Showing papers on "Interatomic potential published in 1996"

Modelling of the thermal dependence of structural and elastic properties of calcite, caco3

Abstract: A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO3; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10−6K−1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10−4K−1 is obtained.

Molecular dynamics study of the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2

Abstract: Molecular dynamics (MD) simulations have been used to calculate the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2 (CMAS) using an interatomic potential model (CMAS94), which is composed of pairwise additive Coulomb, van der Waals, and repulsive interactions. The crystals studied, total of 27, include oxides, Mg meta- and ortho-silicates, Al garnets, and various Ca or Al bearing silicates, with the coordination number of cations ranging 6 to 12 for Ca, 4 to 12 for Mg, 4 to 6 for Al, and 4 and 6 for Si. In spite of the simplicity of the CMAS94 potential and the diversity of the structural types treated, MD simulations are quite satisfactory in reproducing well the observed structural data, including the crystal symmetries, lattice parameters, and average and individual nearest neighbour Ca-O, Mg-O, Al-O, and Si-O distances. In addition MD simulated bulk moduli of crystals in the CMAS system compare well with the observed values.

Structure, Dynamics, and Thermodynamics of Clusters: Tales from Topographic Potential Surfaces

Abstract: Theoretical studies of atomic and molecular clusters often seek to explain structure, dynamics, and thermodynamics in terms of the underlying potential energy surface and the form of the interparticle interaction. One specific example from each of these categories is considered here; the overall approach can be summarized as global analysis of potential surfaces. Changes in the most favorable cluster morphology can be qualitatively understood as a function of the range of the interparticle forces. Thermodynamic properties can be calculated from a representative sample of local minima on the potential energy surface. However, prediction of dynamics requires not only knowledge of minima but also transition states and reaction pathways.

Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves.

Abstract: We provide a systematic test of empirical theories of covalent bonding in solids using an exact procedure to invert ab initio cohesive energy curves. By considering multiple structures of the same material, it is possible for the first time to test competing angular functions, expose inconsistencies in the basic assumption of a cluster expansion, and extract general features of covalent bonding. We test our methods on silicon, and provide direct evidence that the Tersoff-type bond-order formalism correctly describes coordination dependence. For bond-bending forces, we obtain skewed angular functions that favor small angles, unlike existing models. As a proof-of-principle demonstration, we derive a Si interatomic potential which exhibits comparable accuracy to existing models.

Molecular Dynamic Simulation in Titanium Dioxide Polymorphs: Rutile, Brookite, and Anatase

Abstract: Molecular dynamic (MD) simulations with a quantum correction were performed on the titanium dioxide polymorphs. Interatomic potential functions of our new model are composed of Coulomb, short-range repulsion, van der Waals, and Morse interactions. The energy parameters were empirically determined to reproduce the fundamental properties of rutile crystal. The optimized crystal structure of TiO2, rutile, was in very good agreement with experimental data in the literature. For brookite and anatase, our MD simulations reproduced well the crystal structures and several physical properties, including volume thermal expansivity and bulk modulus. The present MD simulations with a new interatomic potential function and parameters successfully predicted the crystal structures of the titanium dioxide polymorphs.

Range and strength of interatomic forces: dispersion and induction contributions to the bonds of dications and of ionic molecules

Abstract: An application of previously introduced correlation formulas in terms of polarizabilities of interacting species permits an assessment of the relative role of dispersion and induction contributions to describe bond lengths and energies in some doubly charged ion-neutral systems (the dications of alkaline earth atoms and rare gases). An extension to ion-ion systems is also presented, on the basis of an empirical analysis of available data on alkali halides, in order to establish the role of both dispersion and induction interactions as compared to Coulomb attraction. An improved version of the Slater-Kirkwood formulation with an appropriate choice for the effective electron numbers is suggested to estimate the long range effective dispersion coefficients. The present approach provides a unifying framework for the characterization of bonds for systems which greatly vary in size and strength and recipes are suggested for interatomic potential energy curves. It is concluded that this approach is also relevant as a starting point for extensions to include anisotropies due both to orbital overlap for open shell partners and to mutual orientation when molecules are considered.

Molecular dynamics simulation of structures, bulk moduli, and volume thermal expansivities of silicate liquids in the system CaO-MgO-Al2O3-SiO2

Abstract: Materials in the system CaO-MgO-Al2O3-SiO2 are important constituents of the Earth's lower crust and mantle Silicate liquids in this geophysically important system have been studied using molecular dynamics(MD) simulation with an empirical interatomic potential (CMAS94) MD simulations are quite satisfactory in reproducing well the observed structure and pressure-volume-temperature equation-of-state parameters of molten enstatite (MgSiO3), wollastonite (CaSiO3), diopside (CaMgSi2O6), and anorthite (CaAl2Si2O8) at 1900 K and 0 GPa However, the MD simulated bulk modulus of molten forsterite (Mg2SiO4) at 2300 K and 0 GPa, K0=180(6) GPa, is found to be much smaller than the value, K0=∼60 GPa at similar temperature and pressure conditions, estimated previously based on melting curve analyses of forsterite In an attempt to investigate the possible occurrence of the density inversion between magmatic liquids and residual crystals in the upper mantle conditions, as proposed by Stolper et al [1981], we have further applied the MD technique with the CMAS94 potential to the diopside system at 1900 K as an example, and have found that the density inversion between crystal and liquid in this system actually occurs at approximately 11 GPa

Solvent Effect on the NMR Chemical Shieldings in Water Calculated by a Combination of Molecular Dynamics and Density Functional Theory

Abstract: The solvent effect on the NMR chemical shielding in liquid water is calculated from a combination of molecular dynamics simulations and quantum chemical calculations for protons and 17O. The simulations are performed with three different potentials, ab initio as well as empirical ones, to study the influence of the force field. From the liquid configurations obtained in these simulations, molecules are randomly chosen together with neighbouring molecules to give clusters of water typical for the liquid at the selected temperature and density. Different cluster sizes are studied. The clusters are treated as supermolecules in quantum chemical calculations of chemical shifts by sum-over-states density functional perturbation theory with individual gauge for localised orbitals. The influence of the quantum chemical method is studied with an ab initio coupled Hartree-Fock gauge including atomic orbitals calculations with different basis sets for a selected cluster. An average over clusters yields the chemical shielding in the liquid at the selected temperature and density. The calculated values for the gas–liquid shift, which are in best agreement with experiment, are –3.2 ppm (exp. –4.26 ppm) for the proton and –37.6 ppm (exp. –36.1 ppm) for 17O, but the results depend strongly on the chosen interatomic potential.

Atomistic simulation of hydroxide ions in inorganic solids

Abstract: This paper describes the derivation of an empirical interatomic potential for the interaction of hydroxide ions with metal oxides. The model is based on the Born model of solids and its major features are firstly that the OH interaction is principally described by a Morse potential, derived originally by Saul et al. using ab initio Hartree-Fock methods, secondly that the parameters describing the short–range interaction of the hydroxyl oxygen with cations follows the approach suggested by Schroder et al. which ensured that the cation-anion equilibrium bond distances were maintained on modifying the anion charge and thirdly that electronic polarizability on the hydroxyl oxygen ion is included. The utility of this approach is described by applying this model to three systems: hydrogen defects in α-quartz; at α-quartz and sodalite surfaces; in modelling non-silicate hydroxide crystal structures, that is Mg(OH)2 and A1(OH)3

Properties of Silicon Nanoparticles: A Molecular Dynamics Study

Abstract: Constant energy molecular dynamics simulations of silicon cluster growth have been conducted for clusters up to 480 atoms using the Stillinger−Weber empirical interatomic potential. It is found that the interior atoms of the 480-atom clusters, at the temperatures used, show bulklike characteristics. The cluster binding energy has been fit to an expression that separates the surface and bulk contributions to the energy over wide temperatures and size ranges. The average surface energy of an atom was found to be independent of cluster size and of a magnitude relative to the bulk, such that all cluster sizes were stable under the conditions studied here (600 < T < 2000 K). The photon density of states is similar to bulk silicon and does not show a strong cluster size dependence. Atomic self-diffusion coefficients have been calculated and compare quite well with experimental data on self-diffusion coefficient measurements of silicon surfaces.

Model interatomic potential for simulations in selenium

Abstract: A three-body, effective interatomic potential is described for selenium. The form is similar to that used for sulfur by Stillinger and Weber, and the parameters are determined using the structures and energies of Se clusters (${\mathrm{Se}}_{2}$-${\mathrm{Se}}_{8}$), known from experiment and density functional calculations, and refined using data for various crystal phases. The potential reproduces the main structural and dynamical features of Se molecules and crystals, and we give results for structures, binding energies, vibrations, and elastic constants of different Se phases. \textcopyright{} 1996 The American Physical Society.

Dynamics of Brittle Fracture with Variable Elasticity.

Abstract: Simulations show that brittle cracks approach six-tenths the Rayleigh speed and follow the highest surface energy path. Using an interatomic potential recently developed by J. P. Sethna, we find that the crack's limiting speed now approaches the theoretical prediction of the Rayleigh speed, but the crack path is still associated with greatest elastic stiffness and surface energy. We conclude that the crack's dynamics is governed by the anisotropic mean-field elasticity associated with large strains ( $\ensuremath{\ge}7%$).

Interatomic potential for theX1?+g state of Be2

Abstract: An extended geminal model has been applied to determine the interatomic potential for the X1Σ+g state Be2. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: Re = 4.67 a.u. (4.63 a.u.) and De = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded −3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v01 = 224.7 cm−1 (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.

Kinetic Energy of Liquid and Solid 4He.

Abstract: We report new path-integral calculations and measurements of the kinetic energy of condensed helium and construct an overall dependence of kinetic energy on temperature for densities less than 70 atoms ${\mathrm{nm}}^{\ensuremath{-}3}$. In the solid phase we find the kinetic energy is almost temperature independent and, surprisingly, has a smaller kinetic energy than the fluid near freezing at the same density. In the high temperature fluid phase, the excess kinetic energy decreases to zero very slowly because of pair scattering from the repulsive interatomic potential.

Solvent effect on the nmr chemical shieldings in water calculated by a combination of molecular dynamics and density functional theory

Abstract: The solvent effect on the NMR chemical shielding in liquid water is calculated from a combination of molecular dynamics simulations and quantum chemical calculations for protons and 17O. The simulations are performed with three different potentials, ab initio as well as empirical ones, to study the influence of the force field. From the liquid configurations obtained in these simulations, molecules are randomly chosen together with neighbouring molecules to give clusters of water typical for the liquid at the selected temperature and density. Different cluster sizes are studied. The clusters are treated as supermolecules in quantum chemical calculations of chemical shifts by sum-over-states density functional perturbation theory with individual gauge for localised orbitals. The influence of the quantum chemical method is studied with an ab initio coupled Hartree-Fock gauge including atomic orbitals calculations with different basis sets for a selected cluster. An average over clusters yields the chemical shielding in the liquid at the selected temperature and density. The calculated values for the gas–liquid shift, which are in best agreement with experiment, are –3.2 ppm (exp. –4.26 ppm) for the proton and –37.6 ppm (exp. –36.1 ppm) for 17O, but the results depend strongly on the chosen interatomic potential.

Structure and thermodynamic properties of liquid transition metals: An embedded-atom-method approach.

Abstract: We have obtained the volume term and effective pair potentials for liquid transition metals using the embedded-atom method (EAM). The EAM embedding functions are fitted to bulk solid-state properties: the experimental Voigt average bulk and shear moduli and sublimation energies. The same fitting procedure is used for all the transition metals. This potential is used in conjunction with the variational modified hypernetted chain (VMHNC) theory of liquids to compute the static structure factors, Helmholtz free energies, internal energies, and entropies of the 3d, 4d, and 5d liquid transition metals. There is overall good qualitative agreement with experiment. The computed thermodynamic properties exhibit trends in accordance with experiment. They also exhibit the correct behavior as a function of temperature. But the calculations also reveal shortcomings in the interatomic potential. \textcopyright{} 1996 The American Physical Society.

Atomistic simulations in ternary Ni - Ti - Al alloys

Abstract: Two different interatomic potentials of the embedded atom type were developed for the Ni - Ti system by empirical fitting to the properties of B2 NiTi. For one of the potentials, the cohesive energy and unrelaxed APB energy of the B2 phase were adjusted to low temperature first principle calculation values. For the other potential, the cohesive energy was adjusted to the experimental values at high temperatures, where the B2 phase is stable. This second interatomic potential also succeeded in predicting the stability of the phase with lattice parameters close to experimental values. The interatomic potentials used for the pure components are the same as those used in our previous work to derive Ni - Al potentials based on B2 NiAl and Ti - Al potentials based on TiAl. This allows the use of the present potentials in conjunction with these previously derived interactions to study ternary Ni - Ti - Al alloys. For both potentials developed here, the phase in the center of the pseudobinary NiAl - NiTi is predicted to be stable and the lattice parameters given by the potentials are close to the experimental values. The potentials predict that Ni substitutes for Al in T-rich Ti trialuminides and Ti substitutes for Al in Ni-rich NiAl. As a test for this ternary EAM model, we present calculations of the APB energies in ternary cubic trialuminides and dislocation cores in NiAl with Ti impurities.

Using An Extended Tersoff Interatomic Potential to Analyze The Static-Fatigue Strength of SiO2 under Atmospheric Influence

Abstract: Calculations of SiO 2 static-fatigue strength are used to show that the strength- degradation behavior of the material under the influence of the ambient atmosphere can be analyzed using an interatomic potential which is based on the Tersoff potential but extended to take charge transfer effects into account. The force-elongation curves of the Si-O interatomic bonds of the SiO2 are calculated with and without H 2 O in the atmosphere. Based on these curves, crack propagation behavior is analyzed, and calculated results are shown to correspond well with experimental results. Moreover, the calculated values of the strength decrease caused by the H 2 O also show fair agreement with the experimental values.

Study of copper precipitates in α-iron by computer simulation. II. Interatomic potential for Fe-Cu interactions and properties of coherent precipitates

Abstract: A pair potential describing Fe[sbnd]Cu interactions has been constructed. The potential was fitted to the vacancy-Cu binding energy in bcc Fe and the dilatation properties of coherent Cu precipitates. Properties of Cu-point defects complexes in the bcc-Fe matrix and point defect-precipitate interactions were calculated. The binding energy of a Cu atom with a small coherent precipitate (up to 180 Cu atoms) was estimated as a function of the precipitate size. This was found to be a non-monotonic function for small precipitates. Dilatation and structural properties of coherent precipitates were studied and the relaxation of the matrix around precipitates was found. The vacancy-precipitate interaction energy and vacancy migration near and within precipitates were also studied. It was found that the anisotropy of vacancy migration and interaction correlates with the anisotropy of the relaxation of the matrix atoms around the precipitate.

Interatomic potentials for ternary Nb - Ti - Al alloys

Abstract: Interatomic potentials of the embedded-atom type were developed for the Nb - Al system via an empirical fitting to the properties of A15 . The cohesive energy and lattice parameters are fitted by the potentials, which also give good agreement with experimental values for the same properties in the phase. A second interatomic potential was developed for the Nb - Ti system via a fitting to the lattice parameters and thermodynamic properties of the disordered BCC phase. The Al and Ti potentials used here are the same as those used in our previous work to derive Ti - Al potentials based on TiAl. This allows the use of the present potentials in conjunction with those previously derived interactions to study ternary Nb - Ti - Al alloys. The potentials were used to calculate the heats of solution of Al and Ti in Nb, and to simulate the orthorhombic phase.

Atomistic simulation of point defects in silicon at high temperature

Abstract: The Stillinger–Weber interatomic potential is used in molecular dynamics simulations to compute estimates of the equilibrium and transport properties of self‐interstitials and vacancies in crystalline silicon at high temperature. Equilibrium configurations are predicted as a 〈110〉 dumbbell for a self‐interstitial, and as an inwardly relaxed configuration for a vacancy. Both structures show considerable delocalization with increasing temperature, which leads to a strong temperature dependence of the entropy of formation, as suggested by diffusion experiments. Diffusion coefficients and mechanisms are predicted as a function of temperature. The predictions are discussed in the context of experiments and first‐principle calculations.

Interatomic Potentials for Atomistic Simulations

Abstract: Atomistic simulations are playing an increasingly prominent role in materials science. From relatively conventional studies of point and planar defects to large-scale simulations of fracture and machining, atomistic simulations offer a microscopic view of the physics that cannot be obtained from experiment. Predictions resulting from this atomic-level understanding are proving increasingly accurate and useful. Consequently, the field of atomistic simulation is gaining ground as an indispensable partner in materials research, a trend that can only continue. Each year, computers gain roughly a factor of two in speed. With the same effort one can then simulate a system with twice as many atoms or integrate a molecular-dynamics trajectory for twice as long. Perhaps even more important, however, are the theoretical advances occurring in the description of the atomic interactions, the so-called “interatomic potential” function. The interatomic potential underpins any atomistic simulation. The accuracy of the potential dictates the quality of the simulation results, and its functional complexity determines the amount of computer time required. Recent developments that fit more physics into a compact potential form are increasing the accuracy available per simulation dollar. This issue of MRS Bulletin offers an introductory survey of interatomic potentials in use today, as well as the types of problems to which they can be applied. This is by no means a comprehensive review. It would be impractical here to attempt to present all the potentials that have been developed in recent years. Rather, this collection of articles focuses on a few important forms of potential spanning the major classes of materials bonding: covalent, metallic, and ionic.