Abstract: Large-scale atomistic simulations of materials heavily rely on interatomic potentials, which predict the system energy and atomic forces. One of the recent developments in the field is constructing interatomic potentials by machine-learning (ML) methods. ML potentials predict the energy and forces by numerical interpolation using a large reference database generated by quantum-mechanical calculations. While high accuracy of interpolation can be achieved, extrapolation to unknown atomic environments is unpredictable. The recently proposed physically-informed neural network (PINN) model improves the transferability by combining a neural network regression with a physics-based bond-order interatomic potential. Here, we demonstrate that general-purpose PINN potentials can be developed for body-centered cubic (BCC) metals. The proposed PINN potential for tantalum reproduces the reference energies within 2.8 meV/atom. It accurately predicts a broad spectrum of physical properties of Ta, including (but not limited to) lattice dynamics, thermal expansion, energies of point and extended defects, the dislocation core structure and the Peierls barrier, the melting temperature, the structure of liquid Ta, and the liquid surface tension. The potential enables large-scale simulations of physical and mechanical behavior of Ta with nearly first-principles accuracy while being orders of magnitude faster. This approach can be readily extended to other BCC metals.

Abstract: Large-scale atomistic computer simulations of materials rely on interatomic potentials providing computationally efficient predictions of energy and Newtonian forces. Traditional potentials have served in this capacity for over three decades. Recently, a new class of potentials has emerged, which is based on a radically different philosophy. The new potentials are constructed using machine-learning (ML) methods and a massive reference database generated by quantum-mechanical calculations. While the traditional potentials are derived from physical insights into the nature of chemical bonding, the ML potentials utilize a high-dimensional mathematical regression to interpolate between the reference energies. We review the current status of the interatomic potential field, comparing the strengths and weaknesses of the traditional and ML potentials. A third class of potentials is introduced, in which an ML model is coupled with a physics-based potential to improve the transferability to unknown atomic environments. The discussion is focused on potentials intended for materials science applications. Possible future directions in this field are outlined.

Abstract: Atomistic computer simulations are capable of providing insights into physical mechanisms responsible for the extraordinary structural stability and strength of immiscible Cu–Ta alloys. To enable reliable simulations of these alloys, we have developed an angular-dependent potential (ADP) for the Cu–Ta system by fitting to a large database of first-principles and experimental data. This, in turn, required the development of a new ADP potential for elemental Ta, which accurately reproduces a wide range of properties of Ta and is transferable to severely deformed states and diverse atomic environments. The new Cu–Ta potential is applied for studying the kinetics of grain growth in nano-crystalline Cu–Ta alloys with different chemical compositions. Ta atoms form nanometer-scale clusters preferentially located at grain boundaries (GBs) and triple junctions. These clusters pin some of the GBs in place and cause a drastic decrease in grain growth by the Zener pinning mechanism. The results of the simulations are well consistent with experimental observations and suggest possible mechanisms of the stabilization effect of Ta.

Abstract: We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.

Abstract: We report on large-scale nonequilibrium molecular dynamics simulations of shock wave compression in tantalum single crystals. Two new embedded atom method interatomic potentials of Ta have been developed and optimized by fitting to experimental and density functional theory data. The potentials reproduce the isothermal equation of state of Ta up to 300 GPa. We examined the nature of the plastic deformation and elastic limits as functions of crystal orientation. Shock waves along (100), (110), and (111) exhibit elastic-plastic two-wave structures. Plastic deformation in shock compression along (110) is due primarily to the formation of twins that nucleate at the shock front. The strain-rate dependence of the flow stress is found to be orientation dependent, with (110) shocks exhibiting the weaker dependence. Premelting at a temperature much below that of thermodynamic melting at the shock front is observed in all three directions for shock pressures above about 180 GPa.

Abstract: We report on large-scale nonequilibrium molecular dynamics simulations of shock wave compression in tantalum single crystals. Two new embedded atom method interatomic potentials of Ta have been developed and optimized by fitting to experimental and density functional theory data. The potentials reproduce the isothermal equation of state of Ta up to 300 GPa. We examined the nature of the plastic deformation and elastic limits as functions of crystal orientation. Shock waves along (100), (110), and (111) exhibit elastic-plastic two-wave structures. Plastic deformation in shock compression along (110) is due primarily to the formation of twins that nucleate at the shock front. The strain-rate dependence of the flow stress is found to be orientation dependent, with (110) shocks exhibiting the weaker dependence. Premelting at a temperature much below that of thermodynamic melting at the shock front is observed in all three directions for shock pressures above about 180 GPa.

Abstract: We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the “local” d band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

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: The ability to predict the behavior of point defects in metals, particularly interstitial defects, is central to accurate modeling of the microstructural evolution in environments with high radiation fluxes. Existing interatomic potentials of embedded atom method type predict disparate stable interstitial defect configurations in vanadium. This is not surprising since accurate first-principles interstitial data were not available when these potentials were fitted. In order to provide the input information required to fit a vanadium potential appropriate for radiation damage studies, we perform a series of first-principles calculations on six different interstitial geometries and vacancies. These calculations identify the 〈111〉 dumbbell as the most stable interstitial with a formation energy of approximately 3.1 eV, at variance with predictions based upon existing potentials. Our potential is of Finnis–Sinclair type and is fitted exactly to the experimental equilibrium lattice parameter, cohesive energy, elastic constants and a calculated unrelaxed vacancy formation energy. Two additional potential parameters were used to obtain the best fit to the set of interstitial formation energies determined from the first-principles calculations. The resulting potential was found to accurately predict both the magnitude and ordering of the formation energies of six interstitial configurations and the unrelaxed vacancy ground state, in addition to accurately describing the migration characteristics of the stable interstitial and vacancy. This vanadium potential is capable of describing the point defect properties appropriate for radiation damage simulations as well as for simulations of more common crystal and simple defect properties.

Abstract: An embedded-atom-method potential for tantalum (Ta) has been carefully constructed by fitting to a combination of experimental and density-functional theory (DFT) data. The fitted data include the elastic constants, lattice constant, cohesive energy, unrelaxed vacancy formation energy, and hundreds of force data calculated by DFT for a variety of structures such as liquids, surfaces, clusters, interstitials, vacancies, and stacking faults. We also fit to the cohesive energy vs volume data from the equation of state for the body-centered-cubic (bcc) Ta and to the calculated cohesive energy using DFT for the face-centered-cubic (fcc) Ta structure. We assess the accuracy of the new potential by comparing several calculated Ta properties with those obtained from other potentials previously reported in the literature. In many cases, the new potential yields superior accuracy at a comparable or lower computational cost.

Abstract: The second nearest-neighbor modified embedded atom method (MEAM) [Phys. Rev. B 62, 8564 (2000)], developed in order to solve problems of the original first nearest-neighbor MEAM on bcc metals, has now been applied to all bcc transition metals, Fe, Cr, Mo, W, V, Nb, and Ta. The potential parameters could be determined empirically by fitting to (∂B/∂P), elastic constants, structural energy differences among bcc, fcc and hcp structures, vacancy-formation energy, and surface energy. Various physical properties of individual elements, including elastic constants, structural properties, point-defect properties, surface properties, and thermal properties were calculated and compared with experiments or high level calculations so that the reliability of the present empirical atomic-potential formalism can be evaluated. It is shown that the present potentials reasonably reproduce nonfitted properties of the bcc transition metals, as well as the fitted properties. The effect of the size of radial cutoff distance on the calculation and the compatibility with the original first nearest-neighbor MEAM that has been successful for fcc, hcp, and other structures are also discussed.

Abstract: The recently published semi-empirical potentials of Finnis and Sinclair for the metals V, Nb, Ta, Mo and W appear to give unphysical results for properties involving small interatomic separation. This is remedied by adding to the potentials cores fitted to electron gas calculations on dimers. The adjusted potentials are shown to predict a more realistic pressure-volume relationship. Interstitial formation energies are calculated for various configurations, using quenched molecular dynamics and static relaxation. Some preliminary results on interstitial migration are presented.

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 set of parameters for the modified embedded atom method (MEAM) potential was developed to describe the perovskite silver tantalate (AgTaO3). First, MEAM parameters for AgO and TaO were determined based on the structural and elastic properties of the materials in a B1 reference structure predicted by density-functional theory (DFT). Then, using the fitted binary parameters, additional potential parameters were adjusted to enable the empirical potential to reproduce DFT-predicted lattice structure, elastic constants, cohesive energy and equation of state for the ternary AgTaO3. Finally, thermal expansion was predicted by a molecular dynamics (MD) simulation using the newly developed potential and compared directly to experimental values. The agreement with known experimental data for AgTaO3 is satisfactory, and confirms that the new empirical model is a good starting point for further MD studies.

Abstract: Interatomic potentials for the Al-Ti, Al-Ta, Al-Zr, Al-Nb and Al-Hf binary systems have been developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The fundamental materials properties (structural, thermodynamic and elastic behaviors of different intermetallics) could be readily described with the potentials using molecular dynamic simulation (MD), in rational agreements with experimental or first principles data. The potentials are further utilized to develop an interatomic potential for the (TiZrNbHfTa)Al₃ high entropy intermetallic compound (HEIC), which open the door to understand atomic scale behavior of HEICs.

Abstract: Interatomic potentials for the Al-Ti, Al-Ta, Al-Zr, Al-Nb and Al-Hf binary systems have been developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The fundamental materials properties (structural, thermodynamic and elastic behaviors of different intermetallics) could be readily described with the potentials using molecular dynamic simulation (MD), in rational agreements with experimental or first principles data. The potentials are further utilized to develop an interatomic potential for the (TiZrNbHfTa)Al₃ high entropy intermetallic compound (HEIC), which open the door to understand atomic scale behavior of HEICs.

Abstract: Atomistic computer simulations are capable of providing insights into physical mechanisms responsible for the extraordinary structural stability and strength of immiscible Cu–Ta alloys. To enable reliable simulations of these alloys, we have developed an angular-dependent potential (ADP) for the Cu–Ta system by fitting to a large database of first-principles and experimental data. This, in turn, required the development of a new ADP potential for elemental Ta, which accurately reproduces a wide range of properties of Ta and is transferable to severely deformed states and diverse atomic environments. The new Cu–Ta potential is applied for studying the kinetics of grain growth in nano-crystalline Cu–Ta alloys with different chemical compositions. Ta atoms form nanometer-scale clusters preferentially located at grain boundaries (GBs) and triple junctions. These clusters pin some of the GBs in place and cause a drastic decrease in grain growth by the Zener pinning mechanism. The results of the simulations are well consistent with experimental observations and suggest possible mechanisms of the stabilization effect of Ta.

Abstract: An angle-dependent interatomic potential has been developed for the Cu-Ta system by crossing two existing potentials for pure Cu and Ta. The cross-interaction functions have been fitted to first-principles data generated in this work. The potential has been extensively tested against first-principles energies not included in the fitting database and applied to molecular dynamics simulations of wetting and dewetting of Cu on Ta. We find that a Cu film placed on a Ta (110) surface dewets from it, forming a Cu droplet on top of a stable Cu monolayer. We also observe that a drop of liquid Cu placed on a clean Ta (110) surface spreads over it as a stable monolayer, while the extra Cu atoms remain in the drop. The stability of a Cu monolayer and instability of thicker Cu films are consistent with recent experiments and first-principles calculations. This agreement demonstrates the utility of the potential for atomistic simulations of Cu-Ta interfaces.

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 pair potential for Ta-He system was developed by fitting to the results obtained from ab initio calculations. The potential model proposed by Juslin and Nordlund was employed to describe the Ta-He interaction. The formation energies of single He atom at different sites were utilized as the fitting targets. Particle swarm optimization scheme was adopted to determine the parameters. The newly developed potential could reproduce the formation energies of single He defects very well. Besides, the binding energies of an additional interstitial He atom to an existing He_n−1V and He_n clusters, and the migration energies of interstitial He atom and HeV₂ cluster were studied. They were found to be in good agreement with available ab initio results.

Abstract: In this paper, we present an interatomic potential for the ternary W-Ta-He system, which is an extension of our previous W-Ta potential. The new potential parameters for the W-He and Ta-He interactions are determined by fitting the results obtained from first-principles calculations. The formation energies of a single He atom at different sites, the binding energies of He-He and He-Vac (Vac = vacancy) in W/Ta, and the binding energies of a single He atom with a solute Ta atom in W are used as the fitting targets. Then, the binding energies of an additional interstitial He atom to existing He_nVac_m clusters in W/Ta are calculated, and the results reported correspond with the results from the first-principles. Furthermore, the effects of solute Ta on the diffusion and aggregation of He in bulk W are studied. We observed that small interstitial He atom clusters (N_He ≤ 4) were easy to diffuse in pure W, and their diffusion activation energies were less than 0.3 eV. However, the binding energies between Ta and these clusters were between 0.5 and 0.9 eV, which has a pinning effect on the He cluster diffusion. At high temperature, the solute Ta cannot qualitatively hinder the agglomeration of He atoms, however, due to the pinning effect compared with pure W, solute Ta in W has a certain delay effect on the agglomeration of He atoms in time.

Abstract: Chemical short-range order (CSRO) in high entropy alloys (HEAs) has attracted interests recently and is believed to be capable for tuning their mechanical properties. However, the characterization of CSRO in HEAs through experimental methods remains challenging. In this work, a modified embedded-atom method interatomic potential with good accuracy for studying CSRO in HfNbTaTiZr alloy system was developed. By employing the potential, molecular dynamic/Monte Carlo simulation was performed to investigate the CSRO in HfNbTaZr HEA. The results indicated that Hf-Zr and Nb-Ta atom pairs were preferred in the BCC solid solution of HfNbTaZr, and a new type of CSRO with topological B2 order was predicted, which can help to understand the mechanical properties of HfNbTaZr HEA. It was also found that forming of CSRO was an incubation process for the precipitation in HfNbTaZr, implying the significance of CSRO on the phase stability or precipitation behavior of HEAs. The findings in the present work can help in understanding CSRO and establishing its relationship with precipitates in HEAs, and more topics related to CSRO and phase stability in HfNbTaTiZr alloy system can be further investigated by atomistic simulation.

Abstract: Refractory multi-principal element alloys (MPEAs) have exceptional mechanical properties, including high strength-to-weight ratio and fracture toughness, at high temperatures. Here we elucidate the complex interplay between segregation, short-range order, and strengthening in the NbMoTaW MPEA through atomistic simulations with a highly accurate machine learning interatomic potential. In the single crystal MPEA, we find greatly reduced anisotropy in the critically resolved shear stress between screw and edge dislocations compared to the elemental metals. In the polycrystalline MPEA, we demonstrate that thermodynamically driven Nb segregation to the grain boundaries (GBs) and W enrichment within the grains intensifies the observed short-range order (SRO). The increased GB stability due to Nb enrichment reduces the von Mises strain, resulting in higher strength than a random solid solution MPEA. These results highlight the need to simultaneously tune GB composition and bulk SRO to tailor the mechanical properties of MPEAs.

Abstract: High Entropy Alloys (HEAs) have attracted much interest over the past 20 years because of their remarkable mechanical properties. Recent works on BCC refractory HEAs have demonstrated high strength even at extreme temperatures with an unusual mix of strength and ductility. They also show excellent strain-hardening behavior. This study focuses on the VNbTaTiZr alloy, which stands out for its favorable qualities including relatively low density, impressive yield strength, and ductility at room temperature. To better understand the atomic behavior and microstructural features inherent to this alloy, a Modified Embedded Atom Method (MEAM) potential is developed, based on first-principles computations. Through accurate modeling of lattice constants, elastic constants, and formation enthalpies, a hybrid Molecular Dynamics/Monte Carlo (MD/MC) simulation of an equimolar VNbTaTiZr refractory HEA was performed to explore the role of local chemical compositions to its mechanical response. The current MEAM potential aligns closely with recent experimental work, validating its effectiveness. Adding Zr to the VNbTaTi alloy induces more lattice distortion, matching recent experimental observations. The potential also predicts that for RHEAs, deformation behavior is dominated by edge dislocations, unlike in pure BCC elements where screw dislocations prevail. Overall, this potential will be useful for unraveling the intricate atomic-level processes that give this alloy its remarkable mechanical performance.

Abstract: Tungsten (W) and W-based alloys are regarded as the most promising candidates for plasma facing materials (PFMs) in future fusion reactors. In this work, new interatomic potentialsfor Ta element and W-Ta alloy have been developed based on the Finnis-Sinclair formalism, in combination with our previously developed potential for W. The potential parameters for Ta were determined by fitting to a set of experimental and first-principles data, including lattice constant, cohesive energy, elastic constants, point defects formation energies and Rose’s equation of state for the bcc lattice. The W-Ta cross parameters were fitted to the first-principles data of the formation energies and binding energies of Ta atom with different point defects in bulk W. The present potentials not only reproduce some important physical properties of various point defects, but also predict the non-degenerate/compact core structure of the 1/2 〈1 1 1〉 screw dislocation in bulk Ta, which is the same as DFT calculations. The developed potentials were expected to be suitable for atomistic simulations of point defects evolution in Ta and W-Ta binary alloys.

Abstract: Metastable high entropy alloy (HEA) with excellent properties have attracted extensive attentions recently. However, as a consequence of limited experiments of high-resolution transmission electron microscopy (HRTEM) and the difficulties of molecular dynamic (MD) simulations for the phase transformation process, the detailed atomic deformation mechanisms in the HEA is not well understood. We carry out the in situ HRTEM observation of the martensitic transformation process and find surprisingly wide phase interface between the parent and the martensite in a typical high strength and high elongation metastable HEA. One specific interatomic potential is developed for the metastable HEA and large-scale MD simulation is carried out to investigate the martensitic transformation process from body-centered cubic to hexagonal close packed structures. The whole processes of the stress-induced martensitic transformation (nucleation, incubation, bursting and propagating of the new phase) are well reproduced in the MD simulations, suggesting its good agreements with the HRTEM observations. The width of the phase interface mainly depends on the competition between interfacial energy and lattice distortion energy during the martensitic transformation process. This wide phase interface acts as a buffer to coordinate the martensitic transformation induced strain and as a buffer storage for dislocation gliding and pile-up. As a result, the metastable HEA achieves a high strength combined with a large tensile elongation. The revealed atomic-scale deformation and corresponding interatomic potential should be useful to guide the design in the new series of high-performance metastable alloy.