Choice Of Interatomic Potential Research Articles

Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework

We present a systematic methodology, built within the Open Knowledgebase of Interatomic Models (OpenKIM) framework (https://openkim.org), for quantifying properties of grain boundaries (GBs) for arbitrary interatomic potentials (IPs), GB character, and lattice structure and species. The framework currently generates results for symmetric tilt GBs in cubic materials, but can be readily extended to other types of boundaries. In this paper, GB energy data are presented that were generated automatically for Al, Ni, Cu, Fe, and Mo with 225 IPs; the system is installed on openkim.org and will continue to generate results for all new IPs uploaded to OpenKIM. The results from the atomistic calculations are compared to the lattice matching model, which is a semi-analytic geometric model for approximating GB energy. It is determined that the energy predicted by all IPs (that are stable for the given boundary type) correlate closely with the energy from the model, up to a multiplicative factor. It thus is concluded that the qualitative form of the GB energy versus tilt angle is dominated more by geometry than the choice of IP, but that the IP can strongly affect the energy level. The spread in GB energy predictions across the ensemble of IPs in OpenKIM provides a measure of uncertainty for GB energy predictions by classical IPs.

Effect of defect guided out-of-plane deformations on the mechanical properties of graphene

In this paper, nanoscale mechanical properties and failure behavior of graphene with Stone-Wales defect concentration were investigated using molecular dynamics simulations with the latest ReaxFFC-2013 potential that can accurately capture bond breakages of graphitic compounds. The choice of interatomic potential plays an essential role in capturing the deformation mechanism accurately. Stable configuration of two-dimensional graphene experiences out-of-plane deformation leading to ripples and wrinkles in graphene. It is observed that the mechanical properties such as Young’s modulus, ultimate tensile strength, and the fracture strain are dependent on the out-of-plane deformation, temperature, defect concentration, defect orientation, defect layout and loading configuration. It is observed that the post transient phase non-homogenous ripples and wrinkles influence the mechanical properties at low and high defect concentrations, respectively.

Overdamped langevin dynamics simulations of grain boundary motion

Macroscopic properties of structural materials are strongly dependent on their microstructure. However, the modeling of their evolution is a complex task because of the mechanisms involved such as plasticity, recrystallization, and phase transformations, which are common processes taking place in metallic alloys. This complexity led to a growing interest in atomistic simulations formulated without any auxiliary hypotheses beyond the choice of interatomic potential. In this context, we propose here a model based on an overdamped stochastic evolution of particles interacting through inter-atomic forces. The model settles to the correct thermal equilibrium distribution in canonical and grand-canonical ensembles and is used to study the grain boundary migration. Finally, a comparison of our results with those obtained by molecular dynamics shows that our approach reproduces the complex atomic-scale dynamics of grain boundary migration correctly.

Semi-grand canonical Monte Carlo simulation for derivation of thermodynamic properties of binary alloy

Semi-grand canonical Monte Carlo (SGCMC) simulations are performed to derive thermodynamic properties of binary alloy from atomistic-based simulations. Particularly, solidus and liquidus compositions are directly derived for Fe-Cr alloy described by two different EAM potentials. Although the SGCMC simulation can derive relationship between the free energy and composition at any temperature straightforwardly, partial phase diagram obtained from SGCMC simulations strongly depends on the choice of interatomic potential.

Dislocation mobility and Peierls stress of c-type screw dislocations in GaN from molecular dynamics

Motion of a single c-type screw dislocation, with [0001] Burgers vector, in single crystal GaN is explored using classical molecular dynamics (MD) simulations with both Tersoff and Stillinger-Weber (SW) interatomic potentials. Three different dislocation core structures (full, small void, and open) along two distinct glide planes ((11¯00) and (1¯1¯20)) are studied. The system is sheared by applying opposing forces to atoms near the surface, with interior atoms maintained at a temperature of 1300 K. This results in glide for screw dislocations with a full core structure, with velocities dependent on the choice of interatomic potential. Full core dislocation glide also results in the nucleation of void defects for both potentials. Small void dislocations glide cleanly with no debris using the SW potential, but glide is not observed for the Tersoff potential. The difference between the potentials is most fully demonstrated from the response of open core dislocations in the (1¯1¯20) slip system. For the Tersoff potential, full core screw dislocations are nucleated from the surface of the open core dislocations, while dislocation glide loops are nucleated for the SW potential. The discrepancy in results using the different potentials is discussed, and attributed to the short cut off distance of the Tersoff potential. Finally, a dislocation dipole system is used to calculate the Peierls stress of the {11¯00}〈0001〉 full core screw dislocation, and compared to experimental results.

Molecular Dynamics Simulations of Atoms Diffusion in Solid

Molecular dynamics (MD) simulations, which treat atoms as point particles and trace their individual trajectories, are always employed to investigate the transport properties of a many-body system. The diffusion coefficients of atoms in solid can be obtained by the Einstein relation and the Green-Kubo relation. An overview of the MD simulations of atoms diffusion in the bulk, surface and grain boundary is provided. We also give an example of the diffusion of helium in tungsten to illustrate the procedure, as well as the importance of the choice of interatomic potentials. MD simulations can provide intuitive insights into the atomic mechanisms of diffusion.

Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study.

Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.

Atomistic simulations of the nanoindentation-induced incipient plasticity in Ni3Al crystal

In this work, the indentation-induced incipient plasticity of Ni3Al crystal is investigated by performing molecular dynamics (MD) simulations. Simulation results reveal that the incipient plasticity of Ni3Al is originated from the homogeneous nucleation of the 1/6〈112〉-type Shockley partial dislocation. The critical load, critical contact pressure, dislocation nucleation site and active slip system are significantly affected by crystallographic orientation, model size, indenter radius and temperature. The choice of interatomic potential has significant implications for the indentation behavior of Ni3Al. Some benchmarks for evaluating the credibility of interatomic potentials are presented. The pop-in phenomena are correlated with dislocation generation, multiplication and reactions. The formation mechanisms of complex stacking faults (CSFs), antiphase boundaries (APBs) and superlattice intrinsic stacking faults (SISFs) are clarified. The highest indentation modulus is obtained in (111) indentation followed by the (110) and (100) cases. The indentation modulus and the depth of nucleation sites increase with increasing indenter radius but the maximum shear stress decreases. The maximum shear stress and indentation modulus decrease linearly with increasing temperature, reflecting the stress-assisted and thermally activated nature of dislocation nucleation.

Material frame representation of equivalent stress tensor for discrete solids

In this paper, we derive expressions for equivalent Cauchy and Piola stress tensors that can be applied to discrete solids and are exact for the case of homogeneous deformation. The main principles used for this derivation are material frame formulation, long wave approximation and decomposition of particle motion into continuum and thermal parts. Equivalent Cauchy and Piola stress tensors for discrete solids are expressed in terms of averaged interparticle distances and forces. No assumptions about interparticle forces are used in the derivation, thereby ensuring our expressions are valid irrespective of the choice of interatomic potential used to model the discrete solid. The derived expressions are used for calculation of the local Cauchy stress in several test problems. The results are compared with prediction of the classical continuum definition (force per unit area) as well as existing discrete formulations (Hardy, Lucy, and Heinz-Paul-Binder stress tensors). It is shown that in the case of homogeneous deformations and finite temperatures the proposed expression leads to the same values of stresses as classical continuum definition. Hardy and Lucy stress tensors give the same result only if the stress is averaged over a sufficiently large volume. Thus, given the lack of sensitivity to averaging volume size, the derived expressions can be used as benchmarks for calculation of stresses in discrete solids.

Molecular dynamics simulations of thermal conductivity of carbon nanotubes: Resolving the effects of computational parameters

Predicting thermal conductivity, k, of carbon nanotubes (CNTs) has been the focus of many molecular dynamics (MD) simulation studies reported in the literature. The values of k obtained in these studies exhibit a large, up to an order of magnitude, variability that is commonly attributed to the variations in the computational setups adopted in different studies. The sensitivity of the computational results to the choice of individual parameters of the simulation setups, however, has not been systematically investigated and is often overlooked when the predicted values of k are compared across the literature. Here we present the results of several series of simulations specifically designed to evaluate the effects of common computational parameters of non-equilibrium MD (NEMD), such as the type of boundary conditions, size and location of heat bath regions, definition of the CNT length, and the choice of interatomic potential, on the computational predictions. The length dependence of thermal conductivity is found to exhibit a gradual transition from a strong increase of k with CNT length for nanotubes that are shorter than ∼200nm to a much weaker dependence for longer CNTs, reflecting the transition from ballistic to diffusive-ballistic heat transport regimes. The effect of increasing length of thermal bath regions is found to be nearly indistinguishable from the effect of increasing length of the unperturbed region between the bath regions, suggesting that the value of k is defined by the total length of the CNT (including the length of the heat bath regions) in NEMD simulations employing uni-directional heat flux. The choice of interatomic potential is shown to be responsible for an up to fourfold variability in predictions of k for otherwise identical simulation conditions. Overall, the results of this study help elucidate the cause of quantitative discrepancies across published data and provide recommendations on the choice of simulation setups that may improve the consistency of the computational predictions.

Nucleation, kinetics and morphology of displacive phase transformations in iron

An extensive, systematic molecular dynamics (MD) study is performed for analysing the nucleation, kinetics and morphology characteristics of thermally-induced, displacive phase transformations from face-centred cubic (fcc) to body-centred cubic (bcc) iron. At the atomic level these transformation characteristics are influenced by a number of factors, including (i) the appearance of free surfaces, (ii) the initial presence of fcc-bcc grain boundaries, (iii) the existence of point defects (i.e., atomic vacancies) near a grain boundary, (iv) the initial thermal velocities of the atoms, and (v) the specific interatomic potential used. Other MD studies that capture the overall transformation behaviour of iron well have often underestimated or ignored the influence by these factors on the transformation response, with the risk of putting the accuracy, generality and physical explanation of the MD results on loose grounds. The present research illustrates the relative contribution of each of the above factors by means of a detailed comparison study for three different interatomic potentials. The accuracy of the interatomic potentials is established by validating for the fcc and bcc phases the calculated elastic moduli, cohesive energy, vacancy formation energy and interfacial energy against experimental and ab initio data reported in the literature. The importance of calibrating material data of both the stable bcc phase and the metastable fcc phase – instead of the stable bcc phase only – is demonstrated. The numerical results call for general caution when interpreting phenomena that start close to instability points and therefore are sensitive to small disturbances; a large spread in the overall transformation time is found under different initial thermal velocities, interfacial lattice incoherence, boundary conditions (free vs. periodic), and interatomic potentials, where for completely transformed atomic systems the discrepancy between the maximum and minimum transformation time appears to be more than a factor of 150. The transformation time is phenomenologically related to the overall activation energy and the cohesive energy difference of the fcc and bcc phases, which, beyond a certain combination of values, may even prevent the transformation process from occurring. Also, the morphology of the bcc product phase is remarkably sensitive to the type of boundary conditions and the choice of interatomic potential, while the influence by both the set of initial thermal velocities and the interfacial lattice incoherence only becomes apparent for specific atomic samples that transform relatively slowly. The presence of fcc-bcc grain boundaries increases the spatial heterogeneity of transformation events, with the appearance of an increasing number of vacancies at the grain boundary giving rise to a larger overall transformation time. The 10 main results following from the present MD study are conveniently summarised at the end of this communication.

Implications of the choice of interatomic potential on calculated planar faults and surface properties in nickel

With the increasing use of molecular simulation to understand deformation mechanisms in transition metals, it is important to assess how well the simulations reproduce physical behavior both near equilibrium and under more extreme conditions. In particular, it is important to examine whether simulations predict unusual deformation paths that are competitive with those experimentally observed. In this work we compare generalized planar fault energy landscapes and surface energies for various interatomic potentials with those from density functional theory calculations to examine how well these more complicated planar faults and surface energies are captured and whether any deformations are energetically competitive with the {111}⟨112⟩ slip observed in FCC crystals. To do this we examine not just the (111) fault orientation, but also the (100), (110), (210), (211), (311), and (331) orientations to test behavior outside of the fitting range of the interatomic potentials. We find that the shape of the (111)[11] stacking fault energy curve varies significantly with potential, with the ratio of unstable to stable stacking fault energies ranging from 1.22 to 14.07, and some deformation paths for non-(111) orientations give activation barriers less than 50% higher than the unstable stacking fault energies. These are important considerations when choosing an interatomic potential for deformation simulations.

Molecular dynamics simulations for the prediction of thermal conductivity of bulk silicon and silicon nanowires: Influence of interatomic potentials and boundary conditions

The reliability of molecular dynamics (MD) results depends strongly on the choice of interatomic potentials and simulation conditions. Five interatomic potentials have been evaluated for heat transfer MD simulations of silicon, based on the description of the harmonic (dispersion curves) and anharmonic (linear thermal expansion) properties. The best interatomic potential is the second nearest-neighbor modified embedded atom method potential followed by the Stillinger-Weber, and then the Tersoff III. However, the prediction of the bulk silicon thermal conductivity leads to the conclusion that the Tersoff III potential gives the best results for isotopically pure silicon at high temperatures. The thermal conductivity of silicon nanowires as a function of cross-section and length is calculated, and the influence of the boundary conditions is studied for those five potentials.

Atomic-scale simulation of screw dislocation/coherent twin boundary interaction in Al, Au, Cu and Ni

The influence of material and choice of interatomic potential on the interaction between an a/2〈110〉{111} screw dislocation and a Σ3{111}〈110〉 coherent twin boundary (CTB) is determined by simulating this process in a range of face-centered cubic metals modeled with a total of 10 embedded-atom method (EAM) potentials. Generalized stacking fault energies are computed, showing a linear relation between the stacking faut (γS) and twin energies, as well as between the unstable stacking fault (γUS) and unstable twinning (γUT) energies. We show that the reaction mechanism (absorption of the dislocation into the CTB or transmission into the twinned region) and reaction stress depend strongly on the potential used, even for a given material and are controlled by the material parameter γS/μbP (where μ is the shear modulus and bP the Shockley partial Burgers vector), rather than the sign of the ratio (γUS−γS)/(γUT−γS), as proposed recently by Jin et al. [1]. Moreover, there exists a critical reaction stress, close to 400MPa, independent of the potential, below which the dislocation is absorbed in the CTB and above which the dislocation is transmitted into the twinned region. The simulations are discussed with respect to in situ transmission electron microscopy straining experiments in Cu that highlight the importance of thermally activated cross-slip in the interaction process and show that transmission across a twin boundary is possible but is most likely an indirect process.

First-principles calculations of intrinsic defects inAl2O3

First-principles plane-wave pseudopotential calculations were performed to study electronic structures, structural relaxation, and energetics of intrinsic vacancies and interstitials in ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}.$ In the presence of the intrinsic point defects, extra levels appeared in the band gap. Considering various charge states for the intrinsic point defects, it was found that each point defect is most stable in its fully ionized state. From the formation energies of individual point defects, Schottky, O Frenkel, and Al Frenkel energies were also evaluated and were compared with previous results by experiment and static lattice calculations. Although previous static lattice calculations showed different relative stabilities of Schottky and Frenkel formation, depending on the choice of interatomic potentials, our calculations revealed that the relative values of formation energies are in the order of $\mathrm{Schottky}l\mathrm{Al}$ $\mathrm{Frenkel}l\mathrm{O}$ Frenkel, which is in good agreement with experimental data.

Kinetics of B2 and D03 Ordering: Theory

AbstractMonte-Carlo simulations (MCS) and the path probability method (PPM) were used to study disorder→order transformations in bcc alloys having the AB3 stoichiometry. Both methods used an explicit vacancy mechanism of ordering and an activated-state rate theory for the vacancy jumps. We studied the evolution of short-range order (SRO) as well as B2 and D03 long-range order (LRO) in alloys that began as random solid solutions. The growth rates of SRO and LRO were significantly higher for the PPM than for the MCS. We attribute this difference to improper handling of correlated vacancy motions in the PPM. The PPM also suffered from an artificial incubation time for the initiation of LRO. Both the MCS and the PPM showed that SRO has a tendency to develop in two stages. In the first stage there is a quick relaxation of the SRO by itself. In the second stage, which occurs with a longer time constant, the SRO and LRO grow simultaneously. Parametric plots of one order parameter against another, here termed “kinetic paths”, are discussed. A variety of different kinetic paths through the B2 and D03 order parameters can be predicted theoretically, depending on the choice of interatomic potentials. This range of calculated kinetic paths is broad enough to encompass our experimental results of SRO and LRO evolution in Fe3Al.

Ejection pattern of sputtered atoms from Cu(100) under 10 keV Ar + ion bombardment

Sputtering of single crystalline Cu(100) has been studied in both experiment and theory. Ejection patterns of sputtered atoms from Cu(100) were observed for 10 keV Ar + ions and the result was compared with computer simulations with a modified MARLOWE code by including a disordering effect in the topmost atomic layer. In experiments, so called Wehner spots were clearly observed in the ejection patterns, suggesting that a crystalline structure remains in the surface region even though the topmost atomic layer seems to be disordered by ion bombardment. In theory the computer simulation has predicted that, when the crystalline structure of the topmost layer is disordered, the ejection pattern turns out to be almost the same as that of an amorphous target. Hence those experimental and theoretical results suggest that the atoms of the topmost layer will again occupy crystalline sites, even though the surface atoms undergo atomic mixing under 10 keV Ar + ion bombardment. A discussion on the choice of interatomic potential and the contribution of simultaneous collisions to the Wehner spot formation is also presented.