DOCSLIB.ORG

Bond Order Potentials for Covalent Elements

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bond Order Potentials for Covalent Elements Bond order potentials for covalent elements. This chapter will be dedicated to a short history of the so called \bond order" potentials [1, 2, 3, 4, 5, 6, 7] (BOPs), that represent an interesting class of the rather scattered family of analytic potentials. Analytic interatomic potentials (sometimes referred to as empirical, semi-empirical or clas- sical potentials) are used for a variety of purposes, ranging from the estimation of minimum energy structures for surface reconstruction, grain boundaries or related defects, to the descrip- tion of the liquid structure. All analytic potentials are de¯ned through a functional form of the interatomic interactions, whose parameters are ¯tted to a selected database. According to Brenner [8], an analytic potential needs to be: ² Flexible: the function should be flexible enough to accommodate the inclusion of a relatively wide range of structures in a ¯tting database. ² Accurate: the potential function must be able to accurately reproduce quantities such energies, bond lengths, elastic constant, and related properties entering a ¯tting database. ² Transferable: the functional form of the potential should be able to reproduce related prop- erties that are not included in the ¯tting database. In practise the potential should be able to give a good description of the energy landscape for any possible realistic con¯guration characterized by the set of atomic positions frig. ² Computationally e±cient: the function should be of such a form that it is tractable for a desired calculation, given the available computing resources. We note that one of the paradigms that has led science through its development, i.e. the Occam razor (\Entities should not be multiplied beyond necessity"), is not mentioned here. This is intentional: as it will become clearer through the chapter, even if bond order potentials are based on the beauty and simplicity of ab initio theories, they achieve computational e±ciency and transferability paying the fee of a proliferation of somewhat ad-hoc adjustments, any of them implying propter-hoc parameters. In other words, on one hand bond order potentials increase transferability, with respect to simple two-body potentials, increasing the number of parameters. On the other hand, they increase computational e±ciency, with respect to ab initio calculations, at the same price of adding parameters. It has to be noted that the focus of bond order potentials is put on their performance, i.e. on the fact that they work. Thus, thinking at the Occam razor, bond order potentials give to \necessity" a meaning that is di®erent from the traditional one. It is indeed necessary to introduce new entities (viz. parameters), for ful¯lling the four requirements stated above. BOPs are all expressed by giving the binding energy of a system as a sum over all pairs: 1 X X £ ¤ E = V R(r ) ¡ b V A(r ) (1.1) b 2 ij ij ij i j6=i R A where V (rij) and V (rij ) are pair-additive interactions representing all interatomic repulsions and all those attractions coming from valence electrons, respectively; rij is the distance between 2 Bond order potentials for covalent elements. atoms i and j and the (scalar) quantity bij is a function of the local environment of atoms i and j, called \bond order". With a meaning indeed close to that used for up-to-date bond-order potentials, the term \bond order" was introduced in 1939 by Coulson [9] in treating the strength of ¼-bonds in polyenes and aromatic molecules. Following this author, if a given molecular orbital of a molecule (ª(n)) is expressed as a linear combination of atomic orbitals (Á(n)) of the individual ¼-electrons: P i ª(n) = a(n)Á(n), with ai a complex number, then the partial mobile bond order (b(n)) of a i i i h i ij (n) 1 (n) (n)¤ (n)¤ (n) ¼-bond between atoms i and j is de¯ned as bij = 2 ai aj + ai aj . The total mobile bond order (bij) of the ¼-bond, between atom i and j, is the sum of the partial bond orders P (n) over all the molecular orbitals involved: bij = (n) bij . The bond order is the total mobile bond order plus one, to account for the σ bond. With this de¯nition, a bond order of value 1 or 2, would correspond to the intuitive concepts of single and double bonds, respectively. In a a benzene molecule the total mobile bond order of each bond is 2=3, and the bond order is 5/3, closer to a double than to a single bond. The form of Eq. 1.1 can be justi¯ed on the basis of the Local Orbital approach (LO) that Abell [10] developed in the framework of Chemical Pseudopotential (CPP) theory [11, 12, 13]. This theory in turn relies on the HÄuckel Molecular-Orbital (HMO) theory [14]. The derivation of Abell is rather instructive: a series of non trivial assumptions lead to two important results. The ¯rst is a motivation of the unexpected alikeness [15] of the shape of the binding energy curves in rather di®erent environments, ranging from pure covalent to metallic bonds; the relevant parameter that identi¯es the type of bonding of a reference atom is the number of its ¯rst neighbours Z. The second is a justi¯cation of the initial guess on the functional form of the ¡1=2 term bij as used in successful BOPs: b = Z . In the following section we will give a brief exposition of the derivation of Eq. 1.1 from LO. The subsequent section (1.2) will suggest an alternative and much more intuitive argument to derive 1.1, based on the moments theorem [16]. In the remainder of the chapter (sections 1.4 and 1.5), a brief overview of BOPs will be given. Focus will be put on those features of the BOPs that are recurrent in all the formulations, underlining analogies and di®erences. Thus, we will often skip the details and we will never give the values of the ¯tted parameters. We will provide a full description of a BOP for the Long range Carbon Bond Order Potential (LCBOP) [7] in section 1.6. The full description is necessary, since an improvement of this potential has been one the early targets of the present thesis work: this modi¯cation is illustrated in section 1.7. 1.1 Localized orbitals model Abell [10], following Anderson [11, 12, 13], writes the Hamiltonian for a system of atoms as: X H = K + Va (1.2) a where K is the total kinetic-energy operator and Va is the e®ective potential due to the presence of atom a in the system and the sum extends over all the atoms. The crucial hypothesis of this approach is that the Va's are short ranged and strongly localized about the corresponding atoms. It is also assumed that only one atomic species is involved. Molecular orbitals (Ãi) end their energies ("i) are the eigenfunctions and eigenvalues of the SCF Hamiltonian: H j Ãi >= "i j Ãi > (1.3) Abell shows that it is possible to ¯nd a suitable basis set, that spans the molecular-orbital sub- space of fÃig, and whose elements are atomic-like orbitals, that allows to write the Hamiltonian as a sum of (environment dependent) pairwise interaction terms. Calling 'm the elements of this searched basis, the Hamiltonian can be rewritten: X X H = [²0 + VR(rkm)] j 'm >< 'm j + m k6=m X X + VA(rkm) j 'm >< 'k j (1.4) m k6=m 1.1 { Localized orbitals model 3 and X Ãi = Cmi'm (1.5) m where the index m runs all over the atoms. The explicit expressions for VR and VA, coming from the CPP theory [13], need the intro- duction of V~m { as the SCF one-electron atomic potential of atom m (including exchange and correlation) appropriated to the isolated atom { and of V~k { as the di®erence from the atomic ~ 0 potential Vm due to the presence of atom k. Introducing the unperturbed atomic orbitals Ám, the energy ²0 of the isolated atom is easily written: 0 ~ 0 ²0 =< Ám j (T + Vm) j Ám > (1.6) and 0 ~ 0 VA(rkm) = < Ák j VkjÁm > 0 ~ 0 0 0 ~ 0 VR(rkm) = < Ám j Vk j Ám > ¡Skm < Ák j Vk j Ám > (1.7) 0 0 0 with Skm =< Ák j Ám >. In the above expressions for VA and VR, the crucial approximation 0 of using the unperturbed atomic orbitals Ám has been adopted . The Hamiltonian in Eq. 1.4 is therefore approximated by the introduction of these VA and VR. The binding energy Eb of the system is de¯ned as the total energy, expressed as the sum of ¤ the energies "i of the occupied orbitals, minus the sum of the energies ²0 of the isolated atoms : X Eb = ni("i ¡ ²0) (1.8) i where ni = 0;1 is the occupancy of the molecular orbital Ãi. De¯ning X : 2 qm = nijCmij (1.9) i X : ¤ bkm = niCkiCmi (1.10) i and using Eqs. 1.4 and 1.5, yields X X X Eb = [qm VR(rkm) + bkmVA(rkm)] (1.11) m k6=m k6=m Note that the de¯nition of bkm explicitly resembles the de¯nition of bond order as given by Coulson [9]. The term qm represents the net electron density on site m. Eq. 1.11 can be particularized for regular structures (in which each atom `sees' the same environment): E X E = b = Z (qV + b V ) (1.12) b N k Rk k Ak k where Eb is the bond energy per atom, Zk is the number of atoms in the k-th shell, bk is the bond order between the reference atom and the atoms in the k-th shell, and q is the number of (valence) electrons per atom.
Load more

Recommended publications
  • A Survey of Some Empirical and Semiempirical Interatomic And
    ui avaiiuai'ua , iuxicu. DUi;au rcererence door; noTto Library, N.W. Bldg D8 taken fr NBS TECHNICAL 246 A Survey of Some Empirical and Semi-Empirical Interatomic SI and Intermolecular Potentials i§ BENJAMIN M. AXILROD or KtHt /T \ U.S. DEPARTMENT OF COMMERCE >rV z *& National Bureau of Standards o \ ^CAU Of * IS — THE NATIONAL BUREAU OF STANDARDS The National Bureau of Standards 1 provides measurement and technical information services essential to the efficiency and effectiveness of the work of the Nation's scientists and engineers. The Bureau serves also as a focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To accomplish this mission, the Bureau is organized into three institutes covering broad program areas of research and services: THE INSTITUTE FOR BASIC STANDARDS . provides the central basis within the United States for a complete and consistent system of physical measurements, coordinates that system with the measurement systems of other nations, and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. This Institute comprises a series of divisions, each serving a classical subject matter area: —Applied Mathematics—Electricity—Metrology—Mechanics —Heat—Atomic Physics—Physical Chemistry—Radiation Physics—Laboratory Astrophysics 2—Radio Standards Laboratory, 2 which includes Radio Standards Physics and Radio Standards Engineering—Office of Standard Refer- ence Data. THE INSTITUTE FOR MATERIALS RESEARCH . conducts materials research and provides associated materials services including mainly reference materials and data on the properties of ma- terials.
    [Show full text]
  • Bond Order Potential for Fesi
    Bond order potential for FeSi P. S¨ule∗ Research Institute for Technical Physics and Material Science, Konkoly Thege u. 29-33, Budapest, Hungary, [email protected],www.mfa.kfki.hu/∼sule, (Dated: October 12, 2018) A new parameter set has been derived for FeSi using the Albe-Erhart-type bond order poten- tial (BOP) and the PONTIFIX code for fitting the parameters on a large training set of various polymorphs. Ab initio calculations are also carried out to study the relative stability of various polymorphs and to use the obtained data in the training set. The original BOP formalism was unable to account for the correct energetic relationship between the B20 (ε-FeSi) and B2 (CsCl) phases and notoriusly slightly favors incorrectly the B2 polymorph. In order to correct this improper behavior the BOP potential has been extended by a Columbic term (BOP+C) in order to account for the partial ionic character of FeSi. Using this potential we are able to account for the correct phase order between the most stable B20 and B2 (CsCl) polymorphs when the net atomic charges are properly set. Although this brings in a new somewhat uncertain parameter (the net charges) one can adjust properly the BOP+C potential for specific problems. To demonstrate this we study under high pressure the B2 phase which becomes more stable vs. B20 as it is found experimentally and expected to be taken place in the Earth mantle. The obtained BOP has also been tested for the metallic and semiconducting disilicides (α-FeSi2 and β-FeSi2) and for the Si/β-FeSi2 heterostruc- ture.
    [Show full text]
  • Molecular Orbital Theory to Predict Bond Order • to Apply Molecular Orbital Theory to the Diatomic Homonuclear Molecule from the Elements in the Second Period
    Skills to Develop • To use molecular orbital theory to predict bond order • To apply Molecular Orbital Theory to the diatomic homonuclear molecule from the elements in the second period. None of the approaches we have described so far can adequately explain why some compounds are colored and others are not, why some substances with unpaired electrons are stable, and why others are effective semiconductors. These approaches also cannot describe the nature of resonance. Such limitations led to the development of a new approach to bonding in which electrons are not viewed as being localized between the nuclei of bonded atoms but are instead delocalized throughout the entire molecule. Just as with the valence bond theory, the approach we are about to discuss is based on a quantum mechanical model. Previously, we described the electrons in isolated atoms as having certain spatial distributions, called orbitals, each with a particular orbital energy. Just as the positions and energies of electrons in atoms can be described in terms of atomic orbitals (AOs), the positions and energies of electrons in molecules can be described in terms of molecular orbitals (MOs) A particular spatial distribution of electrons in a molecule that is associated with a particular orbital energy.—a spatial distribution of electrons in a molecule that is associated with a particular orbital energy. As the name suggests, molecular orbitals are not localized on a single atom but extend over the entire molecule. Consequently, the molecular orbital approach, called molecular orbital theory is a delocalized approach to bonding. Although the molecular orbital theory is computationally demanding, the principles on which it is based are similar to those we used to determine electron configurations for atoms.
    [Show full text]
  • Interatomic Potentials
    Interatomic Potentials Dorothy Duffy October 2020 1 Introduction Interatomic potentials, also commonly referred to as forcefields, are widely used in the materials modelling community for simulating processes and calculating structural properties. They have been employed for several decades in a range of modelling methods, including molecular dynamics, Monte Carlo and, more recently, in rare event methods, such umbrella sampling and metadynamics, discussed in previous lectures of this course. The primary reasons for the popularity and success of methods employing in- teratomic potentials are their computational efficiency. Simulations of hundreds of millions of atoms are now commonplace and molecular dynamics timescales of tens of nanoseconds, or even microseconds, are achievable on high perfor- mance computing platforms. Extending simulation length and time scales is a universal aim of materials modellers, as they endeavor to close the gap between modelling and experiment. The main disadvantage with employing interatomic potentials is, of course, that the results are sensitive to the model. While this is true to some extent for density functional theory calculations, the sensitivity to the model is much stronger in interatomic potential methods. A second significant limitation is that the methods provide no information about electronic structure, therefore calculations of electronic properties, such as band gaps, are inaccessible. Nev- ertheless, carefully parameterised potentials are an invaluable tool for exploring time and length scale
    [Show full text]
  • Unifying Interatomic Potential, G (R), Elasticity, Viscosity, and Fragility of Metallic Glasses: Analytical Model, Simulations, and Experiments
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Home Search Collections Journals About Contact us My IOPscience Unifying interatomic potential, g (r), elasticity, viscosity, and fragility of metallic glasses: analytical model, simulations, and experiments This content has been downloaded from IOPscience. Please scroll down to see the full text. J. Stat. Mech. (2016) 084001 (http://iopscience.iop.org/1742-5468/2016/8/084001) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 131.111.184.102 This content was downloaded on 02/11/2016 at 17:59 Please note that terms and conditions apply. You may also be interested in: Relaxation and physical aging in network glasses: a review Matthieu Micoulaut Computer simulations of glasses: the potential energy landscape Zamaan Raza, Björn Alling and Igor A Abrikosov Length scales in glass-forming liquids and related systems: a review Smarajit Karmakar, Chandan Dasgupta and Srikanth Sastry Dynamical and structural signatures of the glass transition in emulsions Chi Zhang, Nicoletta Gnan, Thomas G Mason et al. Localization model description of diffusion and structural relaxation in glass-forming Cu–Zr alloys Jack F Douglas, Beatriz A Pazmino Betancourt, Xuhang Tong et al. Models of the glass transition J Jackle Exploring the potential energy landscape of glass-forming systems: from inherent structuresvia metabasins to macroscopic transport Andreas Heuer IOP Journal of Statistical Mechanics: Theory and Experiment J. Stat. Mech. 2016 ournal of Statistical Mechanics: Theory and Experiment 2016 J © 2016 IOP Publishing Ltd and SISSA Medialab srl Special Issue on Structure in Glassy and Jammed Systems JSMTC6 Unifying interatomic potential, g r , 084001 ( ) elasticity, viscosity, and fragility of A E Lagogianni et al metallic glasses: analytical model, Mech.
    [Show full text]
  • Valence Bond Theory
    Valence Bond Theory • A bond is a result of overlapping atomic orbitals from two atoms. The overlap holds a pair of electrons. • Normally each atomic orbital is bringing one electron to this bond. But in a “coordinate covalent bond”, both electrons come from the same atom • In this model, we are not creating a new orbital by the overlap. We are simply referring to the overlap between atomic orbitals (which may or may not be hybrid) from two atoms as a “bond”. Valence Bond Theory Sigma (σ) Bond • Skeletal bonds are called “sigma” bonds. • Sigma bonds are formed by orbitals approaching and overlapping each other head-on . Two hybrid orbitals, or a hybrid orbital and an s-orbital, or two s- orbitals • The resulting bond is like an elongated egg, and has cylindrical symmetry. Acts like an axle • That means the bond shows no resistance to rotation around a line that lies along its length. Pi (π) Bond Valence Bond Theory • The “leftover” p-orbitals that are not used in forming hybrid orbitals are used in making the “extra” bonds we saw in Lewis structures. The 2 nd bond in a double bond nd rd The 2 and 3 bonds in a triple bond /~harding/IGOC/P/pi_bond.html • Those extra bonds form only after the atoms are brought together by the formation of the skeletal bonds made by www.chem.ucla.edu hybrid orbitals. • The “extra” π bonds are always associated with a skeletal bond around which they form. • They don’t form without a skeletal bond to bring the p- orbitals together and “support” them.
    [Show full text]
  • Chapter 5 the Covalent Bond 1
    Chapter 5 The Covalent Bond 1. What two opposing forces dictate the bond length? (Why do bonds form and what keeps the bonds from getting any shorter?) The bond length is the distance at which the repulsion of the two nuclei equals the attraction of the valence electrons on one atom and the nucleus of the other. 3. List the following bonds in order of increasing bond length: H-Cl, H-Br, H-O. H-O < H-Cl < H-Br. The order of increasing atom size. 5. Use electronegativities to describe the nature (purely covalent, mostly covalent, polar covalent, or ionic) of the following bonds. a) P-Cl Δχ = 3.0 – 2.1 = 0.9 polar covalent b) K-O Δχ = 3.5 – 0.8 = 2.7 ionic c) N-H Δχ = 3.0 – 2.1 = 0.9 polar covalent d) Tl-Br Δχ = 2.8 – 1.7 = 1.1 polar covalent 7. Name the following compounds: a) S2Cl2 disulfur dichloride b) CCl4 carbon tetrachloride c) PCl5 phosphorus pentachloride d) HCl hydrogen chloride 9. Write formulas for each of the following compounds: a) dinitrogen tetroxide N2O4 b) nitrogen monoxide NO c) dinitrogen pentoxide N2O5 11. Consider the U-V, W-X, and Y-Z bonds. The valence orbital diagrams for the orbitals involved in the bonds are shown in the margin. Use an arrow to show the direction of the bond dipole in the polar bonds or indicate “not polar” for the nonpolar bond(s). Rank the bonds in order of increasing polarity. The bond dipole points toward the more electronegative atom in the bond, which is the atom with the lower energy orbital.
    [Show full text]
  • Carbon Carbon Spsp Hybrids : Acetylene and the : Acetylene And
    CarbonCarbon spsp hybridshybrids:: AcetyleneAcetylene andand thethe TripleTriple bondbond CC2HH2 isis HH--CCCC--HH FormForm spsp onon eacheach CC leavingleaving 2p2px,, 2p2py “unused”“unused” H - sp C sp + +-+ sp C sp H PredictsPredicts linearlinear structure.structure. AboveAbove areare allall σσ bondsbonds H-C-C-H Uses up 2 valence e- for each C in sp (and 2 from 1s H). Leaves 2 valence e - for each C unused. 2py 2py Put last valence 2px e- into ππ orbitals sp formed from H C C H 2px, 2py 2px - - 2 e in πx 2 e in πy Gives two π bonds connecting carbon atoms. π bonds are at right angles to each other. Total C-C bonds are now 3, one σσ, 2 π Short Comparison of Bond Order, Bond Length, Bond Energy C-C C-C C-C Molecule Bond Order Bond Length Bond E, kcal/mole σσ Ethane, C2H6 1 (1 ) 1.54Å 83 σσ Ethylene, C2H4 2 (1 , 1π) 1.35Å 125 σσ Acetylene, C2H2 3 (1 , 2π) 1.21Å 230 ConjugationConjugation andand DelocalizationDelocalization ofof ElectronsElectrons andand BondsBonds Although energy of π* in ethylene < σ*, conjugated polylenes have even lower energy π* levels. These absorb light at longer wavelength- sometimes even in visible (human eye’s light perception). Conjugated polyenes: C=C-C-C=C-C 2 essentially independent double bonds. C=C-C=C-C=C polyene DoubleDouble bondsbonds ALTERNATE!ALTERNATE! Could draw ππ bonds between any 2 C’s ππ* bonds C C C C C C drawn are not unique! ψψ This gives delocalized structure MO = (Const)[2py(1) + 2py(2) + 2py(3) + 2py(4) +2py(5) + 2py(6) +………].
    [Show full text]
  • Machine Learning a General-Purpose Interatomic Potential for Silicon
    PHYSICAL REVIEW X 8, 041048 (2018) Machine Learning a General-Purpose Interatomic Potential for Silicon Albert P. Bartók Scientific Computing Department, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot, OX11 0QX, United Kingdom James Kermode Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom Noam Bernstein Center for Materials Physics and Technology, U.S. Naval Research Laboratory, Washington, D.C. 20375, USA Gábor Csányi Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom (Received 26 May 2018; revised manuscript received 11 October 2018; published 14 December 2018) The success of first-principles electronic-structure calculation for predictive modeling in chemistry, solid-state physics, and materials science is constrained by the limitations on simulated length scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations remains a challenging goal. Here, we present a Gaussian approximation potential for silicon that achieves this milestone, accurately reproducing density-functional-theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations such as finite-temperature phase-boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential’s accuracy for a given atomic configuration.
    [Show full text]
  • Simulations of the Structure and Properties of Amorphous Silica
    Chemical Engineering Science 56 (2001) 4205–4216 www.elsevier.com/locate/ces Simulations of the structure andproperties of amorphous silica surfaces Jeanette M. Stallons, Enrique Iglesia ∗ Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA Received10 December 1999; accepted26 December 2000 Abstract The structure andtransport properties of solidsurfaces have been describedusingmodelsof varying complexity andrigor without systematic comparisons among available methods. Here, we describe the surface of amorphous silica using four techniques: (1) an orderedsurfacecreatedby cutting the structure of a known silica polymorph ( -cristobalite); (2) an unrelaxedamorphous surface obtainedby cutting bulk amorphous silica structures createdby molecular dynamicsmethods;(3) a relaxedamorphous surface createdby relaxing the amorphous surface; and(4) a randomsurface createdby Monte Carlo sphere packing methods. Calculations of the adsorption potential surface and simulation of the surface di4usion of weakly bound adsorbates (N2, Ar, CH4) interacting via Lennard–Jones potentials with these surfaces were used to compare surface models and to judge their ÿdelity by comparisons with available experimental values. Similar heats of adsorption were obtained on the relaxed, unrelaxed, and random surfaces (±0:5kJ=mol), but the relaxed surface showed greater heterogeneity with a wider distribution of adsorption energies. Surface di4usion on the relaxed surface was slower than on the other surfaces, with slightly higher activation energies (0:5–1:0kJ=mol). Rigorous comparisons between simulatedandexperimental surface di4usivitiesare not possible, because of scarce surface di4usion data on well-characterized surfaces. The values obtained from simulations on silica were similar to experimental surface di4usivities reported on borosilicate glasses. ? 2001 Publishedby Elsevier Science Ltd. Keywords: Porous media; Simulation; Transport processes; Di4usion; Surface di4usion; Adsorption 1.
    [Show full text]
  • Disentangling Interatomic Repulsion and Anharmonicity in the Viscosity and Fragility of Glasses
    Disentangling interatomic repulsion and anharmonicity in the viscosity and fragility of glasses J. Krausser,1 A. E. Lagogianni,2 K. Samwer,2 and A. Zaccone1, 3 1Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, CB2 3RA Cambridge, U.K. 2I. Physikalisches Institut, Universit¨atG¨ottingen, Friedrich-Hund-Platz 1, 37077 G¨ottingen,Germany 3Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, U.K. (Dated: February 22, 2017) Within the shoving model of the glass transition, the relaxation time and the viscosity are related to the local cage rigidity. This approach can be extended down to the atomic-level in terms of the interatomic interaction, or potential of mean-force. We applied this approach to both real metallic glass-formers and model Lennard-Jones glasses. The main outcome of this analysis is that in metallic glasses the thermal expansion contribution is mostly independent of composition and is uncorrelated with the interatomic repulsion: as a consequence, the fragility increases upon increasing the interatomic repulsion steepness. In the Lennard-Jones glasses, the scenario is opposite: thermal expansion and interatomic repulsion contributions are strongly correlated, and the fragility decreases upon increasing the repulsion steepness. This framework allows one to tell apart systems where "soft atoms make strong glasses" from those where, instead, "soft atoms make fragile glasses". Hence, it opens up the way for the rational, atomistic tuning of the fragility and viscosity of widely different glass-forming materials all the way from strong to fragile. I. INTRODUCTION fundamental observation in terms of the underlying microstructure, dynamics and interaction picture.
    [Show full text]
  • Bond Orders of the Diatomic Molecules†
    RSC Advances PAPER View Article Online View Journal | View Issue Bond orders of the diatomic molecules† Cite this: RSC Adv.,2019,9,17072 Taoyi Chen and Thomas A. Manz * Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all À Creative Commons Attribution-NonCommercial 3.0 Unported Licence. period 2 homodiatomics plus Mo2,Cr2, ClO, ClO , and Mo2(acetate)4. Using Manz's bond order equation with DDEC6 partitioning, the Mo–Mo bond order was 4.12 in Mo2 and 1.46 in Mo2(acetate)4 with a sum of bond orders for each Mo atom of 4. Our study informs both chemistry research and education. As Received 5th February 2019 a learning aid, we introduce an analogy between bond orders in materials and message transmission in Accepted 10th May 2019 computer networks.
    [Show full text]