Reliable Interatomic Potentials Research Articles

Efficient calculation of unbiased atomic forces in ab initio variational Monte Carlo

quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wave functions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose an efficient method to obtain unbiased atomic forces and pressures in the variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz or the Jastrow antisymmetrized geminal power ansatz, exploiting the gauge-invariant and locality properties of their geminal representation. We demonstrate the effectiveness of our method for H2 and Cl2 molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces. Published by the American Physical Society 2024

Developing an analytical bond-order potential for Hf/Nb/Ta/Zr/C system using machine learning global optimization

Developing an analytical bond-order potential for Hf/Nb/Ta/Zr/C system using machine learning global optimization

An interatomic potential for ternary NiTiHf shape memory alloys based on modified embedded atom method

NiTi-based high temperature shape memory alloys (HTSMAs) can operate in high temperature applications, where binary NiTi cannot function. NiTiHf is among the most popular HTSMAs due to its lower preparation cost and good thermal stability. Various aspects of material properties of NiTiHf and the effect of different factors, such as composition, heat treatment and precipitates, on its behavior is yet to be understood. Molecular dynamics (MD) simulations can provide insights to acquire such an understanding. However, MD simulations of NiTiHf have not been possible due to the absence of a reliable interatomic potential, which is a necessary tool for such simulations. In this study, density functional theory (DFT) simulations were employed and a ternary Second Nearest Neighbor Modified Embedded Atom Method (2NN MEAM) potential was calibrated for NiTiHf. To perform this study, the related unary and binary potentials were calibrated by fitting the values of their reproduced physical properties to the DFT results. The final ternary MEAM potential was checked for reliability and transferability by performing MD simulations. The results showed that the developed potential can appropriately capture the temperature-induced and stress-induced martensitic phase transformations in NiTiHf.

Developing a variable charge potential for Hf/Nb/Ta/Ti/Zr/O system via machine learning global optimization

Despite widespread attentions on the HfNbTaTiZr refractory high-entropy alloy (RHEA) owing to various exceptional properties, insights into nanostructure-property relations are severely hindered by the lack of reliable interatomic potentials in atomistic simulations. In this paper, we propose a supervised machine learning framework powered by the distributed breeder genetic algorithm (DBGA) to train a charge transfer ionic potential (CTIP) for the multi-component Hf/Nb/Ta/Ti/Zr/O system. By combining the DBGA with extensive ab initio training data and a carefully designed objective function, a robust and extrapolative potential with massive internal parameters is effectively optimized. A cross-validation of the CTIP is rigorously performed to verify its accuracy in predicting energetic, structural and mechanical properties of metals, intermetallic compounds, alloys and oxides. Using the developed potential, we further study the atomic structure and its evolution in RHEA to reveal the deformation and oxidation mechanisms in response to mechanical loadings and oxygen atmospheres. The simulation results not only provide valuable atomistic information hardly accessible through experiments and thermodynamic calculations, but also display promising prospects for large-scale reactive simulations of the Hf/Nb/Ta/Ti/Zr/O complex-component system.

Machine learning interatomic potential for silicon-nitride (Si3N4) by active learning.

Silicon nitride (Si3N4) is an extensively used material in the automotive, aerospace, and semiconductor industries. However, its widespread use is in contrast to the scarce availability of reliable interatomic potentials that can be employed to study various aspects of this material on an atomistic scale, particularly its amorphous phase. In this work, we developed a machine learning interatomic potential, using an efficient active learning technique, combined with the Gaussian approximation potential (GAP) method. Our strategy is based on using an inexpensive empirical potential to generate an initial dataset of atomic configurations, for which energies and forces were recalculated with density functional theory (DFT); thereafter, a GAP was trained on these data and an iterative re-training algorithm was used to improve it by learning on-the-fly. When compared to DFT, our potential yielded a mean absolute error of 8 meV/atom in energy calculations for a variety of liquid and amorphous structures and a speed-up of molecular dynamics simulations by 3-4 orders of magnitude, while achieving a first-rate agreement with experimental results. Our potential is publicly available in an open-access repository.

High-Accuracy Neural Network Interatomic Potential for Silicon Nitride.

In the field of machine learning (ML) and data science, it is meaningful to use the advantages of ML to create reliable interatomic potentials. Deep potential molecular dynamics (DEEPMD) are one of the most useful methods to create interatomic potentials. Among ceramic materials, amorphous silicon nitride (SiNx) features good electrical insulation, abrasion resistance, and mechanical strength, which is widely applied in industries. In our work, a neural network potential (NNP) for SiNx was created based on DEEPMD, and the NNP is confirmed to be applicable to the SiNx model. The tensile tests were simulated to compare the mechanical properties of SiNx with different compositions based on the molecular dynamic method coupled with NNP. Among these SiNx, Si3N4 has the largest elastic modulus (E) and yield stress (σs), showing the desired mechanical strength owing to the largest coordination numbers (CN) and radial distribution function (RDF). The RDFs and CNs decrease with the increase of x; meanwhile, E and σs of SiNx decrease when the proportion of Si increases. It can be concluded that the ratio of nitrogen to silicon can reflect the RDFs and CNs in micro level and macro mechanical properties of SiNx to a large extent.

Phase transition in yttrium under shock compression by atomistic simulations

Phase transition in yttrium under shock compression by atomistic simulations

Deep learning interatomic potential for Ca-O system at high pressure

Calcium-containing oxides are fundamental components of the Earth's crust and mantle. Analysis of their structural behavior contributes to our understanding of the Earth's interior, which needs a reliable interatomic potential. Here, we present an interatomic potential for the Ca-O system using the deep neural network method. The initial training data set for the deep interatomic potential (DP) consists of snapshots of prototype binary structures from materials projects and crystal-derived structures based on Ca-O binary compounds, as well as their molecular dynamic trajectories. The accuracy of the DP is evaluated by predicting forces and energies in comparison with those from ab initio calculations. We demonstrate that the vibrational and thermodynamic properties based on DP calculations are in excellent agreement with those from ab initio calculations. Besides, we also construct a temperature-pressure phase diagram of Ca-O compounds with DP at a lower cost compared to ab initio methods. Finally, we use the DP to explore Ca-O structures by combining it with the genetic algorithm, the accuracy of which is validated by a principal component analysis for the local atomic environments. The DP training procedure used in this work is equally applicable to other systems for accurate atomistic simulations as an effective method.

Investigating thermal properties of Kr Gas for temperatures [120–180] K using static fluctuation approximation

Particular thermal properties of internal energy, entropy, specific heat capacity and pressure are indicated using static fluctuation approximation (SFA) for specified temperatures and densities where the interaction between particles is still valid. This ab initio study starts initially from the most reliable krypton interatomic potential and develops with complementary SFA assumptions that depend mainly on substituting the local field mean value instead of its operator, thus developing a numerical solution of a nonlinear close set equation by iteration technique. The results are matched with the ideal gas and show a considerable sense.

Molecular dynamics simulation of metallic Al-Ce liquids using a neural network machine learning interatomic potential.

Al-rich Al-Ce alloys have the possibility of replacing heavier steel and cast irons for use in high-temperature applications. Knowledge about the structures and properties of Al-Ce alloys at the liquid state is vital for optimizing the manufacture process to produce desired alloys. However, reliable molecular dynamics simulation of Al-Ce alloy systems remains a great challenge due to the lack of accurate Al-Ce interatomic potential. Here, an artificial neural network (ANN) deep machine learning (ML) method is used to develop a reliable interatomic potential for Al-Ce alloys. Ab initio molecular dynamics simulation data on the Al-Ce liquid with a small unit cell (∼200 atoms) and on the known Al-Ce crystalline compounds are collected to train the interatomic potential using ANN-ML. The obtained ANN-ML model reproduces well the energies, forces, and atomic structure of the Al90Ce10 liquid and crystalline phases of Al-Ce compounds in comparison with the ab initio results. The developed ANN-ML potential is applied in molecular dynamics simulations to study the structures and properties of the metallic Al90Ce10 liquid, which would provide useful insight into the guiding experimental process to produce desired Al-Ce alloys.

The race between relaxation and nucleation in supercooled liquid and glassy BaS – A molecular dynamics study

Details of the microscopic mechanisms and dynamics of most processes in supercooled liquids (SCL) and glasses remain blurred due to their complexity and the extraordinarily long or inaccessibly short timescales, depending on the supercooling degree. In this paper, we determined the structural relaxation times in an intermediate supercooling window (0.67–0.78 Tm, Tm = melting point) of barium sulfide liquid, used as a model material, through molecular dynamics (MD) simulations based on a reliable two-body interatomic potential. We also inferred these dynamics in the glassy state using extrapolated data and well-accepted models. The average structural α-relaxation times, <tα>, were determined via the intermediate scattering function. Relaxation kinetics were also estimated by the Maxwell relation via the equilibrium shear viscosity and shear modulus, obtained by MD. We found that the viscosity derived (Maxwell) relaxation times are significantly shorter than the intrinsic α -relaxation times, corroborating two recent experimental studies of other substances. For the simulated system, with 36,000 particles and average volume of 1.4x103 nm3, the structural relaxation and nucleus birth time curves cross at the kinetic spinodal temperature, TKS (=0.33 Tm), which is significantly below the glass transition temperature, Tg (=0.44 Tm). However, for larger sample sizes, the TKS occurs at higher temperatures. As for temperatures above TKS, crystal nucleation starts after structural relaxation, and vice-versa, to understand and describe crystal nucleation one must necessarily take the relaxation process into account, however, this is not included in nucleation theories. These discoveries shed light on some obscure aspects of supercooled liquids, i.e., they challenge a critical assumption of nucleation theories (that crystal nucleation always occurs in a fully relaxed SCL), and show that crystallization is BaS ultimate fate, corroborating studies with other substances.

Machine learning interatomic potential developed for molecular simulations on thermal properties of β-Ga2O3.

The thermal properties of β-Ga2O3 can significantly affect the performance and reliability of high-power electronic devices. To date, due to the absence of a reliable interatomic potential, first-principles calculations based on density functional theory (DFT) have been routinely used to probe the thermal properties of β-Ga2O3. DFT calculations can only tackle small-scale systems due to the huge computational cost, while the thermal transport processes are usually associated with large time and length scales. In this work, we develop a machine learning based Gaussian approximation potential (GAP) for accurately describing the lattice dynamics of perfect crystalline β-Ga2O3 and accelerating atomic-scale simulations. The GAP model shows excellent convergence, which can faithfully reproduce the DFT potential energy surface at a training data size of 32 000 local atomic environments. The GAP model is then used to predict ground-state lattice parameters, coefficients of thermal expansion, heat capacity, phonon dispersions at 0 K, and anisotropic thermal conductivity of β-Ga2O3, which are all in excellent agreement with either the DFT results or experiments. The accurate predictions of phonon dispersions and thermal conductivities demonstrate that the GAP model can well describe the harmonic and anharmonic interactions of phonons. Additionally, the successful application of our GAP model to the phonon density of states of a 2500-atom β-Ga2O3 structure at elevated temperature indicates the strength of machine learning potentials to tackle large-scale atomic systems in long molecular simulations, which would be almost impossible to generate with DFT-based molecular simulations at present.

Polytetrahedral short-range order and crystallization stability in supercooled Cu64.5Zr35.5 metallic liquid

Development of reliable interatomic potentials is crucial for theoretical studies of relationship between chemical composition, structure and observable properties in glass-forming metallic alloys. Due to ambiguity of potential parametrization procedure, some crucial properties of the system, such as crystallization stability or symmetry of the ground state crystal phase, may not be correctly reproduced in computer simulations. Here we address this issue for ${\rm Cu_{64.5}Zr_{35.5}}$ alloy described by two modifications of embedded atom model potential as well as by \textit{ab initio} molecular dynamics. We observe that, at low supercooling, both models provide very similar liquid structure, which agrees with that obtained by \textit{ab initio} simulations. Hoverer, deeply supercooled liquids demonstrate essentially different local structure and so different crystallization stability. The system, which demonstrate more pronounced icosahedral sort-range order, is more stable to crystallization that is in agreement with Frank hypothesis.

Effects of pore morphology and pore edge termination on the mechanical behavior of graphene nanomeshes

We report results of a systematic computational study on the mechanical response of graphene nanomeshes (GNMs) to uniaxial tensile straining based on molecular-dynamics simulations of dynamic deformation tests according to a reliable bond-order interatomic potential. We examine the effects on the GNM mechanical behavior under straining along different directions of the nanomesh pore morphology and pore edge passivation by testing GNMs with elliptical pores of various aspect ratios and different extents of edge passivation through termination with H atoms of under-coordinated edge C atoms. We establish the dependences of the ultimate tensile strength, fracture strain, and toughness of the GNMs on the nanomesh porosity, derive scaling laws for GNM strength-density relations, and find the GNMs' mechanical response to uniaxial straining to be anisotropic for pore morphologies deviating from circular pores. We also find that the GNM tensile strength decays exponentially with increasing GNM porosity and that pore edge termination with H atoms causes a reduction in the GNMs' elastic stiffening, strength, deformability, and toughness; this hydrogen embrittlement effect is more pronounced at a high level of pore edge passivation that renders the edge C atoms sp3-hybridized. The underlying mechanisms of crack initiation and propagation and nanomesh failure for the various types of GNMs examined also are characterized in atomistic detail. Overall, even highly porous GNMs remain particularly strong and deformable and, therefore, constitute very promising 2D mechanical metamaterials.

Atomic-Scale Structure and Stress Release Mechanism in Core-Shell Nanoparticles.

Core-shell nanoparticles find applications in catalysts, sensors, and theranostics. The full internal 3D atomic structure, however, cannot be resolved by current imaging and diffraction techniques. We analyzed the atomic positions and stress-release mechanism in a cubic Au-Pd core-shell nanoparticle in approximately 1000 times higher resolution than current experimental techniques using large-scale molecular dynamics simulation to overcome these limitations. The core-shell nanocube of 73 nm size was modeled similarly to solution synthesis by random epitaxial deposition of a 4 nm thick shell of Pd atoms onto a Au core of 65 nm side length using reliable interatomic potentials. The internal structure reveals specific deformations and stress relaxation mechanisms that are caused by the +4.8% lattice mismatch of gold relative to palladium and differential confinement of extended particle facets, edges, and corners by one, two, or three Au-Pd interfaces, respectively. The three-dimensional lattice strain causes long-range, arc-like bending of atomic rows along the faces and edges of the particle, especially near the Au-Pd interface, a bulging deformation of the Pd shell, and stacking faults in the Pd shell at the corners of the particle. The strain pattern and mechanism of stress release were further characterized by profiles of the atomic layer spacing in the principal crystallographic directions. Accordingly, strain in the Pd shell is several times larger in the extended facets than near the edges and corners of the nanoparticle, which likely affects adsorption, optical, and electrochemical properties. The findings are consistent with available experimental data, including 3D reconstructions of the same cubic nanoparticle by coherent diffractive imaging (CDI) and may be verified by more powerful experimental techniques in the future. The stress release mechanisms are representative for cubic core-shell nanoparticles with fcc structure and can be explored for different shapes by the same methods.

A simple embedded atom potential for Pd-H alloys

ABSTRACTMetal Hydride systems are an important research topic in material science because of their many practical, industrial, and scientific applications. Therefore, the development of reliable and efficient interatomic potentials for metal hydrides systems, to be utilised in molecular simulations, can be of great value in accelerating the research in this field. In this paper, a fully analytical interatomic Embedded Atom Potential (EAM) for the Pd-H system has been developed, that can be easily extended to ternary Palladium-based hydride systems. The new potential has fewer fitting parameters than previously developed EAM Pd-H potentials and can better predict the cohesive energy, lattice constant, bulk modulus, elastic constants, and the stable alloy crystal structures during molecular dynamics (MD) simulations for various hydrogen concentrations. The EAM potential also predicts the miscibility gap, the separation of a Pd-H system to dilute (α) and concentrated (β) phases.

Formation and Mechanical Behavior of Nanocomposite Superstructures from Interlayer Bonding in Twisted Bilayer Graphene.

We report a comprehensive study on the design of two-dimensional graphene-diamond nanocomposite superstructures formed through interlayer covalent bonding of twisted bilayer graphene with commensurate bilayers. The interlayer bonding is induced by patterned hydrogenation that leads to the formation of superlattices of two-dimensional nanodiamond domains embedded between the two graphene layers. We generalize a rigorous algorithm for the formation of all possible classes of these superstructures: the structural parameters employed to design such carbon nanocomposites include the commensurate bilayer's twist angle, the stacking type of the nanodomains where the interlayer bonds are formed, the interlayer bond pattern, and the interlayer C-C bond density that is proportional to the concentration of sp3-hybridized interlayer-bonded C atoms. We also analyze systematically the mechanical behavior of these nanocomposite superstructures on the basis of molecular-dynamics simulations of uniaxial tensile straining tests according to a reliable interatomic bond-order potential. We identify a range of structural parameters over which the fracture of these superstructures is ductile, mediated by void formation, growth, and coalescence, contrary to the typical brittle fracture of graphene. We introduce a ductility metric as an order parameter for the brittle-to-ductile transition, demonstrate its direct dependence on the fraction of sp3-hybridized interlayer-bonded C atoms, and show that increasing the fraction of interlayer-bonded C atoms beyond a critical level in certain classes of these superstructures induces their ductile mechanical response.

Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method

Abstract Availability of a reliable interatomic potential is one of the major challenges in utilizing molecular dynamics (MD) for simulations of metals at near the melting temperatures and melting point (MP). Here, we propose a novel approach to address this challenge in the concept of modified-embedded-atom (MEAM) interatomic potential; also, we apply the approach on iron, nickel, copper, and aluminum as case studies. We propose adding experimentally available high temperature elastic constants and MP of the element to the list of typical low temperature properties used for the development of MD interatomic potential parameters. We show that the proposed approach results in a reasonable agreement between the MD calculations of melting properties such as latent heat, expansion in melting, liquid structure factor, and solid-liquid interface stiffness and their experimental/computational counterparts. Then, we present the physical properties of mentioned elements near melting temperatures using the new MEAM parameters. We observe that the behavior of elastic constants, heat capacity and thermal linear expansion coefficient at room temperature compared to MP follows an empirical linear relation (α±β × MP) for transition metals. Furthermore, a linear relation between the tetragonal shear modulus and the enthalpy change from room temperature to MP is observed for face-centered cubic materials.

Size-dependent plastic deformation of twinned nanopillars in body-centered cubic tungsten

Compared with face-centered cubic metals, twinned nanopillars in body-centered cubic (BCC) systems are much less explored partly due to the more complicated plastic deformation behavior and a lack of reliable interatomic potentials for the latter. In this paper, the fault energies predicted by two semi-empirical interatomic potentials in BCC tungsten (W) are first benchmarked against density functional theory calculations. Then, the more accurate potential is employed in large scale molecular dynamics simulations of tensile and compressive loading of twinned nanopillars in BCC W with different cross sectional shapes and sizes. A single crystal, a twinned crystal, and single crystalline nanopillars are also studied as references. Analyses of the stress-strain response and defect nucleation reveal a strong tension-compression asymmetry and a weak pillar size dependence in the yield strength. Under both tensile and compressive loading, plastic deformation in the twinned nanopillars is dominated by dislocation slip on {110} planes that are nucleated from the intersections between the twin boundary and the pillar surface. It is also found that the cross sectional shape of nanopillars affects the strength and the initial site of defect nucleation but not the overall stress-strain response and plastic deformation behavior.

Dynamics of Small Mobile Helium Clusters Near a Symmetric Tilt Grain Boundary of Plasma-Exposed Tungsten

We report the results of a systematic atomic-scale analysis of small helium cluster dynamics near a Σ3<111>{121} symmetric tilt grain boundary (GB) in tungsten based on molecular-dynamics simulations according to a reliable interatomic interaction potential. We find that small, mobile helium clusters (Hen, 1 ≤ n ≤ 7) in the near-GB region are attracted to the GB due to an elastic cluster-GB interaction force. Moreover, as the clusters drift toward the GB, cluster trap mutation (TM) reactions in the near-GB region are activated at rates much higher than those in the bulk of the material's grains. This near-GB cluster dynamics has significant effects on the near-GB defect structures and the amount of helium retained in the material upon plasma exposure. Each TM reaction generates a tungsten vacancy, which traps helium by forming an immobile helium-vacancy complex, and an interstitial tungsten atom in the form of an extended tungsten interstitial complex on the GB. This interstitial configuration is characterized by mobility that depends on the location where the TM reaction occurs: It is immobile when the vacancy produced by the TM reaction is located a few lattice planes away from the GB plane and highly mobile along a specific direction when the produced vacancy is located on the GB. The latter mechanism initiates a potentially fast migration path for W atoms along the GB toward a free surface, which may influence significantly the surface morphology of plasma-exposed tungsten.