOME~~~~

~~~~THE SIMULATION~~~~

Nanoparticle synthesis via gas phase condensation in industrial commercially-relevant processes. Prediction of the nanoparticle size distribution, morphology and internal composition via modelling of the gas phase condensation synthesis process, including homogeneous and 1 USER CASE heterogeneous nucleation, surface and internal chemical kinetics and composition, agglomeration, aggregation.

~~~~Materials: Si, ZnO, Al2O3, Pt nanoparticles in Ar/H2/N2/O2 atmospheres for synthesis processes in plasma, hot wall and flame reactors.~~~~

~~~~MODEL 1 Electronic Density Functional Theory (Electronic)~~~~

~~MODEL 2 Classical MD (Atomistic) CHAIN OF 2 MODELS MODEL 3 Coarse Grained Molecular Dynamics (Mesoscopic) Fluid mechanics, Heat-Flow, Chemistry Reaction Model, MODEL 4 Electromagnetism (Continuum)~~

~~~~3 PUBLICATION N.A.~~~~

Electronic and Atomistic models are based on widely available commercial or open-source licenses packages, such as Quantum ESPRESSO, LAMMPS, ReaxFF, GROMACS, GARFFIELD. The mesoscopic model will be developed within the NanoDome project ACCESS under open-source license. 4 CONDITIONS Continuum models are based on the commercial package ANSYS Fluent and on the open-source package OpenFOAM. Interfacing libraries and the material database for Si/Ar system will be open-source. Material database for reactive materials will be published under commercial license.

~~~~286~~~~

~~~~Model 1: Electronic Density Functional Theory (Electronic)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

Quantum calculations on small clusters: structural and static ASPECT OF THE properties, molecular dynamics (finite temperature) for the 1.1 USER CASE TO BE optimization of the reactive force field, modelling of the very first SIMULATED stages of the nucleation processes, modelling of mutual interaction between clusters, benchmark for classical molecular dynamics.

~~~~1.2 MATERIAL Atoms and small clusters with explicit description of electrons~~~~

~~~~1.3 GEOMETRY Small clusters (less than 50 atoms) in a periodic box~~~~

~~~~1.4 TIME LAPSE Below 1 ns~~~~

~~~~MANUFACTURING PROCESS OR IN- Density and concentration of species, constant volume or constant 1.5 SERVICE pressure CONDITIONS~~~~

~~~~1.6 PUBLICATION n.a.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE 2.0 Quantum mechanics AND NAME~~~~

~~~~2.1 MODEL ENTITY Clusters, atoms, electrons~~~~

~~~~MODEL EQUATIONS Schroedinger equation, Born-Oppenheimer dynamics PHYSICS/ 2.2 CHEMISTRY PHYSICAL Wave function, electron density, total energy EQUATIONS QUANTITIES~~~~

~~~~EQUATIONS Kohn-Sham equation~~~~

~~~~MATERIALS 2.3 PHYSICAL Density functionals, pseudopotentials, plane wave basis RELATIONS QUANTITIES/ set.~~~~

~~~~DESCRIPTORS~~~~

PUBLICATION [1] P. Hohenberg and W. Kohn, Phys. Rev., 136(3B), B864{B871, Nov 1964. [2] W. Kohn and L. J. Sham, Phys. Rev., 140(4A), A1133{A1138, Nov 2.4 1965. [3] "Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods" - Dominik Marx and Jürg Hutter - Cambridge University Press 2010

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Self-consistent field (iterative approach) 3.1 SOLVER~~~~

~~~~287~~~~

~~~~3.2 SOFTWARE TOOL Quantum Espresso, CP2K, Dalton, Gamess~~~~

~~~~PHYSICS Projection of differential equations on finite basis set EQUATIONS~~~~

MATERIAL Interaction among electrons and ions are RELATIONS represented by Local (Coulomb), non-local (exchange) potential from electron density, and gradient of the electron density and pseudo potentials for the implicit core electron.

~~~~COMPUTATIONAL 3.3 MATERIAL Electrons are represented as material points, REPRESENTATION Atoms are represented as ions implicitly including core electrons~~~~

~~~~BOUNDARY Cubic box with periodic boundary conditions. CONDITIONS~~~~

~~~~ADDITIONAL~~~~

~~~~SOLVER n.a.~~~~

~~~~PARAMETERS~~~~

~~~~3.4 TIME STEP Femtoseconds for the molecular dynamics~~~~

[1] Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open- source software project for quantum simulations of materials. J. 3.6 PUBLICATION Phys.: Condens. Matter 2009, 21, 395502. [2] Dalton, a molecular electronic structure program, http://daltonprogram.org.

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED 4.1 OUTPUT IS Atoms and clusters CALCULATED FOR~~~~

~~~~METHODOLOGIES Analysis, by visualization and computational tools, of geometrical 4.2 structure, bonding environment, radial distribution functions etc.~~~~

MARGIN OF ERROR The error depends on input parameters (density functionals, pseudopotentials, basis sets, size of the model system, time step 4.3 and total simulation time) and is different for different physical properties: bonding distances and bonding angles (<5%), bonding energies (about 5%)

~~~~288~~~~

~~~~Model 2: Classical MD (Atomistic)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

Nucleation of atoms from gas phase to form primary nanoparticles and ASPECT OF THE gas phase condensation on nanoparticle surface 1.1 USER CASE TO Mutual interaction between nanoparticles (i.e. agglomeration, sintering) BE SIMULATED

~~~~Atoms (atoms or molecules) in gas and condensed liquid/solid phase 1.2 MATERIAL (nanoparticles)~~~~

~~~~Nanometre sized cubic box, representative a control volume of the 1.3 GEOMETRY reactor~~~~

~~~~1.4 TIME LAPSE Nanosecond to Microseconds.~~~~

~~~~MANUFACTURIN G PROCESS OR Temperature time gradient (cooling), fixed external pressure, species 1.5 IN-SERVICE concentration. CONDITIONS~~~~

~~~~1.6 PUBLICATION n.a.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Classical Molecular Dynamics 2.0 AND NAME~~~~

~~~~2.1 MODEL ENTITY Atoms~~~~

~~~~MODEL EQUATIONS Newton’s equation of motions. PHYSICS/ 2.2 CHEMISTRY PHYSICAL Position, velocity, mass, interatomic potentials. EQUATIONS QUANTITIES~~~~

~~~~EQUATIONS ReaxFF potential functions.~~~~

PHYSICAL ReaxFF parameters includes: MATERIALS QUANTITIES/ 2.3  generic parameters RELATIONS DESCRIPTORS  atom parameters (per element)  atom pairs/bond parameters (combination of two elements)  angle parameters (combination of three elements)  dihedrals (combination of four elements)

PUBLICATION [1] M. Griebel, S. Knapek, and G. Zumbusch. Numerical Simulation in 2.4 ON THIS Molecular Dynamics. Springer, 2007. SIMULATION [2] A.C.T. van Duin et al., J. Phys. Chem. A 105 (2001) 9396-9409

~~~~289~~~~

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Velocity integrator schemes (e.g. Verlet Integration). 3.1 SOLVER~~~~

~~~~SOFTWARE LAMMPS, http://lammps.sandia.gov 3.2 TOOL ReaxFF, http://www.scm.com/ReaxFF~~~~

~~~~PHYSICS Newton’s equation of motion with multibody EQUATIONS interatomic forces.~~~~

~~~~MATERIAL Interatomic potential is represented as sum of RELATIONS functions describing different interaction phenomena (ReaxFF potential definition)~~~~

COMPUTATIONA MATERIAL Atoms are represented are material points. L 3.3 Atoms interactions are represented by interatomic REPRESENTATI potential. ON BOUNDARY Cubic box with periodic boundary conditions. CONDITIONS

~~~~ADDITIONAL NPT constraints. SOLVER Thermostat (i.e. Nosé-Hoover, Langevin). PARAMETERS~~~~

~~~~3.4 TIME STEP Femtoseconds~~~~

~~~~3.6 PUBLICATION N.A.~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Nanoparticles (i.e. grain) 4.1 OUTPUT IS CALCULATED FOR~~~~

METHODOLOGIES Mapping matrix from a set of atomic coordinates to a unique nanoparticle configuration in the mesoscopic system by means of an atom-atom connection criterion. 4.2 Iterative Boltzmann conversion and/or force mapping algorithm to define CG energy functions (i.e. interparticle potentials) from the atomistic energy function.

MARGIN OF ERROR Accuracy of ReaxFF parameters and fitting (8%) Multiparticles interactions are often neglected in favour of binary interaction. 4.3 Application on limited time and domain and to one mechanisms at time (i.e. sintering, nucleation).

~~~~290~~~~

~~~~Model 3: Coarse Grained Molecular Dynamics (Mesoscopic)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

Nanoparticle growth inside a meso-scale control volume and evolution of ASPECT OF THE the nanoparticle ensemble including agglomeration, sintering and 1.1 USER CASE TO chemical reactions in plasma, hot wall and flame nanoparticle synthesis BE SIMULATED processes.

~~~~1.2 MATERIAL Nanoparticles of Si, ZnO, Al3O3, Pt in Ar/H2/N2/O2 atmospheres~~~~

~~~~1.2 GEOMETRY Micrometer sized cubic box representative of the interior of the reactor~~~~

~~~~1.3 TIME LAPSE Milliseconds.~~~~

~~~~MANUFACTURING PROCESS OR IN- 1.4 Temperature time gradient (cooling), fixed external pressure. SERVICE CONDITIONS~~~~

~~~~Sheldon K. Friedlander. Smoke, Dust and Haze. Oxford University Press, 1.6 PUBLICATION 1978~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE 2.0 Coarse Grained Molecular Dynamics AND NAME~~~~

~~~~2.1 MODEL ENTITY Nanoparticles (grains) Equation 1. Langevin’s equation of motions for single particles and particle aggregates:~~~~

~~~~2. Modified Koch and Friedlander equation for sintering process:~~~~

~~~~MODEL PHYSICS/ 3. Diffusion-reaction equation (conservation 2.2 CHEMISTRY of mass) for internal nanoparticle EQUATION concentration profile:~~~~

~~~~Physical 1. Position x, velocity v, mass m and inter- quantities particle forces F.~~~~

~~~~2. Particle area A, coalescence area Af and sintering time . 3. Species radial distribution for each~~~~

~~~~nanoparticle nX (X = A,B), diffusion~~~~

~~~~291~~~~

~~~~coefficient DX and reaction rate constant k.~~~~

~~~~Equation 1. Nanoparticle interaction forces Fi between grains (nanoparticles) based on van der~~~~

~~~~Waals-like potentials: Fi = -V(r) 2. Friction coefficient on a spherical particle a. (Stokes law)~~~~

~~~~b. (Epstein relation) 3. Semi-empirical relation predicting particle sintering~~~~

~~~~time s as function of: MATERIALS 2.3 RELATION~~~~

~~~~4. Nucleation and growth rates from Classical Nucleation Theory Physical 1. Nanoparticle interaction potential V(r)~~~~

~~~~quantities/ 2. Particle radius Ri, gas molecule mass mg, average descriptors gas velocity , gas pressure and temperature p and T.~~~~

3. Material dependant properties (Asint, Esint), temperature T and particles diameter dp. 4. Pressure, temperature and material properties of the condensing species (i.e. surface tension, bulk density, saturation pressure)

PUBLICATION [1] M.L. Eggersdorfer and S.E. Pratsinis. Restructuring of aggregates and their primary particle size distribution during sintering. AIChE 2.5 Journal, 59(4):1118–1126, 2013. [2] W. J. Menz and M. Kraft. A new model for silicon nanoparticles synthesis. Combustion and Flame, 160:947–958, 2013.

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

Time integration via symplectic splitting method for Langevin dynamics. ODE solver for chemical kinetics equations. NUMERICAL 3.1 PDE solver for particle concentration profile. SOLVER The equations are solved coupled together using operator splitting technique (loose coupling).

~~~~3.2 SOFTWARE TOOL In project developed, Open Source.~~~~

PHYSICS Verlet-type algorithm for simulating Langevin EQUATION dynamics in a 3D box. COMPUTATIONAL 3.3 ODE explicit solver for sintering and chemical kinetics. REPRESENTATION PDE explicit solver for particle concentration profile.

~~~~MATERIAL Interaction potential are defined interpolating over~~~~

~~~~292~~~~

~~~~RELATIONS distance dependent database data or fitting functions.~~~~

MATERIAL Particles are point masses while aggregates are rigid bodies. Distance between particles in an aggregate is described by their sintering level. Particle composition is stored for each particle.

~~~~BOUNDARY Periodic boundaries, initial gas phase composition, CONDITIONS temperature and pressure evolution in time.~~~~

~~~~ADDITIONAL User defined time dependent gas phase composition. SOLVER PARAMETERS~~~~

~~~~3.6 TIME STEP Nanoseconds.~~~~

~~~~N. Gronbech-Jensen and O. Farago. A simple and effective verlet-type 3.8 PUBLICATION algorithm for simulating langevin dynamics. Molecular Physics, 11(8):983–991, 2013.~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Finite volume. 4.1 OUTPUT IS Precursor vapour consumption for continuum model coupling. CALCULATED FOR~~~~

~~~~METHODOLOGIES Simple integration on the particle set or particle counting. 4.2 Aggregates properties (e.g. fractal dimension, mass, diameter) obtained by looping on particles structures.~~~~

MARGIN OF Errors related to particle idealization (e.g. spherical shape), chemical ERROR reduction, interparticle forces, sintering mechanism and limited number of particles in the mesoscopic ensemble. 4.3 Using temperature and composition data from a continuum fluid model streamline means that nanoparticle diffusion between continuum regions is neglected. Accuracy

~~~~293~~~~

~~~~Model 4: Fluid mechanics, Heat-Flow, Chemistry Reaction Model, Electromagnetism (Continuum)~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Flow characteristics (e.g. velocity, temperature, species 1.1 USER CASE TO BE concentration) in a gas phase reactor (plasma, flame and hot wall SIMULATED reactors).~~~~

~~~~Gaseous, liquid or solid precursors. 1.2 MATERIAL Si, ZnO, Al2O3, Pt nanoparticle synthesis in Ar/H2/N2/O2 atmospheres.~~~~

~~~~1.2 GEOMETRY Chemical synthesis reactor. Centimetres.~~~~

~~~~1.3 TIME LAPSE Seconds.~~~~

~~~~MANUFACTURING PROCESS OR IN- 1.4 Gas phase condensation synthesis reactor: plasma, flame or hot-wall. SERVICE CONDITIONS~~~~

Colombo, V., Deschenaux, C., Ghedini, E., Gherardi, M., Jaeggi, C., Leparoux, M., Mani, V., Sanibondi, P. Fluid-dynamic characterization 1.6 PUBLICATION of a radio-frequency induction thermal plasma system for nanoparticle synthesis (2012) Plasma Sources Science and Technology, 21 (4), art. no. 045010.

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE 2.0 Fluid Dynamics AND NAME~~~~

~~~~MODEL Finite volumes. 2.1 ENTITY~~~~

EQUATIO 1. Generic transport conservation equation for: 휕휌휙 N + ∇ ∙ (휌푢⃗ 휙) = ∇ ∙ 푞⃗⃗⃗⃗ + 푆 휕푡 휙 휙 a. mass (species) b. momentum (Navier-Stokes) c. energy 2. Turbulence models (Reynolds Averaged Navier Stokes MODEL and/or LES) PHYSICS/ 3. Electromagnetic field equations for plasmas (Maxwell’s 2.2 CHEMISTRY equation under usual Magneto Hydro Dynamics EQUATION simplifications) PHYSICAL 1. The general conservation equation is written for:

~~~~QUANTITI a.  = Yi : qidiffusion flux for species i, Si ES source terms due to chemical reactions and nanoparticle nucleation (from the mesoscale model).~~~~

~~~~b.  = u : qumomentum flux, Su Lorentz forces (plasma)~~~~

~~~~294~~~~

c.  = h : qhheat flux, Sh source terms due to chemical reactions or Joule heating (plasma) with density  and velocity u. 2. Turbulence parameters (e.g. turbulence kinetic energy k) 3. Vector A and scalar V potential (plasma)

~~~~EQUATIO 1. Constitutive equations for:~~~~

~~~~N a. qi using multicomponent (or binary) diffusion, Si from Arrhenius based equations for reaction rates.~~~~

~~~~b. qu assuming Newtonian linear relationship between stress and deformation tensors (Navier-Stokes equation)~~~~

~~~~c. qh heat flux in a multispecies environment. 2. Turbulence:~~~~

~~~~a. for Standard k- RANS and standard closure coefficients MATERIALS b. subgrid scale model for LES 2.3 RELATION 1 3. Simplified Ohm’s law for current density j (thermal plasmas): j = E~~~~

PHYSICAL 1. Descriptors for each equation are: QUANTITIES a. Pre-exponential factor and activation energy for rate / constant calculation for each reaction of the reduced chemical kinetic model and species diffusion DESCRIPTOR coefficients (including thermal diffusion) S b. Fluid transport properties (e.g. viscosity) c. Fluid transport and thermodynamic properties (e.g. thermal conductivity, specific heat). 2. Closure coefficients from the specific model used (e.g. k- e, RSM, Smagorinsky) 3. electrical conductivity and E electric field (plasma)

PUBLICATION Murphy, A.B., Boulos, M.I., Colombo, V., Fauchais, P., Ghedini, E., Gleizes, A., Mostaghimi, J., Proulx, P., Schram, D.C. Advanced thermal plasma 2.5 modelling (2008) High Temperature Material Processes, 12 (3-4), pp. 255- 336

~~~~3 COMPUTATIONAL MODELLING METADATA~~~~

~~~~Finite volumes. NUMERICAL 3.1 Equations are usually solved with loose coupling (segregated solvers) SOLVER due to the high non-linearity of the coefficients and source terms.~~~~

~~~~3.2 SOFTWARE TOOL ANSYS Fluent (commercial), OpenFOAM (open source)~~~~

~~~~-5 -4 3.3 TIME STEP Steady state, or time dependent for LES simulations (10 – 10 ) s~~~~

~~~~COMPUTATIONAL PHYSICS Finite volume discretization of the transport equation. 3.4 REPRESENTATION EQUATION Vector and scalar potential form of the Maxwell’s~~~~

~~~~295~~~~

~~~~equation discretized in a finite volume framework.~~~~

MATERIAL Reaction rates as source terms for species equations. RELATIONS Stress tensor discretization in the Navier-Stokes equation Heat flux constitutive equation used for finite volume surface flux calculation Turbulence transport equations (e.g. k-e) for RANS or subgrid scale models for LES.

~~~~MATERIAL Species densities control volume-wise.~~~~

~~~~BOUNDARY Gas/precursors feeding rates and operating pressure. CONDITIONS Generator power (for plasma sources)~~~~

~~~~ADDITIONAL N.A. SOLVER PARAMETERS~~~~

~~~~3.5 PUBLICATION N.A.~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Flow fields, temperature fields, species concentrations calculated by 4.1 OUTPUT IS the model for the larger (macroscopic) finite volumes (gas phase). CALCULATED FOR~~~~

~~~~METHODOLOGIES Position in time (i.e. streamline), temperature in time, species 4.2 concentration in time calculated for single finite volume.~~~~

MARGIN OF ERROR For plasma simulations, the margin of error in the predicted temperature field is expected to stay below 10% (SIMBA project 4.3 results). Errors related to the limited amount of streamline used for mesoscopic models, chemical reduction, turbulence models.

~~~~296~~~~

~~~~NanoPack~~~~

~~~~NANOPACK (720815)~~~~

~~~~Summary of the project~~~~

NanoPack will develop and demonstrate a solution for extending food shelf life by using novel antimicrobial surfaces, applied in active food packaging products. It will develop, scale up and run pilot lines in operational industrial environments to manufacture antimicrobial polymer films that are commercially feasible and accepted by retailers and consumers alike.

~~~~Migration into food~~~~

Project Acronym and Number: NANOPACK 720815 Project Title: Pilot line production of functional polymer nanocomposites from natural halloysite nanotubes: demonstrating controlled release of active antimicrobials in food packaging applications. Start and End Dates: from 01/01/2017 till 31/12/2019 EU Contribution: 7,665,218.00 € Coordinator: Ester Segal, [email protected] Modeller(s): Angela Stoermer, [email protected]

~~~~297~~~~

~~~~NanoPack~~~~

~~~~MODA Release of essential oils to food, diffusion model NanoPack~~~~

OVERVIEW of the SIMULATION The end user would like to simulate how antimicrobial agents (essential oils) are incorporated in a polymer nano-composites (nanotubes in polyolefin). Initially, before extrusion, the essential oils are located in the nanotubes and 1 USER CASE will be released into the polymer and diffuse to the food contact surface. The release of the antimicrobial agents to food or the surface of the food shall be described during manufacturing and storage and after contact with food. Diffusion model to predict migration of organic molecules into food (and/or polymer layers): Mass transport continuum MODEL 1 model, conservation of mass, Fick’s 2nd law (use of existing CHAIN OF multilayer diffusion models and related software) 2 MODELS

~~~~… …~~~~

Roduit, B., C. H. Borgeat, S. Cavin, C. Fragniere and V. Dudler (2005). PUBLICATION "Application of Finite Element Analysis (FEA) for the simulation of release of 3 ON THIS ONE additives from multilayer polymeric packaging structures." Food Additives & SIMULATION Contaminants 22(10): 945-955.

The modelling tool (model 1) is available as commercial software (AKTS-SML, AKTS AG, 3960 Siders, Switzerland or alternatively MigratestExp, FABES ACCESS 4 GmbH, München, Germany) and as freeware (Safe Food Packaging Portal CONDITIONS http://sfpp3.agroparistech.fr/). The input parameters (diffusion coefficients, partition coefficients) shall be published. Existing diffusion/migration modelling (or better simulation) software is used in which PE/MR and the numerical algorithm are already implemented. For known diffusion and partition coefficients for a given polymer-food system for a defined substance (e.g. from literature), migration can directly be calculated for any time span. All necessary information to solve the Fickian 2nd law by the numerical algorithm is already included with the initial and boundary WORKFLO conditions in the software. 5 W AND ITS RATIONALE For a new material or migrating substance the software can be used to fit the output curve to experimental data by variation of the diffusion and partition coefficients. From the best fit, both parameters for a specific substance in the investigated polymer at a given temperature are obtained. The curve fit procedure is one of several options to experimentally derive diffusion and partition coefficients. Independently how they are derived, they can be used as input parameters for the simulation.

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Polymer (case: polyolefin films or articles) in which a nanomaterial containing a low-molecular weight organic substance (antimicrobial ASPECT OF THE agent = essential oil) is dispersed. The essential oil is initially USER CASE TO 1.1 encapsulated within the nanomaterial and will be released to the BE SIMULATED polymer during extrusion and storage. After filling with food or food simulant, the essential oil diffuses to the food contact surface along the concentration gradient and migrates into food. The model assumes in the first instance homogeneous distribution of the essential oil in the

~~~~298~~~~

~~~~NanoPack~~~~

~~~~polymer. The case described is the release of essential oil into food/food simulant during filling and storage of the food.~~~~

1.2 MATERIAL Polyolefin with Halloysite nanotubes (HNT) any 3D geometry (flat film, pouch, container, etc. will be transposed to 1.3 GEOMETRY a (less complex) 1-dimensional system with the flux of substances only in one direction along the concentration gradient to the food Actual case: storage of food package (days – months) Generally depending on the step of manufacture or storage: 1.4 TIME LAPSE manufacturing nanocomposite in extruder (seconds to minutes), storage of films (hours-months),

~~~~MANUFACTURIN transfer processes at filling and storage of the polymer with food: filling G PROCESS OR and storage at room temperature 1.5 IN-SERVICE CONDITIONS~~~~

~~~~PUBLICATION 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Diffusion in solid polymers: continuum in finite volumes (polymer or food) 2.0 AND NAME and migrating substances on mesoscopic scale~~~~

~~~~MODEL finite volumes 2.1 ENTITY~~~~

휕푐 휕2푐 휕2푐 휕2푐 Equation Fick 2nd law: 푘 = 퐷 ( 푘 + 푘 + 푘) 휕푡 푘 휕푥2 휕푦2 휕푧2 The three dimensional relation is simplified to the flux along the concentration gradient (1 dimensional relation) 휕푐 휕2푐 푘 = 퐷 푘 휕푡 푘 휕푥2 Physical  t time of migration (diffusion), quantities MODEL  2 ≤ k ≤ n index of the medium (layer: polymer, PHYSICS/ food), 2.2 CHEMISTRY  c k local concentration (in mg/l oder µg/l) EQUATION Dk local diffusion coefficient of the substance in the PE medium k  x, y, z 3D-coordinates The (numerical) solution of the differential equation furthermore needs the quantities:  Initial concentrations in the layers (in mg/l oder µg/l)  partition coefficients K between the layers,  density of layers,  thickness of layers (distance) Relation 1. user case input, cooefficients are deduced from experimental data. 2. MATERIALS 2.3 RELATIONS Physical Partition coefficients between each layers describing quantities/ the equilibrium concentrations descriptors for each MR

~~~~SIMULATED 2.4 INPUT~~~~

~~~~299~~~~

~~~~NanoPack~~~~

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS Finite difference method see V. Tosa and P. Mercea (2008) and Tosa et NUMERICAL 3.1 al. (2008) for Migratest Exp software and finite element analysis see SOLVER Roduit et al. (2005) for AKTS-SML software Existing commercial simulation software is used: AKTS-SML, AKTS AG, 3960 Siders, Switzerland (http://www.akts.com/sml-diffusion- SOFTWARE 3.2 migration-multilayer-packaging/download-diffusion-prediction- TOOL software.html) and/or MigratestExp, FABES GmbH, München, Germany (https://www.fabes-online.de/de/software/migratest-exp/)

~~~~3.3 TIME STEP 5 s (10 days simulation)~~~~

PHYSICS EQUATION, use of existing software MATERIAL input parameter: Concentration of organic substance COMPUTATIONAL RELATIONS, (e.g. antimicrobial essential oil (EO) or other substance) 3.4 REPRESENTATION MATERIAL in the polymer at a given moment, including initial content; diffusion coefficient of organic substance in each layer (polymer layers, food); partition coefficients between the layers, thickness of layers; time lapsed • The system packaging/food is isolated: no mass transfer to the environment. • Total mass of the migrant in the system packaging food remains constant (no losses, no chemical reactions) COMPUTATIONA 3.5 L BOUNDARY • Initial homogeneous distribution of substance in the polymer layer CONDITIONS • No boundary resistance at the interface polymer/food • The diffusion coefficient in each layer remains constant at constant temperature • Partition coefficients remain constant at constant temperature

~~~~ADDITIONAL  3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The output of the simulation is time dependent release curves for the OUTPUT migrating substance into the food. Post processing 1: Comparison of the experimental values (migration kinetics) with the simulated curve. Curve fitting by variation of input 4.1 parameters (diffusion and partition coefficients) using the software above.  experimentally obtained diffusion and partition coefficients Post processing 2: Simulated release of essential oils will be fed into existing models for antimicrobial activity

~~~~4.2 METHODOLOGIES~~~~

~~~~MARGIN OF 4.3 ERROR~~~~

~~~~300~~~~

~~~~NEOHIRE (720838)~~~~

~~~~Summary of the project~~~~

NEOHIRE main objective is to reduce the use rare earth elements and critical raw materials like Co and Ga in permanent magnets present in wind turbine generators. The project will develop of a new concept of bonded NdFeB magnets able to substitute the present state-of-the-art sintered magnets for WT, and a new recycling technique for wastes.

~~~~Permanent Magnets for Wind Energy Application~~~~

~~~~continue~~~~

~~~~301~~~~

Project Acronym and Number: NEOHIRE 720838 Project Title: NEOdymium-Iron-Boron base materials, fabrication techniques and recycling solutions to HIghly REduce the consumption of Rare Earths in Permanent Magnets for Wind Energy Application Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution: 4,443,888.75 € Coordinator: JOSE MANUEL MARTIN, [email protected] Modeller(s): Alicia Rodríguez, [email protected] Botja Prieto, [email protected] Klaus Lipp, [email protected] Luis de Prada Martin, [email protected] Rainer Wagener, [email protected] Boris Saje, [email protected]

~~~~302~~~~

~~~~MODA Permanent Magnets for Wind Energy Application NEOHIRE~~~~

OVERVIEW of the simulation NEOHIRE main objective is to reduce the use rare earth elements in the permanent magnets (PM) present in wind turbine generators (WTG). For this purpose, new PM geometries and WTG designs, as well as new 1 USER CASE anisotropic aligning tools (AT) for processing and flow of the thermoplast based anisotropic NdFeB HDDR powder composites (MF) will be modelled and simulated. Continuum model MODEL 1 - Solid mechanics applied to stress distribution of permanent magnet fatigue specimens Continuum model MODEL 2 - Electromagnetic model applied to WTG active parts for electromagnetic predesign Continuum model MODEL 3 - Electromagnetic model for detailed simulation of WTG Continuum model MODEL 4 CHAIN OF - Structural mechanics model of the WTG 2 MODELS Continuum model MODEL 5 - Heat flow model for the analysis of the WTG Continuum model MODEL 6 - Solid mechanics applied to stress distribution of PM in WTG Continuum model (Electromagnetism, magnetics) MODEL 7 - Model for the design of the active parts of the moulding tools for aligning the magnetic material Continuum model (Continuum mechanics, Fluid mechanics) MODEL 8 Non Newtonian model of material flow

~~~~PUBLICATION ON THIS 3 N/A ONE SIMULATION~~~~

ACCESS All models will be treated as “confidential” 4 CONDITIONS The software-tools for the simulations are all commercial Different models are applied to different parts of the system. Interoperability is 5 WORKFLOW shown in the picture

~~~~303~~~~

~~~~MODEL 1: Solid mechanics applied to stress distribution of permanent magnet fatigue specimens~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Analysis of the strains/stresses, stress gradients, highly stressed ASPECT OF THE volume of particular specimens in order to assess the correlation USER CASE TO BE 1.1 between local existing stresses and endurable stresses of the SIMULATED experimental investigation by means of linear elastic calculations (for fatigue assessment)

~~~~1.2 MATERIAL Magnetic Materials to be selected in WP1~~~~

~~~~1.3 GEOMETRY Unnotched and notched small scale specimens to be defined in WP2~~~~

~~~~1.4 TIME LAPSE To be defined in the project~~~~

MANUFACTURING The highly stressed areas of specimen manufactured in different PROCESS OR IN- material states respectively manufacturing routes will be analysed 1.5 SERVICE under axial and probably bending loading according to procedure of CONDITIONS the experimental material characterization (fatigue).

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Solid mechanics: Static strain/stress analysis, linear-elastic calculation 2.0 AND NAME~~~~

~~~~MODEL Finite-Element- 2.1 ENTITY Equation F = k · s MODEL PHYSICS/ Physical displacement, stiffness, force 2.2 CHEMISTRY quantities EQUATION PE~~~~

~~~~Relation Linear elasticity: [] = [E] · []~~~~

~~~~MATERIALS Physical strain/stress, elasticity 2.3 RELATIONS quantities/ descriptors for each MR~~~~

~~~~SIMULATED “N/A (input data obtained via experiments in WP2)”. 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~3.1 NUMERICAL FEM, linear-elastic calculations~~~~

~~~~304~~~~

~~~~SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Abaqus~~~~

~~~~3.3 TIME STEP To be defined~~~~

~~~~PHYSICS EQUATION, COMPUTATIONAL MATERIAL 3.4 REPRESENTATION RELATIONS,~~~~

~~~~MATERIAL~~~~

~~~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Correlation between local strain/stress and endurable stress to be 4.1 OUTPUT used in Model 6 Selection of optimum magnetic material (at least for fatigue) for the PM design in the WTG in Models 2-8.

~~~~4.2 METHODOLOGIES Splining through raw output data~~~~

~~~~MARGIN OF 4.3 Depending on scatter of material and fatigue investigated ERROR~~~~

~~~~305~~~~

~~~~MODEL 2: Electromagnetic model applied to WTG active parts for electromagnetic predesign~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE The user wants to define different PM geometries, together with the USER CASE TO BE active parts (stator and rotor) of a WTG, in order to optimize the 1.1 SIMULATED performance of such a generator in terms of power per unit weight of CRM. PM materials to be selected in WP2. 1.2 MATERIAL Industrial-grade non-oriented electrical steel. Industrial-grade copper conductors.

~~~~1.3 GEOMETRY Geometry to be defined in WP3.~~~~

~~~~1.4 TIME LAPSE To be defined in the project.~~~~

~~~~MANUFACTURING Requirements of WTG specified PROCESS OR IN- 1.5 Electromagnetic boundary conditions (isolating, continuity, etc). SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum electromagnetic model 2.0 AND NAME~~~~

MODEL Finite volumes 2.1 ENTITY Equation Maxwell’s Equations simplified for low frequency fields (displacement current term ignored) with no consideration of the electric polarization phenomenon (Gauss’s law ignored): MODEL PHYSICS/ 2.2 CHEMISTRY

~~~~EQUATION PE Physical Electric field (E). quantities Current density (J). Magnetic flux density (B). Magnetic field intensity (H).~~~~

Relation Magnetic relations: biunivocal B-H relation for PMs (linear, isotropic), copper (linear, isotropic) and electrical steel (spline curve fitted from manufacturer data, anisotropic). Minor hysteresis loops ignored for MATERIALS PMs. Hysteresis loops and induced eddy-currents ignored in the field solution for the electrical steel 2.3 RELATIONS (added later as a post-processing result by considering

~~~~power loss relationships; see below).~~~~

~~~~Electrical relations: Ohm’s law for PMs and copper:~~~~

~~~~306~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

Thermal relations: PM B-H relation dependent on magnet temperature (magnet remanence and intrinsic magnetic field coercitivity dependent on temperature, isotropic) (obtained via experiments in WP2). PM and copper electrical conductivities dependent on temperature (obtained via experiments and manufacturer data in WP2, isotropic).

Physical Electric field (E). quantities/ Current density (J). descriptors Magnetic flux density (B). for each Magnetic field intensity (H). MR Electrical conductivity (σ). Frequency of the main harmonic of the flux density waveform (f) Electrical steel magnetic loss density (kW/kg from manufacturer data).

~~~~SIMULATED Optimum magnetic material (at least for fatigue) postprocessed after 2.4 INPUT Model 1.~~~~

. 3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS PE (Simplified Maxwell’s Equations) (see 2.2) further simplified in order to describe the magnetic field solution in terms of lumped parameters for the different WTG parts (rotor and stator). Use of the concepts of Magnetomotive Force, Magnetic Reluctance and Magnetic NUMERICAL Flux (electrical circuit analogy). Direct algebraic solution of the 3.1 SOLVER magnetic field by considering such a lumped parameter approach. Variable separation method applied to the underlying Poisson Problem (Simplified Maxwell’s Equations) to certain WTG parts (stator slots and air-gap). Field solution given in terms of sum of harmonic functions.

~~~~3.2 SOFTWARE TOOL Code developed by CEIT in MathWorks MATLAB language.~~~~

~~~~3.3 TIME STEP According to WTG design requirements.~~~~

~~~~PHYSICS EQUATION, COMPUTATIONAL 3.4 MATERIAL REPRESENTATION RELATIONS, MATERIAL~~~~

~~~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL SOLVER N/A 3.6 PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Raw output: OUTPUT Electromagnetic field solution (a.k.a. magnetic flux distribution): 4.1 knowledge of the local values of the following physical quantities: electric field (E), current density (J), magnetic flux density (B), magnetic field intensity (H).

~~~~307~~~~

~~~~Electromagnetic torque and output voltages and currents generated by the WTG. Power losses of the WTG. WTG efficiency. WTG power per unit weight of CRM.~~~~

~~~~Optimised PM and active parts to be used in Models 3-8.~~~~

~~~~METHODOLOGIES Computed from classical electrical and magnetic circuit concepts (flux linkage, electrical voltage drop, electromagnetic torque, etc.).~~~~

~~~~Hysteresis and induced eddy-current power losses in the electrical 4.2 steel laminations dependent on magnetic flux density waveform (Generalized Bertotti loss model from manufacturer data):~~~~

~~~~MARGIN OF 4.3 To be defined in the project ERROR~~~~

~~~~MODEL 3: Electromagnetic model for detailed simulation of WTG~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE The user wants to analyse the electromagnetic behaviour of the USER CASE TO BE different PM shapes selected in WP2 , when they are working inside 1.1 SIMULATED of a WTG~~~~

~~~~1.2 MATERIAL Materials selected in WP1~~~~

~~~~1.3 GEOMETRY Geometry selected in Task 3.1 of WP3~~~~

~~~~1.4 TIME LAPSE To be defined in the project.~~~~

~~~~MANUFACTURING Requirements of WTG specified PROCESS OR IN- 1.5 Electromagnetic boundary conditions (isolating, continuity, etc) SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum electromagnetic model 2.0 AND NAME~~~~

~~~~2.1 MODEL ENTITY Finite elements~~~~

~~~~MODEL Equation Maxwell’s Equations PHYSICS/ 2.2 CHEMISTRY EQUATION PE~~~~

~~~~308~~~~

Physical Electric field (E) quantities Electric displacement field (D) Current density (J) Magnetic flux density (B) Magnetic field intensity (H) Relation There are no further materials relations requiring additional equations

~~~~The electrical relation is described by:~~~~

~~~~The magnetic relation is described by:~~~~

Thermal relations: 1) there is a temperature MATERIALS dependence of nonlinear B-H curves for the permanent 2.3 RELATIONS magnets, and 2) the electrical conductivity of the materials is depending on temperature; these relationships are obtained experimentally in WP2.

~~Physical Electrical conductivity: (σ) quantities Permeability (μ) / Electric field (E) descriptor Electric displacement field (D) s for each Magnetic flux density (B) Magnetic field intensity (H) MR~~

~~~~SIMULATED N/A 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL PE 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL COMSOL~~~~

~~~~3.3 TIME STEP According the requirements~~~~

~~~~PHYSICS EQUATION, Written up for finite elements COMPUTATIONAL MATERIAL 3.4 REPRESENTATION RELATIONS, MATERIAL~~~~

~~~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Pure internal numerical solver details, If applicable, like 3.6 SOLVER  Convergence control algorithm PARAMETERS  Time incrementation scheme~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Electromagnetic assessment of the PM selected in WP3 working 4.1 OUTPUT inside the WTG.~~~~

~~~~4.2 METHODOLOGIES Computed from classical electrical and magnetic circuit concepts.~~~~

~~~~4.3 MARGIN OF ERROR To be defined in the project~~~~

~~~~309~~~~

~~~~MODEL 4: Structural mechanics model of WTG critical components~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED The user wants to analyse the status of the stress and strain field in the critical components (such as Axle or bearings) taking into account the ASPECT OF THE geometrical modifications and the most critical load cases. 1.1 USER CASE TO BE Therefore, a frequency response analysis will be carried out in order to SIMULATED know the natural frequency of system and allow us to avoid resonance problems.

~~~~1.2 MATERIAL Materials selected in WP1~~~~

~~~~1.3 GEOMETRY Geometry selected in Task 3.1 of WP3~~~~

~~Studying the information collected through one year of WTG use 1.4 TIME LAPSE (regarding loads, momentums), the load cases analyzed will be the most frequent case (normal use) and some overload cases.~~

~~~~MANUFACTURING In case of frequency study: imposed frequencies PROCESS OR IN- 1.5 In case of stress-strain study, external forces SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Solid mechanics: Static stress analysis procedures and Natural frequency 2.0 AND NAME extraction~~~~

MODEL Finite element 2.1 ENTITY Equation The static stress analysis applied, will find an approximate (finite element) solution for the displacements, deformations, stresses, forces. The exact solution of such problem requires that both force and moment be maintained in equilibrium over a finite number of divisions of the volume of the body. The exact equilibrium statement is written in the form of virtual work statement. Generally, We will use Newton´s method as a numerical technique for solving the nonlinear equilibrium equations, MODEL although modified Newton or quasi-Newton methods can PHYSICS/ be used. 2.2 CHEMISTRY The model of plasticity used (incremental plasticity theory) EQUATION is based on a basic fundamental postulate. The inelastic PE response models the elastic and inelastic responses are distinguished by separation the deformation into recoverable (elastic) and nonrecoverable (inelastic) parts. A more general assumption the total deformation F F=Fel.Fpl is made up of inelastic deformation followed by purely deformation Physical Time, displacement, stress, strain, plastic strain, natural quantities frequency, accelerations, velocity

~~~~Relation Force, Energies, Frequencies, Stress-strain field 2.3 MATERIALS~~~~

~~~~310~~~~

~~~~RELATIONS Physical Force fields in the components quantities/ Energies field descriptors Frequencies field in the system for each Stress-strain field MR~~~~

~~~~SIMULATED Input parameters regarding the maximum torque/load in normal working 2.4 INPUT and overload loadcase, the frequency of the stator-rotor subsystem.~~~~

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS The finite element models are usually nonlinear and can involve from a few NUMERICAL 3.1 to thousands of variables. In terms of these variables the equilibrium SOLVER equations obtained by discretizing the virtual work equation

~~~~SOFTWARE Abaqus 6.14 3.2 TOOL~~~~

~~~~3.3 TIME STEP Depends on the type of analysis. It will be defined in the project~~~~

PHYSICS FN(uM)=0 where FN is the force component conjugate to COMPUTATIO EQUATION, the NTH variable in the problem and uM is the value of the NAL 3.4 MATERIAL MTH variable. The basic problem is to solve the equation REPRESENTAT RELATIONS, above for the uM throughout the history of interest ION MATERIAL

~~~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Pure internal numerical solver details, If applicable, like 3.6 SOLVER  Convergence control algorithm PARAMETERS  Time incrementation scheme~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The raw outputs are: OUTPUT 1. All physical displacement components, including rotations at nodes with rotational degrees of freedom 2. Field of stress, strain, plastic strain velocities and frequencies of 4.1 the nodes/integration points within the finite element, which is part of the component 3. This is post processed into values for the rest of the components. Based on this a selection of the optimal component geometry is chosen

~~~~METHODOLOGIES The results fields are calculated in the integration points or nodes and 4.2 then translated to the rest of the component selection criteria~~~~

~~~~MARGIN OF 4.3 Typically less than 5% ERROR~~~~

~~~~311~~~~

~~~~MODEL 5: Heat flow model applied to WTG~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Heat transfer problems involving conduction, forced convection, and ASPECT OF THE boundary radiation can be analyzed. In these analyses the temperature 1.1 USER CASE TO field is calculated and the stress/deformation state is evaluated in the BE SIMULATED bodies being studied taking into account the temperature change

~~~~1.2 MATERIAL Materials selected~~~~

1.3 GEOMETRY Geometry selected i Studying the information collected through one year of WTG use (regarding temperatures, loads and momentums), the load cases 1.4 TIME LAPSE analyzed will be the most frequent case (normal use) and some overload cases.

~~~~MANUFACTURIN Input parameters regarding the field of temperatures that implies G PROCESS OR thermal dilatations in normal working and overload loadcases. 1.5 IN-SERVICE CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL Heat transfer equation 2.0 TYPE AND NAME~~~~

MODEL Finite element 2.1 ENTITY Equation  qx qy qz  T       Q  c MODEL x y z t   PHYSICS/ 2.2 CHEMISTRY Physical Integration point temperatures, magnitude and components of EQUATION quantities the heat flux vector, current values of uniform distributed heat PE fluxes, Nodal point temperatures

Relation Current values of uniform distributed heat diffusivity Magnitude of the heat diffusivity which PE it completes Temperature degree of freedom n at a node MATERIALS 2.3 Physical Temperature field RELATIONS quantities/ Heat fluxes field in the system descriptors for each MR

~~~~SIMULATED 2.4 INPUT~~~~

~~~~312~~~~

3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS The finite element models are usually nonlinear and can involve from a NUMERICAL 3.1 few to thousands of variables. In terms of these variables the equilibrium SOLVER equations obtained by discretizing the virtual work equation

~~~~3.2 SOFTWARE TOOL Abaqus 6.14, LS dyna~~~~

~~~~3.3 TIME STEP If applicable~~~~

PHYSICS The heat transfer rate is expressed by: EQUATION, Q=-kA(ΔT/Δx) MATERIAL COMPUTATIONAL The convection/diffusion process uses the trapezoidal rule 3.4 RELATIONS, REPRESENTATION for time integration. They include numerical diffusion MATERIAL control (the “upwinding” Petrov-Galerkin method) and, optionally, numerical dispersion control Real boundary conditions, trying to be as close as possible to the reality. COMPUTATIONAL Boundary conditions are very often nonlinear, film coefficients can be 3.5 BOUNDARY functions of surface temperature, the nonlinearities are often mild and CONDITIONS cause little difficulty Pure internal numerical solver details, If applicable, like  Convergence control algorithm ADDITIONAL  Time incrementation scheme 3.6 SOLVER  The software automatically determines a suitable increment size PARAMETERS for each increment of the step.  Regarding the number of DOF we would suggest an initial “time” increment and define a “time” period for the step

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Nodal point temperatures in the whole WTG (check for temperature raise 4.1 OUTPUT in WTG critical components, e.g: PMs, windings, bearings, etc.).~~~~

~~~~METHODOLOGIES The results fields are calculated in the integration points or nodes and 4.2 then translated to the rest of the component~~~~

~~~~4.3 MARGIN OF ERROR Typically less than 2%~~~~

~~~~313~~~~

~~~~MODEL 6: Solid mechanics applied to stress distribution of PM in WTG~~~~

ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED 1 Analysis of the strains/stresses, stress gradients, highly stressed volume ASPECT OF THE of the design of the PM considered for the WTG by means of linear elastic 1.1 USER CASE TO BE calculations and fatigue assessment with regard to lifetime respectively SIMULATED allowable stresses based on the approach of Model 1

~~~~1.2 MATERIAL Finally selected magnetic material~~~~

~~~~1.3 GEOMETRY Proposed PM geometry to be used in the WTG~~~~

~~~~1.4 TIME LAPSE time independent~~~~

MANUFACTURING Assessment of the stress/strain distribution and the highly stressed areas PROCESS OR IN- of prototypes under service load conditions in order to guarantee a reliable 1.5 SERVICE service with regard to fatigue CONDITIONS

~~~~PUBLICATION 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Static strain/stress analysis, linear-elastic calculation 2.0 AND NAME~~~~

~~~~MODEL Finite-Element-Modelling 2.1 ENTITY Equation F = k · s MODEL PHYSICS/ Physical displacement, stiffness, force 2.2 CHEMISTRY quantities EQUATION PE~~~~

~~~~Relation Linear elasticity: [] = [E] · []~~~~

~~~~MATERIALS Physical strain/stress, elasticity 2.3 RELATIONS quantities/ descriptors for each MR~~~~

~~~~SIMULATED Correlation between local strain/stress and endurable stress, output of Model INPUT 2, 2.4 Calculated structural behaviour of the WTG especially of the PM component, Model 4~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~3.1 NUMERICAL FEM, linear-elastic calculations~~~~

~~~~314~~~~

~~~~SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Abaqus~~~~

~~~~3.3 TIME STEP time independent~~~~

~~~~PHYSICS [] = [E] · [] EQUATI Young’s modulus, Poisson’s ratio ON, MATERI COMPUTATIONAL 3.4 AL REPRESENTATION RELATIO NS, MATERI AL~~~~

~~~~COMPUTATIONAL 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Fatigue assessment respectively lifetime estimation 4.1 OUTPUT~~~~

~~~~4.2 METHODOLOGIES Local fatigue concept~~~~

MARGIN OF ERROR Depending on input calculations, scatter of material and fatigue properties 4.3 Estimation of the deviation of the numerical assessment by experimental validation of the PM prototype by means of experimental investigation (fatigue)

~~~~315~~~~

~~~~NEWSOL (720985)~~~~

~~~~Summary of the project~~~~

The project will implement an innovative thermal energy storage design based on the combination of new functional and advanced materials: solid (concrete and filler) and liquid (salts) sensible heat storage media, latent heat storage media and heat insulating materials. All these components will be used to build two innovative system architectures: single concrete thermocline molten salt tank and concrete module.

~~~~Thermal energy storage~~~~

Project Acronym and Number: NEWSOL 720985 Project Title: New StOrage Latent and sensible concept for high efficient CSP Plants Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution4,981,424.27 € Coordinator: Luís Filipe Lopes Guerreiro , [email protected] Modeller(s): Luís Filipe Lopes Guerreiro , [email protected] Pedro Azevedo, [email protected]

~~~~316~~~~

~~~~MODA Thermal energy storage NewSOL~~~~

~~~~OVERVIEW of the simulation~~~~

In order to define the thermal storage capacity of the tan, the behaviour of a thermocline Thermal Energy Storage (TES) tank is to be described. Consortium will define the thermal storage capacity of the tank. 3 different height/diameter ratios will be calculated through. The stacked zones will be defined with regard to number and composition. Inlet temperature will be 1 USER CASE provided by the coordinator. The model will be prepared to work with those conditions. The results will allow further developments and adaptions. Several inlet and outlet mass flows (charge and discharged operations, respectively) will be screened in order to decide the best available conditions to use in the 2D model (commercial code.

~~~~1D energy conservation model (tank axial dimension) to MODEL 1 calculate the temperature along the tank height CHAIN OF 2 MODELS MODEL 2 2D CFD turbulence model~~~~

~~~~… …~~~~

~~~~PUBLICATION 3 ON THIS ONE Not available SIMULATION~~~~

~~~~ACCESS 4 To be defined CONDITIONS~~~~

The thermal behaviour of the tank will be assessed in 2D model of a full CFD flow on a representation of the storage tank. This will be accomplished using a commercial software package. To save effort, a first screening is to be done for predefined in and outlet flows on a simplified (1D) representation of the tank along one or more charging/discharging cycles. For these situations the temperature will be WORKFLOW calculated from which the tank performance and thermocline degradation 5 AND ITS are to be calculated. Then the details of selected cases will be simulated with RATIONALE a 2D CFD model. Considering that only fluid flow thermal phenomena occurring inside the tank are addressed, the CFD approach alone is considered to be able to provide the necessary data to optimize the tank performance considering the chosen parameters (number and composition of layers, inlet and outlet mass flows and walls heat losses) and materials. Thus, heat transfer inside the filler is not in the scope of this work.

~~~~317~~~~

~~~~MODEL 1~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

A simplified (1D) representation of the tank is to be calculated for ASPECT OF THE several cases with predefined in and outlet flows. For these situations 1.1 USER CASE TO BE the temperature should be calculated from which the storage capacity SIMULATED is to be calculated.

The thermocline tank will have cement walls. The interior consists of: 1.2 MATERIAL Molten salt Hitec XL (42-43-15% Ca-K-Na) or other defined by the Consortium in D2.1. Filler preceding from S. Domingos Mines.

Thermal Energy Storage tank with cylindrical shape. Size to be defined. Picture not available. 1.3 GEOMETRY The interior of the tank will have several levels of stacked filler and molten salts (zones with no filler material and zones with filler material. Molten salts will fill the empty spaces).

1 cycle for stored energy or delivered energy (respectively, charge or discharge operation. Eventually up until 7 cycles of charge and 1.4 TIME LAPSE discharge for thermocline degradation along a full week). Model don’t foresee stagnation periods.

MANUFACTURING Several inlet and outlet flows will be screened. PROCESS OR IN- In charging operation, the boundary conditions are the inlet mass flow 1.5 SERVICE and temperature of the hot stream. In discharge operation is the inlet CONDITIONS mass flow and temperature of the cold stream.

~~~~PUBLICATION Not available.~~~~

~~~~1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE AND Heat equation Ch 4.3 of the RoMM. 2.0 NAME~~~~

~~~~2.1 MODEL ENTITY Finite differences representing finite volumes with a single dimension.~~~~

~~~~Equation Main equation: 2 MODEL PHYSICS/ ∂T ṁ ∂T ∂ T~~~~

~~~~CHEMISTRY (ρ. Cp)eff + Cpf . = keff 2 2.2 ∂t A ∂z ∂z EQUATION Physical Cp, Rho, k, ε (porosity), T, ṁ , z, t PE quantities~~~~

~~~~Relation values for the above coefficients will come from MATERIALS 2.3 literature. RELATIONS~~~~

~~~~318~~~~

~~~~Physical quantities/ Not applicable. descriptors for each MR~~~~

~~~~2.4 SIMULATED INPUT NA~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Algebraic. 3.1 SOLVER~~~~

~~~~In house algebraic solutions done in an Excel tool-like software (the 3.2 SOFTWARE TOOL interface in under development).~~~~

~~~~3.3 TIME STEP 5 seconds~~~~

~~~~PHYSICS EQUATION, 1D algebraic equations for mass and energy COMPUTATIONAL 3.4 MATERIAL RELATIONS, conservation (not including radiation). REPRESENTATION MATERIAL~~~~

~~~~COMPUTATIONAL NA 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Not applicable.. 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The output (final temperature profile) allows to determine final stored OUTPUT energy, storage efficiency and the slope of the thermocline, which in turn will allow to determine the thermocline degradation and to foresee an 4.1 operation scheme in order to improve storage efficiency and, thus, increase dispatchability. The optimal situation will be refined in model 2 CFD

METHODOLOGIES Considering the diameter of the TES tank, the amount of energy is calculated for each length step. The integral along the height of the tank is calculated. A slope is determined between the two isothermal “volumes” of the tank. The variation of the slope along time determines 4.2 the thermocline degradation. The spline of the final temperature profile is provided by an excel-like tool. Storage efficiently is calculated as the ratio between stored energy and the maximum stored energy possible.

~~~~MARGIN OF During the validation procedure of the model, an error below 5% was 4.3 ERROR found, considering cumulative error along the total height of the tank (to be confirmed).~~~~

~~~~319~~~~

~~~~MODEL 2~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

The results of model 1 will allow to define the best suitable solutions to ASPECT OF THE test in 2D model of a full CFD flow on a representation of the storage tank. 1.1 USER CASE TO The number of layers and the distribution of filler and fluid in each layer BE SIMULATED will be tested in order to calculate the storage tank performance and thermocline degradation.

Materials both for the bed and for the walls should be available for testing. The thermocline tank will have cement walls. The interior consists of 1.2 MATERIAL Molten salt Hitec XL (42-43-15% Ca-K-Na) or other defined by the Consortium in D2.1. Filler preceding from S. Domingos Mines.

Dimensions both for the bed and for the walls should be available for testing and additional solutions provided after testing. Thermal Energy Storage tank with cylindrical shape. Size provided by model 1 but possible to change depending on the results. Picture not 1.3 GEOMETRY available. The interior of the tank will have several levels of stacked filler and molten salts (zones with no filler material and zones with filler material. Molten salts will fill the empty spaces)

1 cycle for stored energy or delivered energy (respectively, charge or 1.4 TIME LAPSE discharge operation. Eventually up until 7 cycles of charge and discharge for thermocline degradation along a full week).

Model 1 will provide inlet and outlet flows to be tested. Additional tests will be made dependent upon results. MANUFACTURIN In charging operation, the boundary conditions are the inlet mass flow and G PROCESS OR 1.5 temperature of the hot stream. In discharge operation is the inlet mass IN-SERVICE flow and temperature of the cold stream. The walls will also present a CONDITIONS boundary condition. The walls dimensions and heat transfer coefficient will be represented as a heat sink in the walls.

~~~~PUBLICATION t Not available~~~~

~~~~1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Navier-Stokes equations 2.0 AND NAME~~~~

~~~~2.1 MODEL ENTITY Finite volumes in 2D~~~~

~~~~MODEL Equation Continuity equation: 2.2 PHYSICS/ CHEMISTRY EQUATION~~~~

~~~~320~~~~

~~~~PE Momentum conservation equations~~~~

~~~~with~~~~

~~~~Transport equations for the Standard k-w model. This model is envisaged in a first approach and uses the Boussinesq hypothesis for Reynolds stresses modelling.~~~~

~~~~Energy equation~~~~

~~~~Depending on the verified flow pattern, other models can be used.~~~~

Physical For the turbulence model: quantities k: turbulence kinetic energy w: specific dissipation rate; rho: density; u: velocity; x: cell length; Gk: generation of turbulence kinetic energy due to mean velocity gradients; Gw: generation of w; Yk and Yw: dissipation of k and w due to turbulence; Sk and Sw: not used (user-defined terms); x and y: directions (dimensions).

~~~~Relation values for materials coefficients will come from literature and from partners~~~~

~~~~MATERIALS Physical Not applicable 2.3 RELATIONS quantities/ descriptors for each MR~~~~

~~~~SIMULATED Please document the simulated input and with which model it is calculated. 2.4 INPUT~~~~

~~~~321~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Finite volumes solver Pressure-based 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Ansys Fluent (commercial application)~~~~

~~~~5 seconds (depending on results other values may be tested in order to 3.3 TIME STEP allow the modelling of all phenomena and decrease the computational time)~~~~

PHYSICS 1 equation for continuity EQUATION, 1 equation momentum COMPUTATIONAL MATERIAL 3.4 2 equation for viscous model (turbulence) REPRESENTATION RELATIONS, MATERIAL 1 equation for energy Radiation is not considered.

~~~~COMPUTATIONAL Inlet, outlet and walls 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Not applicable 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED The output (final temperature profile) allows to determine final stored OUTPUT energy, storage efficiency and the slope of the thermocline, which in turn will allow to determine the thermocline degradation and to foresee an operation scheme in order to improve storage efficiency and, thus, 4.1 increase dispatchability. Tank performance can decrease due to heat transfer along the walls. Flow pattern near walls will also be an output for minimization of recirculation in the flow.

METHODOLOGIES Considering the diameter of the TES tank, the amount of energy is calculated for each length step. The integral along the height of the tank is calculated. A slope is determined between the two isothermal “volumes” of the tank. The variation of the slope along time determines the thermocline degradation. The spline of the final temperature profile is provided by an excel-like 4.2 tool. Storage efficiently is calculated as the ratio between stored energy and the maximum stored energy possible. Tank performance can decrease due to heat transfer along the walls. Flow pattern near walls will also be analysed for minimization of recirculation in the flow.

~~~~MARGIN OF 4.3 Not yet available ERROR~~~~

~~~~322~~~~

~~~~NEXTOWER (721045)~~~~

~~~~Summary of the project~~~~

Atmospheric solar towers represent one of the best short-term options for large scale power generation in concentrated solar power applications. NEXTOWER focuses on manufacturing better ceramics for high temperature receivers with extended durability (20-25 years) vs. thermal fatigue and thermal shock and on improving thermal storage systems by introducing liquid lead as heat transfer fluid and new steels for coextruded-tubes and liners that are resistant to lead corrosion to enable an all new high temperature thermal storage option in the 600-900°C range.

~~~~Solar towers~~~~

~~~~continue~~~~

~~~~323~~~~

Project Acronym and Number: NEXTOWER 721045 Project Title: Advanced materials solutions for next generation high efficiency concentrated solar power (CSP) tower systems Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution: 4,999,878.88 € Coordinator: Antonio Rinaldi , [email protected] Modeller(s): Santiago Cuesta-Lopez, [email protected] Ivan Di Piazza, [email protected]

~~~~324~~~~

~~~~MODA Thermo-fluid dynamic analysis of a lead/air heat exchanger NEXTOWER~~~~

~~~~OVERVIEW of the simulation~~~~

Thermo-fluid dynamic analysis of a lead/air heat exchanger in a high temperature thermal storage unit for concentrated solar power (called 1 USER CASE SOLEAD). The purpose of the simulation is to design correctly the geometry to assess the overall system circulation in the pool and ensure sufficient thermal power charge and storage

fluid mechanics and thermal model for analysis of the MODEL 1 CHAIN OF overall circulation in in the lead pool of SOLEAD 2 MODELS Tightly coupled system of CFD and heat equations for MODEL 2 analysis of the lead/air heat exchanger alone

~~~~PUBLICATION 3 ON THIS ONE NA SIMULATION~~~~

~~~~ACCESS ANSYS available under commercial licences for parallel computing. 4 CONDITIONS RELAP owned by ENEA (a thermo-hydraulic code of nuclear derivation)~~~~

A coarse simulation will be done to determine the overall circulation of the lead pool (mass transport and natural convection) and the inlet temperature and flow rate in the heat exchanger. Then a more detailed simulation of the sole heat exchanger section will be done to refine the output and design the exchanger. Therefore: - MODEL 1 provides a modelling of the general circulation in the pool and its architecture. - MODEL 2 carries out a correct thermo-fluid dynamic design of the (primary) air/Pb Heat Exchanger alone. This point is crucial for the correct design and operations of the SOLEAD demonstrator in NEXTOWER. RELAP is a design thermohydraulic code from nuclear community and renders a general model of circulation of a WORKFLOW 5 AND ITS reactor/storage system, like the one displayed below. RATIONALE

~~~~The CFD in MODEL 2 is just for one section of the lead pool.~~~~

~~~~325~~~~

~~~~MODEL 1~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE The overall circulation in the pool will be modelled and simulated by 1.1 USER CASE TO BE the System Thermal-Hydraulic code RELAP, assessing flow rate and SIMULATED thermal stratification in the pool.

~~~~The exact design of the heat exchange (HX) and of the position of the 1.3 GEOMETRY pool internals will be fixed by a preliminary engineering design.~~~~

~~~~1.4 TIME LAPSE Stationary simulation~~~~

Adiabatic (hot air) Temperature BC MANUFACTURING (CLARIFYING NOTE: the pool is a closed hydraulic loop with fluid PROCESS OR IN- 1.5 motion ensured by natural convection with temperature gradient SERVICE coming from heat exchange in the primary and secondary heat CONDITIONS exchanger. In the experiment, the pool will be thermo-regulated with "by cables" heating system to never go below 350°C at night. The wall are considered adiabatic in the model)

~~~~PUBLICATION NA 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum models for Fluid Mechanics and energy 2.0 AND NAME~~~~

~~~~MODEL Finite volumes 2.1 ENTITY~~~~

Equation -Continuity Equation (conservation of mass) -Fluid mechanics: Momentum Equation (conservation of MODEL momentum) PHYSICS/ 2.2 CHEMISTRY -Energy Equation (conservation of energy) EQUATION Physical -Pressure PE quantities -Velocity (u) – 1D -Temperature

~~~~Relation - For the physical properties of Lead, correlations as function for the temperature are taken from the Handbook of Liquid metals (see references);~~~~

MATERIALS - The physical properties of air are fully known in 2.3 RELATIONS engineering; - Physical properties for solids are provided by Sandvik - Correlations for friction factor and heat transfer in lead are taken from the Handbook (ref. Handbook [..], NEA-OECD, Science 2015, 2015)

~~~~326~~~~

Physical Physical properties of lead and air (fluids) in 300°C- quantities/ 700°C range: descriptors Viscosity [m2/s] for each MR Density [kg/m3] Specific Heat Capacity [J/kg K] Heat conductivity [W/mK] Physical properties of solids (AISI321 SS/FeCrAl/KANTHAL): Density [kg/m3] Specific Heat Capacity [J/kg K] Heat conductivity [W/mK] Friction factor Heat transfer coefficient

~~~~SIMULATED NA 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL FINITE VOLUE ELEMENTS 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL RELAP (System Thermal Hydraulic code)~~~~

~~~~3.3 TIME STEP not applicable~~~~

PHYSICS EQUATION, Conservation laws integrated in volumes + COMPUTATIONAL MATERIAL correlations for friction factor and heat transfer 3.4 REPRESENTATION RELATIONS, *NB: friction about liquid lead with steel wall

~~~~MATERIAL~~~~

~~~~COMPUTATIONAL Adiabatic conditions of pool walls 3.5 BOUNDARY CONDITIONS~~~~

~~~~Pure internal numerical solver details, If applicable, like ADDITIONAL  Specific tolerances 3.6 SOLVER  Cut-offs, convergence criteria: residuals 10-6 PARAMETERS  Integrator options~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED A graphical post-proc through 1-D plot using the stripped data. 4.1 OUTPUT Output will be given to MODEL 2 in terms of inlet temperature and flow rate in the HX.~~~~

~~~~METHODOLOGIES cross-sectioning of simulated domain (volume averaging to get T and 4.2 v)~~~~

~~~~MARGIN OF 4.3 NA ERROR~~~~

~~~~327~~~~

~~~~MODEL 2~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Thermo Fluid Dynamic behaviour of (primary) air/Pb heat exchanger ASPECT OF THE USER alone. The conjugate heat transfer in the heat exchanger and the 1.1 CASE TO BE fluid dynamics of both air and Lead will be simulated. The purpose is SIMULATED to determine the flux of hot atmospheric air to insure heat transfer from the solar receiver to lead-storage system.

1.2 MATERIAL Pure lead/air/AISI321 SS/FeCrAl/KANTHAL© The exact design of the HX and of the position of the pool internals 1.3 GEOMETRY will be fixed by a preliminary engineering design (a portion of overall geometry from MODEL 1)

~~~~1.4 TIME LAPSE Stationary calculations will be performed (static assumption)~~~~

~~~~MANUFACTURING In service boundary conditions: inlet temperature, inlet mass, PROCESS OR IN- pressure and velocity of lead simulated by MODEL 1. 1.5 SERVICE CONDITIONS~~~~

~~~~PUBLICATION NA 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum models of Fluid Mechanics (first order turbulence model) , 2.0 AND NAME Energy Eq~~~~

MODEL Finite elements/volumes 2.1 ENTITY Equation Reynolds Averaged Navier-Stokes Equations + Turbulence model equations (2 equations) (RANS Approach) RANS Continuity Equation (conservation of mass) RANS Momentum Equation (conservation of momentum) MODEL RANS Energy Equation (conservation of energy) PHYSICS/ Closure Equation for turbulent kinetic energy ‘k’ 2.2 CHEMISTRY EQUATION Closure Equation for turbulent frequency ‘omega’ PE Physical Pressure quantities Velocity components (u, v, w) Temperature Turbulent kinetic energy Turbulent Frequency Relation - For the physical properties of the lead pool, correlations as function for the temperature are taken from the Handbook of Liquid metals (see references); - The physical properties of air are fully known in MATERIALS engineering; 2.3 RELATIONS - Physical properties for solids are provided by Sandvik - Correlations for friction factor and heat transfer in lead are taken from the Handbook (ref. Handbook [..], NEA- OECD, Science 2015), which includes - Kinematic Eddy Viscosity and Closure Coefficients and Auxilary Relation for the turbulent kinetic energy K in the

~~~~328~~~~

~~~~k-omega approach.~~~~

Physical Physical properties of lead and air (fluids) in 300°C-700°C quantities/ range: descriptors Viscosity [m2/s] for each Density [kg/m3] MR Specific Heat Capacity [J/kg K] Heat conductivity [W/mK] Physical properties of solids (AISI321 SS/FeCrAl/KANTHAL): Density [kg/m3] Specific Heat Capacity [J/kg K] Heat conductivity [W/mK]

~~~~SIMULATED Mass flow rate and inlet temperature in the HX component from MODEL 1. 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL ANSYS CFX 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL CFX (Computational Fluid Dynamic module of the ANSYS code)~~~~

~~~~3.3 TIME STEP not applicable~~~~

PHYSICS Reynolds Averaged Navier-Stokes equations + k-omega COMPUTATIONAL EQUATION, SST (Menter) turbulence model. The discretization of the 3.4 REPRESENTATION MATERIAL equation is finite element/finite volume , RELATIONS, MATERIAL

COMPUTATIONAL NA 3.5 BOUNDARY CONDITIONS Pure internal numerical solver details, like  Specific tolerances on geometry to resolve mesh problems (as ADDITIONAL needed) 3.6 SOLVER  Cut-offs, convergence criteria: residuals 10-6 PARAMETERS  Integrator options  Mesh density

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED The output will be post-processed to determine heat fluxes and air 4.1 OUTPUT mass transport~~~~

~~~~METHODOLOGIES cross-sectioning of simulated domain for visualization, volume 4.2 averaging~~~~

~~~~MARGIN OF 4.3 ERROR~~~~

~~~~329~~~~

~~~~MODA#2~~~~

~~~~Ceramic Receiver~~~~

~~~~NEXTOWER~~~~

~~~~OVERVIEW of the simulation~~~~

Stress analysis of solar receiver subject to microstructural damage The purpose of the simulation is to design correctly the solar receiver and 1 USER CASE provide insight about durability and damage trends (cliff edges in stress/gradients distributions). The goal is damage evolution and patterns following field operations and accelerated thermal cycling in furnace testing micromechanics model for stress field tightly coupled to a heat transport equation. No MR is entered for damage, because microcracks patterns in the microstructure and at CHAIN OF MODEL 1 the interfaces/joints between SiSIC and SiC pieces are 2 MODELS given as element removal in the mesh and the overall loss of stiffness measured from compaison of elastic simulations before and after damage.

~~~~PUBLICATION 3 ON THIS ONE NA SIMULATION For AVIZO, ENEA has licence for parallel computing. ACCESS 4 For FEMME, UOXF is proprietary and will make it available to ICCRAM and CONDITIONS ENEA.~~~~

~~~~WORKFLOW 5 AND ITS RATIONALE~~~~

~~~~MODEL 1~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED Comparison of damaged and pristine solar receiver subject under static and cyclic load to assess damage evolution and produce data to estimate ASPECT OF degradation rates and patterns, as well as lifetime of component in service THE USER 1.1 Conditions chosen to match accelerated testing in solar furnace CASE TO BE SIMULATED mechanical constraints + imposed heat fluxes and temperature gradient cycling associated to solar receiver and support (CIEMAT design, including air recirculator) . SiSiC and SiC ceramics (linked to the two receivers foreseen in the 1.2 MATERIAL NEXTOWER) Geometry corresponding to the prototype and smaller samples produced by ENGICER-LIQTECH after CIEMAT design of the receiver 1.3 GEOMETRY geometry from x-ray tomography (rendered by AVIZO software) The x-ray tomography of pristine and aged ceramic receivers will be fed as an input mesh for the finite element simulation of damage

~~~~1.4 TIME LAPSE 6-12 months of thermal cycling~~~~

~~~~MANUFACTURI Static load 1.5 NG PROCESS Mechanical constraint (constrained expansion from connection of receiver OR IN- to metal support) SERVICE~~~~

~~~~330~~~~

~~~~CONDITIONS~~~~

~~~~PUBLICATION N/A 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum models of thermostructural mechanics. Tightly coupled 2.0 AND NAME system of solid mechanics and energy equation~~~~

MODEL Finite volumes and finite elements of full size receiver pieces. Not unit 2.1 ENTITY cell or RVE but actual replica of foam- cellular solid microstructure/geometry/porosity Equation Equations of solid mechanics - Conservation of linear momentum (Cauchy’s equation) - Conservation of angular momentum (with imposed MODEL symmetry of stress tensor) PHYSICS/ 2.2 CHEMISTRY Laplace equation for heat transfer EQUATION

PE Physical - Cauchy stress tensor quantities - Small strain Tensor - Temperature - Heat flux Relation 1. Elastic properties of SiSiC and SiC + joining (as determined by POLITO) 2. Yield behaviour 3. Coefficient of thermal expansion (CTE) of receiver components MATERIALS 2.3 RELATIONS 4. Constitutive relations for finite strain thermo- elastic and plastic)

~~~~Physical 3. Young's modulus and Poisson ration as f(T) quantities/ 4. Temperature (T) and heat fluxes descriptors 5. CTE of materials for each MR 6. densities~~~~

~~~~SIMULATED 2.4 INPUT N/A (there is no earlier model)~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL ANSYS solvers 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL ANSYS~~~~

~~~~3.3 TIME STEP none~~~~

~~~~PHYSICS Solid represented by Finite Elements, COMPUTATIONAL 3.4 EQUATION, REPRESENTATION Microcracks inserted in the mesh by "element removal MATERIAL~~~~

~~~~331~~~~

~~~~RELATIONS, procedure" MATERIAL~~~~

~~~~COMPUTATIONAL N/A 3.5 BOUNDARY CONDITIONS~~~~

~~~~ADDITIONAL Mesh control (e.g. density, shape, order of elements) 3.6 SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Damage parameters defined as %loss of effective stiffness : OUTPUT The output will be post-processed by a standard post-processor for FE simulations (ParaFEM parafem.org.uk/) for peak stress identification 4.1 by analysis of stress and strain fields distribution over the volume. Damage evaluation will proceed from microcrack patterns distribution and from the relative loss of stiffness from pristine conditions

~~~~4.2 METHODOLOGIES visualization tool for strain mapping and damage pattern recognition~~~~

~~~~5 4.3 MARGIN OF ERROR N/A~~~~

~~~~5 Associated to spurious stresses on free boundaries and mesh dependence of stress field in thin walled elements (of solar receiver)~~~~

~~~~332~~~~

~~~~MODA#3~~~~

~~~~Molecular dynamics modelling of the Fe/Pb interface~~~~

~~~~NEXTOWER~~~~

~~~~OVERVIEW of the simulation~~~~

Simulation of the Fe/Pb interface in a model pipe within a demo loop. Emulating loop (plant demo) operation conditions at the atomic level for varying exposure temperatures The purpose of the simulation is to understand correctly the steel-eutectic 1 USER CASE (Fe/Pb) interface and to study the corrosion effects of high-temperature Pb fluid over the Fe surface, giving an exact description at the atomic level of all the steel and eutectic components.

~~~~Classical molecular dynamics of modelling of a Fe/Pb MODEL 1 CHAIN OF interface (Ch 2.3;1) 2 MODELS Quantum molecular dynamics of modelling of the Fe/Pb MODEL 2 interface (Ch 2.3.2)~~~~

~~~~PUBLICATION ON THIS 3 NA ONE SIMULATION~~~~

~~~~ACCESS 4 LAMMPS is an open source code. CPMD is an open source code. CONDITIONS~~~~

Two approaches that are not interlinked giving complementary information (i.e. two separate Models): Model 1 has a reduced representation of the materials at the atomic scale WORKFLO Model 2 without a reduced representation, materials are described in an 5 W AND ITS exact manner at a finer scale. RATIONALE The models run in parallel with NO interoperability. The models will be examined and benchmarked together in the post-processing, establishing what performs better vs. experimental results

~~~~333~~~~

~~~~MODEL 1~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF Classical molecular dynamics of modelling of the Fe/Pb interface. THE USER 1.1 CASE TO BE SIMULATED~~~~

~~~~1.3 GEOMETRY Model interface with PBC at atomic level~~~~

~~~~1.4 TIME LAPSE 1-10 ns~~~~

~~~~MANUFACTURI Emulating loop (plant demo) operation conditions at the atomic level. NG PROCESS Temperature range 500C – 700C 1.5 OR IN- SERVICE CONDITIONS~~~~

~~~~PUBLICATION~~~~

~~~~1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE 2.0 AND NAME Classical MD.~~~~

~~~~2.1 MODEL ENTITY The entity in this materials model is atoms~~~~

~~~~Equation Newton’s equation of motion MODEL Chapter 2.3.1 PHYSICS/ 2.2 CHEMISTRY Physical Atomic positions, EQUATION quantities Atomic velocities, PE Interatomic forces~~~~

~~~~Relation Interatomic potentials~~~~

~~~~MATERIALS Physical form of force field for Fe/Pb, 2.3 RELATIONS quantities/ descriptors for each MR~~~~

~~~~SIMULATED NA 2.4 INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Verlet Algorithm for integration. 3.1 SOLVER~~~~

~~~~334~~~~

~~~~3.2 SOFTWARE TOOL LAMMPS~~~~

~~~~3.3 TIME STEP Femtoseconds~~~~

~~~~PHYSICS COMPUTATIONAL EQUATION, 3.4 REPRESENTATION MATERIAL , RELATIONS, MATERIAL~~~~

~~~~COMPUTATIONAL Periodic Boundary Conditions (PBC) to model particle flow at the 3.5 BOUNDARY interface CONDITIONS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Damage patterns, exchanges of compounds at the surface and within 4.1 OUTPUT the liquid metal flow. Dislocations, defects (and propagation) and mass losses of Fe.~~~~

METHODOLOGIES Dislocation analysis (via Burger’s vector), defect analysis (Wigner Seitz method) and Centro Symetry parameter. Everything will be done via opensource software as OVITO(http://ovito.org/) and self 4.2 developed code (from EU-FP7-RADINTERFACES) RADAMAT-FOAM®. RADIATION DAMAGE IN MATERIALS FOR OPENFOAM. Ekhi Arroyo, Jordi Fradera, Santiago Cuesta, Universidad de Burgos. BU- 59-13. 03/05/2013.

~~~~MARGIN OF ERROR Depending on truncation error, system size and thresholding for 4.3 convergence~~~~

~~~~335~~~~

~~~~MODEL 2~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Quantum molecular dynamics modelling of the Fe/Pb interface. 1.1 USER CASE TO Interface will be designed precisely without a reduced representation. BE SIMULATED~~~~

~~~~Fe/Pb (FeCrAl/KANTHAL©) introducing proper atoms for a more precise 1.2 MATERIAL description of the eutectic (Pb-Bi) and the steel~~~~

~~~~1.3 GEOMETRY Model interface with PBC at atomic level~~~~

~~~~1 ns (simulation scale) but directly induced acceleration of damage 1.4 TIME LAPSE conditions will be tested~~~~

~~~~MANUFACTURI Emulating loop (plant demo) operation conditions at the atomic level. NG PROCESS 1.5 Temperature range 500C – 700C OR IN-SERVICE CONDITIONS~~~~

~~~~PUBLICATION NA~~~~

~~~~1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Ab initio Molecular Dynamics(Car-Parrinello Molecular Dynamics). 2.0 AND NAME Chapter 2.3.2~~~~

~~~~2.1 MODEL ENTITY The entity in this materials model is atoms~~~~

Equation classical equations of motion for the nuclei (They are integrated using the sum of the interatomic potential and the forces derived from the electron potential energy surface. At each time step, the ground- state electronic potential surface can be calculated MODEL using standard quantum mechanical methods (Born- PHYSICS/ Oppenheimer Molecular Dynamics) or introducing 2.2 CHEMISTRY fictitious dynamics for the electrons which follow EQUATION adiabatically the nuclei and are subjected to small readjustments "on the fly" during the nuclei evolution to PE keep them close to the ground state potential surface (Car-Parrinello Molecular Dynamics). (Chapter 2.3.2)

~~~~Physical Atomic positions, velocities and interatomic forces quantities~~~~

Relation Forces derived from Interatomic potentials and the electron potential energy surface MATERIALS 2.3 RELATIONS Physical Positions (atomic arrangement at the interface) quantities/ Electric charge

~~~~descriptors Mass for each MR~~~~

~~~~336~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL Verlet / rattle algorithm 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL CPMD (public)~~~~

~~~~-3 3.3 TIME STEP It will be adjusted during simulation process (1 fs – 10 fs)~~~~

~~~~PHYSICS COMPUTATIONAL EQUATION, 3.4 REPRESENTATION MATERIAL , RELATIONS, MATERIAL~~~~

~~~~COMPUTATIONAL Periodic Boundary Conditions (PBC) to model particle flow at the 3.5 BOUNDARY interface CONDITIONS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Damage patterns, exchanges of compounds at the surface and within OUTPUT the liquid metal flow. Dislocations, defects (and propagation) and mass losses of Fe. 4.1 In addition to the above information, common to the classic approach – MODA 1, we will be able to infer forces and deduce changes mechanical properties.

~~~~MARGIN OF ERROR Depending on truncation error, system size and thresholding for 4.3 convergence~~~~

~~~~337~~~~

~~~~NOVAMAG (686056)~~~~

~~~~Summary of the project~~~~

NOVAMAG aims to develop an automated large computational screening of new and novel intermetallic compounds with uniaxial structures (with high saturation magnetization, magneto- crystalline anisotropy and Curie temperature), which can be used for the rapid development of high performance permanent magnets without the use of critical raw materials.The models will be validated with extensive experimental screening.

~~~~Intermetallic compounds for permanent magnets~~~~

~~~~continue~~~~

~~~~338~~~~

Project Acronym and Number: NOVAMAG 686056 Project Title: NOVel, critical materials free, high Anisotropy phases for permanent MAGnets, by design. Start and End Dates: from 01/04/2016 till 30/09/2019 EU Contribution: 5,562,360 € Coordinator: Naiara ELEJALDE, [email protected] Modeller(s): Santiago Cuesta-Lopez, [email protected] Pablo Nieves, [email protected] Sergiu Arapan, [email protected] Heike Herper, [email protected] Hongbin Zhang, [email protected] Thomas Schrefl, [email protected]

~~~~339~~~~

~~~~Partial PGMs~~~~

~~~~PARTIAL-PGMs (686086)~~~~

~~~~Summary of the project~~~~

The project develops a modelling system for the rational design of smart and innovative nanostructured materials for automotive after-treatment systems, capable to anticipate future emission control regulations. The project will also develop the engine with stratified combustion of spark-ignition engines. The project will evaluate the feasibility of gasoline particulate filters which will contain both viable 3-way catalyst and gasoline particulate oxidation functionality, using either purely base metal components or much lower platinum group metals and rare earth metals loading than the current state-of-the-art.

~~~~nanostructured materials for automotive after-treatment systems~~~~

~~~~continue~~~~

~~~~340~~~~

~~~~Partial PGMs~~~~

Project Acronym and Number: PARTIAL-PGMs 686086 Project Title: Development of novel, high Performance hybrid TWV/GPF Automotive afteR treatment systems by raTIonAL design: substitution of PGMs and Rare earth materials Start and End Dates: from 1/04/2016 till 30/09/2019 EU Contribution: 4,650,001 € Coordinator: Massimo Rinaldi, [email protected] Modeller(s): Emiel Hensen, [email protected] Ivo FILOT, [email protected]

~~~~341~~~~

~~~~POROUS4APP (686163)~~~~

~~~~Summary of the project~~~~

The project addresses upscaling of fabrication of functional metal/metal-oxide nano-porous carbonaceous materials at pilot plant scale from natural resources (polysaccharide). The process for nano-porous carbon fabrication consists of swelling, drying and pyrolysis of natural resources and in this case starch. This technology needs to be up-scaled and modified to enable a full flexibility of the material characteristics to be applied to various industrial applications.

~~~~nano-porous carbon fabrication~~~~

Project Acronym and Number: POROUS4APP 686163 Project Title: Pilot plant production of controlled doped nanoporous carbonaceous materials for energy and catalysis applications Start and End Dates: from 01/03/2016 till 29/02/2020 EU Contribution: 6,535,878 € Coordinator: Joan PARRA, [email protected] Modeller(s): Alejandro Franco, [email protected] Marie-Liesse DOUBLET, [email protected] Nuria Lopez, [email protected]

~~~~342~~~~

~~~~MODA nano-porous carbon fabrication POROUS4APPS~~~~

OVERVIEW of the SIMULATION Elementary kinetics and reactants/products transport processes in porous 1 USER CASE carbonaceous materials supporting catalyst nanoparticles. Electronic structure of the catalyst materials via Density MODEL 1 Functional Theory. Reaction kinetics on catalyst nano-particles surfaces via Kinetic CHAIN OF MODEL 2 Monte Carlo 2 MODELS (coupled to Model 3) Diffusion/convection transport of reactants/products in the full MODEL 3 porous materials via continuum approach (coupled to Model 2) J. Catal. 285, 273-284 (2012), Nature Chem. 4, 739-745 (2012), J. Phys. Chem. C 118, 19023-19031 (2014). M.A. Quiroga, K. Malek, A.A. Franco, J. Electrochem. Soc., 163 (2) 3 PUBLICATION (2016) F59. M.A. Quiroga, A.A. Franco, J. Electrochem. Soc., 162 (7) (2015) E73. A.A. Franco, M.L. Doublet, W. Bessler, Eds., "Multiscale Modeling and Numerical Simulation of Electrochemical Devices for Energy Conversion and Storage", Springer, UK (2015). The electronic structure calculated data will be available through the ioChem-BD.org platform that has been established at ICIQ by the Proof-of- ACCESS Concept BigData4Cat 4 CONDITIONS The coupled continuum/KMC calculations on the full porous materials will be done by using the in-house code MS LIBER-T at CNRS developed since more than 14 years (see: http://modeling-electrochemistry.com/ms-liber-t/ ).

~~~~343~~~~

~~~~MODEL 1: DFT~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Surface process at the elementary step levels 1.1 USER CASE TO BE SIMULATED~~~~

~~~~MATERIAL Metals acting as catalyst. The systems will be clusters, surface, interface and bulk with up to 200 1.3 GEOMETRY atoms.~~~~

~~~~1.4 TIME LAPSE N/A~~~~

~~~~MANUFACTURING bulk of catalyst material and interface between catalyst material and PROCESS OR IN- gas, catalyst nanoparticle. 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Ab initio quantum mechanical models : (Electronic) Quantum Density 2.0 AND NAME Functional Theory~~~~

~~MODEL Electrons 2.1 ENTITY Equations Schrödinger equation MODEL PHYSICS/ 2.2 CHEMISTRY EQUATION Physical Energies, electron density, spin density, wave function quantities for PE’S each equation~~

Equations 1. Kohn-Sham 2. Bloch theorem 3. Hellman-Feymann forces (local energy minimisation procedure to explore the potential energy surface) 4. Transition state theory MATERIALS RELATIONS 5. Themodynamics

Physical quantities/ 1. Electron Density descriptors for 2. Electronic band structure, Phonon band each MR structure, Density of States 3. Equilibrium structures 4. Activation energy barriers 5. Reaction energies , adsorption energies

~~~~SIMULATED Chemical Compositions / Guessed structures 2.4 INPUT~~~~

~~~~344~~~~

~~~~PUBLICATION Publically available standard DFT Density Functional Theory: A Practical 2.5 Introduction D. Scholl, J. A. Steckel~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Kohn-Sham-DFT 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL VASP and Gaussian~~~~

~~~~3.3 TIME STEP Not applicable~~~~

~~~~PHYSICS Written up for the electron density COMPUTATIONAL EQUATION, 3.4 REPRESENTATION MATERIAL RELATIONS, MATERIAL~~~~

~~~~BOUNDARY Periodic boundary conditions~~~~

~~~~CONDITIONS~~~~

ADDITIONAL Pure internal numerical solver details that are often set SOLVER 1. Specific tolerances PARAMETERS 2. Cut-offs, convergence criteria 3. Integrator options All of them employed by default in the programs

~~~~3.5 PUBLICATION~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Adsorption energies, species involved in the surface diffusion, activation OUTPUT IS energies for the elementary reactions 4.1 CALCULATED FOR Destination entity: atoms and molecules for the atomistic/mesoscopic KMC (Model 2)

~~~~4.2 METHODOLOGIES Processing through standard simulation packages,~~~~

~~~~MARGIN OF ERROR 0.4 eV for adsorption energies 4.3 0.1 eV for the kinetic barriers Of the elementary processes~~~~

~~~~345~~~~

~~~~MODEL 2: Atomistic and mesoscopic kMC~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE Operation solving chemical reactions on catalyst nanoparticles with 1.1 USER CASE TO BE particular local SIMULATED partial pressures~~~~

~~~~MATERIAL Catalyst nanoparticles (Pt, Pd)~~~~

~~~~1.3 GEOMETRY Three-dimensional (shape of the nanoparticles)~~~~

~~~~1.4 TIME LAPSE Nanoseconds to days (temporal multi-scale)~~~~

~~~~MANUFACTURING Local partial pressures of reactants and products, temperature, PROCESS OR IN- 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE KMC part of MS LIBER-T 2.0 AND NAME~~~~

~~~~MODEL Atoms, molecules 2.1 ENTITY Equations Markovian equations (Kinetic Monte Carlo approach within the Variable Step Size Method). MODEL~~~~

~~~~PHYSICS/ 2.2 CHEMISTRY Physical Chemical potentials, fluxes, surface concentrations. EQUATION quantities PE’S for each equation~~~~

~~~~Equations Probability functions.~~~~

~~~~MATERIALS RELATIONS Physical Kinetic parameters, surface diffusion quantities/ coefficients, defects surface concentrations descriptors for each MR~~~~

~~~~SIMULATED local partial pressure (calculated by Model 3) 2.4 INPUT~~~~

~~~~2.5 PUBLICATION~~~~

~~~~346~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Variable Step Size Method 3.1 SOLVER MS LIBER-T / MESSI: http://modeling-electrochemistry.com/ms-liber-t/ 3.2 SOFTWARE TOOL~~~~

~~~~3.3 TIME STEP Variable time step~~~~

~~~~PHYSICS EQUATION, The solver represents the materials as a discrete COMPUTATIONAL MATERIAL collection of atoms/molecules. 3.4 REPRESENTATION RELATIONS,~~~~

~~~~MATERIAL~~~~

~~~~BOUNDARY Periodic boundary conditions~~~~

~~~~CONDITIONS~~~~

~~~~ADDITIONAL SOLVER Specific tolerances PARAMETERS Cut-offs, convergence criteria Integrators options~~~~

~~~~3.5 PUBLICATION~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Reaction (production/consumption) rates calculated for finite volume, 4.1 OUTPUT IS the whole bulk? as inputs for the Model 3 CALCULATED FOR~~~~

~~~~4.2 METHODOLOGIES Volume averaging~~~~

~~~~4.3 MARGIN OF ERROR N/A~~~~

~~~~347~~~~

~~~~MODEL 3: CONTINUUM: Diffusion and convection~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~ASPECT OF THE transport by diffusion/convention in the porous component for specific 1.1 USER CASE TO BE local reaction rates SIMULATED catalytic reactor: carbon, catalyst (Pt, Pd) 1.2 MATERIAL~~

~~~~catalytic reactor (thickness = to be defined from the project future 1.3 GEOMETRY specifications)~~~~

~~~~1.4 TIME LAPSE Nanoseconds to days (temporal multi-scale)~~~~

~~~~MANUFACTURING Inlet/outlet reactants/products pressures, temperature PROCESS OR IN- 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum Diffusion and Convection 2.0 AND NAME~~~~

MODEL finite volumes 2.1 ENTITY Equations Set of 20 (in average) coupled Partial Differential Equations and Ordinary Differential Equations formulated within the non- equilibrium thermodynamics approach (mass, energy MODEL conservation equations). PHYSICS/ 2.2 CHEMISTRY EQUATION Physical Chemical potentials, molar fluxes, intermediate reaction species PE’S quantities volume concentrations. for each equation

~~~~Equations Constitutive equations for the reactions and transport coefficients(~~~~

~~~~MATERIALS RELATIONS Physical Diffusion coefficients, pore size distributions, quantities/ particle size distributions descriptors for each MR~~~~

~~~~SIMULATED Reaction rates (Source terms) calculated by the KMC (discrete) part in MS 2.4 INPUT LIBER-T (Model 2).~~~~

~~~~2.5 PUBLICATION~~~~

~~~~348~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Finite Volume Method 3.1 SOLVER MS LIBER-T: http://modeling-electrochemistry.com/ms-liber-t/ 3.2 SOFTWARE TOOL~~~~

~~~~3.3 TIME STEP Variable time step~~~~

~~~~PHYSICS The solver represents the composite electrodes as a COMPUTATIONAL EQUATION, continuum meshed in finite volumes REPRESENTATION 3.4 MATERIAL RELATIONS, MATERIAL~~~~

~~~~BOUNDARY Newman, Dirichlet and mixed boundary conditions CONDITIONS depending on the components (e.g. electrode, separator...) and systems being simulated.~~~~

~~~~ADDITIONAL Specific tolerances SOLVER Cut-offs, convergence criteria PARAMETERS Integrators options~~~~

~~~~3.5 PUBLICATION~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Outlet reactants/products composition, outlet pressure which enters in 4.1 OUTPUT IS the MR (kinetic rate expressions) in the kMC CALCULATED FOR~~~~

~~~~4.2 METHODOLOGIES Averaging~~~~

~~~~4.3 MARGIN OF ERROR N/A~~~~

~~~~349~~~~

~~~~PRODIA (685727)~~~~

~~~~Summary of the project~~~~

The aim of the project is the development of large volume production processes for hybrid nanoporous materials (NPMs) as finished products. The materials addressed are metal-organic frameworks materials which are porous hybrid materials made from an inorganic metal-(oxo) cluster (e.g. Zr, Al, Cu, Fe) and organic linkers and hybrid alumina-silicates which are porous hybrid materials made from an alumina-silicate scaffold using organic surfactants as templating agents. These materials will be formulated, fabricated and up-scaled to pilot capacities to demonstrate the relevance in terms of properties, reproducibility, quality control and costs for industrial applications.

~~~~Heat flow in an adsorber~~~~

Project Acronym and Number: PRODIA 685727 Project Title: Production, control and Demonstration of structured hybrid nanoporous materials for Industrial adsorption Applications Start and End Dates: from 1/1/2015 till 31/10/2018 EU Contribution: 7,030,831 € Coordinator: Richard Blom, [email protected] Modeller(s): Marc Clausse, [email protected]

~~~~350~~~~

~~~~MODA Heat flow in an absorber PRODIA~~~~

~~~~THE SIMULATION GENERAL DESCRIPTION~~~~

~~~~Heat flow in an absorber 1 USER CASE~~~~

~~~~MODEL 1 Continuum heat (energy) transport equation CHAIN OF~~~~

~~~~2 MODELS~~~~

~~~~PUBLICATI 3 ON~~~~

~~~~ACCESS 4 CONDITION S~~~~

~~~~MODEL 1~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF Cycled mass and performance of an adsorber due to heat flow. THE USER 1.1 CASE TO BE SIMULATED~~~~

~~~~1.2 MATERIAL The fluid is water~~~~

The picture below shows a typical geometry of an adsorber dedicated to cold production sorption system. The adsorber is based on fin and tube heat exchanger which gaps are filled with adsorbent material (pellets, beads, etc.). Cooling/heating fluid can flow in the tubes allowing to perform a temperature swing of the adsorber.

~~~~1.3 GEOMETRY~~~~

~~~~351~~~~

Minutes. The cycle time of this system (i.e. the time necessary for an adsorber to go through the various steps (pre-heating, desorption, pre- 1.4 TIME LAPSE cooling and adsorption) is usually about a few tens of minutes depending of thermophysical properties, adsorption equilibrium and adsorber size.

The boundary conditions will consist on three thermal sources: high, MANUFACTUR medium and low temperature as sorption cooling system are 3- ING PROCESS temperature thermodynamic heat pumps. The choice of the temperature 1.5 OR IN- of the sources will be directly linked to the type of sought application. For SERVICE example for solar cooling, typical temperature for the heat sources would CONDITIONS be respectively: 90, 35 and 10 °C

~~~~1.6 PUBLICATION n.a.~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Heat equation applied to describe the dynamic behaviour of an adsorber 2.0 AND NAME~~~~

~~~~MODEL continuum 2.1 ENTITY~~~~

~~~~Equations 1. Energy balance during the desorption step d dq MC  MC  M q C  T  h M d  m C T  T  dt a,M ac ac d p,MeOH d ac dt HW p,HW HW,out HW,in~~~~

2. Energy balance during the adsorption step d MC  MC  M q c  T  dt d,M ac ac a pl,MeOH a dq dq h M a  MC c a T  T  m c T  T  ac dt ac pv,MeOH dt ev a MW p,MW MW ,in MW ,out

MODEL Physical In the energy balance equations the following quantites PHYSICS/ quantities appear: 2.2 CHEMISTRY for each EQUATION  Temperature: desorber (Td), adsorber (Ta), equation heating/cooling fluid (TMW, THW, in and out) PE’S  The adsorption capacity: desorber (qd) and adsorber (qa). It is a function of the temperature and the pressure inside the adsorber. The pressure will be given by that at the evaporator or the condenser (saturation pressure of the refrigerant at Tev or Tcond which are boundary conditions)  The heat capacity (thermal inertia) of the adsorbent, metal and adsorbate (MCac, MCM and Mqc, respectively)   The secondary fluid flow rate and specific heat capacity (mMW and cp) Equations  to describe the heat transfer inside the MATERIALS adsorber (one example hereafter) RELATIONS T T (T T)exp(UA/m C ) out in p

~~~~ to describe the adsorption equilibrium~~~~

~~~~352~~~~

~~~~(various model from the litterature can be used to describe the experimental data: Langmuir familiy, Dubinin family, etc. (one example hereafter with Dubinin-Astakov equation)~~~~

n    P     sat   q  q  Texp  DTln   0 l    P         state equation for the adsorbate (working fluid) Physical quantities/ n.a. descriptors for each MR

~~~~SIMULATED n.a. 2.4 INPUT~~~~

PUBLICATION Clausse M., Meunier F., Coulié J., Herail E., 2009, Comparison of adsorption systems using natural gas fired fuel cell as heat source, for residential air conditioning, Int. J. Refrig., 32(4), 712-719. 2.5 Clausse, M., Alam, K.C.A., Meunier, F., 2008, Residential air conditioning and heating by means of enhanced solar collectors coupled to an adsorption system, Sol. Energy, 82(10), 885-892

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~3.1 NUMERICAL SOLVER Differential Algebraic Equation solver~~~~

~~~~3.2 SOFTWARE TOOL DASPK (Fortran package for DAEs solving)~~~~

~~~~3.3 TIME STEP n.a.~~~~

PHYSICS The DDASPK solver uses the backward EQUATION, differentiation formulas of orders one through five MATERIAL to solve a system of the form G(t,y,y') = 0 for y = RELATIONS, Y and y' = YPRIME. Values for Y and YPRIME at COMPUTATIONAL MATERIAL the initial time must be given as input. These REPRESENTATION values should be consistent, that is, if T, Y, Refers to how your YPRIME are the given initial values, they should computational 3.4 satisfy G(T,Y,YPRIME) = 0. In our case, Y will solver represents content the values id the temperature and the the material, adsorbed quantities of each adsorber while properties, YPRIME will content their derivative as a function equation variables, of time.

~~~~source : http://www.engineering.ucsb.edu/~cse/software.html~~~~

~~~~BOUNDARY Boundary conditions are scalars linked to the heat CONDITIONS source temperatures. They can be directly the~~~~

~~~~temperature or the saturation pressure for this temperature.~~~~

~~~~353~~~~

~~~~ADDITIONAL n.a. SOLVER PARAMETERS~~~~

~~~~3.5 PUBLICATION n.a.~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED the performance: cooling capacity and COP (Coefficient of 4.1 OUTPUT IS Performance). CALCULATED FOR~~~~

~~~~METHODOLOGIES The cyclic average cooling capacity (CACC) can be evaluated by the following expressions:~~~~

~~~~end of adsorptionstep m adsorbatehlvdt begin of adsorptionstep CACC  Cycle time 4.2 The cycle COP (Coefficient of Performance) can be calculated by the following equation:~~~~

~~~~end of adsorptionstep m adsorbateh lvdt begin of adsorptionstep~~~~

~~~~COPcycle  end of cycle time m HWcHW (THW,in  THW,out)dt begin of cycle time~~~~

~~~~4.3 MARGIN OF ERROR n.a.~~~~

~~~~354~~~~

~~~~PROTECT (720851)~~~~

~~~~Summary of the project~~~~

PROTECT aims to up-scale processes for biocompatible antimicrobial and anti- biofilm nano-coating of 2D and 3D surfaces of products including, without being limited to: i) upholstery fabrics for public areas, ii) medical textiles, iii) indwelling medical devices, and iv) water treatment membranes. To this end, PROTECT will build a platform of three pre-commercial manufacturing lines.

~~~~Piezo electric transducer emitting ultrasounds in liquid~~~~

Project Acronym and Number: PROTECT 720851 Project Title: Pre-commercial lines for production of surface nanostructured antimicrobial and anti-biofilm textiles, medical devices and water treatment membranes Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution: 7,746,387.75 € Coordinator: Tzanko TZANOV, [email protected] Modeller(s): Frank CLAEYSSEN, [email protected] Prina Dan, [email protected] Tzanko Tzanov, [email protected]

~~~~355~~~~

~~~~MODA Piezo transducers PROTECT~~~~

~~~~OVERVIEW of the SIMULATION~~~~

~~~~1 USER CASE Piezo electric transducer emitting ultrasounds in liquid~~~~

Tightly coupled set of solid mechanics, fluid mechanics and electrical continuum equations, describing the behaviour of MODEL 1 excitation voltage, electric potential in the piezo ceramics, CHAIN OF strain in the whole transducers, vibration amplitude and 2 MODELS pressures in fluid

J.N.Decarpigny, PhD Thesis, Application of the Finite Element Method to the study of piezo transducers, USTL, France, 1984 PUBLICATION B.Hamonic, PhD Thesis, Contribution to the study of radiating transducers 3 ON THIS ONE based on thin shells, USTL, France, 1987 SIMULATION K.Uchino, J.C.Debus, Application of ATILA FEM software to smart materials, Woodhead Publishing Limited, 2013

~~~~The FEM model is implemented in the commercially available ATILA FEM ACCESS 4 software, developed by IEMN (France) and available CONDITIONS http://www.mmech.com/atila-fem~~~~

WORKFLOW ATILA FEM is dedicated to 2D /3D electro-mechano-acoustic modelling of 5 AND ITS piezo transducers generating acoustic energy in fluid. It has been initially RATIONALE developed by IEMN for French and US Navy for sonars.

~~~~MODEL~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

The piezo transducers for acoustic generation to be developed in the project can be described as : - a transducer composed of one or several stacks of polarised piezoelectric ceramics rings and copper electrodes on which a sinus electric high voltage is applied ASPECT OF THE USER CASE TO BE - a prestress bolt made of steel 1.1 SIMULATED - mechanical parts - a tube linking all the previous parts; the external side of the tube vibrating in the fluid to generate acoustic waves - this transducer is preferably excited at resonance and is working at ultrasonic frequencies

~~~~Steel 1.2 MATERIAL Piezo ceramics (PZT)~~~~

~~~~356~~~~

~~~~typically a tube type structure : See an example below of axial- symmetry FEM of transducers generating acoustic pressure waves in fluid~~~~

~~~~1.3 GEOMETRY~~~~

~~~~1.4 TIME LAPSE A vibration occurs at 20kHz, which means a period of 50*µs.~~~~

~~~~MANUFACTURING PROCESS excitation frequency and voltage on the electrodes 1.5 OR IN-SERVICE CONDITIONS~~~~

~~~~PUBLICATION 1.6 ON THIS ONE SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum solide mechanics applied to piezo transducers and acoustics for 2.0 AND NAME its effect in the fluid~~~~

~~~~MODEL Finite element 2.1 ENTITY~~~~

~~~~Equation Solid mechanics and electrical equations for the piezo transducer in fluid in contained in the following variationals L and Lf : -For the piezo structure~~~~

~~~~MODEL PHYSICS/ 2.2 CHEMISTRY EQUATION PE~~~~

~~~~And for the effects of the transducer on the fluid a derived form of the Navier Stokes equation is used:~~~~

~~~~357~~~~

~~~~The coupling between both variatonal occurs on fluid structure interface~~~~

~~~~Physical U=displacements ; Phi=electric potential ; P=fluid pressure quantities F=Force ; q=electric charge ; Psi= acoustic velocity~~~~

~~~~Relation Piezo materials, elastic materials~~~~

MATERIALS 2.3 RELATIONS Helmoltz equation for fluid Physical T = Stress ; S = Strain ; E = Electric Field ; D = Dielectric quantities/ field descriptors P = Acoustic Pressure ; Psi= acoustic velocity for each MR

~~~~2.4 SIMULATED INPUT~~~~

~~~~3 SOLVER AND COMPUTATIONAL TRANSLATION OF THE SPECIFICATIONS~~~~

~~~~NUMERICAL The software is based on the Finite Element Method in harmonic 3.1 SOLVER analysis involving Cholesky algorithm for the linear solver~~~~

~~~~3.2 SOFTWARE TOOL ATILA~~~~

~~~~3.3 TIME STEP If applicable~~~~

~~~~PHYSICS FEM with nodal values coupled by the following matrix EQUATION, MATERIAL COMPUTATIONAL RELATIONS, 3.4 REPRESENTATION MATERIAL~~~~

~~~~U=displacements ; Phi=electric potential ; P=fluid pressure~~~~

~~~~358~~~~

~~~~F=Force ; q=electric charge ; Psi= acoustic velocity~~~~

Voltage is prescribed on the electrodes. COMPUTATIONAL Displacement of the structure surface is free (ie force = 0), excepted at 3.5 BOUNDARY the fluid interface ; CONDITIONS Velocity at Fluid external surface is 0.

~~~~ADDITIONAL SOLVER Mesh density is chosen in way each element to contain no more 3.6 PARAMETERS than a quater wave length~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Main out put are: OUTPUT Required current I 4.1 Displacements & Stresses in the transducer Pressure in the fluid~~~~

~~~~METHODOLOGIES Electric current : I = ωq 4.2 Electric Impedance : Z = V/I~~~~

~~~~MARGIN OF 4.3 in the range of 10%. ERROR~~~~

~~~~359~~~~

~~~~SIMPHONY (604005)~~~~

~~~~Summary of the project~~~~

SimPhoNy will develop data interoperability interfaces that allow seamless linking and coupling of models each describing material phenomena on a specific scale. These models will be the building blocks for multiscale simulations. One of the main focuses of the SimPhoNy project is to develop a user friendly, extendable and open platform for the integration of various existing open source and commercial simulation and pre- and post-processing software packages. From the application side, SimPhoNy focuses on a cluster of related nano- and microfluidic applications that requires solving of problems not addressable by individual codes alone.

~~~~Flow in a micro or nano channel~~~~

Project Acronym and Number: SIMPHONY 604005 Project Title: Simulation framework for multi-scale phenomena in micro- and nanosystems Start and End Dates: from 1/1/2014 till 31/12/2016 EU Contribution: 3,209,000 € Coordinator: Adham Hashibon, [email protected] Modeller(s): Adham Hashibon, [email protected]

~~~~360~~~~

~~~~MODA Flow in micro or nano channel SIMPHONY~~~~

~~~~OVERVIEW of the SIMULATION~~~~

~~~~Velocity flow profile in a micro or nano channels taking into account the effects 1 USER CASE of micro or nano structure of the channel walls on the flow pattern~~~~

~~~~MODEL 1 Continuum, CFD model CHAIN OF MODEL 2 Atomistic, Molecular Dynamics 2 MODELS … …~~~~

~~~~PUBLICATION 3 ON THE In Preparation. SIMULATION~~~~

~~~~ACCESS Free and open code, see http://github.com/simphony 4 CONDITIONS~~~~

~~~~MODEL 1 CFD~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE USER Velocity profile for liquid flowing in a straight rectangular nano and CASE TO BE micro structured channel. SIMULATED 1.1 AND HOW IT FORMS A PART OF THE TOTAL USER CASE The channel walls are assumed to be made of glass or polystyrene, 1.2 MATERIAL and the fluid is water based. A long rectangular channel, about 1 cm long, and 50µm up to 1.3 GEOMETRY 1000µm in width. Water enters from the right and exits from a left inlet.

~~~~1.4 TIME LAPSE up to 10s of seconds~~~~

~~~~MANUFACTURING There is a constant pressure difference imposed externally across the PROCESS OR IN- channel. 1.5 SERVICE CONDITIONS~~~~

~~~~PUBLICATION Publication documenting the simulation with this single model (if 1.6 ON THIS ONE available and if not included in the overall publication). In Preparation SIMULATION~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum Fluid Mechanics, Fluid Dynamics 2.0 AND NAME~~~~

~~~~2.1 MODEL ENTITY finite volumes~~~~

~~~~361~~~~

~~~~Equations Name and description and mathematical form of the PEs~~~~

~~~~6. The Navier-Stokes(N-S) Equation for incompressible isothermal fluid:~~~~

~~~~∂퐯 ρ [ + (퐯 ⋅ 훁)퐯] = −훁p + μ훁ퟐ퐯 + 퐟 ∂t~~~~

MODEL 7. Mass conservation equation for incompressible fluid PHYSICS/ (liquid): 2.2 CHEMISTRY 훁 ⋅ (퐯) = 0… EQUATION Physical Please name the physics quantities (parameters (constants, PE’S quantities matrices) and variables that appear in these equations e.g. for each wave function, Hamiltonian, spin, velocity, external force). equation 7. N-S equation: ρ: density, 퐯: velocity, p: pressure, μ: dynamic viscosity, f: external body forces (e.g., gravitation) 8. Mass conservation equation: ρ: density, 퐯: velocity In both equations, the independent variables are time t, and position 퐫. MR Equations Strictly speaking, there are no further materials relations requiring additional equations, since the assumption of incompressible, isothermal and Newtonian Fluid viscosity model have already been MATERIALS “consumed” in the general Cauchy relations to obtain RELATIONS the N-S equation. In this case the viscosity and density are just properties of the material (constants).

~~~~Physical quantities/ descriptors for each MR~~~~

SIMULATED After an initial iteration, the MD simulation gives the velocity at the wall as 2.4 INPUT boundary conditions. It is assumed that the velocity is translationally invariant along the walls in steady state. .

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Finite Volume Method 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL SimPhoNy using the OpenFOAM wrapper~~~~

~~~~Dynamic, set by solver to keep accuracy reasonably sufficient, typical 3.3 TIME STEP values 1e-5 seconds~~~~

PHYSICS The computational domain is discretised on a structured EQUATION, mesh. Each mesh element has cell centres and 6 faces. MATERIAL The integral form of the PE from section 1, the MR and the RELATIONS, material is written up for a finite volume mesh. Cell centres COMPUTATIONAL MATERIAL and faces have the following properties: 3.4 REPRESENTATION Cells contain the v and p fields. Faces contain fluxes. Computationally, each equation is represented by a standard data schema as described in the SimPhoNy CDUS and CUBA:

~~~~362~~~~

CUBA.CFD_MODEL, CUBA.INCOMPRESSIBLE_MODEL, CUBA.ISOTHERMAL_MODEL The computational Mesh is also described using CUBA and the CUDS schema: each mesh element has a data property with key-value sets, the keys are standard CUBA.PRESSURE, CUBA.VELOCITY. The material properties such as density and viscosity are described according to the CUDS schema by standard keywords: CUBA.DENSITY and CUBA.VISCOSITY

BOUNDARY Mesh elements that belong to each boundary (inlet, outlet CONDITIONS and channel/pipe walls) can be identified on each of the variables (pressure and velocity) in the PE. Specific boundary conditions are specified to translate the physics boundary conditions and process conditions in section 1 for the walls and the inlet and outlet.  For Velocity: a. on walls: no-slip (fixed velocity, coming from the atomistic model) b. on inlet: pressure inlet velocity, as pressure is fixed and known at inlet, the velocity is evaluated from the flux normal to the inlet c. on outlet: zero gradient on U  For Pressure: a. on channel walls: adjust the pressure gradient so that the boundary flux matches the velocity boundary condition (in OF fixedFluxPressure). b. on inlet: fixed value c. on outlet: fixed value In SimPhoNy this is done by marking the mesh elements that are on boundaries and associating them with the proper boundary conditions using CUBA and CUDS.

~~~~ADDITIONAL Maximum Courant Number, Mesh cell size. SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED velocities and positions of the atoms near the wall 4.1 OUTPUT IS CALCULATED FOR~~~~

~~~~METHODOLOGIES Statistical velocity variations are added which fulfil the classical Maxwell- 4.2 Boltzmann distribution~~~~

~~~~MARGIN OF If the boundary conditions are chosen correctly, the velocity is accurate 4.3 ERROR at the macroscopic level, with a margin of up to 5%.~~~~

~~~~363~~~~

~~~~SINTBAT (685716)~~~~

~~~~Summary of the project~~~~

Sintbat will use modelling and testing to precisely describe the degradation mechanisms in Silicon based lithium-ion batteries for decentralized storage systems for renewable energy. This will be used to improve the battery system based on silicon materials to extend the life time of these batteries up to 25 years. Sintbat will develop functional electrodes and electrolytes substituting carbon-based materials by silicon-based functional materials. This will improve cell energy density and improve life time. A lithium buffer will compensate losses in service (prelithiation of silicon anodes). The project will also develop the required cell manufacturing process.

~~~~deformation and stresses within the battery anode~~~~

Project Acronym and Number: SINTBAT 685716 Project Title: Silicon based materials and new processing technologies for improved lithium-ion batteries Start and End Dates: from 01/03/2016 till 29/02/2020 EU Contribution: 8,334,786 € Coordinator: Martin KREBS, [email protected] Modeller(s): Dhammika Widabalage, [email protected] Lukasz Figiel, [email protected]

~~~~364~~~~

~~~~MODA Stress and strain in anode SINTBAT~~~~

OVERVIEW of the SIMULATION Prediction of the large strain deformation and associated stresses within 1 USER CASE the anode during cycling. To predict the voltage response of the Li-ion Si anode cell with capacity fade due to SEI growth during cycling

~~~~3D Micromechanical model based on the Representative 2 MODEL 1 CHAIN OF Volume Element (RVE) concept MODELS~~~~

~~~~MODEL 2 1D Macro Electrochemical model~~~~

3 PUBLICATION Not yet available The models and post processed data will be distributed among project ACCESS partners. They will be owned by WMG (Nanocomposites Modelling Group 4 CONDITIONS and Energy and Electrical Systems Group) at the University of Warwick. External users may be given access upon contacting the owners.

~~~~Model 1: 3D Micromechanical model~~~~

1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED A 3D micromechanical model for prediction of the deformation and stresses during lithiation/delithiation of the anode will be developed. The micromechanical model will be based on the RVE concept to reflect the in-situ behaviour of the anode. The large deformation ASPECT OF THE behaviour will be driven by the response of Si particles undergoing 1.1 USER CASE TO BE large volumetric deformations. The medium between Si particles will SIMULATED be modelled as an effective nonlinear material governed by the response of binder material. The strains/stresses will be predicted both at the micromechanical level (raw data) and macroscopic level (post-processed data) using nonlinear computational homogenisation.

~~~~1.2 MATERIAL Si particles, effective matrix~~~~

~~~~1.3 GEOMETRY RVE~~~~

~~~~1.4 TIME LAPSE From seconds to hours~~~~

~~~~MANUFACTURING Lithium ion concentration, mechanical constraints PROCESS OR IN- 1.5 SERVICE CONDITIONS~~~~

~~~~1.6 PUBLICATION Not yet available~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE AND Continuum model. 3D Micromechanical model 2.0 NAME~~~~

~~~~2.1 MODEL ENTITY Finite volumes/elements~~~~

~~~~365~~~~

MODEL Equations 1. Stress-strain-like law PHYSICS/ 2. Fick’s-like law 2.2 CHEMISTRY Physical 1. Stresses, strains EQUATION quantities for 2. Concentration, fluxes PE’S each equation Equations 1. Strain energy function 2. Fick’s-like law MATERIALS RELATIONS Physical 1. Material constants: stress-strain tangents, quantities/ cross-link density descriptors for 2. Diffusivity each MR

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL FE 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL ABAQUS~~~~

~~~~3.4 TIME STEP Unclear~~~~

~~~~PHYSICS PDEs EQUATION~~~~

MATERIAL COMPUTATIONAL Stress-strain, Fick’s-like law RELATIONS 3.5 REPRESENTATION MATERIAL Microstructure of the anode will be represented as a composite made of Si particles embedded in an effective matrix, with a possible interphase layer around Si particles

~~~~BOUNDARY Li ion concentration, mechanical constrains~~~~

~~~~CONDITIONS (translational degrees of freedom)~~~~

~~~~ADDITIONAL Relevant parameters governing an iterative- SOLVER incremental Newton-Raphson-like solution scheme PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Macroscopic strain and stress, macroscopic diffusion flux 4.1 OUTPUT IS in finite volumes/elements and RVE used in model 2 CALCULATED FOR~~~~

~~~~4.2 METHODOLOGIES mathematical homogenisation~~~~

~~~~MARGIN OF ERROR Statistical evaluation of the mean and standard error will be 4.3 evaluated by considering various RVE ensembles~~~~

~~~~366~~~~

~~~~Model 2: 1D Macro Electrochemical model~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

~~~~ASPECT OF THE To predict the voltage response of the Li-ion Si anode cell with 1.1 USER CASE TO BE capacity fade due to SEI growth during cycling SIMULATED~~~~

1.2 MATERIAL Current collectors, electrode pair, separator and electrolyte A 1D simplified representation of the current collectors, electrode 1.3 GEOMETRY pair, separator and electrolyte ~ 100 microns

~~~~1.4 TIME LAPSE Seconds-hours~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Continuum model. 1D Macro electrochemical model 2.0 AND NAME~~~~

2.1 MODEL ENTITY Finite volumes Equations 1. Current density for intercalation and for SEI side reaction 2. Mass conservation in electrolyte and solid MODEL phase PHYSICS/ 3. Charge conservation in electrolyte and solid 2.2 CHEMISTRY phase EQUATION Physical 1. Specific surface area, volume fractions, SEI PE’S quantities conductivity for each 2. Diffusion coefficients, particle size equation 3. Solid and electrolyte conductivities

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~~~NUMERICAL Implicit TDMA 3.1 SOLVER~~~~

~~~~3.2 SOFTWARE TOOL Fortran/Matlab~~~~

~~~~3.4 TIME STEP~~~~

~~~~COMPUTATIONAL PHYSICS 3.5 PDE REPRESENTATION EQUATION~~~~

~~~~BOUNDARY Mostly Newman type, BC of solid phase potential CONDITIONS (charge conservation) is governed applied cell charging-discharging current.~~~~

~~~~4 POST PROCESSING~~~~

~~~~PROCESSED SEI thickness/resistance, capacity and power fade 4.1 OUTPUT~~~~

~~~~METHODOLOG Averaging/normalisations and solving a differential equation relating 4.2 IES SEI thickness to rate of reaction~~~~

~~~~4.3 MARGIN OF ERROR~~~~

~~~~367~~~~

~~~~STARCELL (720907)~~~~

~~~~Summary of the project~~~~

The project targets the reduction of critical raw materials in photovoltaic cells. They will develop kesterites formed from low toxicity metals (Cu, Sn, and Zn). The project targets the optimisation of the material processes and the device interfaces to achieve a challenging solar cell efficiency of 18% (16% for a 10x10 cm2 area mini-module) by the end of the project.

~~~~Materials for photovoltaic cells~~~~

Project Acronym and Number: STARCELL 720907 Project Title: Advanced strategies for substitution of critical raw materials in photovoltaics Start and End Dates: from 1/1/2017 till 31/12/2019 EU Contribution: 4,832,185 € Coordinator: Edgardo SAUCEDO, [email protected] Modeller(s): Aron Walsh, [email protected] Matthias Maiberg, [email protected]

~~~~368~~~~

~~~~WALL IN ONE (723574)~~~~

~~~~Summary of the project~~~~

The project aims to provide sustainable insulation solutions to the building industry. This project will develop new advanced insulation products and systems with high energy efficient insolating materials and improved durability and sustainability.

~~~~Heat and moisture transport in insulation products for buidlings~~~~

Project Acronym and Number: WALL IN ONE 723574 Project Title: WALL Insulation NOvel Nanomaterials Efficient systems Start and End Dates: from 1/10/2016 till 30/09/2019 EU Contribution: 4,289,785 € Coordinator: Johann Balau, [email protected] Modeller(s): Mohamad Ibrahil, [email protected]

~~~~369~~~~

~~~~MODA-1 Heat and moisture transport in wall envelop WALL_IN- ONE~~~~

OVERVIEW of the SIMULATION Heat and moisture transfer modeling on system (wall envelope) level to assess the thermal and moisture performance of such systems in different boundary conditions. to analyze the impact of the newly developed 1 USER CASE systems on 1D heat losses, on thermal bridge (2D) heat losses, and on inner surface temperature with a condensation and mould growth risk assessment. Heat transport: continuum model conservation of energy equation (1st law of thermodynamics)  Heat transfer due to conduction (diffusion)  Heat transfer due to convection MODEL 1  Heat transfer due to radiation

~~~~ Fourier's law (conductive flow) CHAIN OF  Newton's law of cooling (convective flow) 2 MODELS  Stefan Boltzmann’s law (radiative flow)~~~~

~~~~Moisture transport: continuum model conservation of mass (moisture transfer)~~~~

~~~~MODEL 2  Fick’s first law (vapour flow)  Darcy’s law (liquid flow)~~~~

~~~~PUBLICATION 3 ON THE SIMULATION~~~~

~~~~ACCESS 4 bought software license (for WUFI or Delphin) CONDITIONS~~~~

~~~~MODEL~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE USER CASE Analyze the impact of adding the newly developed system at TO BE SIMULATED the interior surface of historical brick walls (taken as an e.g.) 1.1 AND HOW IT FORMS A PART on the heat losses, and on inner surface temperature with a OF THE TOTAL USER CASE condensation and mould growth risk assessment e.g.: Brick with Aerogel blanket layer and plaster on the 1.2 MATERIAL interior

~~~~1.3 GEOMETRY Cartesian (1D)~~~~

~~~~1.4 TIME LAPSE 5 years External forces : heat (for e.g. solar radiation) and moisture MANUFACTURING PROCESS 1.5 (for e.g. rain) OR IN-SERVICE CONDITIONS (the source is the weather data)~~~~

~~~~PUBLICATION 1.6 ON THIS ONE SIMULATION~~~~

~~~~370~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Tightly coupled equations: 2.0 AND NAME Heat transport: continuum model Moisture transport: continuum model~~~~

~~~~MODEL finite volumes 2.1 ENTITY~~~~

~~~~푑퐻 휕푇 Equations PE1: = ∇(λ∇T) + ℎ ∇(훿 ∇(휑푃 )) 푑푇 휕푡 푣 푝 푠푎푡~~~~

푑푤 휕휑 PE2: = ∇(퐷 ∇φ + 훿 ∇(휑푃 )) 푑휑 휕푡 휑 푝 푠푎푡 Physical PE1: Physical quantities quantities H=enthalpy (J) for each T = temperature (K) equation 휑 = relative humidity (-) MODEL λ = thermal conductivity (W/(mK)) PHYSICS/ t = time (s) 2.2 CHEMISTRY 훿푝 = water vapour permeability (kg/(msPa)) EQUATION ℎ푣 = evaporation enthalpy (J/kg) PE’S 푃푠푎푡 = water vapour saturation pressure (Pa)

~~~~PE2: Physical quantities w = water content (kg/m3) 휑 = relative humidity (-)~~~~

~~~~퐷휑 = liquid conduction coefficient (kg/(ms)) t = time (s)~~~~

훿푝 = water vapour permeability (kg/(msPa)) 푃푠푎푡 = water vapour saturation pressure (Pa) 1. The material’s thermal conductivity as a function of temperature (for PE1) 2. The material’s thermal conductivity as a function of moisture content (for PE1) 2.3. MATERIALS 3. The material’s specific heat capacity (for PE1) RELATIONS 4. water vapour permeability or water vapour diffusion resistance factor (for PE1 and PE2) 5. the material’s liquid conduction coefficient or liquid absorption coefficient (for PE2) 6. The sorption isotherm curve (for PE2) (all the above are the results of experimental measurments)

~~~~SIMULATED NA 2.4 INPUT~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA~~~~

~~NUMERICAL Finite volume 3.1 SOLVER  Fully implicit for the discretization in time WUFI or Delphine (https://wufi.de/en/ ; http://bauklimatik 3.2 SOFTWARE TOOL dresden.de/delphin/index.php?aLa=en)~~

~~~~3.3 TIME STEP Variable (1h or less)~~~~

~~~~COMPUTATIONAL PHYSICS written up for finite volumes 3.4 REPRESENTATION EQUATION,~~~~

~~~~371~~~~

~~~~MATERIAL RELATIONS, MATERIAL~~~~

~~~~BOUNDARY The physics b.c. are written up for the faces of the~~~~

~~~~CONDITIONS outer finite volumes~~~~

~~~~ADDITIONAL SOLVER PARAMETERS~~~~

~~~~4 POST PROCESSING~~~~

THE PROCESSED Temperatures will be used to estimate the thermal losses/gains OUTPUT IS throughout the envelope 4.1 CALCULATED FOR Relative humidity will be used to estimate the moisture risks (such as condensation)

~~~~METHODOLOGIES physics definition for loss and gain 4.2 literature relations for condensations and mould as function of temperature and humidity~~~~

~~~~4.3 MARGIN OF ERROR~~~~

~~~~372~~~~

~~~~MODA 2 Modeling on a building scale Wall-in One~~~~

OVERVIEW of the simulation Assess the impact of applying the developed internal thermal insulation 1 USER CASE systems to retrofit an old house on the energy demands and thermal comfort. Heat transport: continuum model conservation of energy equation (1st law of thermodynamics)  Heat transfer due to conduction (diffusion)  Heat transfer due to convection CHAIN OF MODEL 1  Heat transfer due to radiation 2 MODELS

~~~~ Fourier's law (conductive flow)  Newton's law of cooling (convective flow)  Stefan Boltzmann’s law (radiative flow)~~~~

~~~~3 PUBLICATION~~~~

~~~~ACCESS 4 Free software (for EnergyPlus) CONDITIONS~~~~

~~~~1 ASPECT OF THE USER CASE/SYSTEM TO BE SIMULATED~~~~

ASPECT OF THE USER CASE TO analyze the impact of adding the newly developed system BE SIMULATED at the interior surface of to retrofit an old house on the 1.1 AND HOW IT FORMS A PART OF heating and/or cooling demands THE TOTAL USER CASE

~~~~1.2 MATERIAL e.g.: an old brick house with Aerogel blanket layer on the interior~~~~

~~~~1.3 GEOMETRY Cartesian~~~~

~~~~1.4 TIME LAPSE 1 year~~~~

~~~~MANUFACTURING Statistical weather conditions 1.5 PROCESS OR IN- SERVICE CONDITIONS~~~~

~~~~2 GENERIC PHYSICS OF THE MODEL EQUATION~~~~

~~~~MODEL TYPE Heat transport: continuum model 2.0 AND NAME~~~~

~~~~MODEL Finite volume 2.1 ENTITY~~~~

~~~~휕푇 Equations PE1: 휌푐푝 = ∇(λ∇T) 2.2 MODEL 휕푡 PHYSICS/~~~~

~~~~373~~~~

CHEMISTRY Physical PE1: Physical quantities EQUATION quantities T = temperature (K) PE’S for each λ = thermal conductivity (W/(mK)) equation t = time (s) 휌 = density (kg/m3) 푐푝 = specific heat (J/(kg.K))

2.3. MATERIALS 1. The material’s thermal conductivity (for PE1) RELATIONS 2. The material’s specific heat capacity and density (for PE1) (all the above are the results of experimental measurements)

~~~~SIMULATED 2.4 INPUT~~~~

~~~~3 SPECIFIC COMPUTATIONAL MODELLING METADATA Finite difference NUMERICAL 3.1 Difference scheme: FullyImplicitFirstOrder SOLVER~~~~

~~~~3.2 SOFTWARE TOOL EnergyPlus (https://energyplus.net/)~~~~

~~~~3.3 TIME STEP 1h or less~~~~

~~~~COMPUTATIONAL PHYSICS EQUATION, written up for finite difference 3.4 REPRESENTATION MATERIAL RELATIONS, MATERIAL~~~~

~~~~BOUNDARY Weather data (temperature, radiation, …)~~~~

~~~~CONDITIONS~~~~

~~~~ADDITIONAL SOLVER Inside face temperature convergence criteria:~~~~

~~~~PARAMETERS <0.0001~~~~

~~~~4 POST PROCESSING~~~~

~~~~THE PROCESSED Temperatures will be used to estimate heating/cooling loads 4.1 OUTPUT IS CALCULATED FOR~~~~

~~~~4.2 METHODOLOGIES physics definition for loss and gain~~~~

~~~~4.3 MARGIN OF ERROR~~~~

~~~~374~~~~

[

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~~~~- Annex III List of software codes used in NMP projects EN~~~~

]

SOFTWARE where they are used by the website NMP projects ABAQUS Continuum solid mechanics (micro and www.3ds.com/fr/products/simulia/p macro); fluid dynamics; process ortfolio/abaqus/overview ABINIT Electronic: quantum mechanical www.abinit.org

ACEFEM Continuum solid mechanics (micro and www.wolfram.com/products/applica macro) tions/acefem ADF Electronic: quantum mechanical and www.scm.com/Products/ADF and many-body and semi-empirical or parametrised electronic models and Atomistic: statistical methods AMBER Atomistic: ab-initio molecular dynamics www.ambermd.org and Quantum Mechanics/Molecular Dynamics AMPAC Electronic: quantum mechanical and www.semichem.com many-body and semi-empirical or parametrised electronic models and Atomistic: statistical methods ANSYS (FLUENT) Continuum solid mechanics (micro and www.ansys.com macro); fluid dynamics ANSYS HFSS Continuum: Electomagnetism www.ansys.com

~~~~BOLTZTRAP Electronic: many-body and semi- www.icams.de/content/departments empirical or parametrised electronic /ams/madsen/boltztrap models CANTERA code.google.com/p/cantera~~~~

CASTEP Electronic: quantum mechanical and www.castep.org Atomistic: ab-initio molecular dynamics and Quantum Mechanics/Molecular Dynamics CHEMKIN Continuum: chemistry www.reactiondesign.com/products/o pen/chemkin CHEMSHELL Continuum: chemistry chemcell.sandia.gov

CFX ANSYS Continuum: fluid mechanics www.ansys.com/Products/Simulatio n+Technology/.../ANSYS+CFX CODICE_DEG Continuum: solid mechanics (micro) www.codice-project.eu/codes and demos CODICE_MEC Continuum: solid mechanics (micro) www.codice-project.eu/codes and demos COMSOL Mesoscopic: statistical methods, www.comsol.com Continuum solid mechanics (micro) ; continuum thermodynamics; electrochemistry; continuum EM CP2K Electronic: quantum mechanical and www.cp2k.org Atomistic: ab-initio molecular dynamics and Quantum Mechanics/Molecular Mechanics

~~~~375~~~~

[

~~~~- CRYSTAL MAKER Electronic: quantum mechanical www.crystalmaker.com 531~~~~

~~~~CTQMC Electronic: many-body and semi- inhouse (GOFAST) -~~~~

~~~~empirical or parametrised electronic ]~~~~

~~~~models CTS studio suite continuum EM www.cst.com/2010~~~~

DALTON Electronic: quantum mechanical www.dirac.chem.sdu.dk/dalton program.org/ DEFORM3D Continuum mechanics (macro) www.deform.com/products/def orm-3d/ DEMON2K Electronic: quantum mechanical www.demon-software.com

~~~~DESSIS Continuum: Device modelling www.iue.tuwien.ac.at/phd/klim a/node8 DETCHEM Continuum: Chemistry www.detchem.com~~~~

DIFFRACMOD Continuum EM www.foservice.com/SOFTWARE /diffractmod DGCA Mesoscopic: micromagnetics, file inhouse (DYNAMAG) compression DL_POLY Electronic: quantum mechanical and http://www.stfc.ac.uk/cse/255

device level 26.aspx DMM Mesoscopic: micromagnetics In-house [DYNAMAG and This is a frequency domain technique MAGNONICS] rather a simulation code ELK Electronic: quantum mechanical www.elk.sourceforge.net

~~~~Elmer Continuum: flow http://www.csc.fi/english/page s/elmer) http://www.simpartix.com/ FDMAX Continuum: Electomagnetics~~~~

FEAP Continuum solid mechanics (micro) and www.ce.berkeley.edu/feap process FEMAP Commercial continuum solid: pre- www.plm.automation.siemens. processor com FEMME Mesoscopic: micromagnetics www.suessco.com/simulations/ solutions/femme-software FIREBALL Electronic: quantum mechanical http://onlinelibrary.wiley.com/d oi/10.1002/pssb.201147259/ab stract;jsessionid=7E7A482F6EF D483AEB9979289EDEE0EE.d03 t04) FLAPW-FLEUR Electronic: quantum mechanical, DFT www.flapw.de

~~~~GARAND Atomistic: statistical methods; drift www.goldstandardsimulations.c diffusion om/services/service- simulations/statistical- variability/atomistic-simulator~~~~

~~~~376~~~~

[

~~~~- GAUSSIAN Electronic: quantum mechanical and www.gaussian.com 531~~~~

~~~~many-body and semi-empirical or -~~~~

~~~~EN parametrised electronic models and~~~~

~~~~- Atomistci Quantum Mechanics/Molecular N~~~~

] Dynamics and Atomistic: statistical methods GPAW Electronic: quantum mechanical www.csc.fi/english/research/sof tware/gpaw GROMACS Electronic: many-body and semi- www.gromacs.org/About_Groma empirical or parametrised electronic cs models and Atomistic: statistical methods, molecular dynamics GROMOS Mesoscopic: molecular dynamics www.gromos.net

HYPERCHEM Electronic: semi-empirical and ab-initio www.hyper.com molecular orbital methods, as well as density functional theory Atomistic: molecular mechanics, molecular dynamics INFOLYTICA Continuum: behaviour of magnets www.infolytica.com/en/products/ magnet

KMC-MD Atomistic: statistical methods www.kintechlab.com/products/m (Molecular Dynamics - kinetic Monte d-kmc Carlo) LAMMPS Atomistic: statistical methods www.lammps.sandia.gov (molecular dynamics) LLG Mesoscopic: Micromagnetics http://llgmicro.home.mindspring. com Madrid/Konstanz Mesoscopic: micromagnetics Inhouse (FEMTOSPIN) code MAGPAR Mesoscopic: micromagnetics www.magpar.net

MARC Continuum mechancis (macro) www.mscsoftware.com/Products/ CAE-Tools/Marc.aspx MATERIALS Electronic: many-body and semi- http://accelrys.com/products/coll STUDIO empirical or parametrised electronic aborative-science/biovia- models and Atomistic: Newton's materials-studio/ equation based and Statistical Mechanics models and Mesoscopic: statistical methods MCGEN Continuum: device modelling Inhouse (SUPERLION)

~~~~MicroMagus Mesoscopic: micromagnetics http://www.micromagus.de/~~~~

MSC.MARC/MENTA Continuum solid mechanics (micro and www.mscsoftware.com T macro); fluid dynamics; process MSINDO Electronic: many-body and semi- www.thch.uni-bonn.de empirical or parametrised electronic models

~~~~MUMAX Mesoscope: micromagnetics code.google.com/p/mumax~~~~

~~~~377~~~~

[

~~~~- NAMD Electronic: many-body and semi- www.ks.uiuc.edu/Research/namd 531~~~~

~~~~empirical or parametrised electronic -~~~~

~~~~EN models and Atomistic: statistical~~~~

~~~~- methods N~~~~

~~~~] NMAG Mesoscopic: micromagnetics www.nmag.soton.ac.uk~~~~

~~~~NMTO Electronic: many-body and semi- www2.fkf.mpg.de/andersen empirical or parametrised electronic models NXNastran Continuum solid mechanics http://www.plm.automation.siem ens.com~~~~

OCTOPUS Electronic: quantum mechanical in www.tddft.org response of time dependent fields OOMMF Mesoscopic: micromagnetics www.ngs.ac.uk/use/applications/ engineering/oommf OpenKIM Atomistic: interatomic potentials and www.openkim.org simulations

~~~~OPENMX Electronic: quantum mechanical www.openmx-square.org~~~~

~~~~OPTILAYER Continuum: EM www.optilayer.com~~~~

~~~~OPTIWAVE Continuum: EM www.optiwave.com~~~~

~~~~PICMC (DSMC) Atomistic: statistical methods Inhouse (ORAMA)~~~~

~~~~POM-POM TUBE Continuum: fluid dynamics: polymer Inhouse (MODIFY) melt rheology This is a constitutive equation not a simulation package! PWM Mesoscopic: micromagnetics inhouse (DYNAMAG)~~~~

~~~~PWSIC Electronic: quantum mechanical Inhouse (ATHENA)~~~~

~~~~QUATRA/CELS Atomistic: semi-classical drift-diffusion inhouse (SMASH) method and quantum kinetic model QLDFT Electronic: quantum mechanical physics.joacobs.university.de/the~~~~

ine/research/qldft/ QUANTUM Electronic: quantum mechanical and www.quantum-espresso.org ESPRESSO Atomistic: ab-initio molecular dynamics QUIP Electronic: quantum mechanical and www.libatoms.org Atomistic: ab-initio molecular dynamics and Quantum Mechanics/Molecular Mechanics RANDOMSPICE Continuum: Device modelling: statistical www.goldstandardsimulations.co circuit simulator m/products/randomspice RETICOLO Continuum: Electromagnetism Inhouse (NIM-NIL)

RIG-VM Atomitsic: Boltzmann transport equation http://www.ist.fraunhofer.de/en/ solver, Direct Simulation Monte-Carlo services/simulation.html and Particle in Cell plasma modelling for coating processes, optical modelling RSPt Electronic: many-body and semi- www.fplmto-rspt.org empirical or parametrised electronic models

~~~~378~~~~

[

~~~~- SE-MARGL Mesoscopic: micromagnetics www.magnonics.org/semargl/ 531~~~~

~~~~This software for post-processing the -~~~~

~~~~EN data from micromagnetic simulations~~~~

]

SIESTA Electronic: quantum mechanical and and www.nanotec.es/products/siesta. many-body and semi-empirical or php parametrised electronic models and Atomistic: statistical methods SIMPARTIX Continuum: flow www.simpartix.com

SPINPM Mesoscopic: micromagnetics www.apl.aip.org/resource/1/appl ab/v96/i2/p022504_s1?view=ref s TIBERCAD Electronic: many-body and semi- www.tibercad.org/ empirical or parametrised electronic models, Atomistic: continuum mechanics (micro) TINKER Electronic: many-body and semi- www.dasher.wustl.edu/ffe/ empirical or parametrised electronic models and Atomistic: statistical methods TURBOMOLE Electronic: quantum mechanical and www.turbomole.com/ quantum mechanical in response of time dependent fields UppASD Atomistic: statistical methods and Inhouse (MONAMI) Mesoscopic: micromagnetics Uppsala code Electronic: quantum mechanical in Inhouse (FEMTOSPIN) response of time dependent fields VASP Electronic: quantum mechanical and www.vasp.at Atomistic: ab-initio molecular dynamics and Quantum Mechanics/Molecular Mechanics WANT Electronic: quantum mechanical Inhouse (ATHENA)

~~~~WIEN2K Electronic: quantum mechanical www.wien2k.at~~~~

~~~~WISETEX Continuum: solid and fluid mechanics www.mtm.kuleuven.be/Onderzoe k/Composites/software/wisetex YORK code Atomistic: statistical methods Inhouse (FEMTOSPIN)~~~~

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~~~~Acknowledgements:~~~~

~~~~Throughout 4 years this Review kept growing via discussions with people who helped with their energy and time to think about the concepts, vocabulary and classification.~~~~

~~~~Major conceptual contributions came from~~~~

Pietro Asinari Emiel Hensen Michal Basista Kersti Hermansson Peter Bobbert Stepan Lomov Jesus Carrete Montana Mathieu Luisier David Cebon Philippe Mainçon Eliodoro Chiavazzo Keijo Mattila Jerome Claracq Nele Moelans Jerome Cornil Eoin O'Reilly Yuwen Cui Mike Payne Michele Fabrizio Heinz Preisig Hans Fangohr Oliver Rott Adam Foster Georg Schmitz Emanuele Ghedini Wolfgang Wenzel Gerhard Goldbeck Erich Wimmer Thomas Hagelien Bjoern Winkler Adham Hashibon

~~~~The intense discussions with all coordinators and modellers in the 130 projects documented in the Review have sharpened the formulations of the concepts.~~~~

~~~~The patience of the owners of models still to be added to the Review made it possible to extract the concepts with which to describe their models.~~~~

~~~~My co-author on the first versions Lula Rosso remained a source of inspiration and without her we would have never embarked on this enterprise.~~~~

~~~~Gigel-Marian Stanusi contributed to the updating of the figures, lay-out of the fiches, hyperlinks…..and stood the data storms.~~~~

~~~~Anne F. de Baas~~~~

~~~~380~~~~

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~~~~How to obtain EU publications -~~~~

]

~~~~Free publications:~~~~

~~~~• one copy: via EU Bookshop (http://bookshop.europa.eu);~~~~

• more than one copy or posters/maps: from the European Union’s representations (http://ec.europa.eu/represent_en.htm); from the delegations in non-EU countries (http://eeas.europa.eu/delegations/index_en.htm); by contacting the Europe Direct service (http://europa.eu/europedirect/index_en.htm) or calling 00 800 6 7 8 9 10 11 (freephone number from anywhere in the EU) (*).

~~~~(*) The information given is free, as are most calls (though some operators, phone boxes or hotels may charge you).~~~~

~~~~Priced publications:~~~~

~~~~• via EU Bookshop (http://bookshop.europa.eu);~~~~

~~~~[Cataloguenumber]~~~~

~~~~KI -~~~~

~~~~197~~~~

~~~~The future of the European industry is associated with a strong modelling capacity. An efficient modelling approach is needed to shorten the development process of materials-enabled products.~~~~

This Review of Materials Modelling describes modelling of materials, their properties and use in industrial applications illustrated by H2020 LEIT NMBP Materials projects. It does not require prior knowledge of the subject. It is written for anybody interested. It contains no equations. The Review is to provide insight into the work of the modellers and help the reader to see the models as more than mere “black boxes”.

This Review of Materials Modelling shows that industry is a very active player both in modelling for production and in modelling research areas. Industry identifies the specifications for material properties and the modelling then finds which material composition can meet the specs and how production can be done. This "Materials by Design" approach has been supported during the last decade in the EU Framework Programmes.

Application areas of modelling span all industrial sectors. The bulk of the projects are applying existing models to new materials, which shows that the current state of the art of modelling can be characterised as "mature".

~~~~Studies and reports~~~~