An interatomic potential for Al-Tb alloy around the composition of Al90Tb10 was developed using the deep neural network (DNN) learning method. The atomic configurations and the corresponding total potential energies and forces on each atom obtained from ab initio molecular dynamics (AIMD) simulations are collected to train a DNN model to construct the interatomic potential for Al-Tb alloy. We show the obtained DNN model can well reproduce the energies and forces calculated by AIMD. Molecular dynamics (MD) simulations using the DNN interatomic potential also accurately describe the structural properties of Al90Tb10 liquid, such as the partial pair correlation functions (PPCFs) and the bond angle distributions, in comparison with the results from AIMD. Furthermore, the developed DNN interatomic potential predicts the formation energies of crystalline phases of Al-Tb system with the accuracy comparable to ab initio calculations. The structure factor of Al90Tb10 metallic glass obtained by MD simulation using the developed DNN interatomic potential is also in good agreement with the experimental X-ray diffraction data.
Developing data-driven machine-learning interatomic potentials for materials containing many elements becomes increasingly challenging due to the vast configuration space that must be sampled by the training data. We study the learning rates and achievable accuracy of machine-learning interatomic potentials for many-element alloys with different combinations of descriptors for the local atomic environments. We show that for a five-element alloy system, potentials using simple low-dimensional descriptors can reach meV/atom-accuracy with modestly sized training datasets, significantly outperform…
We introduce machine-learned potentials for Ag-Pd to describe the energy of alloy configurations over a wide range of compositions. We compare two different approaches. Moment tensor potentials (MTP) are polynomial-like functions of interatomic distances and angles. The Gaussian Approximation Potential (GAP) framework uses kernel regression, and we use the Smooth Overlap of Atomic Positions (SOAP) representation of atomic neighbourhoods that consists of a complete set of rotational and permutational invariants provided by the power spectrum of the spherical Fourier transform of the neighbour d…
In this paper we present new parameters of the TB-SMA interatomic potentials for the Pt/Cu(111) surface alloy. The parameters are fitted using both the experimental and {\it ab initio} data. The potentials reproduce not only the bulk properties of copper and platinum, but also the energy characteristics of the Pt/Cu(111) surface alloy. The potentials can be used for the simulations of the growth of the Pt/Cu(111) surface alloy on the atomic scale.
We develop a fast and accurate machine-learned interatomic potential for the Mo-Nb-Ta-V-W quinary system and use it to study segregation and defects in the body-centred cubic refractory high-entropy alloy MoNbTaVW. In the bulk alloy, we observe clear ordering of mainly Mo-Ta and V-W binaries at low temperatures. In damaged crystals, our simulations reveal clear segregation of vanadium, the smallest atom in the alloy, to compressed interstitial-rich regions like radiation-induced dislocation loops. Vanadium also dominates the population of single self-interstitial atoms. In contrast, due to its…
We have developed a machine learning-based interatomic potential (MLIP) for the quaternary MoNbTaW (R4) and quinary MoNbTaTiW (R5) high entropy alloys (HEAs). MLIPs enabled accurate high throughput calculations of elastic and mechanical properties of various non-equimolar R4 and R5 alloys, which are otherwise very time consuming calculations when performed using density functional theory (DFT). We demonstrate that the MLIP predicted properties compare well with the DFT results on various test cases and are consistent with the available experimental data. The MLIPs are also utilized for high th…
We propose an approach to materials prediction that uses a machine-learning interatomic potential to approximate quantum-mechanical energies and an active learning algorithm for the automatic selection of an optimal training dataset. Our approach significantly reduces the amount of DFT calculations needed, resorting to DFT only to produce the training data, while structural optimization is performed using the interatomic potentials. Our approach is not limited to one (or a small number of) lattice types (as is the case for cluster expansion, for example) and can predict structures with lattice…
Atomistic simulations of liquid alloys face the challenge of correctly modeling basic thermodynamic properties. In this work we present an interatomic potential for the Li-Pb system, as well as a study of physical properties of Li-Pb alloys. Despite the complexity due to Li-Pb being a compound forming system where charge transfer is expected, we show here how the empirical EAM formalism is able to satisfactorily describe several physical properties in a wide range of Li concentration. Application of our potential to Li-Pb eutectic allows us to correctly predict many physical properties observe…
An interatomic potential (termed EAM-21) has been developed with the embedded atomic method (EAM) for CrFeMnNi quaternary HEAs. This potential is based on a previously developed potential for CrFeNi ternary alloys. The parameters to develop the potential were determined by fitting to experimental values, density functional theory (DFT) and thermodynamic calculations, to reproduce the main crystal characteristics, namely: the stability of the fcc phase, elastic constants, and stacking fault energy. Its applicability for the study of plastic deformation mechanisms was checked by calculations of …
Developing reliable interatomic potential models with quantified predictive accuracy is crucial for atomistic simulations. Commonly used potentials, such as those constructed through the embedded atom method (EAM), are derived from semi-empirical considerations and contain unknown parameters that must be fitted based on training data. In the present work, we investigate Bayesian calibration as a means of fitting EAM potentials for binary alloys. The Bayesian setting naturally assimilates probabilistic assertions about uncertain quantities. In this way, uncertainties about model parameters and …
We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution in the entire concentration range but also the energetics of a wider range of configurations including intermetallic phases. We show that an expansion in cluster interactions provides a way to systematically increase the accuracy of the model, and that it is straightforward to generalise this procedure to multicomponent systems. Concentration-dependent intera…
A nanocrystalline metal's strength increases significantly as its grain size decreases, a phenomenon known as the Hall-Petch relation. Such relation, however, breaks down when the grains become too small. Experimental studies have circumvented this problem in a set of Ni-Mo alloys by stabilizing the grain boundaries (GB). Here, using atomistic simulations with a machine learning-based interatomic potential (ML-IAP), we demonstrate that the inverse Hall-Petch relation can be correctly reproduced due to a change in the dominant deformation mechanism as the grain becomes small in the Ni-Mo polycr…
Benchmarking Chemically Scalable Machine-Learning Interatomic Potentials for Large-Scale Simulations of Multicomponent Alloys
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所非线性力学国家重点实验室）；Department of Materials Science and Engineering, Faculty of Mechanical Engineering, Delft University of Technology（代尔夫特理工大学机械工程学院材料科学与工程系）；Faculty of Engineering Technology, University of Twente（特温特大学工程技术学院）；Laboratory for multiscale mechanics and medical science, SV LAB, School of Aerospace, Xi’an Jiaotong University（西安交通大学航天学院SV多尺度力学与医学科学实验室）；College of Physical Science and Technology, Bohai University（渤海大学物理科学与技术学院）
We combine the shoving model of $T$-dependent viscosity of supercooled liquids with the Zwanzig-Mountain formula for the high-frequency shear modulus, using the $g(r)$ of MD simulations of metal alloys as the input. This scheme leads to a semi-analytical expression for the viscosity as a function of temperature, which provides a three-parameter model fitting of experimental data of viscosity for the same alloy for which $g(r)$ was calculated. The model provides direct access to the influence of atomic-scale physical quantities such as the interatomic potential $ϕ(r)$, on the viscosity and frag…
Precipitate phase selection and grain boundary morphology in Cu-Ni-Si-Mn alloys: A machine-learning interatomic potential study
Korea Electrotechnology Research Institute (KERI)（韩国电工技术研究所）；Korea Institute of Materials Science (KIMS)（韩国材料科学研究所）；Seoul National University（首尔大学）；University of Science and Technology (UST)（科学技术联合大学院大学）；Korea Institute for Advanced Study（韩国高等研究院）
We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence-electron o…
The most critical limitation to the wide-scale use of classical molecular dynamics for alloy design is the availability of suitable interatomic potentials. In this work, we demonstrate a simple procedure to generate a library of accurate binary potentials using already-existing single-element potentials that can be easily combined to form multi-component alloy potentials. For the Al-Ni, Cu-Au, and Cu-Al-Zr systems, we show that this method produces results comparable in accuracy to alloy potentials where all parts have been fitted simultaneously, without the additional computational expense. F…
Using the self-consistent field approximation, the static concentration waves approach and the Onsager-type kinetics equations, the descriptions of both the statistical thermodynamics and the kinetics of an atomic ordering of D019 phase are developed and applied for h.c.p.-Ti-Al alloy. The model of order-disorder phase transformation describes the phase transformation of h.c.p. solid solution into the D019 phase. Interatomic-interaction parameters are estimated for both approximations: one supposes temperature-independent interatomic-interaction parameters, while the other one includes the tem…
To enable accurate molecular dynamics simulations of iron-chromium alloys with surfaces, we develop, based on density-functional-theory (DFT) calculations, a new interatomic Fe-Cr potential in the Tersoff formalism. Contrary to previous potential models, which have been designed for bulk Fe-Cr, we extend our potential fitting database to include not only conventional bulk properties but also surface-segregation energies of Cr in bcc Fe. In terms of reproducing our DFT results for the bulk properties, the new potential is found to be superior to the previously developed Tersoff potential and co…
Machine learning interatomic potentials for solid-state precipitation
Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所材料设计与模拟实验室）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院国家新材料计算设计与发现中心）
Patterns and periods of charge density waves (CDW) in transition metal dichalcogenides exhibit complex phase diagrams that depend on pressure, temperature, metal intercalation, or chalcogen alloying. The phase diagrams have been understood in the context of phenomenological Landau free energy model, but the microscopic mechanisms underlying them are still not clear. Here, we present a new microscopic theory based on the interatomic potential, and have explicitly calculated temperature-dependent phase diagrams using the interatomic potential extracted from first-principles calculations. With de…
Accurate Screening of Functional Materials with Machine-Learning Potential and Transfer-Learned Regressions: Heusler Alloy Benchmark
Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science（磁性及自旋材料研究中心，物质材料研究机构）；Digital Transformation Initiative Center for Magnetic Materials (DXMag), National Institute for Materials Science（磁性材料数字化转型倡议中心（DXMag），物质材料研究机构）
Simulations at the atomic scale provide a direct and effective way to understand the mechanical properties of materials. In the regime of classical mechanics, simulations for the thermodynamic properties of metals and alloys can be done by either solving the equations of motion or performing Monte Carlo sampling. The key component for an accurate simulation of such physical systems to produce faithful physical quantities is the use of an appropriate potential or a force field. In this paper, we explore the use of methods from the realm of machine learning to overcome and bypass difficulties en…
In order to design next-generation ferroelectrics, a microscopic understanding of their macroscopic properties is critical. One means to achieving an atomistic description of ferroelectric and dielectric phenomena is classical molecular dynamics simulations. Previously, we have shown that interatomic potentials based on the bond valence molecular dynamics (BVMD) method can be used to study structural phase transitions, ferroelectric domain nucleation, and domain wall migration in several perovskite oxides and fixed-composition binary and ternary alloys. Most modern devices, however, use variab…
Compositionally complex alloys or concentrated solid solutions are the latest frontier in catalyst design, but mixing different elements in one catalyst may result in surface segregation. Atomistic simulations can predict segregation patterns, but standard approaches based on mean-field models, cluster expansion, or classical interatomic potentials are often limited for the description of multicomponent alloys. We present machine learning potentials that can describe surface segregation with near DFT accuracy. The method is used to study a complex Co-Cu-Fe-Mo-Ni quinary alloy. For this alloy, …
Driving force of atomic ordering in Fe$_{1-x}$Pt$_{x}$, investigated by density functional theory and machine-learning interatomic potentials Monte Carlo simulations
Abstract Interatomic potentials constitute the key component of large-scale atomistic simulations of materials. The recently proposed physically-informed neural network (PINN) method combines a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential applicable to both metals and nonmetals. In this paper, we present a modified version of the PINN method that accelerates the potential training process and further improves the transferability of PINN potentials to unknown atomic environments. As an application, a modified PINN …
A critical limitation to the wide-scale use of classical molecular dynamics for alloy design is the limited availability of suitable interatomic potentials. Here, we introduce the Rapid Alloy Method for Producing Accurate General Empirical Potentials or RAMPAGE, a computationally economical procedure to generate binary embedded-atom model potentials from already-existing single-element potentials that can be further combined into multi-component alloy potentials. We present the quality of RAMPAGE calibrated Finnis-Sinclair type EAM potentials using binary Ag-Al and ternary Ag-Au-Cu as case stu…
Laser ablation is often explained by a two-temperature model (TTM) with different electron and lattice temperatures. To realize a classical molecular dynamics simulation of the TTM, we propose an extension of the embedded atom method to construct an interatomic potential that is dependent on the electron temperature. This method is applied to copper, and its validity is demonstrated by comparison of several physical properties, such as the energy-volume curve, phonon dispersion, electronic heat capacity, ablation threshold, and mean square displacement of atoms, with those of finite-temperatur…
The dynamical behavior of liquids is frequently characterized by the fragility, which can be defined from the temperature dependence of the shear viscosity, η. For a strong liquid, the activation energy for η changes little with cooling towards the glass transition temperature, Tg. The change is much greater in fragile liquids, with the activation energy becoming very large near Tg. While fragility is widely recognized as an important concept, for example believed to play an important role in glass formation, the microscopic origin of fragility is poorly understood. Here, we present new experi…
Chemical segregation and structural transitions at interfaces are important nanoscale phenomena, making them natural targets for atomistic modeling, yet interatomic potentials must be fit to secondary physical properties. To isolate the important factors that interatomic potentials must capture in order to accurately model such behavior, the performance of four interatomic potentials was evaluated for the Cu-Zr system, with experimental observations used to provide validation. While experimental results show strong Zr segregation to grain boundary regions and the formation of nanoscale amorpho…
We present an ab initio theory of transport quantities of metallic ferromagnets developed in the framework of the fully relativistic tight-binding linear muffin-tin orbital method. The approach is based on the Kubo-Streda formula for the conductivity tensor, on the coherent potential approximation for random alloys, and on the concept of interatomic electron transport. The developed formalism is applied to pure 3d transition metals (Fe, Co, Ni) and to random Ni-based ferromagnetic alloys (Ni-Fe, Ni-Co, Ni-Mn). High values of the anisotropic magnetoresistance (AMR), found for Ni-rich alloys, ar…
