Abstract: Machine learning interatomic potentials (IPs) can provide accuracy close to that of first-principles methods, such as density functional theory (DFT), at a fraction of the computational cost. This greatly extends the scope of accurate molecular simulations, providing opportunities for quantitative design of materials and devices on scales hitherto unreachable by DFT methods. However, machine learning IPs have a basic limitation in that they lack a physical model for the phenomena being predicted and therefore have unknown accuracy when extrapolating outside their training set. In this paper, we propose a class of Dropout Uncertainty Neural Network (DUNN) potentials that provide rigorous uncertainty estimates that can be understood from both Bayesian and frequentist statistics perspectives. As an example, we develop a DUNN potential for carbon and show how it can be used to predict uncertainty for static and dynamical properties, including stress and phonon dispersion in graphene. We demonstrate two approaches to propagate uncertainty in the potential energy and atomic forces to predicted properties. In addition, we show that DUNN uncertainty estimates can be used to detect configurations outside the training set, and in some cases, can serve as a predictor for the accuracy of a calculation.

Abstract: Machine learning interatomic potentials (IPs) can provide accuracy close to that of first-principles methods, such as density functional theory (DFT), at a fraction of the computational cost. This greatly extends the scope of accurate molecular simulations, providing opportunities for quantitative design of materials and devices on scales hitherto unreachable by DFT methods. However, machine learning IPs have a basic limitation in that they lack a physical model for the phenomena being predicted and therefore have unknown accuracy when extrapolating outside their training set. In this paper, we propose a class of Dropout Uncertainty Neural Network (DUNN) potentials that provide rigorous uncertainty estimates that can be understood from both Bayesian and frequentist statistics perspectives. As an example, we develop a DUNN potential for carbon and show how it can be used to predict uncertainty for static and dynamical properties, including stress and phonon dispersion in graphene. We demonstrate two approaches to propagate uncertainty in the potential energy and atomic forces to predicted properties. In addition, we show that DUNN uncertainty estimates can be used to detect configurations outside the training set, and in some cases, can serve as a predictor for the accuracy of a calculation.

Abstract: Machine learning interatomic potentials (IPs) can provide accuracy close to that of first-principles methods, such as density functional theory (DFT), at a fraction of the computational cost. This greatly extends the scope of accurate molecular simulations, providing opportunities for quantitative design of materials and devices on scales hitherto unreachable by DFT methods. However, machine learning IPs have a basic limitation in that they lack a physical model for the phenomena being predicted and therefore have unknown accuracy when extrapolating outside their training set. In this paper, we propose a class of Dropout Uncertainty Neural Network (DUNN) potentials that provide rigorous uncertainty estimates that can be understood from both Bayesian and frequentist statistics perspectives. As an example, we develop a DUNN potential for carbon and show how it can be used to predict uncertainty for static and dynamical properties, including stress and phonon dispersion in graphene. We demonstrate two approaches to propagate uncertainty in the potential energy and atomic forces to predicted properties. In addition, we show that DUNN uncertainty estimates can be used to detect configurations outside the training set, and in some cases, can serve as a predictor for the accuracy of a calculation.

Abstract: Monolayer and multilayer graphene are promising materials for applications such as electronic devices, sensors, energy generation and storage, and medicine. In order to perform large-scale atomistic simulations of the mechanical and thermal behavior of graphene-based devices, accurate interatomic potentials are required. Here, we present an interatomic potential for multilayer graphene structures referred to as “hNN−Gr_x.” This hybrid potential employs a neural network to describe short-range interactions and a theoretically motivated analytical term to model long-range dispersion. The potential is trained against a large dataset of monolayer graphene, bilayer graphene, and graphite configurations obtained from ab initio total-energy calculations based on density functional theory (DFT). The potential provides accurate energy and forces for both intralayer and interlayer interactions, correctly reproducing DFT results for structural, energetic, and elastic properties such as the equilibrium layer spacing, interlayer binding energy, elastic moduli, and phonon dispersions to which it was not fit. The potential is used to study the effect of vacancies on thermal conductivity in monolayer graphene and interlayer friction in bilayer graphene. The potential is available through the openkim interatomic potential repository at https://openkim.org.

Abstract: Carbon is the most widely studied material today because it exhibits special properties not seen in any other materials when in nano dimensions such as nanotube and graphene. Reduction of material defects created during synthesis has become critical to realize the full potential of carbon structures. Molecular dynamics (MD) simulations, in principle, allow defect formation mechanisms to be studied with high fidelity, and can, therefore, help guide experiments for defect reduction. Such MD simulations must satisfy a set of stringent requirements. First, they must employ an interatomic potential formalism that is transferable to a variety of carbon structures. Second, the potential needs to be appropriately parameterized to capture the property trends of important carbon structures, in particular, diamond, graphite, graphene, and nanotubes. Most importantly, the potential must predict the crystalline growth of the correct phases during direct MD simulations of synthesis to achieve a predictive simulation of defect formation. Because an unlimited number of structures not included in the potential parameterization are encountered, the literature carbon potentials are often not sufficient for growth simulations. We have developed an analytical bond order potential for carbon, and have made it available through the public MD simulation package LAMMPS. We demonstrate that our potential reasonably captures the property trends of important carbon phases. Stringent MD simulations convincingly show that our potential accounts not only for the crystalline growth of graphene, graphite, and carbon nanotubes but also for the transformation of graphite to diamond at high pressure.

Abstract: A semi-empirical interatomic potential for carbon has been developed, based on the modified embedded atom method formalism. The potential describes the structural properties of various polytypes of carbon, elastic, defect and surface properties of diamonds as satisfactorily as the well-known Tersoff potential. Combined with the Lennard-Jones potential, it can also reproduce the physical properties of graphite and amorphous carbon reasonably well. The applicability of the present potential to atomistic approaches on carbon nanotubes and fullerenes is also shown. The potential has the same formalism as previously developed MEAM potentials for bcc, fcc and hcp elements, and can be easily extended to describe various metal–carbon alloy systems.

Abstract: We propose a bond order potential for carbon with built-in long-range interactions. The potential is defined as the sum of an angular and coordination dependent short-range part accounting for the strong covalent interactions and a radial long-range part describing the weak interactions responsible, e.g., for the interplanar binding in graphite. The short-range part is a Brenner type of potential, with several modifications introduced to get an improved description of elastic properties and conjugation. Contrary to previous long-range extensions of existing bond order potentials, we prevent the loss of accuracy by compensating for the additional long-range interactions by an appropriate parametrization of the short-range part. We also provide a short-range bond order potential. In Monte Carlo simulations our potential gives a good description of the diamond to graphite transformation. For thin (111) slabs graphitization proceeds perpendicular to the surface as found in ab initio simulations, whereas for thick layers we find that graphitization occurs layer by layer.

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: An empirical interatomic potential is introduced, which gives a convenient and relatively accurate description of the structural properties and energetics of carbon, including elastic properties, phonons, polytypes, and defects and migration barriers in diamond and graphite. The potential is applied to study amorphous carbon formed in three different ways. Two resulting structures are similar to experimental a−C, but another more diamondlike form has essentially identical energy. The liquid is also found to have unexpected properties.

Abstract: Kinking is a deformation mechanism ubiquitous to layered systems, ranging from the nanometer scale in layered crystalline solids, to the kilometer scale in geological formations. Herein, we demonstrate its origins in the former through multiscale experiments and atomistic simulations. When compressively loaded parallel to their basal planes, layered crystalline solids first buckle elastically, then nucleate atomic-scale, highly stressed ripplocation boundaries – a process driven by redistributing strain from energetically expensive in-plane bonds to cheaper out-of-plane bonds. The consequences are far reaching as the unique mechanical properties of layered crystalline solids are highly dependent upon their ability to deform by kinking. Moreover, the compressive strength of numerous natural and engineered layered systems depends upon the ease of kinking or lack there of.

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 potential function is presented that can be used to model both chemical reactions and intermolecular interactions in condensed-phase hydrocarbon systems such as liquids, graphite, and polymers. This potential is derived from a well-known dissociable hydrocarbon force field, the reactive empirical bond-order potential. The extensions include an adaptive treatment of the nonbonded and dihedral-angle interactions, which still allows for covalent bonding interactions. Torsional potentials are introduced via a novel interaction potential that does not require a fixed hybridization state. The resulting model is intended as a first step towards a transferable, empirical potential capable of simulating chemical reactions in a variety of environments. The current implementation has been validated against structural and energetic properties of both gaseous and liquid hydrocarbons, and is expected to prove useful in simulations of hydrocarbon liquids, thin films, and other saturated hydrocarbon systems.

Abstract: Chemical and structural diversity present in hexagonal boron nitride (h-BN) and graphene hybrid nanostructures provide avenues for tuning various properties for their technological applications. In this paper we investigate the variation of thermal conductivity (κ) of hybrid graphene/h-BN nanostructures: stripe superlattices and BN (graphene) dots embedded in graphene (BN) are investigated using equilibrium molecular dynamics. To simulate these systems, we have parametrized a Tersoff type interaction potential to reproduce the ab initio energetics of the B-C and N-C bonds for studying the various interfaces that emerge in these hybrid nanostructures. We demonstrate that both the details of the interface, including energetic stability and shape, as well as the spacing of the interfaces in the material, exert strong control on the thermal conductivity of these systems. For stripe superlattices, we find that zigzag configured interfaces produce a higher κ in the direction parallel to the interface than the armchair configuration, while the perpendicular conductivity is less prone to the details of the interface and is limited by the κ of h-BN. Additionally, the embedded dot structures, having mixed zigzag and armchair interfaces, affect the thermal transport properties more strongly than superlattices. The largest reduction in thermal conductivity is observed at 50% dot concentration, but the dot radius appears to have little effect on the magnitude of reduction around this concentration.

Abstract: In this work we study the effects of C and Cr enrichment of <1 0 0> dislocation loops (DL) on their absorption and obstacle strength when interacting with an edge dislocation. To do so, we have i) developed a C-Cr cross potential based on density functional theory data as part of a ternary FeCrC interatomic potential; ii) performed exchange Monte Carlo simulations employing the developed interatomic potential to obtain the distribution of the solutes enriching the DL in the energetically optimum configurations; iii) performed large scale molecular dynamics simulations employing the interatomic potential to characterize the interaction between an edge dislocation line and the decorated DL. We found that the obstacle stress scales to the same obstacle strength regardless the DL density. On the other hand, we found that C, the level of Cr enrichment, loop size and interaction temperature have a significant impact on the obstacle strength and level of absorption of the loops. The presented results can be used to help parameterize and validate discrete dislocation dynamics codes and therein integrated constitutive laws to enable accounting for irradiation-induced chemical segregation effects.

Abstract: Unraveling the deformation mechanisms at the atomistic scale of metal matrix-graphene composites is a key step toward designing and fabricating these materials with exceptional mechanical properties. While these composites can be made by embedding graphene into multiple metallic matrices, it is shown that superior mechanical properties can be obtained by combining copper and graphene. In the past few years, molecular dynamics simulations have been used to investigate the fundamental deformation mechanisms at the nanoscale of Cu-graphene composites to facilitate designing these composites with improved mechanical properties. However, in all of the reported works, Lennard-Jones potential has been used for modeling the interaction between copper and carbon atoms. The complexities in the Cu-C interaction emerges the necessity of utilizing more accurate potentials. In this work, a 2NN MEAM (second nearest-neighbor modified embedded atomic method) potential for the copper and carbon atom interaction is developed. Since crystal structures like B1 or B2 are not experimentally available for the Cu-C system, first-principle calculations are used to determine the reference structure and its elastic constants in this work. It is shown that the B1 and B2 structure of Cu-C has positive formation energy, but B1 is dynamically stable. Accordingly, the B1 crystal structure is used as the reference structure for the Cu-C system to develop the interatomic potential. It is shown that the reported potential agrees reasonably well for phonon dispersion frequencies, stacking fault energies, and the atomic forces with the available experimental data and first-principle calculations. The developed potential is utilized to study the mechanical properties of copper-graphene composites subjected to uniaxial loading. Our results show that adding graphene to a defect-free Cu crystal weakens the metallic matrix’s mechanical properties. However, when the graphene is embedded into a Cu matrix with some defects, e.g., in a polycrystalline Cu, it can significantly improve the mechanical properties.

Abstract: Carbon is the most widely studied material today because it exhibits special properties not seen in any other materials when in nano dimensions such as nanotube and graphene. Reduction of material defects created during synthesis has become critical to realize the full potential of carbon structures. Molecular dynamics (MD) simulations, in principle, allow defect formation mechanisms to be studied with high fidelity, and can, therefore, help guide experiments for defect reduction. Such MD simulations must satisfy a set of stringent requirements. First, they must employ an interatomic potential formalism that is transferable to a variety of carbon structures. Second, the potential needs to be appropriately parameterized to capture the property trends of important carbon structures, in particular, diamond, graphite, graphene, and nanotubes. Most importantly, the potential must predict the crystalline growth of the correct phases during direct MD simulations of synthesis to achieve a predictive simulation of defect formation. Because an unlimited number of structures not included in the potential parameterization are encountered, the literature carbon potentials are often not sufficient for growth simulations. We have developed an analytical bond order potential for carbon, and have made it available through the public MD simulation package LAMMPS. We demonstrate that our potential reasonably captures the property trends of important carbon phases. Stringent MD simulations convincingly show that our potential accounts not only for the crystalline growth of graphene, graphite, and carbon nanotubes but also for the transformation of graphite to diamond at high pressure.

Abstract: Machine learning interatomic potentials (MLIPs) for α-iron and carbon binary system have been constructed aiming for understanding the mechanical behavior of Fe–C steel and carbides. The MLIPs were trained using an extensive reference database produced by spin polarized density functional theory (DFT) calculations. The MLIPs reach the DFT accuracies in many important properties which are frequently engaged in Fe and Fe–C studies, including kinetics and thermodynamics of C in α-Fe with vacancy, grain boundary, and screw dislocation, and basic properties of cementite and cementite–ferrite interfaces. In conjunction with these MLIPs, the impact of C atoms on the mobility of screw dislocation at finite temperature, and the C-decorated core configuration of screw dislocation were investigated, and a uniaxial tensile test on a model with multiple types of defects was conducted.

Abstract: Machine learning interatomic potentials (MLIPs) for α-iron and carbon binary system have been constructed aiming for understanding the mechanical behavior of Fe–C steel and carbides. The MLIPs were trained using an extensive reference database produced by spin polarized density functional theory (DFT) calculations. The MLIPs reach the DFT accuracies in many important properties which are frequently engaged in Fe and Fe–C studies, including kinetics and thermodynamics of C in α-Fe with vacancy, grain boundary, and screw dislocation, and basic properties of cementite and cementite–ferrite interfaces. In conjunction with these MLIPs, the impact of C atoms on the mobility of screw dislocation at finite temperature, and the C-decorated core configuration of screw dislocation were investigated, and a uniaxial tensile test on a model with multiple types of defects was conducted.

Abstract: In steels, the interaction between screw dislocations and carbon solutes has a great influence on the yield strength. Fe-C potentials used in molecular dynamics (MD) simulations yield a poor description of screw dislocation properties-their core structure and Peierls barrier-compared to ab initio calculations. Here we combine two EAM potentials from the literature, which greatly improves dislocation property accuracy in FeC alloys. Using this hybrid potential, MD simulations of dislocation glide in random solid solutions confirm a powerful solute strengthening, caused by complex interaction processes. We analyze these processes in a model geometry, where a row of carbon atoms is inserted in the dislocation core with varying separations. We use a combination of MD simulations, minimum-energy path calculations, and a statistical model based on the harmonic transition state theory to explain the strengthening induced by carbon. We unveil that carbon disrupts the glide process, as unpinning requires the successive nucleation of two kink pairs. When solute separation is below about 100 Burgers vectors, the activation enthalpy of both kink pairs are markedly increased compared to pure iron, resulting in a strong dependence of the unpinning stress on solute spacing. Our simulations also suggest an effect of carbon spacing on the kink-pair activation entropy. This work provides elementary processes and parameters that will be useful for larger-scale models and, in particular, kinetic Monte Carlo simulations.

Abstract: Structural, elastic, and thermal properties of cementite (Fe3C) were studied using a modified embedded atom method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single-element potentials were used to develop a Fe-C alloy MEAM potential, using a statistics-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe, and heat of formation of Fe-C alloys in L12 and B1 structures. The stability of cementite was investigated by molecular dynamics simulations at high temperatures. The nine single-crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single-crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments.

Abstract: The iron–carbon EAM potential that we have developed [Comput. Mater. Sci. 40 (2007) 119] was found to predict a saddle point slightly off the tetrahedral position. This problem was fixed by adding a Gaussian function to the Fe–C pairwise function, which does not change neither the position corresponding to the local energy minimum, i.e. the octahedral site, nor the energy of the saddle point. The potential energy landscape around the saddle point is now more realistic, without changing the dynamics properties of the former potential.

Abstract: Stainless steels found in real-world applications usually have some C content in the base Fe–Cr alloy, resulting in hard and dislocation-pinning carbides—Fe3C (cementite) and Cr23C6—being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe–Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell–Brenner–Tersoff form for the entire Fe–Cr–C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe–Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe–Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe.

Abstract: Existing interatomic potentials for the iron-carbon system suffer from qualitative flaws in describing even the simplest of defects. In contrast to more accurate first-principles calculations, all previous potentials show strong bonding of carbon to overcoordinated defects (e.g., self-interstitials, dislocation cores) and a failure to accurately reproduce the energetics of carbon-vacancy complexes. Thus any results from their application in molecular dynamics to more complex environments are unreliable. The problem arises from a fundamental error in potential design—the failure to describe short-ranged covalent bonding of the carbon p electrons. We describe a resolution to the problem and present an empirical potential based on insights from density-functional theory, showing covalent-type bonding for carbon. The potential correctly describes the interaction of carbon and iron across a wide range of defect environments. It has the embedded atom method form and hence appropriate for billion atom molecular-dynamics simulations.

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.

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: Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed.

Abstract: Modified embedded-atom method (MEAM) interatomic potentials for the Fe-Ti-C and Fe-Ti-N ternary systems have been developed based on the previously developed MEAM potentials for sub-unary and binary systems. An attempt was made to find a way to determine ternary potential parameters using the corresponding binary parameters. The calculated coherent interface properties, interfacial energy, work of separation and misfit strain energy between body-centered cubic Fe and NaCl-type TiC or TiN were reasonable when compared with relevant first-principles calculations under the same condition. The applicability of the present potentials for atomistic simulations to investigate nucleation kinetics of TiC or TiN precipitates and their effects on mechanical properties in steels is also demonstrated.

Abstract: We present an Atomic Cluster Expansion (ACE) machine learned potential developed for high-fidelity atomistic simulations of hydrocarbons, targeting pressures and temperatures near and above supercritical fluid regimes for molecular fluids. A diverse set of stoichiometries were covered in training, including 1:0 (pure carbon), 1:4 (methane), and 1:1 (benzene), and rich bonding environments sampled at supercritical temperatures, hydrogen rich, reactive mixtures where metastable stoichiometries arise, including 1:2 (ethylene) and 1:3 (ethane). A high-fidelity training database was constructed by performing large-scale quantum molecular dynamic simulations [density functional theory (DFT) MD] of diamond, graphite, methane, and benzene. A novel approach to selecting structures from DFT MD is also presented, which allows for the rapid selection of unique DFT MD frames from complex trajectories. Comparisons to DFT and experimental data demonstrate that the presented ACE potential accurately reproduces isotherms, carbon melting curves, radial distribution functions, and shock Hugoniots for carbon and hydrocarbon systems for pressures up to 100 GPa and temperatures up to 6000 K for hydrocarbon systems and up to 9000 K for pure carbon systems. This work delivers a potential that can be used for accurate, large-scale simulations of shocked hydrocarbons and demonstrates a methodology for fitting and validating machine learning interatomic potentials to complex molecular environments, which can be applied to energetic materials in future works.

Abstract: We study the performance of eleven reactive force fields (ReaxFF), which can be used to study sp² carbon systems. Among them a new hybrid ReaxFF is proposed combining two others and introducing two different types of C atoms. The advantages of that potential are discussed. We analyze the behavior of ReaxFFs with respect to 1) the structural and mechanical properties of graphene, its response to strain and phonon dispersion relation; 2) the energetics of (n, 0) and (n, n) carbon nanotubes (CNTs), their mechanical properties and response to strain up to fracture; 3) the energetics of the icosahedral C₆₀ fullerene and the 40 C₄₀ fullerene isomers. Seven of them provide not very realistic predictions for graphene, which made us focusing on the remaining, which provide reasonable results for 1) the structure, energy and phonon band structure of graphene, 2) the energetics of CNTs versus their diameter and 3) the energy of C₆₀ and the trend of the energy of the C₄₀ fullerene isomers versus their pentagon adjacencies, in accordance with density functional theory (DFT) calculations and/or experimental data. Moreover, the predicted fracture strain, ultimate tensile strength and strain values of CNTs are inside the range of experimental values, although overestimated with respect to DFT. However, they underestimate the Young’s modulus, overestimate the Poisson’s ratio of both graphene and CNTs and they display anomalous behavior of the stress - strain and Poisson’s ratio - strain curves, whose origin needs further investigation.

Abstract: To investigate the initial chemical events associated with high-temperature gas-phase oxidation of hydrocarbons, we have expanded the ReaxFF reactive force field training set to include additional transition states and chemical reactivity of systems relevant to these reactions and optimized the force field parameters against a quantum mechanics (QM)-based training set. To validate the ReaxFF potential obtained after parameter optimization, we performed a range of NVT−MD simulations on various hydrocarbon/O2 systems. From simulations on methane/O2, o-xylene/O2, propene/O2, and benzene/O2 mixtures, we found that ReaxFF obtains the correct reactivity trend (propene > o-xylene > methane > benzene), following the trend in the C−H bond strength in these hydrocarbons. We also tracked in detail the reactions during a complete oxidation of isolated methane, propene, and o-xylene to a CO/CO2/H2O mixture and found that the pathways predicted by ReaxFF are in agreement with chemical intuition and our QM results. We observed that the predominant initiation reaction for oxidation of methane, propene, and o-xylene under fuel lean conditions involved hydrogen abstraction of the methyl hydrogen by molecular oxygen forming hydroperoxyl and hydrocarbon radical species. While under fuel rich conditions with a mixture of these hydrocarbons, we observed different chemistry compared with the oxidation of isolated hydrocarbons including a change in the type of initiation reactions, which involved both decomposition of the hydrocarbon or attack by other radicals in the system. Since ReaxFF is capable of simulating complicated reaction pathways without any preconditioning, we believe that atomistic modeling with ReaxFF provides a useful method for determining the initial events of oxidation of hydrocarbons under extreme conditions and can enhance existing combustion models.

Abstract: Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed.

Abstract: Silicon oxycarbides show outstanding versatility due to their highly tunable composition and microstructure. Consequently, a key challenge is a thorough knowledge of structure–property relations in the system. In this work, we fit an atomic cluster expansion potential to a set of actively learned density-functional theory training data spanning a wide configurational space. We demonstrate the ability of the potential to produce realistic amorphous structures and rationalize the formation of different morphologies of the turbostratic free carbon phase. Finally, we relate the materials stiffness to its composition and microstructure, finding a delicate dependence on Si-C bonds that contradicts commonly assumed relations to the free carbon phase.

Abstract: Graphene-supported platinum (Pt) and palladium (Pd) nanoclusters have attracted attention as electrocatalysts for proton exchange membrane fuel cell (PEMFC) because of their high activity and resistance to CO poisoning. However, metal nanoparticles are weakly adsorbed to the graphene and easily migrate on the surface, causing sintering and loss of chemical activity. A thorough understanding of structure-adsorption relationship is important to design robust catalysts with high adsorption ability to stabilize metal nanoparticles, but this relationship is still not well understood, particularly in large scale systems (2–5 nm). Therefore, to investigate the structural evolution at atomic scale with atomistic simulations, we have developed interatomic potentials for the Pt-C and Pd-C binary systems, based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. These potentials reproduce various fundamental properties of the alloy systems in reasonable agreement with the experimental data and first-principles calculations. Molecular dynamics simulations employing the 2NN MEAM potential were carried out to analyse structural factors that have decisive effect on the adsorption energy, by changing the symmetry of the nanoparticles and the configuration of the nanoparticles adsorbed to graphene. These factors were characterized via coordination numbers, number of Pt atoms in contact with the graphene and adsorption site. The results of our study suggest avenues for stabilizing and immobilizing metal clusters on graphene in large systems.

Abstract: Graphene-supported platinum (Pt) and palladium (Pd) nanoclusters have attracted attention as electrocatalysts for proton exchange membrane fuel cell (PEMFC) because of their high activity and resistance to CO poisoning. However, metal nanoparticles are weakly adsorbed to the graphene and easily migrate on the surface, causing sintering and loss of chemical activity. A thorough understanding of structure-adsorption relationship is important to design robust catalysts with high adsorption ability to stabilize metal nanoparticles, but this relationship is still not well understood, particularly in large scale systems (2–5 nm). Therefore, to investigate the structural evolution at atomic scale with atomistic simulations, we have developed interatomic potentials for the Pt-C and Pd-C binary systems, based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. These potentials reproduce various fundamental properties of the alloy systems in reasonable agreement with the experimental data and first-principles calculations. Molecular dynamics simulations employing the 2NN MEAM potential were carried out to analyse structural factors that have decisive effect on the adsorption energy, by changing the symmetry of the nanoparticles and the configuration of the nanoparticles adsorbed to graphene. These factors were characterized via coordination numbers, number of Pt atoms in contact with the graphene and adsorption site. The results of our study suggest avenues for stabilizing and immobilizing metal clusters on graphene in large systems.

Abstract: We propose an analytical interatomic potential for modeling platinum, carbon, and the platinum-carbon interaction using a single functional form. The ansatz chosen for this potential makes use of the fact that chemical bonding in both covalent systems and d-transition metals can be described in terms of the Pauling bond order. By adopting Brenner’s original bond-order potential for carbon [Phys. Rev. B 42, 9458 (1990)] we devise an analytical expression that has an equivalent form for describing the C-C/Pt-Pt/Pt-C interactions. It resembles, in the case of the pure metal interaction, an embedded-atom scheme, but includes angularity. The potential consequently provides an excellent description of the properties of Pt including the elastic anisotropy ratio. The parameters for both the Pt-Pt interaction and the Pt-C interaction are systematically adjusted using a combination of experimental and theoretical data, the latter being generated by total-energy calculations based on density-functional theory. This approach offers good chemical accuracy in describing all types of interactions, and has a wide applicability for modeling metal-semiconductor systems.

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: Modified embedded-atom method (MEAM) interatomic potentials for the Ti-C and Ti-N binary systems have been developed using previously developed MEAM potentials of Ti, C and N. The potential parameters were determined by fitting to experimental data on the enthalpy of formation, lattice parameter, elastic constants, thermal linear expansion of NaCl-type TiC and TiN, and dilute heat of solution of carbon and nitrogen atoms in hexagonal close-packed Ti. The potentials can describe fundamental physical properties (structural, elastic, thermal and surface properties) of the alloys well, in good agreement with experimental information or first-principles calculations. The applicability of the potentials to atomistic investigations of interactions between TiC or TiN precipitates and matrix, dislocations or other defects, and their effects on deformation and mechanical behaviors of metallic alloys is discussed.

Abstract: Tungsten (W) is a material of choice for the divertor material due to its high melting temperature, thermal conductivity, and sputtering threshold. However, W has a very high brittle-to-ductile transition temperature, and at fusion reactor temperatures (≥1000 K), it may undergo recrystallization and grain growth. Dispersion-strengthening W with zirconium carbide (ZrC) can improve ductility and limit grain growth, but much of the effects of the dispersoids on microstructural evolution and thermomechanical properties at high temperatures are still unknown. We present a machine learned Spectral Neighbor Analysis Potential for W-ZrC that can now be used to study these materials. In order to construct a potential suitable for large-scale atomistic simulations at fusion reactor temperatures, it is necessary to train on ab initio data generated for a diverse set of structures, chemical environments, and temperatures. Further accuracy and stability tests of the potential were achieved using objective functions for both material properties and high temperature stability. Validation of lattice parameters, surface energies, bulk moduli, and thermal expansion is confirmed on the optimized potential. Tensile tests of W/ZrC bicrystals show that although the W(110)-ZrC(111) C-terminated bicrystal has the highest ultimate tensile strength (UTS) at room temperature, observed strength decreases with increasing temperature. At 2500 K, the terminating C layer diffuses into the W, resulting in a weaker W-Zr interface. Meanwhile, the W(110)-ZrC(111) Zr-terminated bicrystal has the highest UTS at 2500 K.

Abstract: In this work, we developed an interatomic potential for saturated hydrocarbons using the modified embedded-atom method (MEAM), a reactive semi-empirical many-body potential based on density functional theory and pair potentials. We parameterized the potential by fitting to a large experimental and first-principles (FP) database consisting of (1) bond distances, bond angles, and atomization energies at 0 K of a homologous series of alkanes and their select isomers from methane to n-octane, (2) the potential energy curves of H2, CH, and C2 diatomics, (3) the potential energy curves of hydrogen, methane, ethane, and propane dimers, i.e., (H2)2, (CH4)2, (C2H6)2, and (C3H8)2, respectively, and (4) pressure–volume–temperature (PVT) data of a dense high-pressure methane system with the density of 0.5534 g cc−1. We compared the atomization energies and geometries of a range of linear alkanes, cycloalkanes, and free radicals calculated from the MEAM potential to those calculated by other commonly used reactive potentials for hydrocarbons, i.e., second-generation reactive empirical bond order (REBO) and reactive force field (ReaxFF). MEAM reproduced the experimental and/or FP data with accuracy comparable to or better than REBO or ReaxFF. The experimental PVT data for a relatively large series of methane, ethane, propane, and butane systems with different densities were predicted reasonably well by the MEAM potential. Although the MEAM formalism has been applied to atomic systems with predominantly metallic bonding in the past, the current work demonstrates the promising extension of the MEAM potential to covalently bonded molecular systems, specifically saturated hydrocarbons and saturated hydrocarbon-based polymers. The MEAM potential has already been parameterized for a large number of metallic unary, binary, ternary, carbide, nitride, and hydride systems, and extending it to saturated hydrocarbons provides a reliable and transferable potential for atomistic/molecular studies of complex material phenomena involving hydrocarbon–metal or polymer–metal interfaces, polymer–metal nanocomposites, fracture and failure in hydrocarbon-based polymers, etc. The latter is especially true since MEAM is a reactive potential that allows for dynamic bond formation and bond breaking during simulation. Our results show that MEAM predicts the energetics of two major chemical reactions for saturated hydrocarbons, i.e., breaking a C–C and a C–H bond, reasonably well. However, the current parameterization does not accurately reproduce the energetics and structures of unsaturated hydrocarbons and, therefore, should not be applied to such systems.