A spectral neighbor analysis potential for Nb-Mo-Ta-W developed by Xiangguo Li (2019) v000

Hui Zheng; Xiangguo Li; Chi Chen; Ong, Shyue Ping

doi:10.25950/c34c3362

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SNAP_LiChenZheng_2019_NbTaWMo__MO_560387080449_000

Interatomic potential for Molybdenum (Mo), Niobium (Nb), Tantalum (Ta), Tungsten (W).
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Title A single sentence description.	A spectral neighbor analysis potential for Nb-Mo-Ta-W developed by Xiangguo Li (2019) v000
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	A spectral neighbor analysis potential for Nb-Mo-Ta-W chemistries. The potential is trained against diverse and large materials data, including undistorted ground state structures for Nb, Mo, Ta, W; distorted structures constructed by applying different strains to a bulk supercell; surface structures of elemental structures; solid solution random binary structures; special quasi-random structures for ternary and quaternary systems; ab-initio molecular dynamics (AIMD) simulated random structures at different temperatures for elementary bulk and special quasi-random structures. The potential gives accurate predictions of structural energies, forces, elasticity, lattice parameters, free energies, melting point, surface energies, generalized stacking fault energies, dislocation core structures, critical resolved shear stress of screw and edge dislocations. It can also successfully predict the short-range order and segregation effects in the multi-principal element NbMoTaW alloy.
Species The supported atomic species.	Mo, Nb, Ta, W
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	This potential is designed for Nb-Mo-Ta-W chemistries, including the elementary, binary, ternary and quaternary systems. The potential was trained using LAMMPS version 17Nov2016. Newer LAMMPS may see energy differences, but the relative values should remain to be the same.
Content Other Locations	https://arxiv.org/abs/1912.01789

Contributor	Xiangguo Li
Maintainer	Xiangguo Li
Developer	Hui Zheng Xiangguo Li Chi Chen Ong, Shyue Ping
Published on KIM	2020
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Li X-G, Chen C, Zheng H, Zuo Y, Ong SP. Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy. npj Computational Materials. 2020;6(1). doi:10.1038/s41524-020-0339-0 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information. [2] Zheng H, Li X, Chen C, Ong SP. A spectral neighbor analysis potential for Nb-Mo-Ta-W developed by Xiangguo Li (2019) v000. OpenKIM; 2020. doi:10.25950/c34c3362 [3] Afshar Y, Thompson AP, Swiler LP, Trott CR, Foiles SM, Tucker GJ. Spectral neighbor analysis potential (SNAP) model driver v000. OpenKIM; 2019. doi:10.25950/f4fae493 [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. 99 Citations (61 used) Show Model Used Show All Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the . S. He, X.-Z. Zhou, D. Mordehai, and J. Marian, “Thermal Super-Jogs Control High-Temperature Strength in Nb-Mo-Ta-W Alloys,” SSRN Electronic Journal. 2022. link Times cited: 0 Abstract: Refractory multi-element alloys (RMEA) with body-centered cu… read more Abstract: Refractory multi-element alloys (RMEA) with body-centered cubic (bcc) structure have been the object of much research over the last decade due to their high potential as candidate materials for high-temperature applications. Most of these alloys display a remarkable strength at temperatures above 1000 ˝ C, which cannot be explained by the standard model of bcc plasticity dominated by thermally-activated screw dislocation motion. Recent research on Nb-Mo-Ta-W alloys points to a heightened role of edge dislocations during mechanical deformation, which is generally attributed to atomic-level chemical ﬂuctuations in the material and their interactions with dislocation cores during slip. However, while this e ﬀ ect accounts for levels of strength that are much larger than what might be found in a pure metal, it is not su ﬃ cient to explain the high yield stress found at high temperature in Nb-Mo-Ta-W. In this work, we propose a new strengthening mechanism based on the existence of thermal super-jogs in edge dislocation lines that act as strong obstacles to dislocation motion, conferring an extra strength to the alloy that turns out to be in very good agreement with experimental measurements. The basis for the formation of these super-jogs is found in the unique properties of RMEA, which display vacancy formation energy distributions with tails that extend into negative values. This leads to spontaneous, i.e., athermal, vacancy formation at edge dislocation cores, which subsequently relax into atomic-sized super-jogs on the dislocation line. At the same time, these super-jogs can displace di ﬀ usively along the glide direction, relieving with their motion some of the extra stress, thus countering the hardening e ﬀ ect due to jog-pinning We implement these mechanisms into a specially-designed hybrid kinetic Monte Carlo / Discrete Dislocation Dynamics approach (kMC / DD) parameterized with vacancy formation and migration energy distributions obtained with machine-learning potentials designed speciﬁcally for the Nb-Mo-Ta-W system. The kMC module sets the timescale dictated by thermally-activated events, while the DD module relaxes the dislocation line conﬁguration in between events in accordance with the applied stress. We ﬁnd that the balance between super-jog pinning and superjog di ﬀ usion confers an extra strength to edge dislocations at intermediate-to-high temperatures that is in remarkable agreement with experimental measurements in equiatomic Nb-Mo-Ta-W and several other RMEA. We derive an analytical model based on the computational results that captures this improved understanding of plastic processes in these alloys and and explains the experimental data. read less I. Geiger, J. Luo, E. Lavernia, P. Cao, D. Apelian, and T. Rupert, “Influence of chemistry and structure on interfacial segregation in NbMoTaW with high-throughput atomistic simulations,” Journal of Applied Physics. 2022. link Times cited: 4 Abstract: Refractory multi-principal element alloys exhibiting promisi… read more Abstract: Refractory multi-principal element alloys exhibiting promising mechanical properties such as excellent strength retention at elevated temperatures have been attracting increasing attention. Although their inherent chemical complexity is considered a defining feature, a challenge arises in predicting local chemical ordering, particularly in grain boundary regions with an enhanced structural disorder. In this study, we use atomistic simulations of a large group of bicrystal models to sample a wide variety of interfacial sites (grain boundary) in NbMoTaW and explore emergent trends in interfacial segregation and the underlying structural and chemical driving factors. Sampling hundreds of bicrystals along the [001] symmetric tilt axis and analyzing more than one hundred and thirty thousand grain boundary sites with a variety of local atomic environments, we uncover segregation trends in NbMoTaW. While Nb is the dominant segregant, more notable are the segregation patterns that deviate from expected behavior and mark situations where local structural and chemical driving forces lead to interesting segregation events. For example, incomplete depletion of Ta in low-angle boundaries results from chemical pinning due to favorable local compositional environments associated with chemical short-range ordering. Finally, machine learning models capturing and comparing the structural and chemical features of interfacial sites are developed to weigh their relative importance and contributions to segregation tendency, revealing a significant increase in predictive capability when including local chemical information. Overall, this work, highlighting the complex interplay between the local grain boundary structure and chemical short-range ordering, suggests tunable segregation and chemical ordering by tailoring grain boundary structure in multi-principal element alloys. read less T. Lee et al., “Atomic-scale origin of the low grain-boundary resistance in perovskite solid electrolyte Li0.375Sr0.4375Ta0.75Zr0.25O3,” Nature Communications. 2022. link Times cited: 9 H. Zheng et al., “Multi-scale investigation of short-range order and dislocation glide in MoNbTi and TaNbTi multi-principal element alloys,” npj Computational Materials. 2022. link Times cited: 8 X. Wang, F. Maresca, and P. Cao, “The Hierarchical Energy Landscape of Screw Dislocation Motion in Refractory High-entropy Alloys,” Acta Materialia. 2022. link Times cited: 18 W. Jian, Y. Su, S. Xu, W. Ji, and I. Beyerlein, “Effect of interface structure on dislocation glide behavior in nanolaminates,” Journal of Materials Research. 2021. link Times cited: 6 Abstract: The ultra-high strength of nanolaminates arises from the eff… read more Abstract: The ultra-high strength of nanolaminates arises from the effect of the fine layering on dislocation motion. Using atomistic simulations, we investigate the effect of the interface structure on the behavior of an edge dislocation driven to glide within a nanolayer of a nanolaminate. Three classes of interface structures are studied, including Cu/Nb or Cu/Cu incoherent interfaces and Nb/Nb coherent interface. Glide behavior is jerky when the interface is incoherent and composed of discrete misfit dislocation arrays. The resistance to glide is non-uniform among parallel glide planes, where planes with intersection lines coinciding with misfit dislocation lines experience greater resistances than those that do not. Interfaces containing misfit dislocations, which extend from the interface into a glide plane in the layer, severely obstruct glide, causing the dislocation to transfer to a parallel plane. Coherent interfaces, while posing the least resistance to initiate and promote smooth glide, lead to strain hardening. read less X. Zhou, S. He, and J. Marian, “Temperature dependence of the strength of Nb-Mo-Ta-W alloys due to screw dislocations,” Scripta Materialia. 2024. link Times cited: 0 C. Hu, R. Dingreville, and B. L. Boyce, “Computational modeling of grain boundary segregation: A review,” Computational Materials Science. 2024. link Times cited: 0 D. Hua et al., “Revealing the deformation mechanisms of <110> symmetric tilt grain boundaries in CoCrNi medium-entropy alloy,” International Journal of Plasticity. 2023. link Times cited: 0 S. Shuang, Y. Liang, X. Zhang, F. Yuan, G. Kang, and X. Zhang, “Impact of local chemical ordering on deformation mechanisms in single-crystalline CuNiCoFe high-entropy alloys: a molecular dynamics study,” Modelling and Simulation in Materials Science and Engineering. 2023. link Times cited: 0 Abstract: High-entropy alloys (HEAs), composed of multiple constituent… read more Abstract: High-entropy alloys (HEAs), composed of multiple constituent elements with concentrations ranging from 5% to 35%, have been considered ideal solid solution of multi-principal elements. However, recent experimental and computational studies have demonstrated that complex enthalpic interactions among constituents lead to a wide variety of local chemical ordering (LCO) at lower temperatures. HEAs containing Cu typically decompose by forming of Cu-rich phases during annealing, thus affecting mechanical properties. In this study, CuNiCoFe HEA was chosen as a model with a tendency for Cu segregation at low temperatures. The formation of LCO and its impact on the deformation behaviors in the single-crystalline CuNiCoFe HEA were studied via molecular dynamics simulations. Our results demonstrate that CuNiCoFe HEA decomposes by Cu clustering, in agreement with prior experimental and computational studies, owing to insufficient configuration entropy to compete against the mixing enthalpy at lower temperatures. A softening in ultimate stress in the LCO models was observed compared to the random solid solution models. The softening is due to the lower unstable stacking fault energy, which determines the nucleation event of dislocations, thereby rationalizing the dislocation nucleation in the Cu-rich regions and the softening of the overall ultimate strength in the LCO models. Additionally, the inhomogeneous FCC–BCC transformation is closely associated with concentration inhomogeneity. CuNiCoFe HEA with LCO can be regarded as composites, consisting of clusters with different properties. Consequently, concentration inhomogeneity induced by LCO profoundly impacts the mechanical properties and deformation behaviors of the HEA. This study provides insights into the effect of LCO on the mechanical properties of CuNiCoFe HEAs, which is crucial for developing HEAs with tailored properties for specific applications. read less X.-T. Li, X. Tang, and Y.-F. Guo, “Inhibition effect of segregation and chemical order on grain boundary migration in NbMoTaW multi-principal element alloy,” Scripta Materialia. 2023. link Times cited: 0 H. Umashankar, D. Scheiber, V. Razumovskiy, and M. Militzer, “Modeling solute-grain boundary interactions in a bcc Ti-Mo alloy using density functional theory,” Computational Materials Science. 2023. link Times cited: 1 S. Chen et al., “Crack Tip Dislocation Activity in Refractory High-Entropy Alloys,” International Journal of Mechanical Sciences. 2023. link Times cited: 0 A. A. Mamun, S. Xu, X.-G. Li, and Y. Su, “Comparing interatomic potentials in calculating basic structural parameters and Peierls stress in tungsten-based random binary alloys,” Physica Scripta. 2023. link Times cited: 0 Abstract: The field of machine learning-based interatomic potentials (… read more Abstract: The field of machine learning-based interatomic potentials (ML-IAPs) has seen increasing development in recent years. In this work, we compare three widely used ML-IAPs–the moment tensor potential (MTP), the spectral neighbor analysis potential (SNAP), and the tabulated Gaussian approximation potential (tabGAP)with a conventional non-ML-IAP, the embedded atom method (EAM) potential. We evaluated these potentials on the basis of their accuracy and efficiency in determining basic structural parameters and Peierls stress under equivalent conditions. Three tungsten (W)-based alloys (Mo-W, Nb-W, and Ta-W) are considered, and their lattice parameter, formation energy, elastic tensor, and Peierls stress of edge dislocation are calculated. Compared with DFT results, MTP demonstrates the highest accuracy in predicting the lattice parameter and the best computational efficiency among the three ML-IAPs, while tabGAP accurately predicts two independent elastic constants, C 11 and C 12. Despite being the slowest, SNAP shows the highest accuracy in predicting the third independent elastic constant C 44 and its Peierls stress value is comparable to that based on MTP. read less Y.-F. Wu, W. Yu, and S. Shen, “Developing an analytical bond-order potential for Hf/Nb/Ta/Zr/C system using machine learning global optimization,” Ceramics International. 2023. link Times cited: 0 A. Chen, Y. Pan, J. Dai, W. Fu, and X. Song, “Theoretical study on the element distribution characteristics and the effects of oxygen in TiZrHfNb high entropy alloys,” Materials Today Communications. 2023. link Times cited: 1 P. Ouyang et al., “Atomic Local Ordering and Alloying Effects on the Mg3(Sb1-xBix)2 Thermoelectric Material.,” ACS applied materials & interfaces. 2023. link Times cited: 1 Abstract: Mg3(Sb1-xBix)2 alloy has been extensively studied in the las… read more Abstract: Mg3(Sb1-xBix)2 alloy has been extensively studied in the last 5 years due to its exceptional thermoelectric (TE) performance. The absence of accurate force field for inorganic alloy compounds presents great challenges for computational studies. Here, we explore the atomic microstructure, thermal, and elastic properties of the Mg3(Sb1-xBix)2 alloy at different solution concentrations through atomic simulations with a highly accurate machine learning interatomic potential (ML-IAP). We find atomic local ordering in the optimized structure with the Bi-Bi pair inclined to join adjacent layers and Sb-Sb pair preferring to stay within the same layer. The thermal conductivity changes with the solution concentrations can be correctly predicted through ML-IAP-based molecular dynamics simulations. Spectral thermal conductance analysis shows that the continuous movement of low-frequency peak to high frequency is responsible for the reduction of the thermal conductivity upon alloying. Elastic calculations reveal that similar to the thermal conductivity, solid solution alloying can reduce the overall elastic properties at both Mg3Sb2 and Mg3Bi2 ends, while anisotropic behavior is clearly observed with linear interpolation relationship upon alloying along the interlayer direction and nonlinearity along the intralayer direction. Although the atomic local ordering shows little effects on the properties of the Mg3(Sb1-xBix)2 alloy with only two alloying elements, it possesses potential important impacts on multiprincipal element inorganic TE alloys. This work provides a recipe for computational studies on the TE alloy systems and thus can accelerate the discovery and optimization of TE materials with high TE performance. read less S. Lyu, W. Li, Y. Xia, Y. Chen, and A. Ngan, “Effects of chemical randomness on strength contributors and dislocation behaviors in a bcc multiprincipal element alloy,” Physical Review Materials. 2023. link Times cited: 0 Y. Chen, X. Liao, R. Qiu, L. Liu, W. Hu, and H. Deng, “Primary radiation damage in tungsten-based high-entropy alloy: Interatomic potential and collision cascade simulations,” Journal of Nuclear Materials. 2023. link Times cited: 1 W. Chen, L. Li, Q. Zhu, and H. Zhuang, “Chemical short-range order in complex concentrated alloys,” MRS Bulletin. 2023. link Times cited: 1 Abstract: Complex concentrated alloys (CCAs) have drawn immense attent… read more Abstract: Complex concentrated alloys (CCAs) have drawn immense attention from the materials research community and beyond. Because the vast compositional and structural degrees of freedom in CCAs can lead to novel properties (e.g., structural and functional) with a wide range of applications, the structure–property relationships of CCAs are of critical interest. One salient feature in the atomic structures of CCAs is the presence of chemical short-range ordering (CSRO). Understanding the roles of CSRO on properties, especially phase stability, requires joint efforts from experimental and computational approaches. In this article, we first briefly survey the most recent experimental efforts in identifying and characterizing CSRO of various CCAs. We then focus on the theoretical and computational techniques that have been deployed to investigate the CSRO effects. These computational methods include density functional theory (DFT), molecular dynamics (MD), and statistical mechanics methods such as cluster expansions and machine learning methods such as creating transferable interatomic potentials. Finally, we outline the challenges and future directions of CSRO research in CCAs. read less Y.-F. Wu, W. Yu, and S. Shen, “Developing a variable charge potential for Hf/Nb/Ta/Ti/Zr/O system via machine learning global optimization,” Materials & Design. 2023. link Times cited: 1 R. Zhao et al., “Development of a Neuroevolution Machine Learning Potential of Pd-Cu-Ni-P Alloys,” SSRN Electronic Journal. 2023. link Times cited: 2 W. Yuxiang, K. Lingchao, C. Yongxiong, T. Yonggang, and L. Xiubing, “Femtosecond laser melting NbMoTaW refractory high entropy alloy: A micro-scale thermodynamic simulation,” Applied Surface Science. 2023. link Times cited: 3 S. Chen et al., “Short-range ordering alters the dislocation nucleation and propagation in refractory high-entropy alloys,” Materials Today. 2023. link Times cited: 6 A. Ferrari, F. Körmann, M. Asta, and J. Neugebauer, “Simulating short-range order in compositionally complex materials,” Nature Computational Science. 2023. link Times cited: 5 J. Mo, Y. Wan, Z. Zhang, B. Shen, and X. Liang, “The structure and mechanical properties of NbHfTaW refractory high-entropy alloy: A combined theoretical and experimental study,” International Journal of Refractory Metals and Hard Materials. 2023. link Times cited: 2 I. Lobzenko, Y. Shiihara, H. Mori, and T. Tsuru, “Influence of group IV element on basic mechanical properties of BCC medium-entropy alloys using machine-learning potentials,” Computational Materials Science. 2023. link Times cited: 1 Y.-J. Hu, “First-principles approaches and models for crystal defect energetics in metallic alloys,” Computational Materials Science. 2023. link Times cited: 4 S. Xu, W. Jian, and I. Beyerlein, “Ideal simple shear strengths of two HfNbTaTi-based quinary refractory multi-principal element alloys,” APL Materials. 2022. link Times cited: 4 Abstract: Atomistic simulations are employed to investigate chemical s… read more Abstract: Atomistic simulations are employed to investigate chemical short-range ordering in two body-centered cubic refractory multi-principal element alloys, HfMoNbTaTi and HfNbTaTiZr, and its influence on their ideal simple shear strengths. Both the alias and affine shear strengths are analyzed on the {110} and {112} planes in the two opposing [Formula: see text] directions. In both quinary alloys, local ordering of NbNb, TaTa, HfNb, HfTa, and NbTa is preferred as the annealing temperature decreases from 900 to 300 K. The pair that achieves the highest degree of local ordering is TiTi in HfMoNbTaTi and HfTi in HfNbTaTiZr. Subject to the affine shear, these alloys yield by first phase transformation at the most likely pairs followed by deformation twinning at those sites. read less S. He, X. Zhou, D. Mordehai, and J. Marian, “Thermal super-jogs control high-temperature strength plateau in Nb-Mo-Ta-W alloys,” Acta Materialia. 2022. link Times cited: 4 S. Rao, C. Woodward, and B. Akdim, “Solid solution softening and hardening in binary BCC alloys,” Acta Materialia. 2022. link Times cited: 8 M. L. H. Chandrappa, J. Qi, C. Chen, S. Banerjee, and S. Ong, “Thermodynamics and Kinetics of the Cathode–Electrolyte Interface in All-Solid-State Li–S Batteries,” Journal of the American Chemical Society. 2022. link Times cited: 9 Abstract: Lithium–sulfur batteries (LSBs) are among the most promising… read more Abstract: Lithium–sulfur batteries (LSBs) are among the most promising energy storage technologies due to the low cost and high abundance of S. However, the issue of polysulfide shuttling with its corresponding capacity fading is a major impediment to its commercialization. Replacing traditional liquid electrolytes with solid-state electrolytes (SEs) is a potential solution. Here, we present a comprehensive study of the thermodynamics and kinetics of the cathode–electrolyte interface in all-solid-state LSBs using density functional theory based calculations and a machine learning interatomic potential. We find that among the major solid electrolyte chemistries (oxides, sulfides, nitrides, and halides), sulfide SEs are generally predicted to be the most stable against the S8 cathode, while the other SE chemistries are predicted to be highly electrochemically unstable. If the use of other SE chemistries is desired for other reasons, several binary and ternary sulfides (e.g., LiAlS2, Sc2S3, Y2S3) are predicted to be excellent buffer layers. Finally, an accurate moment tensor potential to study the S8\|β-Li3PS4 interface was developed using an active learning approach. Molecular dynamics (MD) simulations of large interface models (>1000s atoms) revealed that the most stable Li3PS4(100) surface tends to form interfaces with S8 with 2D channels and lower activation barriers for Li diffusion. These results provide critical new insights into the cathode–electrolyte interface design for next-generation all-solid-state LSBs. read less J. F. Q. Rodrigues, V. Coluci, M. del Grosso, G. da Silva Padilha, W. R. Osório, and A. D. Bortolozo, “Modeling and characterization of MoNbTiW refractory multi-principal element alloy,” Journal of Alloys and Compounds. 2022. link Times cited: 1 M. Pozuelo and J. Marian, “Microscale Deformation Controlled by Compositional Fluctuations in Equiatomic Nb-Mo-Ta-W Alloys,” SSRN Electronic Journal. 2022. link Times cited: 5 X. Zhou, S. He, and J. Marian, “Vacancy Energetics and Diffusivities in the Equiatomic Multielement Nb-Mo-Ta-W Alloy,” Materials. 2022. link Times cited: 6 Abstract: In this work, we study vacancy energetics in the equiatomic … read more Abstract: In this work, we study vacancy energetics in the equiatomic Nb-Mo-Ta-W alloy, especially vacancy formation and migration energies, using molecular statics calculations based on a spectral neighbor analysis potential specifically developed for Nb-Mo-Ta-W. We consider vacancy properties in bulk environments as well as near edge dislocation cores, including the effect of short-range order (SRO) by preparing supercells through Metropolis Monte-Carlo relaxations and temperature on the calculation. The nudged elastic band (NEB) method is applied to study vacancy migration energies. Our results show that both vacancy formation energies and vacancy migration energies are statistically distributed with a wide spread, on the order of 1.0 eV in some cases, and display a noticeable dependence on SRO. We find that, in some cases, vacancies can form with very low energies at edge dislocation cores, from which we hypothesize the formation of stable ‘superjogs’ on edge dislocation lines. Moreover, the large spread in vacancy formation energies results in an asymmetric thermal sampling of the formation energy distribution towards lower values. This gives rise to effective vacancy formation energies that are noticeably lower than the distribution averages. We study the effect that this phenomenon has on the vacancy diffusivity in the alloy and discuss the implications of our findings on the structural features of Nb-Mo-Ta-W. read less X. Zhang et al., “Design of NbNiTaTi refractory high-entropy alloy via NiTi eutectic phase,” Journal of Alloys and Compounds. 2022. link Times cited: 5 D. Yang, B. Chen, S. Li, X. Ding, and J. Sun, “Effect of local lattice distortion on the core structure of edge dislocation in NbMoTaW multi-principal element alloys and the subsystems,” Materials Science and Engineering: A. 2022. link Times cited: 4 P. A. Santos-Flórez et al., “Short-range order and its impacts on the BCC MoNbTaW multi-principal element alloy by the machine-learning potential,” Acta Materialia. 2022. link Times cited: 1 B. Jiao et al., “New insights into the recrystallization behavior of large-size Mo-3Nb single crystal based on multi-scale characterization,” Journal of Materials Research and Technology. 2022. link Times cited: 1 X. Liu et al., “Atomistic understanding of incipient plasticity in BCC refractory high entropy alloys,” Journal of Alloys and Compounds. 2022. link Times cited: 16 Z. Fan, B. Xing, and P. Cao, “Predicting path-dependent diffusion barrier spectra in vast compositional space of multi-principal element alloys via convolutional neural networks,” Acta Materialia. 2022. link Times cited: 9 B. Xing, X. Wang, W. Bowman, and P. Cao, “Short-range order localizing diffusion in multi-principal element alloys,” Scripta Materialia. 2022. link Times cited: 25 F. Z. Dai, B. Wen, Y. Sun, Y. Ren, H. Xiang, and Y. Zhou, “Grain boundary segregation induced strong UHTCs at elevated temperatures: a universal mechanism from conventional UHTCs to high entropy UHTCs,” Journal of Materials Science & Technology. 2022. link Times cited: 12 S. Xu, J. Y. Cheng, Z. Li, N. Mara, and I. Beyerlein, “Phase-field modeling of the interactions between an edge dislocation and an array of obstacles,” Computer Methods in Applied Mechanics and Engineering. 2022. link Times cited: 10 S. Xu, S. Chavoshi, and Y. Su, “On calculations of basic structural parameters in multi-principal element alloys using small atomistic models,” Computational Materials Science. 2022. link Times cited: 9 T. Li, J. Miao, Y. Lu, T. Wang, and T. Li, “Effect of Zr on the as-cast microstructure and mechanical properties of lightweight Ti2VNbMoZrx refractory high-entropy alloys,” International Journal of Refractory Metals and Hard Materials. 2022. link Times cited: 25 J. Startt, A. Kustas, J. Pegues, P. Yang, and R. Dingreville, “Compositional effects on the mechanical and thermal properties of MoNbTaTi refractory complex concentrated alloys,” Materials & Design. 2022. link Times cited: 7 B. Zhang, J. Ding, and E. Ma, “Chemical short-range order in body-centered-cubic TiZrHfNb high-entropy alloys,” Applied Physics Letters. 2021. link Times cited: 14 R. Romero, S. Xu, W. Jian, I. Beyerlein, and C. Ramana, “Atomistic simulations of the local slip resistances in four refractory multi-principal element alloys,” International Journal of Plasticity. 2021. link Times cited: 23 D. E. Farache, J. C. Verduzco, Z. D. McClure, S. Desai, and A. Strachan, “Active learning and molecular dynamics simulations to find high melting temperature alloys,” Computational Materials Science. 2021. link Times cited: 9 N. K. Aragon, S. Yin, H. Lim, and I. Ryu, “Temperature dependent plasticity in BCC micropillars,” Materialia. 2021. link Times cited: 3 R. Eleti, N. Stepanov, N. Yurchenko, D. Klimenko, and S. Zherebtsov, “Plastic deformation of solid-solution strengthened Hf-Nb-Ta-Ti-Zr body-centered cubic medium/high-entropy alloys,” Scripta Materialia. 2021. link Times cited: 32 X. Wang, S. Xu, W. Jian, X.-G. Li, Y. Su, and I. Beyerlein, “Generalized stacking fault energies and Peierls stresses in refractory body-centered cubic metals from machine learning-based interatomic potentials,” Computational Materials Science. 2021. link Times cited: 30 M. Klimova, D. Shaysultanov, A. Semenyuk, S. Zherebtsov, G. Salishchev, and N. Stepanov, “Effect of nitrogen on mechanical properties of CoCrFeMnNi high entropy alloy at room and cryogenic temperatures,” Journal of Alloys and Compounds. 2020. link Times cited: 66 W. Jian, S. Xu, and I. Beyerlein, “On the significance of model design in atomistic calculations of the Peierls stress in Nb,” Computational Materials Science. 2020. link Times cited: 15 L. Smith, Y. Su, S. Xu, A. Hunter, and I. Beyerlein, “The effect of local chemical ordering on Frank-Read source activation in a refractory multi-principal element alloy,” International Journal of Plasticity. 2020. link Times cited: 43 A. Natarajan, P. Dolin, and A. V. der Ven, “Crystallography, thermodynamics and phase transitions in refractory binary alloys,” Acta Materialia. 2020. link Times cited: 26 S. Xu, A. A. Mamun, S. Mu, and Y. Su, “Uniaxial deformation of nanowires in 16 refractory multi-principal element alloys,” Journal of Alloys and Compounds. 2023. link Times cited: 1 F. Wang et al., “Atomic-scale simulations in multi-component alloys and compounds: A review on advances in interatomic potential,” Journal of Materials Science & Technology. 2023. link Times cited: 9 X. Liu et al., “A statistics-based study and machine-learning of stacking fault energies in HEAs,” Journal of Alloys and Compounds. 2023. link Times cited: 0 S. Xu, Y. Su, W. Jian, and I. Beyerlein, “Local slip resistances in equal-molar MoNbTi multi-principal element alloy,” Acta Materialia. 2021. link Times cited: 48 M. Hodapp, “Machine learning is funny but physics makes the money: How machine-learning potentials can advance computer-aided materials design in metallurgy,” Computational Materials Science. 2024. link Times cited: 0 M. L. Taheri et al., “Understanding and leveraging short-range order in compositionally complex alloys,” MRS Bulletin. 2023. link Times cited: 0 M. C. Barry, J. R. Gissinger, M. Chandross, K. Wise, S. Kalidindi, and S. Kumar, “Voxelized atomic structure framework for materials design and discovery,” Computational Materials Science. 2023. link Times cited: 0 S. Röcken and J. Zavadlav, “Accurate machine learning force fields via experimental and simulation data fusion,” ArXiv. 2023. link Times cited: 0 Abstract: Machine Learning (ML)-based force fields are attracting ever… read more Abstract: Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties remained largely unperturbed. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials. read less A. Anand, S.-J. Liu, and C. V. Singh, “Recent advances in computational design of structural multi-principal element alloys,” iScience. 2023. link Times cited: 1 Z. Ma and Z. Pan, “Efficient machine learning of solute segregation energy based on physics-informed features,” Scientific Reports. 2023. link Times cited: 0 V. Sotskov, E. Podryabinkin, and A. Shapeev, “A machine-learning potential-based generative algorithm for on-lattice crystal structure prediction,” Journal of Materials Research. 2023. link Times cited: 1 Abstract: We propose a method for crystal structure prediction based o… read more Abstract: We propose a method for crystal structure prediction based on a new structure generation algorithm and on-lattice machine learning interatomic potentials. Our algorithm generates the atomic configurations assigning atomic species to sites of the given lattice, and uses cluster expansion or low-rank potential to evaluate their energy. We demonstrate two benefits of such approach. First, our structure generation algorithm offers a ``smart'' configurational space sampling, targeting low-energy structures which significantly reduces computational costs. Second, the application of machine learning interatomic potentials significantly reduces the number of DFT calculations. We discuss how our algorithm resembles the latent diffusion models for image generation. We demonstrate the efficiency of our method by constructing the convex hull of Nb-Mo-Ta-W system, including binary and ternary Nb-W and Mo-Ta-W subsystems. We found new binary, ternary, and quaternary stable structures that are not reported in the AFLOW database which we choose as our baseline. Due to the computational efficiency of our method we anticipate that it can pave the way towards efficient high-throughput discovery of multicomponent materials. read less K. Elder, J. Berry, B. Bocklund, S. McCall, A. Perron, and J. McKeown, “Computational discovery of ultra-strong, stable, and lightweight refractory multi-principal element alloys. Part I: design principles and rapid down-selection,” npj Computational Materials. 2023. link Times cited: 0 W. Ji and M. Wu, “Retainable short-range order effects on the strength and toughness of NbMoTaW refractory high-entropy alloys,” Intermetallics. 2022. link Times cited: 2 X. Liu, J. Zhang, and Z. Pei, “Machine Learning for High-entropy Alloys: Progress, Challenges and Opportunities,” Progress in Materials Science. 2022. link Times cited: 41 J. Byggmästar, K. Nordlund, and F. Djurabekova, “Simple machine-learned interatomic potentials for complex alloys,” Physical Review Materials. 2022. link Times cited: 5 Abstract: Developing data-driven machine-learning interatomic potentia… read more Abstract: Developing data-driven machine-learning interatomic potentials for materials containing many elements becomes increasingly challenging due to the vast conﬁguration space that must be sampled by the training data. We study the learning rates and achievable accuracy of machine-learning interatomic potentials for many-element alloys with diﬀerent combinations of descriptors for the local atomic environments. We show that for a ﬁve-element alloy system, potentials using simple low-dimensional descriptors can reach meV/atom-accuracy with modestly sized training datasets, signiﬁcantly outperforming the high-dimensional SOAP descriptor in data eﬃciency, accuracy, and speed. In particular, we develop a computationally fast machine-learned and tabulated Gaussian approximation potential (tabGAP) for Mo–Nb–Ta–V–W alloys with a combination of two-body, three-body, and a new simple scalar many-body density descriptor based on the embedded atom method. read less A. Pandey, J. Gigax, and R. Pokharel, “Machine Learning Interatomic Potential for High-Throughput Screening of High-Entropy Alloys,” JOM. 2022. link Times cited: 1 E. Huang et al., “Machine-learning and high-throughput studies for high-entropy materials,” Materials Science and Engineering: R: Reports. 2022. link Times cited: 39 S. Zhao, “Application of machine learning in understanding the irradiation damage mechanism of high-entropy materials,” Journal of Nuclear Materials. 2021. link Times cited: 14 G. Hart, T. Mueller, C. Toher, and S. Curtarolo, “Machine learning for alloys,” Nature Reviews Materials. 2021. link Times cited: 169 H. Yanxon, D. Zagaceta, B. Tang, D. Matteson, and Q. Zhu, “PyXtal_FF: a python library for automated force field generation,” Machine Learning: Science and Technology. 2020. link Times cited: 15 Abstract: We present PyXtal_FF—a package based on Python programming l… read more Abstract: We present PyXtal_FF—a package based on Python programming language—for developing machine learning potentials (MLPs). The aim of PyXtal_FF is to promote the application of atomistic simulations through providing several choices of atom-centered descriptors and machine learning regressions in one platform. Based on the given choice of descriptors (including the atom-centered symmetry functions, embedded atom density, SO4 bispectrum, and smooth SO3 power spectrum), PyXtal_FF can train MLPs with either generalized linear regression or neural network models, by simultaneously minimizing the errors of energy/forces/stress tensors in comparison with the data from ab-initio simulations. The trained MLP model from PyXtal_FF is interfaced with the Atomic Simulation Environment (ASE) package, which allows different types of light-weight simulations such as geometry optimization, molecular dynamics simulation, and physical properties prediction. Finally, we will illustrate the performance of PyXtal_FF by applying it to investigate several material systems, including the bulk SiO2, high entropy alloy NbMoTaW, and elemental Pt for general purposes. Full documentation of PyXtal_FF is available at https://pyxtal-ff.readthedocs.io. read less H. Inui, K. Kishida, and Z. Chen, “Recent Progress in Our Understanding of Phase Stability, Atomic Structures and Mechanical and Functional Properties of High-Entropy Alloys,” MATERIALS TRANSACTIONS. 2022. link Times cited: 13 Abstract: This paper reviews a current trend and recent progress in re… read more Abstract: This paper reviews a current trend and recent progress in research on phase stability, atomic structures, mechanical and functional properties of high-entropy alloys. The survey is carried out based partly on the special issue published in April, 2020, in Materials Transactions (Vol. 61, No. 4). Research on high-entropy alloys has spread worldwide since the year of 2004, as many of them exhibit attractive properties for structural and functional applications, which have never been achieved in conventional alloys. Signi ﬁ cant progress has been made in recent years in our understanding of high-entropy alloys in terms of processing, characterization, modeling and simulation, and so on. Some of them are brie ﬂ y described in this paper. [doi:10.2320 read less M. Minotakis, H. Rossignol, M. Cobelli, and S. Sanvito, “Machine-learning surrogate model for accelerating the search of stable ternary alloys,” Physical Review Materials. 2023. link Times cited: 1 Abstract: The prediction of phase diagrams in the search for new phase… read more Abstract: The prediction of phase diagrams in the search for new phases is a complex and computationally intensive task. Density functional theory provides, in many situations, the desired accuracy, but its throughput becomes prohibitively limited as the number of species involved grows, even when used with local and semi-local functionals. Here, we explore the possibility of integrating machine-learning models in the workflow for the construction of ternary convex hull diagrams. In particular, we train a set of spectral neighbour-analysis potentials (SNAPs) over readily available binary phases and we establish whether this is good enough to predict the energies of novel ternaries. Such a strategy does not require any new calculations specific for the construction of the model, but just avails of data stored in binary-phase-diagram repositories. We find that a so-constructed SNAP is capable of accurate total-energy estimates for ternary phases close to the equilibrium geometry but, in general, is not able to perform atomic relaxation. This is because during a typical relaxation path a given phase traverses regions in the parameter space poorly represented by the training set. Different metrics are then investigated to assess how an unknown structure is well described by a given SNAP model, and we find that the standard deviation of an ensemble of SNAPs provides a fast and non-specie-specific metric. read less X.-G. Li, S. Xu, Q. Zhang, S. Liu, and J. Shuai, “Complex strengthening mechanisms in nanocrystalline Ni-Mo alloys revealed by a machine-learning interatomic potential,” Journal of Alloys and Compounds. 2023. link Times cited: 2 B. Waters, D. S. Karls, I. Nikiforov, R. Elliott, E. Tadmor, and B. Runnels, “Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework,” Computational Materials Science. 2022. link Times cited: 5 X. Wang, N.-D. Tran, S. Zeng, C. Hou, Y. Chen, and J. Ni, “Element-wise representations with ECNet for material property prediction and applications in high-entropy alloys,” npj Computational Materials. 2022. link Times cited: 2 C. D. Woodgate and J. Staunton, “Short-range order and compositional phase stability in refractory high-entropy alloys via first-principles theory and atomistic modeling: NbMoTa, NbMoTaW, and VNbMoTaW,” Physical Review Materials. 2022. link Times cited: 4 Abstract: Using an all-electron, first principles, Landau-type theory,… read more Abstract: Using an all-electron, first principles, Landau-type theory, we study the nature of short-range order and compositional phase stability in equiatomic refractory high entropy alloys, NbMoTa, NbMoTaW, and VNbMoTaW. We also investigate selected binary subsystems to provide insight into the physical mechanisms driving order. Our approach examines the short-range order of the solid solutions directly, infers disorder/order transitions, and also extracts parameters suitable for atomistic modelling of diffusional phase transformations. We find a hierarchy of relationships between the chemical species in these materials which promote ordering tendencies. The most dominant is a relative atomic size difference between the 3d element, V, and the other 4d and 5d elements which drives a B32-like order. For systems where V is not present, ordering is dominated by the difference in filling of valence states; pairs of elements which are isoelectronic remain weakly correlated to low temperatures, while pairs with a valence difference present B2-like order. Our estimated order-disorder transition temperature in VNbMoTaW is sufficiently high for us to suggest that SRO in this material may be experimentally observable. read less I. Novikov, O. Kovalyova, A. Shapeev, and M. Hodapp, “AI-accelerated materials informatics method for the discovery of ductile alloys,” Journal of Materials Research. 2022. link Times cited: 3 Abstract: In computational materials science, a common means for predi… read more Abstract: In computational materials science, a common means for predicting macroscopic (e.g., mechanical) properties of an alloy is to define a model using combinations of descriptors that depend on some material properties (elastic constants, misfit volumes, etc.), representative for the macroscopic behavior. The material properties are usually computed using special quasi-random structures, in tandem with density functional theory (DFT). However, DFT scales cubically with the number of atoms and is thus impractical for a screening over many alloy compositions. Here, we present a novel methodology which combines modeling approaches and machine-learning interatomic potentials. Machine-learning interatomic potentials are orders of magnitude faster than DFT, while achieving similar accuracy, allowing for a predictive and tractable high-throughput screening over the whole alloy space. The proposed methodology is illustrated by predicting the room temperature ductility of the medium-entropy alloy Mo–Nb–Ta. Graphical abstract read less R. Wang et al., “Classical and machine learning interatomic potentials for BCC vanadium,” Physical Review Materials. 2022. link Times cited: 3 Abstract: BCC transition metals (TMs) exhibit complex temperature and … read more Abstract: BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behaviour controlled by individual crystal lattice defects. Classical empirical and semi-empirical interatomic potentials have limited capability in modelling defect properties such as the screw dislocation core structures and Peierls barriers in the BCC structure. Machine learning (ML) potentials, trained on DFT-based datasets, have shown some successes in reproducing dislocation core properties. However, in group VB TMs, the most widely-used DFT functionals produce erroneous shear moduli C 44 which are undesirably transferred to machine-learning interatomic potentials, leaving current ML approaches unsuitable for this important class of metals and alloys. Here, we develop two interatomic potentials for BCC vanadium (V) based on (i) an extension of the partial electron density and screening parameter in the classical semi-empirical modiﬁed embedded-atom method (XMEAM-V) and (ii) a recent hybrid descriptor in the ML Deep Potential framework (DP-HYB-V). We describe distinct features in these two disparate approaches, including their dataset generation, training procedure, weakness and strength in modelling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties (vacancy, self-interstitials, surface, dislocation) relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with C 44 near experimental value. XMEAM-V also naturally exhibits the anomalous slip at 77 K widely observed in group VB and VIB TMs and outperforms all existing, publically available interatomic potentials for V. The XMEAM thus provides a practical path to developing accurate and efﬁcient interatomic potentials for nonmagnetic BCC TMs and possibly multi-principal element TM alloys. read less D. Aksoy et al., “Chemical order transitions within extended interfacial segregation zones in NbMoTaW,” Journal of Applied Physics. 2022. link Times cited: 2 Abstract: Interfacial segregation and chemical short-range ordering in… read more Abstract: Interfacial segregation and chemical short-range ordering influence the behavior of grain boundaries in complex concentrated alloys. In this study, we use atomistic modeling of a NbMoTaW refractory complex concentrated alloy to provide insight into the interplay between these two phenomena. Hybrid Monte Carlo and molecular dynamics simulations are performed on columnar grain models to identify equilibrium grain boundary structures. Our results reveal extended near-boundary segregation zones that are much larger than traditional segregation regions, which also exhibit chemical patterning that bridges the interfacial and grain interior regions. Furthermore, structural transitions pertaining to an A2-to-B2 transformation are observed within these extended segregation zones. Both grain size and temperature are found to significantly alter the widths of these regions. An analysis of chemical short-range order indicates that not all pairwise elemental interactions are affected by the presence of a grain boundary equally, as only a subset of elemental clustering types are more likely to reside near certain boundaries. The results emphasize the increased chemical complexity that is associated with near-boundary segregation zones and demonstrate the unique nature of interfacial segregation in complex concentrated alloys. read less C. Liu et al., “Medical high-entropy alloy: Outstanding mechanical properties and superb biological compatibility,” Frontiers in Bioengineering and Biotechnology. 2022. link Times cited: 5 Abstract: Medical metal implants are required to have excellent mechan… read more Abstract: Medical metal implants are required to have excellent mechanical properties and high biocompatibility to handle the complex human environment, which is a challenge that has always existed for traditional medical metal materials. Compared to traditional medical alloys, high entropy alloys (HEAs) have a higher design freedom to allow them to carry more medical abilities to suit the human service environment, such as low elastic modulus, high biocompatible elements, potential shape memory capability. In recent years, many studies have pointed out that bio-HEAs, as an emerging medical alloy, has reached or even surpassed traditional medical alloys in various medical properties. In this review, we summarized the recent reports on novel bio-HEAs for medical implants and divide them into two groups according the properties, namely mechanical properties and biocompatibility. These new bio-HEAs are considered hallmarks of a historic shift representative of a new medical revolution. read less D. Marchand and W. Curtin, “Machine learning for metallurgy IV: A neural network potential for Al-Cu-Mg and Al-Cu-Mg-Zn,” Physical Review Materials. 2022. link Times cited: 7 X. Zhou and J. Marian, “Temperature and Stress Dependence of Screw Dislocation Mobility in Nb-V-Ta Alloys Using Kinetic Monte Carlo Simulations,” Frontiers in Materials. 2021. link Times cited: 4 Abstract: In this work we present simulations of thermally-activated s… read more Abstract: In this work we present simulations of thermally-activated screw dislocation motion in Nb-Ta-V alloys for two distinct scenarios, one where kink propagation is solely driven by chemical energy changes, i.e., thermodynamic energy differences, and another one where a migration barrier of 1.0 eV is added to such changes. The simulations have been performed using a kinetic Monte Carlo model for screw dislocation kinetics modified for complex lattice-level chemical environments. At low stresses, we find that dislocation motion in the case with no barrier is controlled by long waiting times due to slow nucleation rates and extremely fast kink propagation. Conversely, at high stress, the distribution of sampled time steps for both kink-pair nucleation and kink propagation events are comparable, resulting in continuous motion and faster velocities. In the case of the 1.0-eV kink propagation energy barrier, at low stresses kink motion becomes the rate-limiting step, leading to slow dynamics and large kink lateral pileups, while at high stresses both kink pair nucleation and kink propagation coexist on similar time scales. In the end, dislocation velocities differ by more than four orders of magnitude between both scenarios, emphasizing the need to have accurate calculations of kink energy barriers in the complex chemical environments inherent to these alloys. read less H. Zhuang, “Sudoku-Inspired High-Shannon-Entropy Alloys,” Acta Materialia. 2021. link Times cited: 5 S. Yin et al., “Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order,” Nature Communications. 2021. link Times cited: 121 J. Byggmästar, K. Nordlund, and F. Djurabekova, “Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: Defects and segregation,” Physical Review B. 2021. link Times cited: 32 Abstract: We develop a fast and accurate machine-learned interatomic p… read more Abstract: We develop a fast and accurate machine-learned interatomic potential for the Mo–Nb–Ta–V–W quinary system and use it to study segregation and radiation damage in the body-centred cubic refractory high-entropy alloy MoNbTaVW. In the bulk alloy, we observe clear ordering of mainly Mo–Ta and V–W binaries at low temperatures. In damaged crystals, our simulations reveal clear segregation of vanadium, the smallest atom in the alloy, to compressed interstitial-rich regions like radiation-induced dislocation loops. Vanadium also dominates the population of single selfinterstitial atoms. In contrast, due to its larger size and low surface energy, niobium segregates to spacious regions like the inner surfaces of voids. When annealing samples with supersaturated concentrations of defects, we find that in complete contrast to W, interstitial atoms in MoNbTaVW cluster to create only small (∼ 1 nm) experimentally invisible dislocation loops enriched by vanadium. By comparison to W, we explain this by the reduced but three-dimensional migration of interstitials, the immobility of dislocation loops, and the increased mobility of vacancies in the high-entropy alloy, which together promote defect recombination over clustering. read less G. Nikoulis, J. Byggmästar, J. Kioseoglou, K. Nordlund, and F. Djurabekova, “Machine-learning interatomic potential for W–Mo alloys,” Journal of Physics: Condensed Matter. 2021. link Times cited: 9 Abstract: In this work, we develop a machine-learning interatomic pote… read more Abstract: In this work, we develop a machine-learning interatomic potential for W x Mo1−x random alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Vienna ab initio simulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of W x Mo1−x compositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler–Biersack–Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom. read less Z. Leong, U. Ramamurty, and T. L. Tan, “Microstructural and compositional design principles for Mo-V-Nb-Ti-Zr multi-principal element alloys: a high-throughput first-principles study,” Acta Materialia. 2021. link Times cited: 13 N. Birbilis, S. Choudhary, J. Scully, and M. Taheri, “A perspective on corrosion of multi-principal element alloys,” npj Materials Degradation. 2021. link Times cited: 49 J. Qi et al., “Bridging the gap between simulated and experimental ionic conductivities in lithium superionic conductors,” Materials Today Physics. 2021. link Times cited: 33 S. Nikolov et al., “Data-driven magneto-elastic predictions with scalable classical spin-lattice dynamics,” npj Computational Materials. 2021. link Times cited: 25 X. Liu, J. Zhang, J. Yin, S. Bi, M. Eisenbach, and Y. Wang, “Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: A data-driven approach,” Computational Materials Science. 2020. link Times cited: 35 Y.-J. Hu, A. Sundar, S. Ogata, and L. Qi, “Screening of generalized stacking fault energies, surface energies and intrinsic ductile potency of refractory multicomponent alloys,” Acta Materialia. 2020. link Times cited: 41
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_560387080449_000
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	SNAP_LiChenZheng_2019_NbTaWMo__MO_560387080449_000
DOI	10.25950/c34c3362 https://doi.org/10.25950/c34c3362 https://commons.datacite.org/doi.org/10.25950/c34c3362
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver SNAP__MD_536750310735_000
Driver	SNAP__MD_536750310735_000
KIM API Version	2.0
Potential Type	snap

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 7.49106e-10 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
P The model is C^1 continuous. This means that the model has continuous energy and continuous first derivative.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
P No memory leak detected.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
N/A Unable to perform verification check due to an error.	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: W

Species: Ta

Species: Mo

Species: Nb

Cohesive Energy Graph

This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.

Species: Ta

Species: Mo

Species: W

Species: Nb

Diamond Lattice Constant

This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Nb

Species: Mo

Species: W

Species: Ta

Dislocation Core Energies

This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.

(No matching species)

FCC Elastic Constants

This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Nb

Species: Ta

Species: W

Species: Mo

FCC Lattice Constant

This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: W

Species: Mo

Species: Ta

Species: Nb

FCC Stacking Fault Energies

This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

(No matching species)

FCC Surface Energies

This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

(No matching species)

SC Lattice Constant

This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Ta

Species: Nb

Species: W

Species: Mo

Cubic Crystal Basic Properties Table

Species: Mo

Species: Nb

Species: Ta

Species: W

Tests

Disclaimer From Model Developer

This potential is designed for Nb-Mo-Ta-W chemistries, including the elementary, binary, ternary and quaternary systems. The potential was trained using LAMMPS version 17Nov2016. Newer LAMMPS may see energy differences, but the relative values should remain to be the same.

CohesiveEnergyVsLatticeConstant__TD_554653289799_003

Cohesive energy versus lattice constant curve for monoatomic cubic lattices v003

Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5

This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Cohesive energy versus lattice constant curve for bcc Mo v004	view	3653
Cohesive energy versus lattice constant curve for bcc Nb v004	view	2904
Cohesive energy versus lattice constant curve for bcc Ta v004	view	2994
Cohesive energy versus lattice constant curve for bcc W v004	view	3004
Cohesive energy versus lattice constant curve for diamond Mo v004	view	4212
Cohesive energy versus lattice constant curve for diamond Nb v004	view	3387
Cohesive energy versus lattice constant curve for diamond Ta v004	view	3313
Cohesive energy versus lattice constant curve for diamond W v004	view	3313
Cohesive energy versus lattice constant curve for fcc Mo v004	view	3093
Cohesive energy versus lattice constant curve for fcc Nb v004	view	3083
Cohesive energy versus lattice constant curve for fcc Ta v004	view	2974
Cohesive energy versus lattice constant curve for fcc W v004	view	3123
Cohesive energy versus lattice constant curve for sc Mo v004	view	2964
Cohesive energy versus lattice constant curve for sc Nb v004	view	3018
Cohesive energy versus lattice constant curve for sc Ta v004	view	3092
Cohesive energy versus lattice constant curve for sc W v004	view	2805

ElasticConstantsCubic__TD_011862047401_006

Elastic constants for cubic crystals at zero temperature and pressure v006

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f

Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for bcc Mo at zero temperature v006	view	13660
Elastic constants for bcc Nb at zero temperature v006	view	3164
Elastic constants for bcc Ta at zero temperature v006	view	11529
Elastic constants for bcc W at zero temperature v006	view	7739
Elastic constants for diamond W at zero temperature v001	view	27320
Elastic constants for fcc Mo at zero temperature v006	view	8992
Elastic constants for fcc Nb at zero temperature v006	view	4198
Elastic constants for fcc Ta at zero temperature v006	view	3415
Elastic constants for fcc W at zero temperature v006	view	3948
Elastic constants for sc Mo at zero temperature v006	view	2851
Elastic constants for sc Nb at zero temperature v006	view	2538
Elastic constants for sc Ta at zero temperature v006	view	2569
Elastic constants for sc W at zero temperature v006	view	3133

EquilibriumCrystalStructure__TD_457028483760_003

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v003

Creators:
Contributor: ilia
Publication Year: 2025
DOI: https://doi.org/10.25950/866c7cfa

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium crystal structure and energy for Mo in AFLOW crystal prototype A_cF4_225_a v003	view	200015
Equilibrium crystal structure and energy for Nb in AFLOW crystal prototype A_cF4_225_a v003	view	185282
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_cF4_225_a v003	view	173591
Equilibrium crystal structure and energy for W in AFLOW crystal prototype A_cF4_225_a v003	view	184882
Equilibrium crystal structure and energy for Mo in AFLOW crystal prototype A_cI2_229_a v003	view	167587
Equilibrium crystal structure and energy for Nb in AFLOW crystal prototype A_cI2_229_a v003	view	169989
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_cI2_229_a v003	view	162958
Equilibrium crystal structure and energy for W in AFLOW crystal prototype A_cI2_229_a v003	view	192809
Equilibrium crystal structure and energy for W in AFLOW crystal prototype A_cP8_223_ac v003	view	195100
Equilibrium crystal structure and energy for Mo in AFLOW crystal prototype A_hP1_191_a v003	view	153784
Equilibrium crystal structure and energy for Mo in AFLOW crystal prototype A_hP4_194_ac v003	view	165814
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_tP22_136_af2i v003	view	355507
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_tP30_136_af2ij v003	view	508125
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_tP4_127_g v003	view	199935

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_002

Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v002

Creators: Brandon Runnels
Contributor: brunnels
Publication Year: 2019
DOI: https://doi.org/10.25950/4723cee7

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Mo v000		view	288223656
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Mo v000		view	561591535

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v003

Creators:
Contributor: brunnels
Publication Year: 2022
DOI: https://doi.org/10.25950/2c59c9d6

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in bcc Mo v001		view	311243079
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Mo v001		view	525966027

LatticeConstantCubicEnergy__TD_475411767977_007

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium zero-temperature lattice constant for bcc Mo v007	view	2130
Equilibrium zero-temperature lattice constant for bcc Nb v007	view	1942
Equilibrium zero-temperature lattice constant for bcc Ta v007	view	2130
Equilibrium zero-temperature lattice constant for bcc W v007	view	1880
Equilibrium zero-temperature lattice constant for diamond Mo v007	view	2632
Equilibrium zero-temperature lattice constant for diamond Nb v007	view	2569
Equilibrium zero-temperature lattice constant for diamond Ta v007	view	2193
Equilibrium zero-temperature lattice constant for diamond W v007	view	2381
Equilibrium zero-temperature lattice constant for fcc Mo v007	view	2036
Equilibrium zero-temperature lattice constant for fcc Nb v007	view	2162
Equilibrium zero-temperature lattice constant for fcc Ta v007	view	1786
Equilibrium zero-temperature lattice constant for fcc W v007	view	2193
Equilibrium zero-temperature lattice constant for sc Mo v007	view	2318
Equilibrium zero-temperature lattice constant for sc Nb v007	view	1880
Equilibrium zero-temperature lattice constant for sc Ta v007	view	2193
Equilibrium zero-temperature lattice constant for sc W v007	view	1629

LatticeConstantHexagonalEnergy__TD_942334626465_005

Equilibrium lattice constants for hexagonal bulk structures at zero temperature and pressure v005

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32

Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium lattice constants for hcp Mo v005	view	32677
Equilibrium lattice constants for hcp Nb v005	view	36061
Equilibrium lattice constants for hcp Ta v005	view	30453
Equilibrium lattice constants for hcp W v005	view	32427

LinearThermalExpansionCoeffCubic__TD_522633393614_002

Linear thermal expansion coefficient of cubic crystal structures v002

Creators:
Contributor: mjwen
Publication Year: 2024
DOI: https://doi.org/10.25950/9d9822ec

This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for a cubic lattice (fcc, bcc, sc, diamond) of a single given species.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Linear thermal expansion coefficient of bcc Mo at 293.15 K under a pressure of 0 MPa v002	view	12900928
Linear thermal expansion coefficient of bcc Ta at 293.15 K under a pressure of 0 MPa v002	view	9863748
Linear thermal expansion coefficient of bcc W at 293.15 K under a pressure of 0 MPa v002	view	8366105

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

High-symmetry surface energies in cubic lattices and broken bond model v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6

Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by:

E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c

E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.

In Python, these two fits take the following form:

def BrokenBondFCC(params, index):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]

def BrokenBondBCC(params, x, y, z):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Broken-bond fit of high-symmetry surface energies in bcc Mo v004	view	157245
Broken-bond fit of high-symmetry surface energies in bcc Nb v004	view	224855
Broken-bond fit of high-symmetry surface energies in bcc Ta v004	view	142301
Broken-bond fit of high-symmetry surface energies in bcc W v004	view	129174

VacancyFormationMigration__TD_554849987965_001

Vacancy formation and migration energies for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd

Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Vacancy formation and migration energy for bcc Mo	view	2573036
Vacancy formation and migration energy for bcc Nb	view	7168502
Vacancy formation and migration energy for bcc W	view	2220247

Errors

DislocationCoreEnergyCubic__TD_452950666597_002

Test	Error Categories	Link to Error page
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [0, 0, 1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 0] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 2] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 3] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 4] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 5] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 6] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 7] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, -1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, -2] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, 1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, 3] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, -1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, -3] v000	other	view

ElasticConstantsCubic__TD_011862047401_006

Test	Error Categories	Link to Error page
Elastic constants for diamond Mo at zero temperature v001	other	view
Elastic constants for diamond Nb at zero temperature v001	other	view
Elastic constants for diamond Ta at zero temperature v001	other	view

ElasticConstantsHexagonal__TD_612503193866_004

Test	Error Categories	Link to Error page
Elastic constants for hcp Mo at zero temperature v004	other	view
Elastic constants for hcp Nb at zero temperature v004	other	view
Elastic constants for hcp Ta at zero temperature v004	other	view
Elastic constants for hcp W at zero temperature v004	other	view

EquilibriumCrystalStructure__TD_457028483760_003

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_tP22_81_g5h v003	other	view
Equilibrium crystal structure and energy for Ta in AFLOW crystal prototype A_tP30_113_c3e2f v003	other	view

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Test	Error Categories	Link to Error page
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Mo v001	other	view
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Mo v001	other	view

VacancyFormationEnergyRelaxationVolume__TD_647413317626_001

Test	Error Categories	Link to Error page
Monovacancy formation energy and relaxation volume for bcc Mo	other	view
Monovacancy formation energy and relaxation volume for bcc Nb	other	view
Monovacancy formation energy and relaxation volume for bcc W	other	view

No Driver

Verification Check	Error Categories	Link to Error page
MemoryLeak__VC_561022993723_004	other	view

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CMakeLists.txt
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NbMoTaW_Li_Arxiv2019.snapcoeff
NbMoTaW_Li_Arxiv2019.snapparam
kimprovenance.edn
kimspec.edn

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SNAP_LiChenZheng_2019_NbTaWMo__MO_560387080449_000

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BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

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