Empirical Interatomic Potentials Research Articles

Neural network potential for dislocation plasticity in ceramics

Dislocations in ceramics are increasingly recognized for their promising potential in applications such as toughening intrinsically brittle ceramics and tailoring functional properties. However, the atomistic simulation of dislocation plasticity in ceramics remains challenging due to the complex interatomic interactions characteristic of ceramics, which include a mix of ionic and covalent bonds, and highly distorted and extensive dislocation core structures within complex crystal structures. These complexities exceed the capabilities of empirical interatomic potentials. Therefore, constructing neural network potentials (NNPs) emerges as the optimal solution. Yet, creating a training dataset that includes dislocation structures proves difficult due to the complexity of their core configurations in ceramics and the computational demands of density functional theory for large atomic models containing dislocation cores. In this work, we propose a training dataset from properties that are easier to compute via high-throughput calculation. Using this dataset, we have successfully developed NNPs for dislocation plasticity in ceramics, specifically for three typical functional ceramics: ZnO, GaN, and SrTiO3. These NNPs effectively capture the nonstoichiometric and charged core structures and slip barriers of dislocations, as well as the long-range electrostatic interactions between charged dislocations. The effectiveness of this dataset was further validated by measuring the similarity and uncertainty across snapshots derived from large-scale simulations, alongside extensive validation across various properties. Utilizing the constructed NNPs, we examined dislocation plasticity in ceramics through nanopillar compression and nanoindentation, which demonstrated excellent agreement with experimental observations. This study provides an effective framework for constructing NNPs that enable the detailed atomistic modeling of dislocation plasticity, opening new avenues for exploring the plastic behavior of ceramics.

Incorporating static intersite correlation effects in vanadium dioxide through DFT+V

We analyze the effects on the structural and electronic properties of vanadium dioxide (VO2) due to adding an empirical interatomic potential within the density-functional theory+V (DFT+V) framework. We use the DFT+V machinery founded on the extended Hubbard model to apply an empirical self-energy correction between nearest-neighbor vanadium atoms in both rutile and monoclinic phases, and for a set of structures interpolating between these two cases. We observe that imposing an explicit intersite interaction V along the vanadium–vanadium chains enhances the characteristic bonding-antibonding splitting of the relevant bands in the monoclinic phase, thus favoring electronic dimerization and the formation of a bandgap. We then explore the effect of V on the structural properties and the relative energies of the two phases, finding an insulating global energy minimum for the monoclinic phase, consistent with experimental observations. With increasing V, this minimum becomes deeper relative to the rutile structure, and the transition from the metallic to the insulating state becomes sharper. We also analyze the effect of applying the +V correction either to all or only to selected vanadium–vanadium pairs and both in the monoclinic as well as the metallic rutile phase. Our results suggest that DFT+V can indeed serve as a computationally inexpensive unbiased way of modeling VO2 which is well suited for studies that, e.g., require large system sizes. Published by the American Physical Society 2024

Empirical interatomic potential development and classical molecular dynamics simulation of monolayer group-III monochalcogenides: insights into thermal transport properties

Abstract This research addresses the lack of comprehensive studies utilizing classical molecular dynamics simulations for monolayer group-III monochalcogenide materials. These materials, including GaS, GaSe, and InSe, have shown promise for diverse applications but lack well-defined empirical interatomic potentials in the literature. This study is concentrated on the development of empirical interatomic potential parameters for these materials using the particle swarm optimization method, filling a gap in the literature regarding classical molecular dynamics simulations. The parameters are optimized based on fundamental physical characteristics such as the lattice constants, bond lengths, phonon dispersions, and the equation of state, obtained from first-principles calculations. The developed potential parameters are then employed to predict lattice thermal conductivity through non-equilibrium classical molecular dynamics simulations, providing insights into the thermal transport properties of these materials.

Thermal transport in disordered wurtzite ScAlN alloys using machine learning interatomic potentials

Disordered wurtzite ScAlN alloy is an emerging material with a strong piezoelectric coefficient that promotes its application in 5 G communication devices. To extend the service lifetime of the device, it is an urgent task to understand the thermal transport properties of this alloy for thermal management. Yet a thorough understanding of the thermal transport in the disordered ScAlN alloy is hindered by the inaccuracy of empirical interatomic potentials adopted for atomistic simulations. Herein, we developed an accurate and efficient neuro-evolution potential and combined it with Allen and Feldman theory and molecular dynamics to investigate thermal transport properties of disordered ScAlN alloys with varying ratios. This potential is shown to have the same computational accuracy as first principles by comparing the phonon spectrum and radial distribution function. Based on the homogeneous non-equilibrium molecular dynamics simulations, the lattice thermal conductivity of the disordered alloys reaches its maximum value (less than 12 W/m·K) at room temperature. Further investigation of the temperature effects on the vibrational modes shows that it affects the mode lifetimes for the propagons and the mode heat capacities for the diffusions. In addition, it was found that both mode lifetime and diffusivity decrease with increasing Sc concentration. This work aims to train a universal machine learning interatomic potential of disordered ScAlN alloys, seeking to accelerate the thermal management design of related devices.

Interatomic Interaction Models for Magnetic Materials: Recent Advances

Abstract Atomistic modeling is a widely employed theoretical method of computational materials science. It has found particular utility in the study of magnetic materials. Initially, magnetic empirical interatomic potentials or spin-polarized density functional theory (DFT) served as the primary models for describing interatomic interactions in atomistic simulations of magnetic systems. Furthermore, in recent years, a new class of interatomic potentials known as magnetic machine-learning interatomic potentials (magnetic MLIPs) has emerged. These MLIPs combine the computational efficiency, in terms of CPU time, of empirical potentials with the accuracy of DFT calculations. In this review, our focus lies on providing a comprehensive summary of the interatomic interaction models developed specifically for investigating magnetic materials. We also delve into the various problem classes to which these models can be applied. Finally, we offer insights into the future prospects of interatomic interaction model development for the exploration of magnetic materials.

Interatomic Potential For Carbon Based Quantum‐Technology Applications

AbstractTo optimize parameters for laser processing of quantum‐technology relevant materials, such as diamond, precise atomistic simulations of the light‐matter interaction on large scales (on the order of atoms) are essential. Classical empirical interatomic potentials are commonly employed for simulating such a large number of atoms, however they fail to accurately capture all relevant effects of light‐matter interaction. Conversely, ab initio methods like Density Functional Theory (DFT) can effectively incorporate quantum properties arising from photon excitations, but their applicability is limited to small systems containing at most approximately atoms. Consequently, bridging the gap between achieving DFT precision and handling millions of atoms necessitates the development of innovative classes of interatomic potentials. In this paper, the construction of a highly accurate interatomic potential for diamond is presented, derived from an extensive dataset of DFT calculations. The parameters of the interatomic potential depend on the electronic temperature (). The findings demonstrate that this newly developed interatomic potential can aptly describe the laser processing of diamond for nanophotonic applications, achieving accuracy comparable to ab initio methods for large systems.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids.

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

Line shapes of isotropic and depolarized CILS spectra of neon: Interaction potential and pair polarizability

The present work proposes three interaction potentials between two gaseous neon atoms and applies them to the study of models representing the anisotropy and trace of the induced pair polarizability tensor. The proposed empirical interatomic potentials for the gaseous Ne-Ne interaction are developed by fitting the Improved Lennard-Jones (ILJ), Modified Tang-Toennies (MTT) and Barker et al. (BFW) potentials simultaneously to the spectroscopic and transport properties over a wide temperature range. The validity of the proposed interatomic potentials is verified by comparing the calculated and experimental second pressure virial coefficient over a wide temperature range. In addition to this, the results show satisfactory accordance between the experimental and calculated vibrational energy levels using the deduced pair potential parameters compared to those reported for neon gas. These comparisons exhibit acceptable accuracy when the present work potential parameters are inserted to reproduce the transport and thermo-physical properties, besides the spectral moments and the spectral line-shape intensities for neon gas. The isotropic and depolarized collision-induced light scattering (CILS) spectra are produced and analyzed as functions of the potential considered. They exhibit sensitivity to both the attractive part of the potential and the short-range values of the polarizability anisotropy or mean at intermediate and high frequencies. Mean and anisotropy are deduced directly from spectral line shapes using a new inversion method.

Interatomic potentials for cubic zirconia and yttria-stabilized zirconia optimized by genetic algorithm

Yttria stabilized zirconia (YSZ) is an important engineering ceramic oxide used for various applications, including solid electrolytes in solid oxide fuel cells due to its high ionic conductivity. Accurate and computationally inexpensive interatomic potentials for cubic ZrO2 and YSZ are required to accommodate the large number of defect configurations originating from high concentrations of Y and oxygen vacancies and to statistically understand their properties in realistic time. In this study, a genetic algorithm has been used to optimize empirical interatomic potential parameters for cubic ZrO2 and 10Y2O3 mol% YSZ using energies, forces acting on atoms, and stresses generated by ab initio calculations as training data. The optimized potentials reproduce the structural, mechanical, and thermal properties as well as the ionic conduction properties more accurately than previously reported empirical interatomic potentials. The developed potentials will be useful for a statistical characterization of YSZ properties, combined with more accurate ab initio calculations.

Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential

The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

Microstructure evolution under thermo-mechanical operating of rocksalt-structure TiN via neural network potential.

In the process of high temperature service, the mechanical properties of cutting tools decrease sharply due to the peeling of the protective coating. However, the mechanism of such coating failure remains obscure due to the complicated interaction between atomic structure, temperature, and stress. This dynamic evolution nature demands both large system sizes and accurate description on the atomic scale, raising challenges for existing atomic scale calculation methods. Here, we developed a deep neural network (DNN) potential for Ti-N binary systems based on first-principles study datasets to achieve quantum-accurate large-scale atomic simulation. Compared with empirical interatomic potential based on the embedded-atom-method, the developed DNN-potential can accurately predict lattice constants, phonon properties, and mechanical properties under various thermodynamic conditions. Moreover, for the first time, we present the atomic evolution of the fracture behavior of large-scale rocksalt-structure (B1) TiN systems coupled with temperature and stress conditions. Our study validates that interatomic brittle fractures occur when TiN stretches beyond its tensile yield point. Such simulation of coating fracture and cutting behavior based on large-scale atoms can shed new light on understanding the microstructure and mechanical properties of coating tools under extreme operating conditions.

Empirical interatomic potentials for ZrO2 and YSZ polymorphs: Application to a tetragonal ZrO2 grain boundary

Yttria stabilized zirconia (YSZ) ceramics have been used for various engineering applications including structural ceramics, biomedical materials, and thermal barrier coatings. The versatile and excellent properties of YSZ stem from its unique microstructure consisting of monoclinic, tetragonal, and cubic phases, whose stability depends on yttria concentration and temperature. However, there are no empirical interatomic potentials (EIPs) that can reproduce the structures and energies of ZrO2 and YSZ polymorphs, limiting the atomic-scale investigation of lattice defect structures and their interactions that affect the YSZ microstructure and properties. Here, using a genetic algorithm and ab initio training datasets, we have optimized EIPs to sufficiently reproduce the structures and stability of ZrO2 and YSZ polymorphs, as well as the properties of the tetragonal and cubic phases at finite temperature. The potentials have also been applied to the search for a tetragonal grain boundary structure, showing that the obtained grain boundary structure is consistent with that obtained by ab initio calculations. The developed EIPs will aid in revealing the microstructure-property relationships in YSZ by performing large-scale and systematic calculations, which are practically difficult to perform with ab initio and machine-learning-potential calculations.

Development of machine learning and empirical interatomic potentials for the binary Zr-Sn system

Zirconium alloys are pivotal structural materials in nuclear reactors. Enhancing their properties and performance necessitates a profound understanding of the interactions between alloying elements and lattice defects. However, the atomic-level mechanisms that account for the effects of tin (Sn) on irradiation-induced defect evolution in zirconium (Zr) are not well understood yet. To bridge this gap, we conducted extensive first-principles calculations and utilized the obtained data to develop two interatomic potentials for the Zr-Sn system: a Zr-Sn moment tensor machine learning interatomic potential (MTP) and a modified embedded atom potential (MEAM) built upon existing unary ones. The reliability of the constructed potentials was validated through systematically comparing relevant physical properties of pure Zr, Sn metals, and Zr-Sn solid solutions, calculated using these potentials, to values obtained from density functional theory calculations and/or experiments. The developed potentials exhibit high fidelity and accuracy in capturing the behavior of the Zr-Sn system. Their applicability in terms of both reliability and computational efficiency was also discussed. These potentials provide a solid foundation for further exploration of the atomic-scale behavior of the Zr-Sn alloy systems, thereby facilitating the continuous optimization and application of the zirconium alloys.

Construction of machine-learning interatomic potential under heat flux regularization and its application to power spectrum analysis for silver chalcogenides

We propose a data-driven approach for constructing machine-learning interatomic potentials (MLIPs) trained under a regularization with the aim of avoiding nonphysical heat flux that arises from the many-body effect of MLIPs and is sensitive to their initial weight parameters. Specifically, we introduce a regularization term for the heat flux into the cost function of MLIPs to be minimized. Since the treatment of heat flux using MLIPs with regularization can be decomposed into elemental contributions or conducted in frequency space, this approach is expected to be useful for investigating the origin of thermal conductivity obtained from the Green-Kubo formula. However, the strength of regularization needs to be appropriately set because it may reduce not only the nonphysical part but also the intrinsic heat flux one. To this end, we investigated the conditions for constructing MLIPs that can reproduce the power spectra of heat flux associated with the empirical interatomic potential of Ag2Se, which consists of pairwise functions and do not contain a nonphysical heat flux. The power spectrum is useful because it helps to verify the effect of regularization and also contains the information on thermal conductivity and phonon. The appropriate strength could be estimated from the variation of the magnitude of regularization term as well as root mean square errors for total potential energy, atomic force, and virial stress with respect to the strengths, without reference spectrum data. As an application example, we explored the differences in power spectra between superionic and nonsuperionic conducting phases based on the heat flux regularization to MLIPs trained with the first-principles calculation data of Ag2S. Furthermore, our results demonstrate that training with the regularization improves the robustness of MLIPs as well as the reduction of the nonphysical heat flux.

Ab initio calculations and empirical potential assessments of the energy and structure of symmetric tilt grain boundaries in tungsten

Molecular statics/dynamics (MS/MD) based on empirical interatomic potentials (IAPs) is an effective means for conducting grain boundary (GB) related studies. The accuracy of these MS/MD simulations, however, can be greatly affected by the IAP used. Unfortunately, the large discrepancies between the ab-initio values make it difficult to evaluate, improve and further develop IAPs. Motivated by this issue, in the present work we perform a systematic investigation of 〈100〉 and 〈110〉 symmetric tilt GBs in tungsten (W) via atomistic simulations, including the stable structure, GB energy, work of separation, excess volume, and vacancy formation energy. We here use a two-step relaxation process, initially obtaining the candidate structures from MS and then performing DFT validation of these structures to determine the ground state structure, where six empirical IAPs and four exchange–correlation (xc) functionals are used. And the step-like feature is revealed that can be used to reduce the cost of time-consuming optimization processes. Taking the results yielded by PBEsol xc-functional as a benchmark, it is shown that for the same xc-functional, the relative errors of GB energy and work of separation are almost identical, independent of the GB character. The performance of six typical empirical IAPs considered for W is also evaluated by comparing it with the DFT data. The quantities chosen for the comparison include the structure and energetic properties of GBs, as mentioned before. We demonstrate that these empirical IAPs tend to better describe only part of the properties of GBs; for example, some IAPs can predict the energetic properties well, while others can better describe the structure. This suggests that a fully reliable description of GBs remains an elusive objective, requiring further efforts in the development and optimization of the IAP.

Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations.

Metal-organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Simulation studies of the stability and growth kinetics of Pt-Sn phases using a machine learning interatomic potential

The thermodynamic stability and growth kinetics of Pt-Sn phases are investigated by atomistic simulations utilizing a neural-network machine learning (NN-ML) interatomic potential. The physical properties of Pt-Sn crystalline phases described by the NN-ML interatomic potential, such as equation of states, formation energy convex hull, and phonon vibrational spectrum, are in in accord well with first-principles calculations and experimental data. The calculations of temperature dependent Gibbs free energies of the crystalline Pt-Sn phases by the NN-ML potential are in the efficiency of empirical interatomic potentials and accuracy of density functional theory (DFT). The developed NN-ML potential is also used to investigate the structures and dynamics of liquid phases of Pt-Sn alloys by molecular dynamics (MD) simulations. The crystallization of PtSn and Pt3Sn phases from the solid–liquid interface are also studied by MD simulations using the NN-ML potential. The results obtained from our studies provide useful insight into thermodynamics stability and growth kinetics of Pt-Sn binary phases.

Interatomic-Potential-Free, Data-Driven Molecular Dynamics

We present a Data-Driven (DD) paradigm that enables molecular dynamics calculations to be performed directly from sampled force-field data such as obtained, e. g., from ab initio calculations, thereby eschewing the conventional step of modeling the data by empirical interatomic potentials entirely. The data required by the DD solvers consists of local atomic configurations and corresponding atomic forces and is, therefore, fundamental, i. e., it is not beholden to any particular model. The resulting DD solvers, including a fully explicit DD-Verlet algorithm, are provably convergent and exhibit robust convergence with respect to the data in selected test cases. We present an example of application to C60 buckminsterfullerenes that showcases the feasibility, range and scope of the DD molecular dynamics paradigm.

Computational study of Na diffusion and conduction in P2- and O3-Na2x[NixTi1-x]O2 materials with machine-learning interatomic potentials

Sodium-ion batteries (SIBs) provide a feasible solution for large-scale energy storage applications of sustainable energy resources like wind and solar energy. Layered sodium nickel titanates (Na2x[NixTi1-x]O2) (SNTL) are considered a promising electrode material for SIBs since they can function as either a positive or negative electrode due to the coexistence of high redox potential element Ni (V = 3.7 V vs. Na/Na+) and low redox potential element Ti (V = 0.7 V vs. Na/Na+). There have been both experimental and computational studies on the family of Na2x[NixTi1-x]O2 materials, investigating their structures, electrochemical performance, electronic and ionic conductivity, etc. However, the current understanding of the Na migration mechanism is still very limited at an atomic level because of the restrictions of simulation methods: density-functional theory (DFT) simulation is restricted to a small length and time scale, whereas the conventional empirical interatomic potential (IP) is restricted by a limited accuracy. To solve this efficiency-versus-accuracy dilemma, herein we developed a neural network (NN)-based machine-learning interatomic potential (MLIP), which is trained using DFT data. Our MLIP demonstrates a DFT-approaching accuracy in terms of atomic forces. Moreover, the extracted Na self-diffusivity, ionic conductivity, and activation energy values from MLIP-MD simulation agree well with experimental data. In general, P2-SNTL demonstrates a higher Na self-diffusivity and ionic conductivity than O3-SNTL, mainly due to the larger bottleneck size through which Na ions migrate. We also employed the incoherent density correlation function to study the Na migration mechanism. The Singwi-Sjölander (SS) model and Chudley-Elliot (CE) model were used to fit the jump-diffusion behavior in P2- and O3-SNTL, respectively. The obtained jump distance values match well with the typical distance between the nearest Na sites in P2- and O3-SNTL, confirming that the hopping events happen mostly between neighboring Na sites in SNTL. The decrease of residence time and jump distance values with temperature is a result of higher ion mobility and level of delocalization, as validated by the nuclear density maps. In addition, our study also confirmed that both the “straight” and “curved” Na migration paths exist in O3-SNTL, in contrast to previous studies which only mention the “curved” migration path. In the end, our calculated Haven ratios have a value <1, indicating that it is more likely for the Na hopping events to occur via a concerted migration of several atoms other than the jump of an isolated atom.