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 interatomic potentials can be built upon almost any type of potential for the pure elements including embedded atom method (EAM), modified EAM, bond-order, and Stillinger-Weber type potentials. In general, composition-dependent N-body terms in the total energy lead to explicit (N+1)-body forces, which potentially renders them computationally expensive. We present an algorithm that overcomes this problem and that can speed up the calculation of the forces for composition-dependent pair potentials in such a way as to make them computationally comparable in efficiency and scaling behaviour to standard EAM potentials. We also discuss the implementation in Monte-Carlo simulations. Finally, we exemplarily review the composition-dependent EAM model for the Fe-Cr system [PRL 95, 075702 (2005)].
A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.
Recent application of neural networks (NNs) to modeling interatomic interactions has shown the learning machines' encouragingly accurate performance for select elemental and multicomponent systems. In this study, we explore the possibility of building a library of NN-based models by introducing a hierarchical NN training. In such a stratified procedure NNs for multicomponent systems are obtained by sequential training from the bottom up: first unaries, then binaries, and so on. Advantages of constructing NN sets with shared parameters include acceleration of the training process and intact des…
A theory of two-phase eutectic growth for a multicomponent alloy is presented. This theory employs the thermodynamic equilibrium at the solid/liquid interface and thus makes it possible to use standard CALPHAD databases to determine the effects of multicomponent phase equilibrium on eutectic growth. Using the same hypotheses as the Jackson Hunt theory, we find that the growth law determined for binary alloys in the Jackson Hunt theory can be generalized to systems with N elements. In particular, a new model is derived from this theory for ternary two-phase eutectics. The use of this model to p…
Microalloying elements tend to segregate to the matrix-precipitate phase boundaries to reduce the interfacial energy. The segregation mechanism is emerging as a novel design strategy for developing precipitation-hardened alloys with significantly improved coarsening resistance for high temperature applications. In this paper, we report a nanoscopic diffuse-interface thermodynamic model that describes multicomponent segregation behavior in two-phase substitutional alloys. Following classical approaches for grain boundaries, we employ the regular solution thermodynamics to establish segregation …
The generalized stacking fault energy is a key ingredient to mesoscale models of dislocations. Here we develop an approach to quantify the dependence of generalized stacking fault energies on the degree of chemical disorder in multicomponent alloys. We introduce the notion of a "configurationally-resolved planar fault" (CRPF) energy and extend the cluster expansion method from alloy theory to express the CRPF as a function of chemical occupation variables of sites surrounding the fault. We apply the approach to explore the composition and temperature dependence of the unstable stacking fault e…
We develop an approach to apply Wang-Landau algorithm to multicomponent alloys in semi-grand-canonical ensemble. Although the Wang-Landau algorithm has great advantages over conventional sampling methods, there are few applications to alloys. This is because calculating compositions in semi-grand-canonical ensemble using the Wang-Landau algorithm requires a multi-dimensional density of states in terms of total energy and compositions. However, constructing the multi-dimensional density of states is difficult. In this study, we develop a simple approach to calculate the alloy phase diagram usin…
Why is EXAFS analysis for multicomponent metals so hard? Challenges and opportunities for measuring ordering in complex concentrated alloys using x-ray absorption spectroscopy
Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Meanwhile, further optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging, which would require systematic predictions of the correlated alloy properties across a vast compositional space. In the present work, we performed first-principles calculations with the special quasi-random structure (SQS) method to predict the unstable stacking fault energy ($γ_{usf}$) of the $(1…
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.
The near-rapid solidification conditions during additive manufacturing can lead to selection of non-equilibrium phases. Sharp interface models via interface response functions have been used earlier to explain the microstructure selection under such solidification conditions. However, most of the sharp interface models assume linear superposition of contributions of alloying elements without considering the non-linearity associated with the phase diagram. In this report, both planar and dendritic Calphad coupled sharp interface models have been implemented and used to explain the growth-contro…
Interest in high entropy alloy thermoelectric materials is predicated on achieving ultralow lattice thermal conductivity $κ\sub{L}$ through large compositional disorder. However, here we show that for a given mechanism, such as mass contrast phonon scattering, $κ\sub{L}$ will be minimized along the binary alloy with the highest mass contrast, such that adding an intermediate-mass atom to increase atomic disorder can increase thermal conductivity. Only when each component adds an independent scattering mechanism (such as adding strain fluctuation to an existing mass fluctuation) is there a bene…
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）
The chemical pathways leading to gamma-prime(L1_2)-nucleation from nondilute Ni-5.2 Al-14.2 Cr at.%, gamma(f.c.c.), at 873 K are followed with radial distribution functions and isoconcentration surface analyses of direct-space atom-probe tomographic images. Although Cr atoms initially are randomly distributed, a distribution of congruent Ni3Al short-range order domains (SRO), <R> =0.6 nm, results from Al diffusion during quenching. Domain site occupancy develops as their number density increases leading to Al-rich phase separation by gamma-prime-nucleation, <R>=0.75 nm, after SRO occurs.
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…
Element-Specific Solute Trapping and Grain Structure Evolution during Laser Powder Bed Fusion of Multicomponent Alloys
University of Michigan, Dearborn（密歇根大学迪尔伯恩分校）；Texas A&M University（德克萨斯农工大学）；AlphaSTAR Technology Solutions（AlphaSTAR技术解决方案）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
University of California, Irvine（加州大学尔湾分校）；University of New Mexico（新墨西哥大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Massachusetts Institute of Technology（麻省理工学院）；University of California, San Diego（加州大学圣地亚哥分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；Stony Brook University（石溪大学）；University of Arizona（亚利桑那大学）；Los Alamos National Lab（洛斯阿拉莫斯国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
This paper compares two approaches for investigating the near-surface composition profile that results from surface segregation in the so-called Cantor alloy, an equi-molar alloy of CoCrFeMnNi. One approach consists of atomistic computer simulations by a combination of Monte Carlo, molecular dynamics and molecular statics techniques, and the other is a nearest neighbor analytical calculation performed in the regular solution approximation with a multilayer model, developed here for the first time for a N-component system and tested for the 5-component Cantor alloy. This type of comparison is u…
Short-range ordering (SRO) tendency for disordered alloys is considered as competition between chemical ordering and geometric (mainly, difference in atomic radius for constituents) effects. Especially for multicomponent (including the so-called high entropy alloys (HEAs) near equiatomic composition), it has been considered as difficult to systematically characterize the SRO tendency only by geometric effects, due mainly to the fact that (i) chemical effects typically plays significant role, (ii) near equiatomic composition, we cannnot classify which elements belong to solute or solvent, and (…
We developed new modified embedded-atom method (MEAM) interatomic potentials for the Mg-Al alloy system using a first-principles method based on density functional theory (DFT). The materials parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, were used to determine the MEAM parameters. Face-centered cubic, hexagonal close packed, and cubic rock salt structures were used as the reference structures for Al, Mg, and MgAl, respectively. The applicability of the new MEAM potentials to atomistic simulations for investigating Mg-Al alloys was demonstrated by perform…
First-principles calculations of the thermodynamic factor of multicomponent alloys
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）；Materials department, University of California, Santa Barbara（加州大学圣巴巴拉分校材料系）
Dynamic Kinetic Evaluation Favors Compositionally Diverse Multicomponent Alloy Nanoparticles for Hydrogen Evolution
The University of Tokyo（东京大学）；National Institute for Materials Science（物质材料研究机构）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
The superconducting high-entropy alloys (HEAs) recently attract considerable attention due to their exciting properties, such as the robustness of superconductivity against atomic disorder and extremely high-pressure. The well-studied crystal structure of superconducting HEAs is body-centered-cubic (bcc) containing Nb, Ti, and Zr atoms. The same elements are contained in Al5Nb24Ti40V5Zr26, which is a recently discovered bcc HEA and shows a gum-metal-like behavior after cold rolling. The gum metal is also an interesting system, exhibiting superelasticity and low Young's modulus. If gum metals s…
Estimating the diffusion coefficients experimentally in a four-component inhomogeneous alloy following the conventional diffusion couple method by intersecting three couples at the same composition is difficult unless a small composition range of constant diffusivity is identified. Additionally, the intrinsic diffusion coefficients of the components cannot be estimated in a system with more than two components. To solve these issues, we have followed the pseudo-binary and pseudo-ternary diffusion couple methods for estimating the diffusion coefficients at the equiatomic composition of NiCoFeCr…
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 develop a new approach to determining LJ-EAM potentials for alloys and use these to determine the solid-liquid phase diagrams for binary metallic alloys using Kofke's Gibbs-Duhem integration technique combined with semigrand canonical Monte Carlo simulations. We demonstrate that it is possible to produce a wide-range of experimentally observed binary phase diagrams (with no intermetallic phases) by reference to the atomic sizes and cohesive energies of the two elemental materials. In some cases, it is useful to employ a single adjustable parameter to adjust the phase diagram (we provided a …
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…
Among crystal structures of N-component metal alloys, far fewer examples are known with N>=4 than with N=2 or 3, in apparent contradiction to the exponentially growing number of possible combinations of elements. Two effects contribute to this shortfall. Since the N-component composition space resides within a d-dimensional simplex with d=N-1, the vanishing volume in high dimensions reduces the distinct N-component compositions. Additionally, the increasing surface area makes it more probable that stable structures reside on the surface of the simplex (containing fewer than N components) as op…
Mechanical properties of engineering alloys are strongly correlated to their microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka type is one of the principal mechanisms through which the scale of the microstructural features are determined during solidification. In contrast to binary systems, in multicomponent alloys with arbitrary interdiffusivities, the growth rate as well as the maximally growing wavelengths characterizing these instabilities depend on the the dynamically selected equilibrium tie-lines and the steady state growth velocity. In this study, we derive…
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…
High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEA's exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr-Mo-Nb-V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-pri…
Lattice models parameterized using first-principles calculations constitute an effective framework to simulate the thermodynamic behavior of physical systems. The cluster expansion method is a flexible lattice-based method used extensively in the study of multicomponent alloys. Yet despite its prevalent use, a well-defined understanding of expansion terms has remained elusive. In this letter, we introduce the cluster decomposition as a unique and basis-agnostic decomposition of any general function of the atomic configuration in a crystal. We demonstrate that cluster expansions constructed fro…
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…
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 …
