Abstract: Classical interatomic potentials for Nickel are essential for large-scale atomistic simulations, yet many existing models suffer from thermal-inconsistency biases by mixing zero-Kelvin predictions with finite-temperature experimental data. To address this, a new angular-dependent potential for elemental Nickel was developed and validated, parameterized using a comprehensive first-principles Density Functional Theory reference dataset. The dataset included diverse ground-state, strained, high-temperature, surface, and defect configurations. Optimized via force-matching, the potential shows high fidelity to the Density Functional Theory training data. Its performance was benchmarked against experimental data and three other representative interatomic potentials, demonstrating excellent agreement for the lattice constant, bulk modulus, longitudinal elastic constants, and phonon dispersion relations. While it shows strong agreement for most properties, deviations were observed in the shear elastic constant, intrinsic stacking-fault energy, and vacancy energetics. This angular-dependent potential offers a robust alternative at an intermediate computational cost, suitable for large-scale simulations where lattice dynamics and equilibrium bulk properties are critical.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors—atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors—using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.

Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors—atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors—using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.

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.

Abstract: In recent years, efficient interatomic potentials approaching the accuracy of density functional theory (DFT) calculations have been developed using rigorous atomic descriptors satisfying strict invariances, for example, for translation, rotation, permutation of homonuclear atoms, among others. In this paper, we generalize the spectral neighbor analysis potential (SNAP) model to bcc-fcc binary alloy systems. We demonstrate that machine-learned SNAP models can yield significant improvements even over the well-established high-performing embedded atom method (EAM) and modified EAM potentials for fcc Cu and Ni. We also report on the development of a SNAP model for the fcc Ni-bcc Mo binary system by machine learning a carefully constructed large computed data set of elemental and intermetallic compounds. We demonstrate that this binary Ni-Mo SNAP model can achieve excellent agreement with experiments in the prediction of a Ni-Mo phase diagram as well as near-DFT accuracy in the prediction of many key properties, such as elastic constants, formation energies, melting points, etc., across the entire binary composition range. In contrast, the existing Ni-Mo EAM has significant errors in the prediction of the phase diagram and completely fails in binary compounds. This paper provides a systematic model development process for multicomponent alloy systems, including an efficient procedure to optimize the hyperparameters in the model fitting, and paves the way for long-time large-scale simulations of such systems.

Abstract: Primary radiation damage formation in solid materials typically involves collisions between atoms that have up to a few hundred keV of kinetic energy. During these collisions, the distance between two colliding atoms can approach 0.05 nm. At such small atomic separations, force fields fitted to equilibrium properties tend to significantly underestimate the potential energy of the colliding dimer. To enable molecular dynamics simulations of high-energy collisions, it is common practice to use a screened Coulomb force field to describe the interactions and to smoothly join this to the equilibrium force field at a suitable interatomic spacing. However, there is no accepted standard method for choosing the parameters used in the joining process, and our results prove that defect production is sensitive to how the force fields are linked. A new procedure is presented that involves the use of ab initio calculations to determine the magnitude and spatial dependence of the pair interactions at intermediate distances, along with systematic criteria for choosing the joining parameters. Results are presented for the case of nickel, which demonstrate the use and validity of the procedure.

Abstract: The two-phase solid–liquid coexisting structures of Ni, Cu, and Al are studied by molecular dynamics (MD) simulations using the second nearest-neighbor (2NN) modified-embedded atom method (MEAM) potential. For this purpose, the existing 2NN-MEAM parameters for Ni and Cu were modified to make them suitable for the MD simulations of the problems related to the two-phase solid–liquid coexistence of these elements. Using these potentials, we compare calculated low-temperature properties of Ni, Cu, and Al, such as elastic constants, structural energy differences, vacancy formation energy, stacking fault energies, surface energies, specific heat and thermal expansion coefficient with experimental data. The solid–liquid coexistence approach is utilized to accurately calculate the melting points of Ni, Cu, and Al. The MD calculations of the expansion in melting, latent heat and the liquid structure factor are also compared with experimental data. In addition, the solid–liquid interface free energy and surface anisotropy of the elements are determined from the interface fluctuations, and the predictions are compared to the experimental and computational data in the literature.

Abstract: A new interatomic potential for the Ni–Zr system is presented. This potential was developed specifically to match experimental scattering data from Ni, Zr and NiZr2 liquids. Both ab initio and published thermodynamic data were used to optimise the potential to study the liquid and amorphous structure of the NiZr2 alloy. This potential has the C16 phase, being more stable than C11b phase in the NiZr2 alloy, consistent with experiments. The potential leads to the correct glass structure in the molecular dynamics simulation and, therefore, can be used to study the liquid–glass transformation in the NiZr2 alloy.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: Modified embedded atom method (MEAM) potentials for fcc elements Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb have been newly developed using the original first nearest-neighbor MEAM and the recently developed second nearest-neighbor MEAM formalisms. It was found that the original MEAM potentials for fcc elements show some critical shortcomings such as structural instability and incorrect surface reconstructions on (100), (110), and/or (111) surfaces. The newly developed MEAM potentials solve most of the problems and describe the bulk properties (elastic constants, structural energy differences), point defect properties (vacancy and interstitial formation energy and formation volume, activation energy of vacancy diffusion), planar defect properties (stacking fault energy, surface energy, surface relaxation and reconstruction), and thermal properties (thermal expansion coefficients, specific heat, melting point, heat of melting) of the fcc elements considered, in good agreement with relevant experimental information. It has been shown that in the MEAM the degree of many-body screening (C_min) is an important material property and that structural stability at finite temperatures should be included as a checkpoint during development of semiempirical potentials.

Abstract: We demonstrate an approach to the development of many-body interatomic potentials for monoatomic metals with improved accuracy and reliability. The functional form of the potentials is that of the embedded-atom method, but the interesting features are as follows: (1) The database used for the development of a potential includes both experimental data and a large set of energies of different alternative crystalline structures of the material generated by ab initio calculations. We introduce a rescaling of interatomic distances in an attempt to improve the compatibility between experimental and ab initio data. (2) The optimum parametrization of the potential for the given database is obtained by alternating the fitting and testing steps. The testing step includes a comparison between the ab initio structural energies and those predicted by the potential. This strategy allows us to achieve the best accuracy of fitting within the intrinsic limitations of the potential model. Using this approach we develop reliable interatomic potentials for Al and Ni. The potentials accurately reproduce basic equilibrium properties of these metals, the elastic constants, the phonon-dispersion curves, the vacancy formation and migration energies, the stacking fault energies, and the surface energies. They also predict the right relative stability of different alternative structures with coordination numbers ranging from 12 to 4. The potentials are expected to be easily transferable to different local environments encountered in atomistic simulations of lattice defects.

Abstract: A detailed derivation of the simplest form of the effective medium theory for bonding in metallic systems is presented, and parameters for the fcc metals Ni, Pd, Pt, Cu, Ag and Au are given. The derivation of parameters is discussed in detail to show how new parameterizations can be made. The method and the parameterization is tested for a number of surface and bulk problems. In particular we present calculations of the energetics of metal atoms deposited on metal surfaces. The calculated energies include heats of adsorption, energies of overlayers, both pseudomorphic and relaxed, as well as energies of atoms alloyed into the first surface layer.

Abstract: This paper addresses the energy associated with the trapping of hydrogen to defects in a nickel lattice. Several dislocations and grain boundaries which occur in nickel are studied. The dislocations include an edge, a screw, and a Lomer dislocation in the locked configuration, i.e. a Lomer-Cottrell lock (LCL). For both the edge and screw dislocations, the maximum trap site energy is approximately 0.1 eV occurring in the region where the lattice is in tension approximately 3-4 angstroms from the dislocation core. For the Lomer-Cottrell lock, the maximum binding energy is 0.33 eV and is located at the core of the a/6(110) dislocation. Several low-index coincident site lattice grain boundaries are investigated, specifically the Sigma 3(112), Sigma 9(221) and Sigma 11(113) tilt boundaries. The boundaries all show a maximum binding energy of approximately 0.25 eV at the tilt boundary. Relaxation of the boundary structures produces an asymmetric atomic structure for both the Sigma 3 and Sigma 9 boundaries and a symmetric structure for the Sigma 11 tilt boundary. The results of this study can be compared to recent experimental studies showing that the activation energy for hydrogen-initiated failure is approximately 0.3-0.4 eV in the Fe-based superalloy IN903. From the results of this comparison it can be concluded that the embrittlement process is likely associated with the trapping of hydrogen to grain boundaries and Lomer-Cottrell locks.

Abstract: The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic "five-frequency formula," which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's "Tm" model.

Abstract: Using the approach of Finnis and Sinclair, N-body potentials for copper, silver, gold and nickel have been constructed. The total energy is regarded as consisting of a pair-potential part and a many body cohesive part. Both these parts are functions of the atomic separations only and are represented by cubic splines, fitted to various bulk properties. For the noble metals, the pair-potentials were fitted at short range to pressure-volume relationships calculated by Christensen and Heine so that interactions at separations smaller than that of the first-nearest neighbours can be treated in this scheme. Using these potentials, point defects, surfaces (including the surface reconstructions) and grain boundaries have been studied and satisfactory agreement with available experimental data has been found.

Abstract: A consistent set of embedding functions and pair interactions for use with the embedded-atom method [M.S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] have been determined empirically to describe the fcc metals Cu, Ag, Au, Ni, Pd, and Pt as well as alloys containing these metals. The functions are determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys. The validity of the functions is tested by computing a wide range of properties: the formation volume and migration energy of vacancies, the formation energy, formation volume, and migration energy of divacancies and self-interstitials, the surface energy and geometries of the low-index surfaces of the pure metals, and the segregation energy of substitutional impurities to (100) surfaces.

Abstract: The Morse parameters were calculated using experimental values for the energy of vaporization, the lattice constant, and the compressibility. The equation of state and the elastic constants which were computed using the Morse parameters, agreed with experiment for both face-centered and body-centered cubic metals. All stability conditions were also satisfied for both the face-centered and the body-centered metals. This shows that the Morse function can be applied validly to problems involving any type of deformation of the cubic metals.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: A detailed derivation of the simplest form of the effective medium theory for bonding in metallic systems is presented, and parameters for the fcc metals Ni, Pd, Pt, Cu, Ag and Au are given. The derivation of parameters is discussed in detail to show how new parameterizations can be made. The method and the parameterization is tested for a number of surface and bulk problems. In particular we present calculations of the energetics of metal atoms deposited on metal surfaces. The calculated energies include heats of adsorption, energies of overlayers, both pseudomorphic and relaxed, as well as energies of atoms alloyed into the first surface layer.

Abstract: The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic "five-frequency formula," which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's "Tm" model.

Abstract: A consistent set of embedding functions and pair interactions for use with the embedded-atom method [M.S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] have been determined empirically to describe the fcc metals Cu, Ag, Au, Ni, Pd, and Pt as well as alloys containing these metals. The functions are determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys. The validity of the functions is tested by computing a wide range of properties: the formation volume and migration energy of vacancies, the formation energy, formation volume, and migration energy of divacancies and self-interstitials, the surface energy and geometries of the low-index surfaces of the pure metals, and the segregation energy of substitutional impurities to (100) surfaces.

Abstract: An Ag–Ni semi-empirical potential was developed to simulate the segregation of Ni solutes at Ag grain boundaries (GBs). The potential combines a new Ag potential fitted to correctly reproduce the stable and unstable stacking fault energies in this metal and the existing Ni potential from Mendelev et al (2012 Phil. Mag. 92 4454–69). The Ag–Ni cross potential functions were fitted to ab initio data on the liquid structure of the Ag₈₀Ni₂₀ alloy to properly incorporate the Ag–Ni interaction at small atomic separations, and to the Ni segregation energies at different sites within a high-energy Σ9 (221) symmetric tilt GB. By deploying this potential with hybrid Monte Carlo/molecular dynamics simulations, it was found that heterogeneous segregation and clustering of Ni atoms at GBs and twin boundary defects occur at low Ni concentrations, 1 and 2 at%. This behavior is profoundly different from the homogeneous interfacial dispersion generally observed for the Cu segregation in Ag. A GB transformation to amorphous intergranular films was found to prevail at higher Ni concentrations (10 at%). The developed potential opens new opportunities for studying the selective segregation behavior of Ni solutes in interface-hardened Ag metals and its effect on plasticity.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Molecular dynamics simulations were used to study the deposition and growth of a thin film of high-entropy CoCrFeMnNi alloy on an Al(100) substrate. Interatomic interactions were modeled using Morse potentials, which were developed with mixing rules adopted for regular solutions. A total of 50000 atoms with an incident energy of 10 eV were deposited for 100 ns, forming a film with a thickness of 6.1 nm. The resulting film exhibited face-centered cubic, body-centered cubic, hexagonal close-packed, and amorphous phases. Radial distribution function analysis determined the nearest neighbor distances and lattice parameters, which showed good agreement with experimental data.

Abstract: A set of embedded atom model (EAM) interatomic potentials was developed to represent highly idealized face-centered cubic (FCC) mixtures of Fe–Ni–Cr–Co–Al at near-equiatomic compositions. Potential functions for the transition metals and their crossed interactions are taken from our previous work for Fe–Ni–Cr–Co–Cu [D. Farkas and A. Caro: J. Mater. Res. 33 (19), 3218–3225, 2018], while cross-pair interactions involving Al were developed using a mix of the component pair functions fitted to known intermetallic properties. The resulting heats of mixing of all binary equiatomic random FCC mixtures not containing Al is low, but significant short-range ordering appears in those containing Al, driven by a large atomic size difference. The potentials are utilized to predict the relative stability of FCC quinary mixtures, as well as ordered L1₂ and B2 phases as a function of Al content. These predictions are in qualitative agreement with experiments. This interatomic potential set is developed to resemble but not model precisely the properties of this complex system, aiming at providing a tool to explore the consequences of the addition of a large size-misfit component into a high entropy mixture that develops multiphase microstructures.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Interatomic potentials for the Ni-Co binary and Ni-Al-Co ternary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials describe structural, thermodynamic, deformation and defect properties of solid solution phases or compound phases in reasonable agreements with experiments or first-principles calculations. The results demonstrate the transferability of the potentials and their applicability to large-scale atomistic simulations to investigate the effect of an alloying element, cobalt, on various microstructural factors related to mechanical properties of Ni-based superalloys on an atomic scale.

Abstract: Ni–Al–Co is a promising system for ferromagnetic shape memory applications. This paper reports on the development of a ternary embedded-atom potential for this system by fitting to experimental and first-principles data. Reasonably good agreement is achieved for physical properties between values predicted by the potential and values known from experiment and/or first-principles calculations. The potential reproduces basic features of the martensitic phase transformation from the B2-ordered high-temperature phase to a tetragonal CuAu-ordered low-temperature phase. The compositional and temperature ranges of this transformation and the martensite microstructure predicted by the potential compare well with existing experimental data. These results indicate that the proposed potential can be used for simulations of the shape memory effect in the Ni–Al–Co system.

Abstract: Classical effective potentials are indispensable for any large-scale atomistic simulations, and the relevance of simulation results crucially depends on the quality of the potentials used. For complex alloys such as quasicrystals, however, realistic effective potentials are almost non-existent. We report here our efforts to develop effective potentials especially for quasicrystalline alloy systems. We use the so-called force-matching method, in which the potential parameters are adapted so as to reproduce the forces and energies optimally in a set of suitably chosen reference configurations. These reference data are calculated with ab-initio methods. As a first application, embedded-atom method potentials for decagonal Al–Ni–Co, icosahedral Ca–Cd, and both icosahedral and decagonal Mg–Zn quasicrystals have been constructed. The influence of the potential range and degree of specialization on the accuracy and other properties is discussed and compared.

Abstract: Classical effective potentials are indispensable for any large-scale atomistic simulations, and the relevance of simulation results crucially depends on the quality of the potentials used. For complex alloys such as quasicrystals, however, realistic effective potentials are almost non-existent. We report here our efforts to develop effective potentials especially for quasicrystalline alloy systems. We use the so-called force-matching method, in which the potential parameters are adapted so as to reproduce the forces and energies optimally in a set of suitably chosen reference configurations. These reference data are calculated with ab-initio methods. As a first application, embedded-atom method potentials for decagonal Al–Ni–Co, icosahedral Ca–Cd, and both icosahedral and decagonal Mg–Zn quasicrystals have been constructed. The influence of the potential range and degree of specialization on the accuracy and other properties is discussed and compared.

Abstract: Ordered L1₂ γ′ Ni₃Al intermetallics are essential strengthening components to maintain the high strength of Ni-based superalloys and recently developed high entropy alloys at elevated temperatures. Under service conditions, structural disorder is usually encountered in these intermetallics, resulting in significant loss of their strengthening functionality. Thus, retaining the degree of order of the L1₂ intermetallics is vital for their long-term reliability and serviceability. In this study, atomistic simulations and rate equation analysis are employed to highlight a notable enhancement in the reordering ability of L1₂ intermetallics by incorporating multiple principal elements. Specifically, we examine the effects of Co and Ti addition on the irradiation-induced disordering and kinetic reordering process of L1₂ intermetallics. Our results reveal that the incorporation of Ti in the Al sublattice can maintain comparable disordering resistance as Ni₃Al. Better yet, the introduction of Ti or Co fosters vacancy migration, which accelerates the kinetic reordering rate during the defect diffusion stage. A synergistic effect of Ti and Co in promoting kinetic reordering is also observed. Our work thus suggests a promising approach for designing irradiation-resistant multicomponent intermetallics, which can retain a high degree of structural order under irradiation with chemical disorder contributed by desirable compositions.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Micro-twinning is the major creep deformation mechanism in Ni-based superalloys at temperatures above 700 °C. Recent experiments suggest that superlattice stacking faults in γ′ phase may serve as the precursors to twin formation. Segregation of alloying elements to these precursors may have a significant effect on formation and extension of micro-twins. Using atomistic modeling we investigate and explain the effects of Nb and Cr alloying additions on these processes. The simulation shows that Nb increases the creep resistance which is mostly associated with impeding the reordering of the high energy double complex stacking fault. Cr, on the other hand, promotes twin growth, degrading the high temperature creep properties. These results can help to understand the effects of elemental composition of the alloy on creep resistance.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Fe-Ni-based alloys have been considered as candidate structural materials for advanced nuclear reactors, and some of their excellent properties are particularly associated with L1₂ precipitates dispersed in the alloys. For a better understanding of the irradiation response, classical molecular dynamics is an essential tool to simulate the irradiation-induced defect formation and subsequent microstructural evolution. We here develop an interatomic potential for L1₂ (Ni, Fe)₃Al precipitates in the ternary Fe-Ni-Al system. The fitting parameters are tuned to describe the lattice and elastic constants of NiFe solid solutions and defect formation/vacancy migration energies in the fcc matrix. Furthermore, the lattice properties and defect energies of L1₂ (Ni, Fe)₃Al are considered for the fitting. We demonstrate the developed potential reproduces the lattice and defect properties with reasonable accuracy by comparison with density functional theory calculations, existing empirical potentials, and experimental data. This potential will be useful to investigate the defect formation and evolution of (Ni, Fe)₃Al precipitates in the alloys under irradiation, which would provide critical insights into the materials design strategy to achieve enhanced properties.

Abstract: This paper addresses the energy associated with the trapping of hydrogen to defects in a nickel lattice. Several dislocations and grain boundaries which occur in nickel are studied. The dislocations include an edge, a screw, and a Lomer dislocation in the locked configuration, i.e. a Lomer-Cottrell lock (LCL). For both the edge and screw dislocations, the maximum trap site energy is approximately 0.1 eV occurring in the region where the lattice is in tension approximately 3-4 angstroms from the dislocation core. For the Lomer-Cottrell lock, the maximum binding energy is 0.33 eV and is located at the core of the a/6(110) dislocation. Several low-index coincident site lattice grain boundaries are investigated, specifically the Sigma 3(112), Sigma 9(221) and Sigma 11(113) tilt boundaries. The boundaries all show a maximum binding energy of approximately 0.25 eV at the tilt boundary. Relaxation of the boundary structures produces an asymmetric atomic structure for both the Sigma 3 and Sigma 9 boundaries and a symmetric structure for the Sigma 11 tilt boundary. The results of this study can be compared to recent experimental studies showing that the activation energy for hydrogen-initiated failure is approximately 0.3-0.4 eV in the Fe-based superalloy IN903. From the results of this comparison it can be concluded that the embrittlement process is likely associated with the trapping of hydrogen to grain boundaries and Lomer-Cottrell locks.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: As the operating temperature of jet turbine engines increase, creep becomes the life-limiting property for turbine disks and blades. At intermediate temperatures, around 600-800 °C, microtwinning contributes significantly to creep strain in these alloys. Therefore, understanding how microtwins form and grow is critical to improving the creep life of future Ni-base superalloy components. In addition, exploring the effect of different alloying elements, such as Nb and Ta, on the formation of microtwins is critical for future alloy development. Several mechanisms of microtwinning have been proposed among which the Kolbe mechanism, based on thermally activated reordering, is believed to be dominant. In this work we employ atomistic simulation to investigate the effects of Nb solutes on the Kolbe mechanism. The simulation demonstrates that Nb atoms significantly slow down the reordering processes, explaining the experimentally observed improvement in the creep resistance.

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: As the operating temperature of jet turbine engines increase, creep becomes the life-limiting property for turbine disks and blades. At intermediate temperatures, around 600-800 °C, microtwinning contributes significantly to creep strain in these alloys. Therefore, understanding how microtwins form and grow is critical to improving the creep life of future Ni-base superalloy components. In addition, exploring the effect of different alloying elements, such as Nb and Ta, on the formation of microtwins is critical for future alloy development. Several mechanisms of microtwinning have been proposed among which the Kolbe mechanism, based on thermally activated reordering, is believed to be dominant. In this work we employ atomistic simulation to investigate the effects of Nb solutes on the Kolbe mechanism. The simulation demonstrates that Nb atoms significantly slow down the reordering processes, explaining the experimentally observed improvement in the creep resistance.

Abstract: Second nearest neighbor modified embedded-atom method (2NN-MEAM) interatomic potentials are developed for binary aluminum (Al) alloys applicable from room temperature to the melting point. The binary alloys studied in this work are Al-Cu, Al-Fe and Al-Ni. Sensitivity and uncertainty analyses are performed on potential parameters based on the perturbation approach. The outcome of the sensitivity analysis shows that some of the MEAM parameters interdependently influence all MEAM model outputs, allowing for the definition of an ordered calibration procedure to target specific MEAM outputs. Using these 2NN-MEAM interatomic potentials, molecular dynamics (MD) simulations are performed to calculate low and high-temperature properties, such as the formation energies of stable phases and unstable intermetallics, lattice parameters, elastic constants, thermal expansion coefficients, enthalpy of formation of solids, liquid mixing enthalpy, and liquidus temperatures at a wide range of compositions. The computed data are compared with the available first principle calculations and experimental data, showing high accuracy of the 2NN-MEAM interatomic potentials. In addition, the liquidus temperature of the Al binary alloys is compared to the phase diagrams determined by the CALPHAD method.

Abstract: An interatomic potential for the Ni–Al system is presented within the third-generation charge optimized many-body (COMB3) formalism. The potential has been optimized for Ni₃Al, or the γ' phase in Ni-based superalloys. The formation energies predicted for other Ni–Al phases are in reasonable agreement with first-principles results. The potential further predicts good mechanical properties for Ni₃Al, which includes the values of the complex stacking fault (CSF) and the anti-phase boundary (APB) energies for the (1 1 1) and (1 0 0) planes. It is also used to investigate dislocation propagation across the Ni₃Al (1 1 0)–Ni (1 1 0) interface, and the results are consistent with simulation results reported in the literature. The potential is further used in combination with a recent COMB3 potential for Al₂O₃ to investigate the Ni₃Al (1 1 1)–Al₂O₃ (0 0 0 1) interface, which has not been modeled previously at the classical atomistic level due to the lack of a reactive potential to describe both Ni₃Al and Al₂O₃ as well as interactions between them. The calculated work of adhesion for this interface is predicted to be 1.85 J m⁻², which is in agreement with available experimental data. The predicted interlayer distance is further consistent with the available first-principles results for Ni (1 1 1)–Al₂O₃ (0 0 0 1).

Abstract: We construct an interatomic potential for the Ni-Al system within the embedded-atom method formalism. The potential is based on previously developed accurate potentials for pure Ni and Al. The cross-interactions are fitted to experimental cohesive energy, lattice parameter and elastic constants of B2-NiAl, as well as to ab initio formation energies of several real or imaginary intermetallic compounds with different crystal structures and chemical compositions. The potential accurately reproduces a variety of physical properties of the NiAl and Ni3Al phases, and shows reasonable agreement with experimental and ab initio data for phase stability across the Ni-Al phase diagram. Most of the properties reproduced by the new potential were not involved in the fitting process, which demonstrates its excellent transferability. Advantages and certain weaknesses of the new potential in comparison with other existing potentials are discussed in detail. The potential is expected to be especially suitable for simulations of heterophase interfaces and mechanical behavior of Ni-Al alloys.

Abstract: Complex equilibria and phase transformations involving diffusion can now be calculated quickly and efficiently. Detailed examples are given for cases which involve varying degrees of non-equilibrium and therefore time-dependence. Despite very good agreement between such calculations and experimental results, many potential end-users are still not convinced that such techniques could be usefully applied to their own specific problems. Friendly graphic interface versions of calculating software are now generally available, so the authors conclude that the most likely source of the reluctance to use such tools lies in the formulation of relevant questions and the interpretation of the results. Although the potential impact of such tools was foreseen many years ago [M. Hillert, Calculation of phase equilibria, in: Conference on Phase Transformations, 1968], few changes in the relevant teaching curricula have taken into account the availability and power of such techniques.
This paper has therefore been designed not only as a collection of interesting problems, but also highlights the critical steps needed to achieve a solution. Each example includes a presentation of the "real" problem, any simplifications that are needed for its solution, the adopted thermodynamic formulation, and a critical evaluation of the results. The availability of such examples should facilitate changes in subject matter that will both make it easier for the next generation of students to use these tools, and at the same time reduce the time and effort currently needed to solve such problems by less efficient methods.
The first set of detailed examples includes the deoxidation of steel by aluminum; heat balance calculations associated with ladle additions to steel; the determination of conditions that avoid undesirable inclusions; the role of methane in sintering atmospheres; interface control during the physical vapour deposition of cemented carbide; oxidation of γ-TiAl materials; and simulation of the thermolysis of metallorganic precursors for Si-C-N ceramics and interface reaction of yttrium silicates with SiC-coated C/C-SiC composites for heat shield applications.
A second set of examples, more dependent on competitive nucleation and growth, includes segregation and carburization in multicomponent steels and features a series of sophisticated simulatons using DICTRA software.
Interfacial and strain energies become increasingly important in defining phase nucleation and morphology in such problems, but relatively little information is available compared to free energy and diffusion databases. The final section therefore demonstrates how computational thermodynamics, semi-empirical atomistic approaches and first-principles calculations are being used to aid filling this gap in our knowledge.

Abstract: A new embedded-atom potential has been developed for Ni₃Al by fitting to experimental and first-principles data. The potential describes lattice properties of Ni₃Al, point defects, planar faults, as well as the γ and γ′ fields on the Ni–Al phase diagram. The potential is applied to calculate the energies of coherent Ni/Ni₃Al interphase boundaries with three different crystallographic orientations. Depending on the orientation, the interface energy varies between 12 and 46 mJ/m2. Coherent γ/γ′ interfaces existing at high temperatures are shown to be more diffuse and are likely to have a lower energy than Ni/Ni₃Al interfaces.

Abstract: An embedded-atom potential has been constructed for the intermetallic compound B2−NiAl by fitting to both experimental properties and ab initio data. The ab initio data have been generated in the form of energy-volume relations for a number of alternative structures of NiAl and Ni3Al, as well as for Ni and Al. The potential accurately reproduces the basic lattice properties of B2−NiAl, planar faults, and point-defect characteristics. It also reproduces the energetics and stability of all other structures included in the fit. The potential is applied to calculate equilibrium point-defect concentrations in B2−NiAl as functions of temperature and composition near the stoichiometry. In contrast to previous calculations, the defect formation entropies arising from atomic vibrations are included in our calculation within the quasiharmonic approximation. Such entropies tend to increase the concentrations of thermal point defects in B2−NiAl at high temperatures, but the atomic disorder mechanism remains triple-defect type up to the melting point.

Abstract: An interatomic potential for the Ni–Al system is presented within the third-generation charge optimized many-body (COMB3) formalism. The potential has been optimized for Ni₃Al, or the γ' phase in Ni-based superalloys. The formation energies predicted for other Ni–Al phases are in reasonable agreement with first-principles results. The potential further predicts good mechanical properties for Ni₃Al, which includes the values of the complex stacking fault (CSF) and the anti-phase boundary (APB) energies for the (1 1 1) and (1 0 0) planes. It is also used to investigate dislocation propagation across the Ni₃Al (1 1 0)–Ni (1 1 0) interface, and the results are consistent with simulation results reported in the literature. The potential is further used in combination with a recent COMB3 potential for Al₂O₃ to investigate the Ni₃Al (1 1 1)–Al₂O₃ (0 0 0 1) interface, which has not been modeled previously at the classical atomistic level due to the lack of a reactive potential to describe both Ni₃Al and Al₂O₃ as well as interactions between them. The calculated work of adhesion for this interface is predicted to be 1.85 J m⁻², which is in agreement with available experimental data. The predicted interlayer distance is further consistent with the available first-principles results for Ni (1 1 1)–Al₂O₃ (0 0 0 1).

Abstract: Complex concentrated alloys (CCAs) are a new generation of metallic alloys composed of three or more principal elements with physical and mechanical properties that can be tuned by adjusting their compositions. The extensive compositional workspace of CCAs makes it impractical to perform a comprehensive search for a specific material property using experimental measurements. The use of computational methods can rapidly narrow down the search span, improving the efficiency of the design process. We carried out a high-throughput parameterization of modified embedded atom method (MEAM) interatomic potentials for combinations of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn using a genetic algorithm. Unary systems were parameterized based on DFT calculations and experimental results. MEAM potentials for 28 binary and 56 ternary combinations of the elements were parameterized to DFT results that were carried out with semi-automated frameworks. Specific attention was made to reproduce properties that impact compositional segregation, material strength, and mechanics.

Abstract: Interatomic potentials for the Ni-Ti and Ni-Al-Ti systems have been developed based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism. The Ni-Ti binary potential reproduces fundamental materials properties (structural, elastic, thermodynamic, and thermal stability) of alloy systems in reasonable agreement with experiments, first-principles calculations and thermodynamic calculations. Atomistic simulations using the Ni-Al-Ti ternary potential validate that the potential can be applied successfully to atomic-scale investigations to clarify the effects of titanium on important materials phenomena (site preference in γ', γ-γ' phase transition, and segregation on grain boundaries) in Ni-Al-Ti ternary superalloys.

Abstract: A computational approach combining dispersion-corrected density functional theory (DFT) and classical molecular dynamics is employed to characterize the geometrical and thermomechanical properties of a recently proposed 2D transition metal dihalide NiCl₂. The characterization is performed using a classical interatomic force field whose parameters are determined and verified through the comparison with the results of DFT calculations. The developed force field is used to study the mechanical response, thermal stability, melting and solidification of a NiCl₂ monolayer on the atomistic level of detail. The 2D NiCl₂ sheet is found to be thermally stable at temperatures below its melting point of ~695 K. At higher temperatures, several subsequent structural transformations of NiCl₂ are observed, namely a transition into a porous 2D sheet and a 1D nanowire. The MD simulations of NiCl₂ cooling show that the molten NiCl₂ system solidifies into an amorphous porous 2D structure at T ~450 K. The resulting structure has lower cohesive energy with respect to the initial 2D sheet. The computational methodology presented through the case study of NiCl₂ can also be utilized to study the properties of other novel 2D materials, including recently synthesized NiO₂, NiS₂, and NiSe₂.

Abstract: High Entropy Alloys (HEA) attract attention as possible radiation resistant materials, a feature observed in some experiments that has been attributed to several unique properties of HEA, in particular to the disorder-induced reduced thermal conductivity and to the peculiar defect properties originating from the chemical complexity. To explore the origin of such behavior we study the early stages (less than 0.1 ns), of radiation damage response of a HEA using molecular dynamics simulations of collision cascades induced by primary knock-on atoms (PKA) with 10, 20 and 40 keV, at room temperature, on an idealized model equiatomic quinary fcc FeNiCrCoCu alloy, the corresponding "Average Atom" (AA) material, and on pure Ni. We include accurate corrections to describe short-range atomic interactions during the cascade. In all cases the average number of defects in the HEA is lower than for pure Ni, which has been previously used to help claiming that HEA is radiation resistant. However, simulated defect evolution during primary damage, including the number of surviving Frenkel Pairs, and the defect cluster size distributions are nearly the same in all cases, within our statistical uncertainty. The number of surviving FP in the alloy is predicted fairly well by analytical models of defect production in pure materials. All of this indicates that the origin of radiation resistance in HEAs as observed in experiments may not be related to a reduction in primary damage due to chemical disorder, but is probably caused by longer-time defect evolution.

Abstract: A set of embedded atom method model interatomic potentials is presented to represent a high-entropy alloy with five components. The set is developed to resemble but not model precisely face-centered cubic (fcc) near-equiatomic mixtures of Fe–Ni–Cr–Co–Cu. The individual components have atomic sizes deviating up to 3%. With the heats of mixing of all binary equiatomic random fcc mixtures being less than 0.7 kJ/mol and the corresponding value for the quinary being −0.0002 kJ/mol, the potentials predict the random equiatomic fcc quinary mixture to be stable with respect to phase separation or ordering and with respect to bcc and hcp random mixtures. The details of lattice distortion, strain, and stress states in this phase are reported. The standard deviation in the individual nearest neighbor bond lengths was found to be in the range of 2%. Most importantly, individual atoms in the alloy were found to be under atomic strains up to 0.5%, corresponding to individual atomic stresses up to several GPa.

Abstract: The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C₁₂ − C₄₄, which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.

Abstract: Although high-entropy alloys (HEAs) are attracting interest, the physical metallurgical mechanisms related to their properties have mostly not been clarified, and this limits wider industrial applications, in addition to the high alloy costs. We clarify the physical metallurgical reasons for the materials phenomena (sluggish diffusion and micro-twining at cryogenic temperatures) and investigate the effect of individual elements on solid solution hardening for the equiatomic CoCrFeMnNi HEA based on atomistic simulations (Monte Carlo, molecular dynamics and molecular statics). A significant number of stable vacant lattice sites with high migration energy barriers exists and is thought to cause the sluggish diffusion. We predict that the hexagonal close-packed (hcp) structure is more stable than the face-centered cubic (fcc) structure at 0 K, which we propose as the fundamental reason for the micro-twinning at cryogenic temperatures. The alloying effect on the critical resolved shear stress (CRSS) is well predicted by the atomistic simulation, used for a design of non-equiatomic fcc HEAs with improved strength, and is experimentally verified. This study demonstrates the applicability of the proposed atomistic approach combined with a thermodynamic calculation technique to a computational design of advanced HEAs.