Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors—atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors—using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.

Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors—atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors—using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.

Abstract: An optimized interatomic potential has been constructed for silicon using a modified Tersoff model. The potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature, and other properties. The proposed potential is compared with three other potentials from the literature. The potentials demonstrate reasonable agreement with first-principles binding energies of small Si clusters as well as single-layer and bilayer silicenes. The four potentials are used to evaluate the thermal stability of free-standing silicenes in the form of nanoribbons, nanoflakes, and nanotubes. While single-layer silicene is found to be mechanically stable at zero Kelvin, it is predicted to become unstable and collapse at room temperature. By contrast, the bilayer silicene demonstrates a larger bending rigidity and remains stable at and even above room temperature. The results suggest that bilayer silicene might exist in a free-standing form at ambient conditions.

Abstract: Silicene, the silicon-based counterpart of graphene with a two-dimensional honeycomb lattice, has attracted tremendous interest both theoretically and experimentally due to its significant potential industrial applications. From the aspect of theoretical study, the widely used classical molecular dynamics simulation is an appropriate way to investigate the transport phenomena and mechanisms in nanostructures such as silicene. Unfortunately, no available interatomic potential can precisely characterize the unique features of silicene. Here, we optimized the Stillinger-Weber potential parameters specifically for a single-layer Si sheet, which can accurately reproduce the low buckling structure of silicene and the full phonon dispersion curves obtained from ab initio calculations. By performing equilibrium and nonequilibrium molecular dynamics simulations and anharmonic lattice dynamics calculations with the new potential, we reveal that the three methods consistently yield an extremely low thermal conductivity of silicene and a short phonon mean-free path, suggesting silicene as a potential candidate for high-efficiency thermoelectric materials. Moreover, by qualifying the relative contributions of lattice vibrations in different directions, we found that the longitudinal phonon modes dominate the thermal transport in silicene, which is fundamentally different from graphene, despite the similarity of their two-dimensional honeycomb lattices.

Abstract: Silicene, the silicon-based counterpart of graphene with a two-dimensional honeycomb lattice, has attracted tremendous interest both theoretically and experimentally due to its significant potential industrial applications. From the aspect of theoretical study, the widely used classical molecular dynamics simulation is an appropriate way to investigate the transport phenomena and mechanisms in nanostructures such as silicene. Unfortunately, no available interatomic potential can precisely characterize the unique features of silicene. Here, we optimized the Stillinger-Weber potential parameters specifically for a single-layer Si sheet, which can accurately reproduce the low buckling structure of silicene and the full phonon dispersion curves obtained from ab initio calculations. By performing equilibrium and nonequilibrium molecular dynamics simulations and anharmonic lattice dynamics calculations with the new potential, we reveal that the three methods consistently yield an extremely low thermal conductivity of silicene and a short phonon mean-free path, suggesting silicene as a potential candidate for high-efficiency thermoelectric materials. Moreover, by qualifying the relative contributions of lattice vibrations in different directions, we found that the longitudinal phonon modes dominate the thermal transport in silicene, which is fundamentally different from graphene, despite the similarity of their two-dimensional honeycomb lattices.

Abstract: A force-matching method is employed to optimize the parameters of the Stillinger–Weber (SW) interatomic potential for calculation of the lattice thermal conductivity of silicon. The parameter fitting is based on first-principles density functional calculations of the restoring forces for atomic displacements. The thermal conductivities of bulk crystalline Si at 300–500 K estimated using nonequilibrium molecular dynamics with the modified parameter set show excellent agreement with existing experimental data. We also briefly discuss how the force-matching-based parameterization can provide the improved estimation of thermal conductivity, as compared to the original SW parameter set, through analysis of phonon density of states and phonon dispersion relations.

Abstract: A force-matching method is employed to optimize the parameters of the Stillinger–Weber (SW) interatomic potential for calculation of the lattice thermal conductivity of silicon. The parameter fitting is based on first-principles density functional calculations of the restoring forces for atomic displacements. The thermal conductivities of bulk crystalline Si at 300–500 K estimated using nonequilibrium molecular dynamics with the modified parameter set show excellent agreement with existing experimental data. We also briefly discuss how the force-matching-based parameterization can provide the improved estimation of thermal conductivity, as compared to the original SW parameter set, through analysis of phonon density of states and phonon dispersion relations.

Abstract: Mobile single interstitials can grow into extended interstitial defect structures during thermal anneals following ion implantation. The silicon tetra‐interstitials present an important intermediate structure that can either provide a chain‐like nucleation site for extended structures or form a highly stable compact interstitial cluster preventing further growth. In this paper, dimer searches using the tight‐binding (TB) model by Lenosky et al. and density functional calculations show that the compact ground‐state I^a₄ and the I₄‐chain are surrounded by high‐lying neighboring local minima.\nTo furthermore explore the phase space of tetra‐interstitial structures an empirical potential is optimized to a database of silicon defect structures. The minima hopping method combined with this potential extensively searches the energy landscape of tetra‐interstitials and discovers several new low‐energy I₄ structures. The second lowest‐energy I₄ structure turns out to be a distorted ground‐state tri‐interstitial bound with a single interstitial, which confirms that the ground‐state tri‐interstitial may serve as a nucleation center for the extended defects in silicon.

Abstract: The Tersoff potential is one of the most widely used interatomic potentials for silicon. However, its poor description of the elastic constants and melting point of diamond silicon is well known. In this research, three bond-order type interatomic potentials have been developed: the first one is fitted to the elastic constants by employing the Tersoff potential function form, the second one is fitted to both the elastic constants and melting point by employing the Tersoff potential function form and the third one is fitted to both the elastic constants and melting point by employing the modified Tersoff potential function form in which the angular-dependent term is improved. All of developed potentials well reproduce the elastic constants of diamond silicon as well as the cohesive energies and equilibrium bond lengths of silicon polytypes. The third potential can reproduce the melting point, while the second one cannot reproduce that. The elastic constants and melting point calculated using the third potential turned out to be C₁₁ = 166.4 GPa, C₁₂ = 65.3 GPa, C₄₄ = 77.1 GPa and T_m = 1681 K. It was also found that only elastic constants can be reproduced using the original Tersoff potential function, and that our proposed angular-dependent term is a key to reproducing the melting point.

Abstract: A semi-empirical interatomic potential for silicon has been developed, based on the modified embedded atom method formalism. This potential describes elastic, structural, point defect, surface, thermal (except melting point), and cluster properties as satisfactorily as any other empirical potential ever developed. When compared to the previously developed MEAM Si potential [M.I. Baskes, J.S. Nelson, A.F. Wright, Phys. Rev. B 40 (1989) 6085], for example, improvements were made in the description of surface relaxations, thermal expansion, and amorphous structure. This potential has the same formalism as already developed MEAM potentials for bcc, fcc, and hcp elements, and can be easily extended to describe various metal–silicon multi-component systems.

Abstract: We fit an empirical potential for silicon using the modified embedded atom (MEAM) functional form, which contains a nonlinear function of a sum of pairwise and three-body terms. The three-body term is similar to the Stillinger-Weber form. We parametrized our model using five cubic splines, each with 10 fitting parameters, and fitted the parameters to a large database using the force-matching method. Our model provides a reasonable description of energetics for all atomic coordinations, Z, from the dimer (Z = 1) to fcc and hcp (Z = 12). It accurately reproduces phonons and elastic constants, as well as point defect energetics. It also provides a good description of reconstruction energetics for both the 30° and 90° partial dislocations. Unlike previous models, our model accurately predicts formation energies and geometries of interstitial complexes - small clusters, interstitial-chain and planar {311} defects.

Abstract: We have measured the velocity of a running crack in brittle single crystal silicon as a function of energy flow to the crack tip. The experiments are designed to permit direct comparison with molecular dynamics simulations; therefore the experiments provide an indirect but sensitive test of interatomic potentials. Performing molecular dynamics simulations of brittle crack motion at the atomic scale we find that experiments and simulations disagree showing that interatomic potentials are not yet well understood.

Abstract: We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with theoretically motivated functional forms that capture chemical and physical trends as explained in a companion paper. The numerical parameters in the functional form are obtained by fitting to a set of ab initio results from quantum-mechanical calculations based on density-functional theory in the local-density approximation, which include various bulk phases and defect structures. We test the potential by applying it to the relaxation of point defects, core properties of partial dislocations and the structure of disordered phases, none of which are included in the fitting procedure. For dislocations, our model makes predictions in excellent agreement with ab initio and tight-binding calculations. It is the only potential known to describe both the 30°- and 90°-partial dislocations in the glide set {111}. The structural and thermodynamic properties of the liquid and amorphous phases are also in good agreement with experimental and ab initio results. Our potential is capable of simulating a quench directly from the liquid to the amorphous phase, and the resulting amorphous structure is more realistic than with existing empirical preparation methods. These advances in transferability come with no extra computational cost, since force evaluation with our model is faster than with the popular potential of Stillinger-Weber, thus allowing reliable atomistic simulations of very large atomic systems.

Abstract: The widely used Stillinger-Weber potential for silicon interactions has been modified to provide an accurate description of the Si(111)-(7 × 7) surface including the highly reactive adatom and rest-atom sites. This modified potential also provides a good representation of bulk silicon, and the Si(001)-(1 × 1), Si(001)-(2 × 1), Si(111)-(1 × 1) and Si(111)-(2 × 1) surfaces. Above the melting temperature of 1683 K, however, the original Stillinger-Weber potential is probably superior.

Abstract: An empirical potential for silicon has been developed. Molecular-dynamics methods and simulated annealing techniques have been used to study the structural properties of small silicon clusters with this potential. A detailed comparison has been made between our results and those obtained from other theoretical methods. It is found that our results are close to those obtained using ab initio techniques. A significant improvement over other empirical potentials has been made.

Abstract: We have performed a comparative study of six classical many-body potentials for silicon (Pearson, Takai, Halicioglu, and Tiller; Biswas and Hamann; Stillinger and Weber; Dodson, Tersoff 2, and Tersoff 3). Extensive static calculations have been performed using these potentials on Si_n clusters (n=2–6), bulk point defects, elastic constants, polytypes, pressure-induced phase transformations, and surfaces [(111), (100), and (110)]. Similarities and differences between the six potentials have been identified, and their transferability as well as their accuracy with respect to experiment and first-principles methods have been assessed. In general, all of these potentials do a relatively poor job of modeling the energetics of small clusters as well as the various reconstructions of the Si(111) surface. They provide a fair to good description of the properties of bulk diamond cubic silicon, its intrinsic defects, and the Si(100) surface. Besides the fact that none of them models π bonding, their inability to be more transferable lies in their inadequate description of the angular forces. Each potential has its strengths and limitations, but none of them appears to be clearly superior to the others, and none is totally transferrable. However, despite their shortcomings we feel that some of these potentials will be useful in large-scale simulations of materials-related problems. They can give valuable insights into phenomena that are otherwise intractable to investigate either experimentally or via first-principles methods.

Abstract: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of system configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for "simple" liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.

Abstract: In a comprehensive study, the modified embedded-atom method is extended to a variety of cubic materials and impurities. In this extension, all functions are analytic and computationally simple. The basic equations of the method are developed and applied to 26 elements: ten fcc, ten bcc, three diamond cubic, and three gaseous materials. The materials modeled include metals, semiconductors, and diatomic gases, all of which exhibit different types of bonding. Properties of these materials, including equation of state, elastic moduli, structural energies and lattice constants, simple defects, and surfaces, are calculated. The formalism for applying the method to combinations of these elements is developed and applied to the calculation of dilute heats of solution. In all cases, comparison is made to experiment or higher-level calculations when possible.

Abstract: A modified form of the Tersoff empirical interatomic potential for Si is proposed to improve simulation of adatom behaviors on Si surfaces. The modified form of the potential is consistent with local-density-approximation calculations of the surface electronic band structure of Si(001) 2×1. It is demonstrated that the addition of a screened-Morse-potential tail to the bulk Tersoff interaction behavior when tetrahedral coordination is disrupted improves the results significantly. The surface structure is calculated and shown to yield substantial differences with respect to the original potential form. In particular, anomalous abrupt variations in adatom bonding energy are eliminated and the probability of a successful deposition of the adatom on a lattice site is increased.

Abstract: An interatomic potential for silicon is proposed, which is a significant improvement over the Stillinger-Weber model. This potential is valid for clusters with more than six atoms, where π bonding is not significant because of the large degree of coordination. Guided by ab initio electronic calculations, we introduced four-body interactions to the potential, which were essential to give good agreement with the melting point of the crystal and the geometries and the energies of the ground and low metastable states of silicon clusters.

Abstract: In a critical evaluation, we show that existing classical potentials are not suitable for calculating the energy of realistic atomic processes in Si. We present a new potential which is especially suited to simulate processes in the diamond lattice rather than in high-energy bulk structures of Si. Our potential is based on a very large quantum-mechanical data base. It consists of two- and three-body terms with short-range separable forms, and reproduces accurately the energy surface for atomic exchange in Si. Thus, it is ideally suited for molecular dynamics simulations of atomic processes in Si.

Abstract: Based on the idea that bonding energies of many substances can be modeled by pairwise interactions moderated by the local environment, we propose a new universal interatomic potential for tetrahedrally bonded materials. We obtain two basic relationships linking equilibrium interatomic distances and cohesive energies to the coordination number for a large range of phases of silicon. The relationships are also valid for germanium and carbon, covering, in the latter case, double and triple carbon-carbon bonds, where π bonding is important. Based on these ideas we discuss the construction of the universal interatomic potential for these three substances. This potential, which uses very few parameters, should be useful, particularly for surface studies.

Abstract: Empirical interatomic potentials permit the calculation of structural properties and energetics of complex systems. A new approach for constructing such potentials, by explicitly incorporating the dependence of bond order on local environment, permits an improved description of covalent materials. In particular, a new potential for silicon is presented, along with results of extensive tests which suggest that this potential provides a rather realistic description of silicon. The limitations of the potential are discussed in detail.

Abstract: An alternative parametrization is given for a previous empirical interatomic potential for silicon. The new potential is designed to more accurately reproduce the elastic properties of silicon, which were poorly described in the earlier potential. The properties of liquid Si are also improved, but energies of surfaces are less accurate. Detailed tests of the new potential are described.

Abstract: A theory of classical two- and three-body interatomic potentials is developed. The ability of the classical potentials to model quantum-mechanical local-density-functional calculations for a wide range of silicon structures is explored. In developing classical models it was found to be necessary to perform new local-density-functional calculations for self-interstitial and layered silicon structures. Two different potentials are derived from fits and tests to energies of bulk, surface, layered, and self-interstitial structures. One potential models bulk energies and high-pressure properties well; the other is more appropriate for properties of the tetrahedral structure. Simulated annealing is used to find low-energy structures for silicon-atom clusters.

Abstract: An empirical interatomic potential for covalent systems is proposed, incorporating bond order in an intuitive way. The potential has the form of a Morse pair potential, but with the bond-strength parameter depending upon local environment. A model for Si accurately describes bonding and geometry for may structures, including highly rebonded surfaces.

Abstract: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of system configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for "simple" liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.

Abstract: Metal-semiconductor nanostructures are key objects for multifunctional electronics and optical design. We report a new interatomic potential for atomistic simulation of a ternary Si-Au-Al system. The development procedure was based on the force-matching method that allowed us to create the potential without use of experimental data at the fitting. Extensive validation including elastic, thermophysical and defect properties demonstrates a wide range of the potential applicability. Special attention was paid to the description of the silicon-metal alloys in liquid and amorphous states. We used the new potential for study of crystallization and glass transition in the undercooled melt. The simulation results revealed the beneficial conditions for the formation of the unique metal-semiconductor nanocrystalline structure, which is highly important for various applications in the field of nanophotonics.

Abstract: A set of modified embedded-atom method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab initio calculations, with adjustment to reproduce the ab initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab initio simulations and experiments. Single elements in their ground-state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal atomistic simulation environment (ASE), are distributed to facilitate reproducibility of the results.

Abstract: In this work we studied crystallization of the liquid Si-Au system at rapid cooling. For this purpose we performed atomistic simulation with novel interatomic potential. Results of the simulations showed that crystallization proceeds in different ways for pure silicon and Si-Au melt. For the studied binary system, the main factor limiting crystallization is diffusion of Au atoms in the liquid state. Threshold cooling rate for crystallization significantly depends on the Au content.

Abstract: A quaternary element Modified Embedded Atom Method (MEAM) potential comprising Fe, Mn, Si, and C is developed by employing a hierarchical multiscale modeling paradigm to simulate low-alloy steels. Experimental information alongside first-principles calculations based on Density Functional Theory served as calibration data to upscale and develop the MEAM potential. For calibrating the single element potentials, the cohesive energy, lattice parameters, elastic constants, and vacancy and interstitial formation energies are used as target data. The heat of formation and elastic constants of binary compounds along with substitutional and interstitial formation energies serve as binary potential calibration data, while substitutional and interstitial pair binding energies aid in developing the ternary potential. Molecular dynamics simulations employing the developed potentials predict the thermal expansion coefficient, heat capacity, self-diffusion coefficients, and stacking fault energy for steel alloys comparable to those reported in the literature.

Abstract: The effects of various process variables on the formation of polytypes during SiC single crystal growths have been investigated using atomistic simulations based on an empirical potential (the second nearest-neighbor MEAM) and first-principles calculation. It is found out that the main role of process variables (temperature, surface type, growth rate, atmospheric condition, dopant type, etc.) is not to directly change the relative stability of SiC polytypes directly but to change the formation tendency of point defects. The biaxial local strain due to the formation of point defects is found to have an effect on the relative stability of SiC polytypes and is proposed in the present study as a governing factor that affects the selective growth of SiC polytypes. Based on the present local strain scheme, the competitive growth among SiC polytypes, especially the 4H and 6H-SiC, available in literatures can be reasonably explained by interpreting the effect of each process variable in terms of defect formation and the resultant local strain. Those results provide an insight into the selective growth of SiC polytypes and also help us obtain high quality SiC single crystals.

Abstract: Using a combination of random configuration sampling, molecular dynamics simulated annealing with empirical potential, and ensuing structural refinement by first-principles density functional calculations, we perform an extensive ground-state search for the most stable configurations of small carbon interstitial clusters in SiC. Our search reveals a "magic" cluster number of three atoms, where the formation energy per interstitial shows a distinct minimum. A carbon tri-interstitial cluster with trigonal C_3v symmetry is discovered, in which all carbon atoms are fourfold coordinated. In addition to its special thermodynamic stability, its localized vibrational modes are also in a very good agreement with the experimental photoluminescence spectra of the D_II center in both 3C- and 4H-SiC. The D_II center is one of the most persistent defects in SiC, and we propose that the discovered carbon tri-interstitial is responsible for this center.

Abstract: An effective interatomic interaction potential for SiC is proposed. The potential consists of two-body and three-body covalent interactions. The two-body potential includes steric repulsions due to atomic sizes, Coulomb interactions resulting from charge transfer between atoms, charge-induced dipole-interactions due to the electronic polarizability of ions, and induced dipole-dipole (van der Waals) interactions. The covalent characters of the Si–C–Si and C–Si–C bonds are described by the three-body potential. The proposed three-body interaction potential is a modification of the Stillinger-Weber form proposed to describe Si. Using the molecular dynamics method, the interaction potential is used to study structural, elastic, and dynamical properties of crystalline (3C), amorphous, and liquid states of SiC for several densities and temperatures. The structural energy for cubic (3C) structure has the lowest energy, followed by the wurtzite (2H) and rock-salt (RS) structures. The pressure for the structural transformation from 3C-to-RS from the common tangent is found to be 90 GPa. For 3C-SiC, our computed elastic constants (C₁₁, C₁₂, and C₄₄), melting temperature, vibrational density-of-states, and specific heat agree well with the experiments. Predictions are made for the elastic constant as a function of density for the crystalline and amorphous phase. Structural correlations, such as pair distribution function and neutron and x-ray static structure factors are calculated for the amorphous and liquid state.

Abstract: We present an analytical bond-order potential for silicon, carbon, and silicon carbide that has been optimized by a systematic fitting scheme. The functional form is adopted from a preceding work [Phys. Rev. B 65, 195124 (2002)] and is built on three independently fitted potentials for Si-Si, C-C, and Si-C interaction. For elemental silicon and carbon, the potential perfectly reproduces elastic properties and agrees very well with first-principles results for high-pressure phases. The formation enthalpies of point defects are reasonably reproduced. In the case of silicon stuctural features of the melt agree nicely with data taken from literature. For silicon carbide the dimer as well as the solid phases B1, B2, and B3 were considered. Again, elastic properties are very well reproduced including internal relaxations under shear. Comparison with first-principles data on point defect formation enthalpies shows fair agreement. The successful validation of the potentials for configurations ranging from the molecular to the bulk regime indicates the transferability of the potential model and makes it a good choice for atomistic simulations that sample a large configuration space.

Abstract: We present an analytical bond-order potential for silicon, carbon, and silicon carbide that has been optimized by a systematic fitting scheme. The functional form is adopted from a preceding work [Phys. Rev. B 65, 195124 (2002)] and is built on three independently fitted potentials for Si-Si, C-C, and Si-C interaction. For elemental silicon and carbon, the potential perfectly reproduces elastic properties and agrees very well with first-principles results for high-pressure phases. The formation enthalpies of point defects are reasonably reproduced. In the case of silicon stuctural features of the melt agree nicely with data taken from literature. For silicon carbide the dimer as well as the solid phases B1, B2, and B3 were considered. Again, elastic properties are very well reproduced including internal relaxations under shear. Comparison with first-principles data on point defect formation enthalpies shows fair agreement. The successful validation of the potentials for configurations ranging from the molecular to the bulk regime indicates the transferability of the potential model and makes it a good choice for atomistic simulations that sample a large configuration space.

Abstract: We have calculated the displacement threshold energies (E_d) for C and Si primary knock-on atoms (PKA) in β-SiC using molecular dynamic simulations. The interactions between atoms were modeled using a modified form of the Tersoff potential in combination with a realistic repulsive potential obtained from density-functional theory calculations. The simulation cell was cubic, contained 8000 atoms and had periodic boundaries. The temperature of the simulation was about 150 K. Our results indicate strong anisotropy in the E_d values for both Si and C PKA. The displacement threshold for Si varies from about 36 eV along [001] to 113 eV along [111], while E_d for C varies from 28 eV along [111] to 71 eV along [111]. These results are in good agreement with experimental observations.

Abstract: While ordering in alloy crystals is well understood, short-range ordering in amorphous alloys remains controversial. Here, by studying computer-generated models of amorphous SiC, we show that there are two principal factors controlling the degree of chemical order in amorphous covalent alloys. One, the chemical preference for mixed bonds, is much the same in crystalline and amorphous materials. However, the other factor, the atomic size difference, is far less effective at driving ordering in amorphous material than in the crystal. As a result, the amorphous phase may show either strong ordering (as in GaAs), or weaker ordering (as in SiC), depending upon the relative importance of these two factors.

Abstract: The energies of carbon defects in silicon are calculated, using an empirical classical potential, and used to infer defect properties and reactions. Substitutional carbon is found to react with silicon interstitials, with the carbon "kicked out" to form a (100) split interstitial. This interstitial can in turn bind to a second substitutional carbon, relieving stress, in three configurations with similar energies. The results here accord well with a variety of experimental data, including defect structures, activation energies for defect motion, and coupling to strain. A discrepancy with the accepted values for carbon solubility in silicon suggests a reinterpretation of the experimental data.

Abstract: A general form is proposed for an empirical interatomic potential for multicomponent systems. This form interpolates between potentials for the respective elements to treat heteronuclear bonds. The approach is applied to C-Si and Si-Ge systems. In particular, the properties of SiC and its defects are well described.

Abstract: Bond-order potentials have been developed for the Ti₃AlC₂ and Ti₃SiC₂ MAX phases within the Tersoff formalism. Parameters were determined by independently considering each interatomic interaction present in the system and fitting them to the relevant structural, elastic, and defect properties for a number of unary, binary, and ternary structures. A number of material properties, including those not used in the fitting procedure, are reproduced with a high degree of accuracy when compared to experiment and ab initio calculations. Additionally, well-documented MAX phase behaviors such as plastic anisotropy and kinking nonlinear elasticity are demonstrated to be captured by the potentials. As a first highly accurate atomistic model for MAX phases, these potentials provide the opportunity to study some of the fundamental mechanisms behind unique MAX phase properties. Additionally, the fitting procedure employed is highly transferable and should be applicable to numerous other MAX phases.

Abstract: A general form is proposed for an empirical interatomic potential for multicomponent systems. This form interpolates between potentials for the respective elements to treat heteronuclear bonds. The approach is applied to C-Si and Si-Ge systems. In particular, the properties of SiC and its defects are well described.

Abstract: Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well-known silicon dioxide, there are phases with different stoichiometric composition and nanostructured composites. One of the key challenges in understanding the Si-O system is therefore to accurately account for its nanoscale heterogeneity beyond the length scale of individual atoms. Here we show that a unified computational description of the full Si-O system is indeed possible, based on atomistic machine learning coupled to an active-learning workflow. We showcase applications to very-high-pressure silica, to surfaces and aerogels, and to the structure of amorphous silicon monoxide. In a wider context, our work illustrates how structural complexity in functional materials beyond the atomic and few-nanometre length scales can be captured with active machine learning.

Abstract: Silica (SiO₂) is an abundant material with a wide range of applications. Despite much progress, the atomistic modelling of the different forms of silica has remained a challenge. Here we show that by combining density-functional theory at the SCAN functional level with machine-learning-based interatomic potential fitting, a range of condensed phases of silica can be accurately described. We present a Gaussian approximation potential model that achieves high accuracy for the thermodynamic properties of the crystalline phases, and we compare its performance (and performance-cost trade-off) with that of multiple empirically fitted interatomic potentials for silica. We also include amorphous phases, assessing the ability of the potentials to describe structures of melt-quenched glassy silica, their energetic stability, and the high-pressure structural transition to a mainly sixfold-coordinated phase. We suggest that rather than standing on their own, machine-learned potentials for silica may be used in conjunction with suitable empirical models, each having a distinct role and complementing the other, by combining the advantages of the long simulation times afforded by empirical potentials and the near-quantum-mechanical accuracy of machine-learned potentials. This way, our work is expected to advance atomistic simulations of this key material and to benefit further computational studies in the field.

Abstract: An interatomic potential model that can simultaneously describe metallic, covalent, and ionic bonding is suggested by combining the second nearest-neighbor modified embedded-atom method (2NNMEAM) and the charge equilibration (Qeq) method, as a further improvement of a series of existing models. Paying special attention to the removal of known problems found in the original Qeq model, a mathematical form for the atomic energy is newly developed, and carefully selected computational techniques are adapted for energy minimization, summation of Coulomb interaction, and charge representation. The model is applied to the Ti-O and Si-O binary systems selected as representative oxide systems for a metallic element and a covalent element. The reliability of the present 2NNMEAM+Qeq potential is evaluated by calculating the fundamental physical properties of a wide range of titanium and silicon oxides and comparing them with experimental data, density functional theory calculations, and other calculations based on (semi-)empirical potential models.

Abstract: A parameter set for Tersoff potential has been developed to investigate the structural properties of Si-O systems. The potential parameters have been determined based on ab initio calculations of small molecules and the experimental data of α-quartz. The structural properties of various silica polymorphs calculated by using the new potential were in good agreement with their experimental data and ab initio calculation results. Furthermore, we have prepared SiO₂ glass using molecular dynamics (MD) simulations by rapid quenching of melted SiO₂. The radial distribution function and phonon density of states of SiO₂ glass generated by MD simulation were in excellent agreement with those of SiO₂ glass obtained experimentally.

Abstract: Current experimental research aims to reduce the size of quartz crystal oscillators into the submicrometer range. Devices then comprise multimillion atoms and operating frequencies will be in the gigahertz regime. Such characteristics make direct atomic scale simulation feasible using large scale parallel computing. Here, we describe molecular-dynamics simulations on bulk and nanoscale device systems focusing on elastic constants and flexural frequencies. Here we find (a) in order to achieve elastic constants within 1% of those of the bulk requires approximately one million atoms; precisely the experimental regime of interest; (b) differences from continuum mechanical frequency predictions are observable for 17 nm devices; (c) devices with 1% defects exhibit dramatic anharmonicity. A subsequent paper describes the direct atomistic simulation of operating characteristics of a micrometer scale device. A PAPS cosubmission gives algorithmic details.

Abstract: Large-scale molecular dynamics simulations of amorphous silica are carried out on systems containing up to 41472 particles using an effective interatomic potential consisting of two-body and three-body covalent interactions. The intermediate-range order represented by the first sharp diffraction peak (FSDP) in the neutron static structure factor shows a significant dependence on the system size. Correlations in the range 0.4–1.1 nm are found to play a vital role in determining the shape of the FSDP correctly. The calculated structure factor for the largest system is in excellent agreement with neutron diffraction experiments, including the height of the FSDP.

Abstract: An interaction potential consisting of two-body and three-body covalent interactions is proposed for SiO₂. The interaction potential is used in molecular-dynamics studies of structural and dynamical correlations of crystalline, molten, and vitreous states under various conditions of densities and temperatures. The two-body contribution to the interaction potential consists of steric repulsion due to atomic sizes, Coulomb interactions resulting from charge transfer, and charge-dipole interaction to include the effects of large electronic polarizability of anions. The three-body covalent contributions include O-Si-O and Si-O-Si interactions which are angle dependent and functions of Si-O distance. In lattice-structure calculations with the total potential function, α-cristobalite and α-quartz are found to have the lowest and almost degenerate energies, in agreement with experiments. The energies for β-cristobalite, β-quartz, and keatite are found to be higher than those for α-cristobalite and α-quartz. Molecular-dynamics calculations with this potential function correctly describe the short- and intermediate-range order in molten and vitreous states.\nIn the latter, partial pair-distribution functions give Si-O, O-O, and Si-Si bond lengths of 1.62, 2.65, and 3.05 Å, respectively. The vitreous state consists of nearly ideal Si(O_1/2)₄ tetrahedra in corner-sharing configurations. The Si-O-Si bond-angle distribution has a peak at 142° and a full width at half maximum (FWHM) of 25° in good agreement with nuclear magnetic resonance experiments. The calculated static structure factor is also in agreement with neutron-diffraction experiments. Partial static structure factors reveal that intermediate-range Si-Si, O-O, and Si-O correlations between 4 and 8 Å give rise to the first sharp diffraction peak (FSDP). The FSDP is absent in charge-charge structure factor, which indicates that charge neutrality prevails over length scales between 4 and 8 Å. Dynamical correlations in vitreous and molten states, phonon densities of states of crystalline and vitreous SiO₂, infrared spectra of crystalline, vitreous and molten states, isotope effect, distribution of rings and their structure in molten and vitreous states, and structural transformations at high pressures will be discussed in subsequent papers.

Abstract: Uranium-silicide (U-Si) fuels are being pursued as a possible accident tolerant fuel (ATF). This uranium alloy fuel benefits from higher thermal conductivity and higher fissile density compared to uranium dioxide (UO2). In order to perform engineering scale nuclear fuel performance simulations, the material properties of the fuel must be known. Currently, the experimental data available for U-Si fuels is rather limited. Thus, multiscale modeling efforts are underway to address this gap in knowledge. In this study, a semi-empirical modified Embedded-Atom Method (MEAM) potential is presented for the description of the U-Si system. The potential is fitted to the formation energy, defect energies and structural properties of U3Si2. The primary phase of interest (U3Si2) is accurately described over a wide temperature range and displays good behavior under irradiation and with free surfaces. The potential can also describe a variety of U-Si phases across the composition spectrum.