Using DL_POLY to understand radiation damage effects and soft matter (glasses, liquids, supercritical fluids)

Kostya Trachenko

Queen Mary University of London Collaborators:

Martin Dove, Volker Heine

Vadim Brazhkin

William Smith, Ilian Todorov, Michael Seaton

Chenxing Yang, Dima Bolmatov, Eva Zarkadoula, Ling Wang, Aaron Diver

Support from MCC Consortium and Prof R Catlow Starting from 2017, DL_POLY is taught in Queen Mary in third year.

Twice the number of students we expected (40-50). I started 20 years ago, working on glasses with Martin and Volker. DL_POLY 2 (now “Classic”) Two-level systems

PRL 1998 Glasses under pressure

Explains how glasses relax under pressure ~ln(t) Glasses under pressure

We vs two PRLs: a story about 1-order in SiO2 glass:

experiment vs theory

PRL 2004 Radiation damage effects

Future of nuclear industry is linked to safe encapsulation of nuclear waste

1. Radiation damage in materials to be used to encapsulate highly radioactive nuclear waste: ceramic materials

2. Radiation damage in nuclear fuels in current and future nuclear reactors: metals 3. Radiation damage in future fusion reactors: metals Crystalline ceramics as waste forms

. Safe and more durable alternative to glasses: CaTiO3, CaZrTi2O7, BaAl2Ti6O16 and TiO2 - geochemically stable minerals which have immobilised uranium and thorium for billions of years. Can incorporate high-level radioactive waste (Pu, Sr, Ba, Cs) . Pyrochlore (Gd, Sm, Hf-based)-rich titanate phases for Pu encapsulation: high waste load plus criticality control (neutron absorbants)

. Other potential “waste forms”: ZrSiO4, ZrO2, Gd2Zr2O7 and so on

What are the effects of radiation damage? How do they affect performance of waste forms? Effect of radiation-induced amorphization on

What are long-term (millions of years) effects of irradiation on the performance of waste forms?

Case study: zircon ZrSiO4 minerals are ~1 billion years old, completely amorphous yet intact Absorbs large ions like Pu on Zr site Can we learn from Nature?

What are the effects of radiation damage? Processes are too fast and collision cascades are too small for experiments -> MD simulations

Challenge of large energy and large size: Recoil energies: 100-500 keV Require very large MD boxes Not achievable previously Molecular dynamics simulation of radiation damage: challenge of large energy and large size Details: 1. Empirical potentials; short-range ZBL potential at short <~1 Å distances

2. Perfectly scalable MD code based on domain decomposition strategy (DL_POLY 3 and 4)

3. Parallel computers (Cambridge HPC, HPCx, HECToR, Archer)

4. Adapted MD code to handle out-of-equilibrium conditions (variable time step, boundary scaling) High-energy U recoils in ZrSiO4 50 keV U recoil and their overlap

Density variations appeared inside cascades and during their overlap

Density variations later confirmed in diffuse X-ray scattering The value of percolation threshold in the continuum percolation is pc=0.3 (approx.) (non-trivial because it is continuous percolation)

This gives channels of increased diffusion and explains percolation-type increases of transport (Geisler et al, Trachenko et al, 2003, 2004) Amorphizability

A material is amorphizable if it is able to form a covalent network Resistant vs amorphizable materials

Some materials are easily amorphized (silicates and titanates)

Others are extremely resistant to amorphization (e.g., ZrO2, Gd2Zr2O7)

What is the nature of the process of resistance to amorphization by radiation damage?

The same question is relevant in other areas: GaN and ZnO are considerably more resistant than GaAs, GaSb, Si etc Understanding resistance to amorphization to radiation damage

Resistance is governed by activation barriers for damage recovery and the nature of the bond

(but may or may not correlate with ratio of ionic “radii”, topology, coordinations, defect disorder energetics etc) Look at the process in detail

Rutile TiO2 Two types of damage relaxation:

1. Elastic reversible relaxation of crystalline lattice around the swollen cascade – large peak in Ndef

2. Irreversible topological damage

1-2 ps 50-100 ps Resistance to amorphization

50 keV U recoil Poor recovery Intermediate recovery Good and perfect recovery

SiO2 GeO2 TiO2 MgO Al2O3

t=1 ps

t=5, 50 ps

MD simulations reproduce experimental behaviour of resistance to amorphization. Damage increases with the stiffness of O-O interaction Trachenko, Todorov, Dove, Artacho and W. Smith, PRB 2006 Why do empirical potentials reproduce activation barriers that govern damage recovery? Resistance to amorphization

. Classical MD simulations reproduce experimental behaviour of resistance to amorphization

. MD simulations can be used to predict highly resistant materials where resistance to amorphization operates on the time scale of picoseconds. Successfully predicted resistance of series of pyrochlores.

. Slower recovery processes are possible. Even then, predictions work if the barriers are sufficiently high (cascade size in MD simulations on ps time scale=in billion-year-old samples from NMR experiments) Radiation damage in Simulate radiation damage in fusion reactors: ~1 Mev Fe recoil atoms from 14 MeV neutrons Also relevant for nuclear fuels: fission products (many MeVs)

These energies were not studied before, yet are important to simulate Require up to 1 billion atoms in MD box DL_POLY development work supported by the EPSRC grant, in collaboration with Ilian Todorov and Michael Seaton

Radiation damage-specific developments: - Identification of radiation damage and defects - Electronic energy loss mechanism (friction term and two- models)

General developments related to very large system sizes: -Calculation of properties on the fly (one configuration of 250 mln atoms is about 100 Gb, ~10,000-frame history file is ~10-100 Tb in size) - Change the paradigm of how to run&analyze MD results – MD of the future - Relevant for many interested in phenomena operating on microscale: shock, fracture, initiation of micro-cracks, micro-structural changes, interfacial effects, macromolecules, biological systems and so on Current work: finish the development work

Calculation on the fly of: - elastic constants - velocity correlation functions (thermal conductivity, density of states etc) - New algorithms of defect identification

Write it up and include in the next release. Our new postdoc is happy to lead. 0.2 - 0.5 MeV Fe recoils in iron

These energies have not been simulated before • Many-body (embedded atom) potential optimized against several defect energies in alpha-iron • 100-500 million atoms, system size ~100-200 nm • 24,000-65,000 parallel HeCTOR processors • Fearless PhD student

1. What does the collision cascade actually look like? First visualization of high-energy cascades

2. Novel insights into the cascade structure: continuous damage morphology vs sub-cascade branching Iron movies

Can defects induced by shock waves be permanent? 500 keV Fe recoils in iron anharmonicity displaced atoms defect atoms

Look at defects locally: Novel large (~100 atoms) clusters of interstitials and vacancies. Quantify and discuss their stability. IoP Selected Highlight and News Story in JPCM 2013 Current work: interfaces in Y2O3-ZrO2

0% Y 5% Y 8% Y 10% Y

11% Y 12% Y 15% Y 20% Y

Cubic phase Orthorhombic (not monoclinic) phase Liquids gases: solids: fluidity density viscosity duality of liquids bulk modulus … No theory

Trachenko and Brazhkin, Reports on Progress in Physics 2016 Energy and heat capacity of matter

E =3NT/2 Gases, solids gas Esolid=3NT

Liquids Eliquid=? A Granato JNCS 2002

Landau school: “liquids have no small parameter” Landau&Lifshitz, Statistical Physics: “The absence of smallness of particle vibrations… Interactions in a liquid are both strong and system-specific Liquid energy can not be calculated in general form 3 N E  NT  U (r)g(r)dV 2 2 

Allen and Tildesley “Computer simulation of liquids” Frenkel reduction

τ - time between particle jumps

t<τ : solid t>τ : liquid

ω>ωF=1/τ : liquid supports solid-like collective modes. Frequency gap. ω<ωF=1/τ : hydrodynamic modes

Prediction: liquid supports two transverse modes with ω>ωF and one longitudinal mode (propagating in two different regimes) Experiments: liquid Hg

• Van Der Waals, hard-spheres models of liquids etc: ideal-gas cv=3kB/2

• Can liquid cv be understood on the basis of collective modes as in solids? Supercritical fluids

Food industry, e.g. Purification and extraction decaffination (non-toxic) of unwanted solvents, CO2

of coffee and tea, CO2

supercritical fluids: green and effective Supercritical H2 in Jupiter, Saturn, exoplanets, brown dwarfs

plants to treat toxic and hazardous

wastes: “supercritical H2O oxidation” as alternative to Extraction and removing of incineration and landfills actinides in nuclear waste, CO2 New proposal: the Frenkel line in the supercritical region

Textbooks: no difference Our proposal: the new Frenkel between a gas and a liquid line separates two distinct states above the critical point.

2012-2013: Physics Today 2012, PRL 2013, Nature Comm. 2013

Recently reviewed in Rep. Prog. Phys. 2016 Thermodynamic crossover at the Frenkel line

Shear modes at ω>1/τ

Frenkel line corresponds to τ≈τD

Important change is the inability to support rigidity (solid-like shear modes) at ANY frequency: rigidity is lost completely

the supercritical system crosses over from “rigid” liquid to “non-rigid” gas- like fluid What kind of shear modes can propagate  in liquids and supercritical fluids? ds P 1 dP  1 1 d         P  dt G dt  G dt  1  d  1 P    dt  1  dv   2v    p dt     d  dv   2v  1   p 1  dt  dt  k  k   gap c  2v  2v dv    x2 t 2 dt K-gap!  2v  2v 1 dv c2   (rather than frequency gap ω=1/τ, 2  2 x t dt frequency gap =0)  t  v exp exp( i t)   2  1  c2k 2  Rep. Prog. Phys. 2016  2 MD simulations: DL_POLY

LJ potential, calculate transverse current correlation function for several

C(k,t)=, J=Σ[kvi]exp(-ikri(t)).

Rather than using a fitting function, we average over 20 different runs

Fourier transform gives intensity maps (structure factor) Intensity maps C(k,ω) 1 PRL 2017 k  k  gap c

T=250 K T=300 K

T=350 K T=400 K

T=450 K T=500 K Dispersion curves

Supercritical Ar 1 k  k  gap c

Subcritical Ar

Supercritical CO2 What does this imply from the point of view of field theory?

1. Epc – relativistic particle. No gap.

2. (c=1) – non-relativistic particle. Gap in energy or mass. Gap in Y-axis

3. ( ). Liquid (quasiparticles). Gap in k-space, or momentum. Gap in X-axis. Not seem anywhere else.

Except in tachyons!

What is the corresponding field theory? What is Lagrangian? Need to involve TWO fields propagating in the opposite space-time directions (arXiv:1710.01390) Back to liquid thermodynamics:

6 ω Energy of two transverse modes Et : 2 1 ω where ωF=1/τ

ω Add all other terms: 3 ω

As temperature increases, ωF=1/τ increases and the range of transverse modes shrinks. The energy slope decreases and cv decreases from 3 to 2. Theory and experiment:

Take experimental τ and calculate cv=dE/dT directly. Experimental SUPERCRITICAL data are from NIST Theory and MD simulations: calculate τ directly (Wang et al PRE 2017) Ar Fe

ρ=1.5 g/cm3 ρ=8 g/cm3 ρ

ρ=1.9 g/cm3 ρ=11 g/cm3 Can a theory of liquid heat capacity, in fact, exist?

. Good agreement for 21 metallic, noble, molecular and network - bonded liquids in a wide range of temperature and pressure

. No fitting parameters used. Parameters correspond to physically sensible

τD~0.1 ps (τD is fixed at their solid experimental values)

. Despite many pessimistic statements, liquids emerge as exciting systems amenable to theoretical understanding in a consistent picture THANK YOU