Showing papers on "Interatomic potential published in 2006"

Thickness of graphene and single-wall carbon nanotubes

Abstract: Young's modulus and the thickness of single wall carbon nanotubes (CNTs) obtained from prior atomistic studies are largely scattered. In this paper we establish an analytic approach to bypass atomistic simulations and determine the tension and bending rigidities of graphene and CNTs directly from the interatomic potential. The thickness and elastic properties of graphene and CNTs can also be obtained from the interatomic potential. But the thickness, and therefore elastic moduli, also depend on type of loading (e.g., uniaxial tension, uniaxial stretching, equibiaxial stretching), as well as the nanotube radius $R$ and chirality when $Rl1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. This explains why the thickness obtained from prior atomistic simulations is scattered. This analytic approach is particularly useful in the study of multiwall CNTs since their stress state may be complex even under simple loading (e.g., uniaxial tension) due to the van der Waals interactions between nanotube walls. The present analysis also provides an explanation of Yakobson's paradox that the very high Young's modulus reported from the atomistic simulations together with the shell model may be due to the not-well-defined CNT thickness.

A new self-consistent empirical interatomic potential model for oxides, silicates, and silica-based glasses.

Abstract: A new empirical pairwise potential model for ionic and semi-ionic oxides has been developed. Its transferability and reliability have been demonstrated by testing the potentials toward the prediction of structural and mechanical properties of a wide range of silicates of technological and geological importance. The partial ionic charge model with a Morse function is used, and it allows the modeling of the quenching of melts, silicate glasses, and inorganic crystals at high-pressure and high-temperature conditions. The results obtained by molecular dynamics and free energy calculations are discussed in relation to the prediction of structural and mechanical properties of a series of soda lime silicate glasses.

Crystal-melt interfacial free energies in hcp metals: A molecular dynamics study of Mg

Abstract: Crystal-melt interfacial free energies $(\ensuremath{\gamma})$ are computed for hcp Mg by employing equilibrium molecular-dynamics (MD) simulations and the capillary-fluctuation method (CFM). This work makes use of a newly developed embedded-atom-method (EAM) interatomic potential for Mg fit to crystal, liquid, and melting properties. We describe how the CFM, which has previously been applied to cubic systems only, can be generalized for studies of hcp metals by employing a parametrization for the orientation dependence of $\ensuremath{\gamma}$ in terms of hexagonal harmonics. The method is applied in the calculation of the Turnbull coefficient $(\ensuremath{\alpha})$ and crystalline anisotropies of $\ensuremath{\gamma}$. We obtain a value of $\ensuremath{\alpha}=0.48$, with interfacial free energies for different high-symmetry orientations differing by approximately 1%. These results are compared to those obtained in previous MD-CFM studies for cubic EAM metals as well as experimental studies of solid-liquid interfaces in hcp alloys. In addition, the implications of our results for the prediction of dendrite growth directions in hcp metals are discussed.

Phonon transport in molecular dynamics simulations: Formulation and thermal conductivity prediction.

Abstract: Publisher Summary This chapter discusses the phonon transport in molecular dynamics (MD) simulations. The chapter presents a formulation for studying the thermal transport in dielectric materials using MD simulations. The simulations allow for analysis in both the real and phonon spaces. The natural inclusion of anharmonic effects through the form of the interatomic potential presents a significant advantage over harmonic theories. The chapter describes, examines, and compares two major approaches for predicting thermal conductivity from MD simulations (the Green–Kubo method [GK] and direct methods). Each has advantages and disadvantages, and the method chosen strongly depends on the problem of interest. Generally, the GK method is superior for bulk phase simulations, while the direct method is best for finite structures. In terms of applying MD simulations to real systems, current computational resources cannot accurately model anything close to a micron in size on an atom-by-atom level. The upscaling of MD results to larger length scale models is a promising and exciting avenue. Upscaling has been applied in a different context to phonon transport across material interfaces by Schelling and Phillpot.

Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials

Abstract: Preface. 1 Background Knowledge. 1.1 The Subject and its Specificity. 1.2 A Brief Historical Survey. 1.3 The Concept of Interatomic Potential and Adiabatic Approximation. 1.4 General Classification of Intermolecular Interactions. References. 2 Types of Intermolecular Interactions: Qualitative Picture. 2.1 Direct Electrostatic Interactions. 2.2 Resonance Interaction. 2.3 Polarization Interactions. 2.4 Exchange Interaction. 2.5 Retardation Effects in Long-Range Interactions and the Influence of Temperature. 2.6 Relativistic (Magnetic) Interactions. 2.7 Interaction Between Macroscopic Bodies. References. 3 Calculation of Intermolecular Interactions. 3.1 Large Distances. 3.2 Intermediate and Short Distances. References. 4 Nonadditivity of Intermolecular Interactions. 4.1 Physical Nature of Nonadditivity and the Definition of Many-Body Forces. 4.2 Manifestations of Nonadditive Effects. 4.3 Perturbation Theory and Many-Body Decomposition. 4.4 Many-Body Effects in Atomic Clusters. 4.5 Atom-Atom Potential Scheme and Nonadditivity. References. 5 Model Potentials. 5.1 Semiempirical Model Potentials. 5.2 Determination of Parameters in Model Potentials. 5.3 Reconstructing Potentials on the Basis of Experimental Data. 5.4 Global Optimization Methods. References. Appendix 1: Fundamental Physical Constants and Conversion Table of Physical Units. Appendix 2: Some Necessary Mathematical Apparatus. A2.1 Vector and Tensor Calculus. A2.1.1 Definition of vector the addition law. A2.1.2 Scalar and vector products triple scalar product. A2.1.3 Determinants. A2.1.4 Vector analysis gradient, divergence and curl. A2.1.5 Vector spaces and matrices. A2.1.6 Tensors. A2.2 Group Theory. A2.2.1 Properties of group operations. A2.2.2 Representations of groups. A2.2.3 The permutation group. A2.2.4 The linear groups. The three-dimensional rotation group. A2.2.5 Point groups. A2.2.6 Irreducible tensor operators. Spherical tensors. References. Appendix 3: Methods of Quantum-Mechanical Calculations of Many-Electron Systems. A3.1 Adiabatic Approximation. A3.2 Variational Methods. A3.2.1 Self-consistent field method. A3.2.2 Methods taking into account the electron correlation. A3.2.2.1 r12-dependent wave functions. A3.2.2.2 Configuration interaction. A3.2.2.3 Coupled cluster method. A3.2.2.4 Density functional theory approach. A3.3 Perturbation Theory. A3.3.1 Rayleigh-Schr odinger perturbation theory. A3.3.2 Moller-Plesset perturbation theory. A3.3.3 Operator formalism and the Brillouin-Wigner perturbation theory. A3.3.4 Variational perturbation theory. A3.3.5 Asymptotic expansions Pade approximants. References. Index.

Defect Chemistry, Surface Structures, and Lithium Insertion in Anatase TiO2

Abstract: Atomistic simulation techniques are used to investigate the defect properties of anatase TiO2 and LixTiO2 both in the bulk and at the surfaces. Interatomic potential parameters are derived that reproduce the lattice constants of anatase, and the energies of bulk defects and surface structures are calculated. Reduction of anatase involving interstitial Ti is found to be the most favorable defect reaction in the bulk, with a lower energy than either Frenkel or Schottky reactions. The binding energies of selected defect clusters are also presented: for the Ti3+−Li+ defect cluster, the binding energy is found to be approximately 0.5 eV, suggesting that intercalated Li ions stabilize conduction band electrons. The Li ion migration path is found to run between octahedral sites, with an activation energy of 0.45−0.65 eV for mole fractions of lithium in LixTiO2 of x ≤ 0.1. The calculated surface energies are used to predict the crystal morphology, which is found to be a truncated bipyramid in which only the (101...

A surface Cauchy-Born model for nanoscale materials

Abstract: We present an energy-based continuum model for the analysis of nanoscale materials where surface effects are expected to contribute significantly to the mechanical response. The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continuum is derived from an underlying crystal structure and interatomic potential. The key to the success of the proposed method lies in decomposing the potential energy of the material into bulk (volumetric) and surface area components. In doing so, the method naturally satisfies a variational formulation in which the bulk volume and surface area contribute independently to the overall system energy. Because the surface area to volume ratio increases as the length scale of a body decreases, the variational form naturally allows the surface energy to become important at small length scales; this feature allows the accurate representation of size and surface effects on the mechanical response. Finite element simulations utilizing the proposed approach are compared against fully atomistic simulations for verification and validation. Copyright © 2006 John Wiley & Sons, Ltd.

Extended Finnis–Sinclair potential for bcc and fcc metals and alloys

Abstract: We propose an extended Finnis?Sinclair (FS) potential by extending the repulsive term into a sextic polynomial for enhancing the repulsive interaction and adding a quartic term to describe the electronic density function. It turns out that for bcc metals the proposed potential not only overcomes the 'soft' behaviour of the original FS potential, but also performs better than the modified FS one by Ackland et al, and that for fcc metals the proposed potential is able to reproduce the lattice constants, cohesive energies, elastic constant, vacancy formation energies, equations of state, pressure?volume relationships, melting points and melting heats. Moreover, for some fcc?bcc systems, e.g.?the Ag?refractory metal systems, the lattice constants, cohesive energies and elastic constants of some alloys are reproduced by the proposed potential and are quite compatible with those directly determined by ab initio calculations.

Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures

Abstract: In this paper, we extend the quasicontinuum approach for a multiscale analysis of silicon nanostructures at finite temperature. The quasicontinuum method uses the classical continuum mechanics framework, but the constitutive response of the system is determined by employing an atomistic description. For finite-temperature solid systems under isothermal conditions, the constitutive response is determined by using the Helmholtz free energy density. The static part of the Helmholtz free energy density is obtained directly from the interatomic potential while the vibrational part is calculated by using the theory of quantum-mechanical lattice dynamics. Specifically, we investigate three quasiharmonic models, namely the real space quasiharmonic model, the local quasiharmonic model, and the reciprocal space quasiharmonic model, to compute the vibrational free energy. Using the finite-temperature quasicontinuum method, we compute the effect of the temperature and strain on the phonon density of states, phonon Gruneisen parameters, and the elastic properties of the Tersoff silicon. We also compute the mechanical response of silicon nanostructures for various external loads and the results are compared to molecular dynamics simulations.

Silicon carbide nanowires under external loads: An atomistic simulation study

Abstract: The nanomechanical response properties of $3\mathrm{C}\text{\ensuremath{-}}\mathrm{SiC}$ nanowires are investigated using molecular dynamics simulation with Tersoff bond-order interatomic potential. Under axial compression and tensile strain, the computed Young's modulus and structural changes at elastic limit do not depend appreciably on the diameter of the nanowire except for the nanowire of the smallest diameter $(\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ under compression. The elastic modulus and structural failure near the elastic limit regime, for nonaxial bending and torsional strains, are found to depend strongly on the nanowire diameters through a power-law behavior. The exponent of the power-law behavior and mechanisms of the material failure under different types of loading strains are described in this work.

The origin of (001) texture evolution in FePt thin films on amorphous substrates

Abstract: A theoretical study has been performed to rationalize the strong evolution of (001) texture during postannealing of deposited Fe50Pt50 thin films on amorphous substrates, by comparing calculated strain energies of several crystals with different orientations under presumed strain conditions. An atomistic calculation method based on an empirical interatomic potential (MEAM) was used to calculate strain and surface energies and atomic force microscope experiments were carried out to confirm the surface energy calculation. The (001) texture evolution could not be explained using traditional factors, the surface energy anisotropy and the in-plane strain. It was found that the strain from the L10 ordering transformation that occurs during postannealing can make the (001) crystal (crystal with [001] crystallographic orientation into the surface normal) energetically most stable among those with various orientations. It is proposed that the occurrence of anisotropic strain due to ordering transformations should be considered as a key factor that affects the texture evolution and that enhanced ordering and recrystallization kinetics is necessary to maximize the strain effect.

A progressive fracture model for carbon nanotubes

Abstract: An atomistic-based progressive fracture model for simulating the mechanical performance of carbon nanotubes by taking into account initial topological and vacancy defects is proposed. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space-frame structures. The finite element method is used to analyze the nanotube structure and the modified Morse interatomic potential to simulate the non-linear force field of the C–C bonds. The model has been applied to defected single-walled zigzag, armchair and chiral nanotubes subjected to axial tension. The defects considered were: 10% weakening of a single bond and one missing atom at the middle of the nanotube. The predicted fracture evolution, failure stresses and failure strains of the nanotubes correlate very well with molecular mechanics simulations from the literature.

Atomistic calculation of elastic moduli in strained silicon

Abstract: Strained silicon is becoming a new technology in silicon industry where the novel strain-induced features are utilized. In this paper we present a molecular dynamic prediction for the elastic stiffnesses C11, C12 and C44 in strained silicon as functions of the volumetric strain level. Our approach combines basic continuum mechanics with the classical molecular dynamic approach, supplemented with the Stillinger–Weber potential. Using our approach, the bulk modulus, effective elastic stiffnesses C11, C12 and C44 of the strained silicon, including also the effective Young's modulus and Poisson's ratio, are all calculated and presented in terms of figures and formulae. In general, our simulation indicates that the bulk moduli, C11 and C12, increase with increasing volumetric strain whilst C44 is almost independent of the volumetric strain. The difference between strained moduli and those at zero strain can be very large, and therefore use of standard free-strained moduli should be cautious.

On the atomic structures, mobility and interactions of extended defects in GaN: dislocations, tilt and twin boundaries

Abstract: Results obtained by atomic computer simulation based on an adapted Stillinger–Weber (SW) potential concerning the structure and relative stability of lattice dislocations, tilt and twin boundaries in GaN are discussed. The method used for the search and description of all possible atomic configurations depends on the crystallographic structure; consequently it is of general application and the results are transferable to the wurtzite binary compounds. On the contrary, the relaxed structures and their relative energetic stability are potential dependent. The results presented here correspond to a GaN model described by a pair potential. Whenever it has been possible our results have been compared with experiments or with ab initio calculations. We present the core shape and energy of and crystal dislocations of both edge and screw character; [0001] tilt boundaries of misorientation angles from 9.3° (corresponding to Σ37) to θ = 44.8° (corresponding to Σ43) and ( ) twin boundaries (n = 1, 2, 3) 1, 2, 3, 4. ...

Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes

Abstract: It is of fundamental value to understand the thermo-mechanical properties of carbon nanotubes. In this paper, by using molecular dynamics simulation, a systematic numerical investigation is carried out to explore the natural thermal vibration behaviors of single-walled carbon nanotubes and their quantitative contributions to the apparent thermal contraction behaviors. It is found that the thermo-mechanical behavior of single-walled carbon nanotubes is exhibited through the competition between quasi-static thermal expansion and dynamic thermal vibration, while the vibration effect is more prominent and induces apparent contraction in both radial and axial directions. With increasing temperature, the anharmonic interatomic potential helps to increase the bond length, which leads to thermally induced expansion. On the other hand, the higher structural entropy and vibrational entropy of the system cause the carbon nanotube to vibrate, and the apparent length of nanotube decreases due to various vibration modes. Parallel analytical and finite element analyses are used to validate the vibration frequencies and provide helpful insights. The unified multi-scale study has successfully decoupled and systematically analyzed both thermal expansion and contraction behaviors of single-walled carbon nanotube from 100 to 800 K, and obtained detailed information on various vibration modes as well as their quantitative contributions to the coefficient of thermal expansion in axial and radial directions. The results of this paper may provide useful information on the thermo-mechanical integrity of single-walled carbon nanotubes, and become important in practical applications involving finite temperature.

Analytic bond-order potential for atomistic simulations of zinc oxide

Abstract: An interatomic potential for zinc oxide and its elemental constituents is derived based on an analytical bond-order formalism. The model potential provides a good description of the bulk properties of various solid structures of zinc oxide including cohesive energies, lattice parameters, and elastic constants. For the pure elements zinc and oxygen the energetics and structural parameters of a variety of bulk phases and in the case of oxygen also molecular structures are reproduced. The dependence of thermal and point defect properties on the cutoff parameters is discussed. As exemplary applications the irradiation of bulk zinc oxide and the elastic response of individual nanorods are studied.

In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics

Abstract: The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2 to 217 nm and temperatures from 300 to 1000 K. The relation between the bulk pho.-non mean free path (A) and the film thickness (d s ) spans from the ballistic regime (A ≥ d s ) at 300 K to the diffusive, bulk-like regime (Λ «d s ) at 1000 K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300 K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debye's temperature.

Quasiharmonic models for the calculation of thermodynamic properties of crystalline silicon under strain

Abstract: Quasiharmonic models with Tersoff Phys. Rev. B 38, 9902 1988 interatomic potential are used to study the thermodynamic properties of crystalline silicon. It is shown that, compared to the molecular dynamics simulation data, the reciprocal space quasiharmonic model accurately predicts the thermal properties for temperatures up to 800 K. For higher temperatures, anharmonic effects become significant. With a significantly higher computational cost, the results from the real space quasiharmonic model approach the results from the reciprocal space quasiharmonic model as the number of atoms increases. The local quasiharmonic model does not accurately describe the thermal properties as it neglects the vibrational coupling of the atoms. We also investigate the effect of the strain on the thermodynamic properties. The variation of the thermodynamic properties with temperature under a tension, compression, and a shear deformation state is computed. © 2006 American Institute of Physics. DOI: 10.1063/1.2185834 I. INTRODUCTION Thermodynamic properties of crystalline silicon have long been a focus of interest because of their important role in elucidating the material behavior. Computational analysis is a powerful approach to investigate the thermodynamic properties of materials. First-principles quantum-mechanical methods are generally most accurate for predicting the material properties. Ab initio local density functional techniques have been used to determine the thermodynamic properties of silicon 1 and other materials. 2 However, due to the complexity of these methods and the need for large computational resources, ab initio calculations are limited to very small systems. Empirical and semi-empirical interatomic potentials 3‐5 have been developed to provide a simpler and yet a reasonably accurate description of materials. The various parameters in these potentials are determined by a weighted fitting of the material property databases obtained from experiments or ab initio calculations. Molecular dynamics MD and Monte Carlo MC simulations are the two popular methods that are based on interatomic potentials. In these methods, the thermal statistics are gathered to calculate the ensemble average of the thermal properties. MD calculations on the thermodynamic properties of crystalline silicon were carried out in Ref. 6, where the Tersoff potential 4 was

Two-stage melting of Au-Pd nanoparticles.

Abstract: Several series of molecular dynamics runs were performed to simulate the melting transition of bimetallic cuboctahedral nanoparticles of gold−palladium at different relative concentrations to study their structural properties before, in, and after the transition. The simulations were made in the canonical ensemble, each series covering a range of temperatures from 300 to 980 K, using the Rafii−Tabar version of the Sutton and Chen interatomic potential for metallic alloys. We found that the melting transition temperature has a strong dependence on the relative concentrations of the atomic species. We also found that, previous to the melting transition, the outer layer of the nanoparticle gets disordered in what can be thought as a premelting stage, where Au atoms near the surface migrate to the surface and remain there after the particle melts as a whole. The melting of the surface below Tm is consistent with studies of the interaction of a TEM electron beam with Au and Au−Pd nanoparticles.

A modified embedded-atom method interatomic potential for the Fe-C system

Abstract: A modified embedded-atom method (MEAM) interatomic potential for the Fe–C binary system has been developed using previous MEAM potentials of Fe and C. The potential parameters were determined by fitting to experimental information on the dilute heat of solution of carbon, the vacancy–carbon binding energy and its configuration, the location of interstitial carbon atoms and the migration energy of carbon atoms in body-centered cubic (bcc) Fe, and to a first-principles calculation result for the cohesive energy of a hypothetical NaCl-type FeC. The potential reproduces the known physical properties of carbon as an interstitial solute element in bcc Fe and face-centered cubic Fe very well. The applicability of this potential to atomistic approaches for investigating interactions between carbon interstitial solute atoms and other defects such as vacancies, dislocations and grain boundaries, and also for investigating the effects of carbon on various deformation and mechanical behaviors of iron is demonstrated.

Use of a variable-charge interatomic potential for atomistic simulations of bulk, oxygen vacancies, and surfaces of rutile TiO 2

Abstract: In this paper, interatomic potential models used for atomistic simulations of insulating oxides are revisited through the example of ${\mathrm{TiO}}_{2}$ rutile. The cohesive energy of oxides comprises an electrostatic part and a short-range part whose relative importance differs with the models. The electrostatic part can be evaluated by considering either point fixed atomic charges or, alternatively, charges that are allowed to vary in response to the local atomic environment, with a shielding correction to coulombic interactions at short range. We deeply analyzed this latter approach in the framework of the Rapp\'e and Goddard QEq charge equilibration scheme. We conclude that it is an efficient model to describe heterogeneous situations due to point defects or surfaces. Moreover, whatever the description of the electrostatic part of the energy is, several short-range interatomic potentials are found to describe in an acceptable way the crystal bulk properties (cohesive energy, elastic constants, etc). To compare the efficiency of various short-range potentials, we selected the ${\mathrm{TiO}}_{2}$ rutile whose experimental formation energy of the oxygen vacancy is available. By combining it with the cohesive energy, we have been able to accurately analyze the energetics of ${\mathrm{TiO}}_{2}$ as a function of those potentials. In this paper we show first that Morse potential is not adapted to oxygen-oxygen interactions and that pair-wise potentials between $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{O}$ pairs are not suitable to describe defects. As a result, we propose a model that combines the QEq description for electrostatic energy, a Buckingham potential for $\mathrm{O}\text{\ensuremath{-}}\mathrm{O}$ interactions and a $N$-body potential for the covalent part of the $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{O}$ interactions. This model efficiency has been tested on bulk, oxygen vacancy, and surfaces of rutile and turned out to provide results which fit very satisfactorily the experimental data.