EAM potential (LAMMPS cubic hermite tabulation) for Nb developed by Fellinger, Park and Wilkins (2010) v005

Michael Fellinger; Hyoungki Park; John W. Wilkins

doi:10.25950/befb2eea

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EAM_Dynamo_FellingerParkWilkins_2010_Nb__MO_102133002179_005

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Interatomic potential for Niobium (Nb).
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Title A single sentence description.	EAM potential (LAMMPS cubic hermite tabulation) for Nb developed by Fellinger, Park and Wilkins (2010) v005
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.	An embedded-atom method potential for Nb developed by Fellinger, Park and Wilkins (2010). The potential was constructed from density-functional theory calculations of forces, energies, and stresses using a force-matching algorithm for Nb structures for a wide range of strains and temperatures.
Species The supported atomic species.	Nb
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	http://www.ctcms.nist.gov/potentials/Nb.html

Contributor	Michael Fellinger
Maintainer	Michael Fellinger
Developer	Michael Fellinger Hyoungki Park John W. Wilkins
Published on KIM	2018
How to Cite	Click here to download this 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. 107 Citations (59 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 . J. J. Moller et al., “110 planar faults in strained bcc metals: Origins and implications of a commonly observed artifact of classical potentials,” Physical Review Materials. 2018. link Times cited: 18 Abstract: Large-scale atomistic simulations with classical potentials … read more Abstract: Large-scale atomistic simulations with classical potentials can provide valuable insights into microscopic deformation mechanisms and defect-defect interactions in materials. Unfortunately, these assets often come with the uncertainty of whether the observed mechanisms are based on realistic physical phenomena or whether they are artifacts of the employed material models. One such example is the often reported occurrence of stable planar faults (PFs) in body-centered cubic (bcc) metals subjected to high strains, e.g., at crack tips or in strained nano-objects. In this paper, we study the strain dependence of the generalized stacking fault energy (GSFE) of {110} planes in various bcc metals with material models of increasing sophistication, i.e., (modified) embedded atom method, angular-dependent, Tersoff, and bond-order potentials as well as density functional theory. We show that under applied tensile strains the GSFE curves of many classical potentials exhibit a local minimum which gives rise to the formation of stable PFs. These PFs do not appear when more sophisticated material models are used and have thus to be regarded as artifacts of the potentials. We demonstrate that the local GSFE minimum is not formed for reasons of symmetry and we recommend including the determination of the strain-dependent (110) GSFE as a benchmark for newly developed potentials. read less J. Bian, L. Yang, X. Niu, and G. Wang, “Orientation-dependent deformation mechanisms of bcc niobium nanoparticles,” Philosophical Magazine. 2017. link Times cited: 12 Abstract: Nanoparticles usually exhibit pronounced anisotropic propert… read more Abstract: Nanoparticles usually exhibit pronounced anisotropic properties, and a close insight into the atomic-scale deformation mechanisms is of great interest. In present study, atomic simulations are conducted to analyse the compression of bcc nanoparticles, and orientation-dependent features are addressed. It is revealed that surface morphology under indenter predominantly governs the initial elastic response. The loading curve follows the flat punch contact model in [1 1 0] compression, while it obeys the Hertzian contact model in [1 1 1] and [0 0 1] compressions. In plastic deformation regime, full dislocation gliding is dominated in [1 1 0] compression, while deformation twinning is prominent in [1 1 1] compression, and these two mechanisms coexist in [0 0 1] compression. Such deformation mechanisms are distinct from those in bulk crystals under nanoindentation and nanopillars under compression, and the major differences are also illuminated. Our results provide an atomic perspective on the mechanical behaviours of bcc nanoparticles and are helpful for the design of nanoparticle-based components and systems. read less X.-G. Li, C. Chen, H. Zheng, Y. Zuo, and S. Ong, “Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy,” npj Computational Materials. 2019. link Times cited: 114 X. Chen, R. Huang, T.-M. Shih, and Y. Wen, “Shape Stability of Metallic Nanoplates: A Molecular Dynamics Study,” Nanoscale Research Letters. 2019. link Times cited: 3 K. Kowalczyk-Gajewska and M. Maździarz, “Effective stiffness tensor of nanocrystalline materials of cubic symmetry: The core-shell model and atomistic estimates,” International Journal of Engineering Science. 2019. link Times cited: 5 H. Sun, Z. Jian, B. Jiang, J. Xu, and T. Zhang, “Relation between superheated temperature and cooling rate for deep supercooled niobium melt,” RSC Advances. 2019. link Times cited: 1 Abstract: Research into the conditions for forming uniform melt-free c… read more Abstract: Research into the conditions for forming uniform melt-free crystal sites and the effect of the melt state on solidification behaviors is theoretically significant and has valuable applications. However, there are no quantitative data on these aspects due to rigorous experimental requirements. In this study, the variation of the melt structure at different superheating temperatures and the cooling rate during the deep solidification of cold niobium melt was investigated by a large-scale molecular dynamics simulation method. The solid/liquid coexistence method, the radial distribution function, an energy–temperature analysis, the average energy, an atomic cluster analysis, and a visualization analysis were adopted to analyze the variations in microstructure transitions. The temperature vs. undercooling plots of Nb melt at different superheating temperatures suggested that the metal melt structure should be classified into three regions (regions 1 and 2, each with different melt structures that vary with temperature, and region 3, whose melt structure does not change with temperature); the critical cooling rate of the crystal–amorphous transition was 1.0 × 1012.5 K s−1 and the solidification undercooling increased with increasing superheating temperature until maximal undercooling was obtained. Simultaneously, it was found that the maximal undercooling occurred at ∼0.432Tm (Tm is the melting point) and the maximal superheating occurred at ∼1.216Tm. read less S. Waheed et al., “Temperature-dependent plastic hysteresis in highly confined polycrystalline Nb films,” Modelling and Simulation in Materials Science and Engineering. 2018. link Times cited: 1 Abstract: In this study, the effect of temperature on the cyclic defor… read more Abstract: In this study, the effect of temperature on the cyclic deformation behaviour of a confined polycrystalline Nb film is investigated. Micropillars encapsulating a thin niobium interlayer are deformed under cyclic axial compression at different test temperatures. A distinct plastic hysteresis is observed for samples tested at elevated temperatures, whereas negligible plastic hysteresis is observed for samples tested at room temperature. These results are interpreted using planar discrete dislocation plasticity incorporating slip transmission across grain boundaries. The effect of temperature-dependent grain boundary energy and dislocation mobility on dislocation penetration and, consequently, the size of plastic hysteresis is simulated to correlate with the experimental results. It is found that the decrease in grain boundary energy barrier caused by the increase in temperature does not lead to any appreciable change in the cyclic response. However, dislocation mobility significantly affects the size of plastic hysteresis, with high mobilities leading to a larger hysteresis. Therefore, it is postulated that the experimental observations are predominantly caused by an increase in dislocation mobility as the temperature is increased above the critical temperature of body-centred cubic niobium. read less Z. Shi and C. V. Singh, “Competing twinning mechanisms in body-centered cubic metallic nanowires,” Scripta Materialia. 2016. link Times cited: 39 H. Lim, L. Hale, J. Zimmerman, C. Battaile, and C. Weinberger, “A multi-scale model of dislocation plasticity in α-Fe: Incorporating temperature, strain rate and non-Schmid effects,” International Journal of Plasticity. 2015. link Times cited: 64 D. Tafen and M. Gao, “Oxygen Atom Adsorption on and Diffusion into Nb(110) and Nb(100) from First Principles,” JOM. 2013. link Times cited: 9 D. Lin, S. S. Wang, D. Peng, M. Li, and X. D. Hui, “An n-body potential for a Zr–Nb system based on the embedded-atom method,” Journal of Physics: Condensed Matter. 2013. link Times cited: 49 Abstract: A novel n-body potential for an Zr–Nb system was developed i… read more Abstract: A novel n-body potential for an Zr–Nb system was developed in the framework of the embedded-atom method. All the parameters of the constructed potential have been systematically evaluated by fitting to the ground state properties obtained from experimental measurements and first-principles calculations for pure elements and some alloys. It is shown that most of the static thermodynamics properties for Zr and Nb can be well reproduced by using the present potential. Some calculation results based on the present model are even closer to the experimental data than those based on previous potential models. The ground state properties of hypothetical Zr–Nb alloys were also calculated and found to be in agreement with first-principles calculations. Furthermore, the formation energies of random solid solutions of Zr–Nb with lattices of body centered cubic (bcc) and hexagonal close packed (hcp) type were calculated by fitting the energy–volume relations to Rose’s equation of state. These values were compared with those obtained by first-principles calculations based on special quasirandom structure models and the Miedema-ZSL-07 model (the improved Miedema model proposed by Zhang, Sheng and Liu in 2007). It is indicated that our n-body constructed potential for a Zr–Nb alloy provides an effective description for the interaction between the dissimilar ion interactions for hcp–bcc systems. read less H. Park et al., “Ab initio based empirical potential used to study the mechanical properties of molybdenum,” Physical Review B. 2012. link Times cited: 70 Abstract: Density-functional theory energies, forces, and elastic cons… read more Abstract: Density-functional theory energies, forces, and elastic constants determine the parametrization of an empirical, modified embedded-atom method potential for molybdenum. The accuracy and transferability of the potential are verified by comparison to experimental and density-functional data for point defects, phonons, thermal expansion, surface and stacking fault energies, and ideal shear strength. Searching the energy landscape predicted by the potential using a genetic algorithm verifies that it reproduces not only the correct bcc ground state of molybdenum but also all low-energy metastable phases. The potential is also applicable to the study of plastic deformation and used to compute energies, core structures, and Peierls stresses of screw and edge dislocations. Molybdenum's high strength and high-temperature stability make this refractory metal very attractive for use in advanced process technologies. The motion of dislocations is generally accepted to be responsible for the complex deformation behavior of this transition metal. 1-8 In recent years progress has been made on the description of the properties of screw dislocations using density-functional theory (DFT), tight- binding calculations, and empirical potentials. 9-19 However, DFT and tight-binding techniques are limited to small system sizes, which is problematic due to the long-range strain field of dislocations, and current empirical potentials lack the required accuracy for the description of the dislocation structure. Simulations of dislocation motion and interactions require efficient interatomic potentials which accurately describe the dislocation energies, core structures, and motion. In this work we develop an empirical potential for Mo which predicts the ideal shear strength, generalized stacking fault en- ergies, energies of dislocations, and the Peierls stress and core structure of the � 111� /2 screw dislocation. The potential form is given by the modified embedded-atom method (MEAM) and the potential parameters are optimized usingabinitio energies, lattice parameters, forces, and elastic constants. Section II describes the calculations for the DFT database, the functional form of the MEAM potential, and the optimization of the potential parameters to the DFT database. The accuracy of the potential for structural, elastic, and defect properties is verified in Sec. III by comparison to DFT results and experiments. A genetic algorithm search of the energy landscape of the MEAM potential confirms that the potential reproduces the correct bcc ground state and predicts several low-energy metastable structures whose energies agree well with DFT results. Results of the MEAM potential for formation energies of point defects, phonon dispersion, thermal expansion, surface energies, ideal shear strength, and generalized stacking faults for the MEAM potential closely match DFT results and available experimental data. In Sec. IV we apply the potential to determine energies and Peierls stresses of the screw and edge dislocation in bcc Mo. The results show that the MEAM potential accurately describes the structural and mechanical properties of Mo and should be applicable to simulate the motion of dislocations and the plastic deformation of Mo. read less L. Wu, Y. Zhu, H. Wang, and M. Li, “Crystal–melt coexistence in fcc and bcc metals: a molecular-dynamics study of kinetic coefficients,” Modelling and Simulation in Materials Science and Engineering. 2021. link Times cited: 5 Abstract: As a sequel to the previous paper on the calculation of the … read more Abstract: As a sequel to the previous paper on the calculation of the crystal–melt interface free energy (2021 Materialia 15 100962), here we report the results on the kinetic coefficients using molecular dynamics simulations performed on six fcc metals and four bcc metals with the intention to compare the crystal structural influence. We found that the calculated kinetic coefficients are well described by the model by Broughton, Gilmer and Jackson (1982 Phys. Rev. Lett. 49 1496), and in particular, they exhibit varying degrees of anisotropy. We reveal that the anisotropies are related to the fluctuation of the crystal–melt interfaces, which causes the increase of the actual interface area in melting or solidification. The kinetic coefficients always display asymmetry between the solidification and melting process, and the difference is much more pronounced for the (111) interfaces in fcc metals which have the highest anisotropy. We found that the atomic mechanisms of the kinetic behaviors of these interfaces are closely related to the formation of twin-crystal domains during solidification, which delays the solidification process and consequently causes a decrease in the calculated kinetic coefficients. read less H. Duan, Y. Yang, Y. Ma, and P. He, “The growth progress of Nb films on Cu: a molecular dynamics simulation,” Radiation Detection Technology and Methods. 2023. link Times cited: 0 V. Jain, K. Das, A. Chaudhuri, M. Manna, S. Pal, and M. Ghosh, “Modelling of thermal behaviour in Niobium during Electron Beam Welding,” Materials Today Communications. 2023. link Times cited: 0 S. Kazanç and C. Canbay, “Investigation of microstructural development of liquid Nb in dependence of cooling rate: Molecular dynamics simulation study,” Vacuum. 2023. link Times cited: 1 M. N. Magomedov, “Study of the melting temperature baric dependence for Au, Pt, Nb,” Vacuum. 2023. link Times cited: 0 A. Rajput and S. Paul, “Influence of hard inclusion on Bauschinger effect and cyclic deformation behaviour: An atomistic simulation on single-crystal and polycrystal aluminium,” Materials Today Communications. 2022. link Times cited: 1 V. Popov, M. E. Stupak, and M. G. Urazaliev, “Atomistic Simulation of Grain Boundaries in Niobium: Structure, Energy, Point Defects and Grain-Boundary Self-Diffusion,” Journal of Phase Equilibria and Diffusion. 2022. link Times cited: 4 Z. Qi et al., “Coupling Between Ductile Damage Evolution and Phase Transition in Single Crystal Niobium Subjected to High Strain Rate Loading,” Journal of Materials Engineering and Performance. 2022. link Times cited: 0 P. Li et al., “Crystallographic-orientation-dependence plasticity of niobium under shock compressions,” International Journal of Plasticity. 2022. link Times cited: 8 W. Lu et al., “Atomistic Simulation Study of the FCC and BCC Crystal-Melt Interface Stresses,” Surfaces and Interfaces. 2021. link Times cited: 4 N. Zotov and B. Grabowski, “Molecular dynamics simulations of screw dislocation mobility in bcc Nb,” Modelling and Simulation in Materials Science and Engineering. 2021. link Times cited: 8 Abstract: The screw dislocation mobility in bcc Nb has been studied by… read more Abstract: The screw dislocation mobility in bcc Nb has been studied by molecular dynamics (MD) simulations at different strain rates and temperatures using an embedded-atom method (EAM) potential. Static properties of the screw dislocation, as determined with the EAM potential, are in agreement with previous density-functional-theory calculations. The elementary slip plane of the screw dislocation remains (110) for all studied strain rates (in the range 6.3 × 107–6.3 × 109 s−1) and temperatures (5 to 550 K). However, the consecutive cross-slip on different symmetry-equivalent (110) planes leads to an effective glide on (112) planes. It is demonstrated that the screw dislocation trajectories, velocities and waviness of the screw dislocation depend on the crystallographic indices, (110) or (112), of the maximum resolved shear stress plane. The waiting time for the start of the screw dislocation motion increases exponentially with decreasing strain rate, substantiating the necessity to apply in future accelerated MD techniques in order to compare with macroscopic stress-strain experiments. read less Z. Wu, R. Wang, L. Zhu, S. Pattamatta, and D. Srolov, “Revealing and Controlling the Core of Screw Dislocations in BCC Metals.” 2021. link Times cited: 0 Abstract: Body-centred-cubic (BCC) transition metals (TMs) tend to b… read more Abstract: Body-centred-cubic (BCC) transition metals (TMs) tend to be brittle at low temperatures, posing significant challenges in their processing and major concerns for damage tolerance in critical load-carrying applications. The brittleness is largely dictated by the screw dislocation core structure; the nature and control of which has remained a puzzle for nearly a century. Here, we introduce a universal model and a physics-based material index χ that guides the manipulation of dislocation core structure in all pure BCC metals and alloys. We show that the core structure, commonly classified as degenerate (D) or non-degenerate (ND), is governed by the energy difference between BCC and face-centred cubic (FCC) structures and χ robustly captures this key quantity. For BCC TMs alloys, the core structure transition from ND to D occurs when χ drops below a threshold, as seen in atomistic simulations based on nearly all extant interatomic potentials and density functional theory (DFT) calculations of W-Re/Ta alloys. In binary W-TMs alloys, DFT calculations show that χ is related to the valence electron concentration at low to moderate solute concentrations, and can be controlled via alloying. χ can be quantitatively and efficiently predicted via rapid, low-cost DFT calculations for any BCC metal alloys, providing a robust, easily applied tool for the design of ductile and tough BCC alloys. read less S. Starikov and D. Smirnova, “Optimized interatomic potential for atomistic simulation of Zr-Nb alloy,” Computational Materials Science. 2021. link Times cited: 15 L. Zhao, H. Zong, X. Ding, and T. Lookman, “Anomalous dislocation core structure in shock compressed bcc high-entropy alloys,” Acta Materialia. 2021. link Times cited: 38 L. Wu, H. Wang, Y. Zhu, and M. Li, “Crystal-melt coexistence in FCC and BCC metals: A molecular-dynamics study of crystal-melt interface free energies,” Materialia. 2021. link Times cited: 6 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 B. Lin, J. Li, Z. Wang, and J. Wang, “Dislocation nucleation from Zr–Nb bimetal interfaces cooperating with the dynamic evolution of interfacial dislocations,” International Journal of Plasticity. 2020. link Times cited: 13 D. Singh, P. Sharma, and A. Parashar, “Atomistic simulations to study point defect dynamics in bi-crystalline niobium,” Materials Chemistry and Physics. 2020. link Times cited: 7 S. Xu, E. Hwang, W. Jian, Y. Su, and I. Beyerlein, “Atomistic calculations of the generalized stacking fault energies in two refractory multi-principal element alloys,” Intermetallics. 2020. link Times cited: 39 D. Fernández-Pello, J. M. Fernández-Díaz, M. A. Cerdeira, C. González, and R. Iglesias, “Energetic, electronic and structural DFT analysis of point defects in refractory BCC metals,” Materials today communications. 2020. link Times cited: 1 D. Errandonea et al., “Experimental and theoretical confirmation of an orthorhombic phase transition in niobium at high pressure and temperature,” Communications Materials. 2020. link Times cited: 40 K. Krylova, I. Lobzenko, A. Semenov, A. Kudreyko, and S. Dmitriev, “Spherically localized discrete breathers in bcc metals V and Nb,” Computational Materials Science. 2020. link Times cited: 22 D. Singh and A. Parashar, “A Comparison between ∑3 Asymmetrical Tilt Grain Boundary Energies in Niobium Obtained Analytically and through Molecular Dynamics Based Simulations,” Materials Science Forum. 2020. link Times cited: 2 Abstract: Niobium is an important constituent of Zr-Nb alloys being us… read more Abstract: Niobium is an important constituent of Zr-Nb alloys being used widely in the nuclear industries as fuel claddings and pressure tubes. In this article, MD based simulations are performed to obtain grain boundary (GB) energies in ∑3 symmetrical and asymmetrical tilt grain boundaries (ATGBs) along <110> tilt axis. Grain boundary energies are also obtained analytically by utilizing the equation establishing the relationship between inclination angle and grain boundary energy for ATGBs. It is observed that in both the cases the GB energies increase with the increase in inclination angle of the ATGBs. The increase in the GB energy follows the same trend with a little offset between the results obtained analytically and MD based simulations. The offset between both the results can be attributed to the limitations of the potentials employed for the simulations. MD based simulations thus provide an accurate method to calculate the GB energies. read less P. Garg, C. Muhich, L. Cooley, T. Bieler, and K. Solanki, “Possible role of grain-boundary and dislocation structure for the magnetic-flux trapping behavior of niobium: A first-principles study,” Physical Review B. 2020. link Times cited: 7 E. Fransson and P. Erhart, “Defects from phonons: Atomic transport by concerted motion in simple crystalline metals,” Acta Materialia. 2019. link Times cited: 11 S. Kramynin and É. Akhmedov, “Equation of state and properties of Nb at high temperature and pressure,” Journal of Physics and Chemistry of Solids. 2019. link Times cited: 10 S. Kramynin and É. Akhmedov, “Baric and dimensional changes of niobium properties,” Journal of Physics: Conference Series. 2019. link Times cited: 0 Abstract: We have calculated the baric dependencies of thermophysical … read more Abstract: We have calculated the baric dependencies of thermophysical properties and melting temperature as well as the thermal equation of state for niobium based on the pair interatomic Mi-Lenard-Jones potential and the crystal Einstein model for niobium (Nb). Baric dependencies computations made along two isotherms 300 K and 3000 K are in good agreement with the experimental data for niobium. We have obtained the charts of pressure dependencies for the following properties: Debye temperature, the first, second and third Gruneisen parameters, isothermal compression modulus, isochoric and isobaric heat capacity, volumetric coefficient of thermal expansion and the melting temperature. The article investigates size dependencies of both specified properties and the melting temperature of niobium using an RP-model of nanocrystal. read less G. Song and S. Lee, “Effects of temperature on surface-controlled dislocation multiplication in body-centered-cubic metal nanowires,” Computational Materials Science. 2019. link Times cited: 2 C. Yang and L. Qi, “Modified embedded-atom method potential of niobium for studies on mechanical properties,” Computational Materials Science. 2019. link Times cited: 17 D. Singh, P. Sharma, S. Jindal, P. Kumar, P. Kumar, and A. Parashar, “Atomistic simulations to study crack tip behaviour in single crystal of bcc niobium and hcp zirconium,” Current Applied Physics. 2019. link Times cited: 33 S. Abdeslam and T. Chihi, “Molecular dynamics study of size and cooling rate effects on physical properties of Niobium nanoclusters,” Chinese Journal of Physics. 2018. link Times cited: 7 D. Smirnova, S. Starikov, and A. Vlasova, “New interatomic potential for simulation of pure magnesium and magnesium hydrides,” Computational Materials Science. 2018. link Times cited: 17 D. Singh and A. Parashar, “Effect of symmetric and asymmetric tilt grain boundaries on the tensile behaviour of bcc-Niobium,” Computational Materials Science. 2018. link Times cited: 26 S. J. Yang, L. Hu, L. Wang, and B. Wei, “Heterogeneous nucleation and dendritic growth within undercooled liquid niobium under electrostatic levitation condition,” Chemical Physics Letters. 2017. link Times cited: 7 X. Zhou and J. Song, “Effect of local stress on hydrogen segregation at grain boundaries in metals,” Materials Letters. 2017. link Times cited: 19 A. Parashar and D. Singh, “Molecular dynamics based study of an irradiated single crystal of niobium,” Computational Materials Science. 2017. link Times cited: 19 S. Shi, L. Zhu, H. Zhang, and Z. Sun, “Strength and ductility of niobium alloys with nonmetallic elements: A first-principles study,” Materials Letters. 2017. link Times cited: 19 M. A. Cerdeira, S. L. Palacios, C. González, D. Fernández-Pello, and R. Iglesias, “Ab initio simulations of the structure, energetics and mobility of radiation-induced point defects in bcc Nb,” Journal of Nuclear Materials. 2016. link Times cited: 17 Z. Liu, Y.-X. Feng, and J. Shang, “Characterizing twist grain boundaries in BCC Nb by molecular simulation: Structure and shear deformation,” Applied Surface Science. 2016. link Times cited: 11 E. Hahn and M. Meyers, “Grain-size dependent mechanical behavior of nanocrystalline metals,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2015. link Times cited: 162 C. Coupeau et al., “Atomic reconstruction of niobium (111) surfaces,” Surface Science. 2015. link Times cited: 8 B. Huang, J. Shang, Z. Liu, and Y. Chen, “Atomic simulation of bcc niobium Σ5〈001〉310 grain boundary under shear deformation,” Acta Materialia. 2014. link Times cited: 20 L. Hale, J. Zimmerman, and C. Weinberger, “Simulations of bcc tantalum screw dislocations: Why classical inter-atomic potentials predict 1 1 2 slip,” Computational Materials Science. 2014. link Times cited: 27 C. R. Weinberger, B. L. Boyce, and C. Battaile, “Slip planes in bcc transition metals,” International Materials Reviews. 2013. link Times cited: 214 Abstract: Slip in face centred cubic (fcc) metals is well documented t… read more Abstract: Slip in face centred cubic (fcc) metals is well documented to occur on {111} planes in 〈110〉 directions. In body centred cubic (bcc) metals, the slip direction is also well established to be 〈111〉, but it is much less clear as to the slip planes on which dislocations move. Since plasticity in metals is governed by the collective motion and interaction of dislocations, the nature of the relevant slip planes is of critical importance in understanding and modelling plasticity in bcc metals. This review attempts to address two fundamental questions regarding the slip planes in bcc metals. First, on what planes can slip, and thus crystallographic rotation, be observed to occur, i.e. what are the effective slip planes? Second, on what planes do kinks form along the dislocation lines, i.e. what are the fundamental slip planes? We review the available literature on direct and indirect characterisation of slip planes from experiments, and simulations using atomistic models. Given the technological importance of bcc transition metals, this review focuses specifically on those materials. read less 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 D. Singh and A. Parashar, “Effect of symmetrical tilt grain boundary on dislocation nucleation and growth in Niobium bi-crystal,” Materials Today: Proceedings. 2019. link Times cited: 0 V. R. Ikkurthi et al., “Multi-scale Computational Approach for Modelling Spallation at High Strain Rates in Single-Crystal Materials☆,” Procedia Engineering. 2017. link Times cited: 11 H. Sun and A. Samanta, “Exploring structural transitions at grain boundaries in Nb using a generalized embedded atom interatomic potential,” Computational Materials Science. 2023. link Times cited: 0 P. Pleskunov et al., “A multi-timescale model predicts the spherical-to-cubic morphology crossover of magnetron-sputtered niobium nanoparticles,” Applied Surface Science. 2023. link Times cited: 2 M. E. Stupak, M. G. Urazaliev, and V. Popov, “Atomistic Modeling of Symmetric and Asymmetric Σ5 \documentclass[12pt]minimal \usepackageamsmath \usepackagewasysym \usepackageamsfonts \usepackageamssymb \usepackageamsbsy \usepackagemathrsfs \usepackageupgreek \setlength\oddsidemargin-69pt \begindocument$$\left⟨\text,” Physics of Metals and Metallography. 2023. link Times cited: 0 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 S. Sharma et al., “Machine Learning Methods for Multiscale Physics and Urban Engineering Problems,” Entropy. 2022. link Times cited: 0 Abstract: We present an overview of four challenging research areas in… read more Abstract: We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations. read less S. Kramynin, “Changes in the Pressure Dependences of Thermophysical Properties upon Changing the Size of Niobium Nanocrystals,” Physics of Metals and Metallography. 2022. link Times cited: 0 Y. Kurniawan et al., “Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials.,” The Journal of chemical physics. 2021. link Times cited: 6 Abstract: In this paper, we consider the problem of quantifying parame… read more Abstract: In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models. read less J. A. Vita and D. Trinkle, “Exploring the necessary complexity of interatomic potentials,” Computational Materials Science. 2021. link Times cited: 8 A. H. M. Faisal and C. Weinberger, “Modeling twin boundary structures in body centered cubic transition metals,” Computational Materials Science. 2021. link Times cited: 6 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 S. Kramynin, “Change of baric dependencies of thermophysical properties under variation of the size and shape of niobium nanocrystal,” Journal of Physics and Chemistry of Solids. 2020. link Times cited: 4 C. Cheng et al., “Development and application of EAM potentials for Ti, Al and Nb with enhanced planar fault energy of Ti,” Computational Materials Science. 2020. link Times cited: 4 D. Smirnova and S. Starikov, “An interatomic potential for simulation of Zr-Nb system,” Computational Materials Science. 2017. link Times cited: 37 A. Lipnitskii and V. Saveliev, “Development of n-body expansion interatomic potentials and its application for V,” Computational Materials Science. 2016. link Times cited: 20 L. Hale, H. Lim, J. Zimmerman, C. Battaile, and C. Weinberger, “Insights on activation enthalpy for non-Schmid slip in body-centered cubic metals,” Scripta Materialia. 2015. link Times cited: 17 V. Stegailov and P. Zhilyaev, “Pressure in electronically excited warm dense metals,” Contributions to Plasma Physics. 2015. link Times cited: 11 Abstract: Non‐equilibrium two‐temperature warm dense metals consist of… read more Abstract: Non‐equilibrium two‐temperature warm dense metals consist of the ion subsystem that is subjected to structural transitions and involved in the mass transfer, and the electron subsystem that in various pulsed experiments absorbs energy and then evolves together with ions to equilibrium. Definition of pressure in such non‐equilibrium systems causes certain controversy. In this work we make an attempt to clarify this definition that is vital for proper description of the whole relaxation process. Using the density functional theory we analyze on examples of Al and Au electronic pressure components in warm dense metals. Appealing to the Fermi gas model we elucidate a way to find a number of free delocalized electrons in warm dense metals. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) read less Q.-J. Hong and A. van de Walle, “Solid-liquid coexistence in small systems: A statistical method to calculate melting temperatures.,” The Journal of chemical physics. 2013. link Times cited: 49 Abstract: We propose an efficient and accurate scheme to calculate the… read more Abstract: We propose an efficient and accurate scheme to calculate the melting point (MP) of materials. This method is based on the statistical analysis of small-size coexistence molecular dynamics simulations. It eliminates the risk of metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated MPs. The method converges to the exact result in the limit of large system size. An accuracy within 100 K in MP is usually achieved when simulation contains more than 100 atoms. Density functional theory examples of tantalum, high-pressure sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the MP is a design criterion. read less V. Hizhnyakov, M. Haas, A. Liivand, A. Shelkan, and M. Klopov, “Modeling of self-localized vibrations and defect formation in solids,” Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms. 2013. link Times cited: 12 Y. Dai, C. H. Lu, Q. Ren, L. Lu, J. Li, and B. Liu, “A long-range U–Nb potential for the calculation of some chemical and physical properties of the U–Nb system,” Journal of Nuclear Materials. 2012. link Times cited: 12 D. E. Smirnova, S. Starikov, S. Starikov, V. Stegailov, and V. Stegailov, “Interatomic potential for uranium in a wide range of pressures and temperatures,” Journal of Physics: Condensed Matter. 2012. link Times cited: 3 Abstract: Using the force-matching method we develop an interatomic po… read more Abstract: Using the force-matching method we develop an interatomic potential that allows us to study the structure and properties of α-U, γ-U and liquid uranium. The potential is fitted to the forces, energies and stresses obtained from ab initio calculations. The model gives a good comparison with the experimental and ab initio data for the lattice constants of α-U and γ-U, the elastic constants, the room-temperature isotherm, the normal density isochore, the bond-angle distribution functions and the vacancy formation energies. The calculated melting line of uranium at pressures up to 80 GPa and the temperature of the α–γ transition at 3 GPa agree well with the experimental phase diagram of uranium. read less O. Chirayutthanasak et al., “Universal function for grain boundary energies in bcc metals,” Scripta Materialia. 2024. link Times cited: 0 E. Rothchild, Q. J. Li, and E. Ma, “On the validity of using the Debye model to quantitatively correlate the shear modulus with vibrational properties in cubic metals,” Scripta Materialia. 2019. link Times cited: 1 D. Caillard, B. Bienvenu, and E. Clouet, “Anomalous slip in body-centred cubic metals,” Nature. 2022. link Times cited: 8 Y. Kurniawan et al., “Extending OpenKIM with an Uncertainty Quantification Toolkit for Molecular Modeling,” 2022 IEEE 18th International Conference on e-Science (e-Science). 2022. link Times cited: 0 Abstract: Atomistic simulations are an important tool in materials mod… read more Abstract: Atomistic simulations are an important tool in materials modeling. Interatomic potentials (IPs) are at the heart of such molecular models, and the accuracy of a model's predictions depends strongly on the choice of IP. Uncertainty quantification (UQ) is an emerging tool for assessing the reliability of atomistic simulations. The Open Knowledgebase of Interatomic Models (OpenKIM) is a cyberinfrastructure project whose goal is to collect and standardize the study of IPs to enable transparent, reproducible research. Part of the OpenKIM framework is the Python package, KIM-based Learning-Integrated Fitting Framework (KLIFF), that provides tools for fitting parameters in an IP to data. This paper introduces a UQ toolbox extension to KLIFF. We focus on two sources of uncertainty: variations in parameters and inadequacy of the functional form of the IP. Our implementation uses parallel-tempered Markov chain Monte Carlo (PTMCMC), adjusting the sampling temperature to estimate the uncertainty due to the functional form of the IP. We demonstrate on a Stillinger–Weber potential that makes predictions for the atomic energies and forces for silicon in a diamond configuration. Finally, we highlight some potential subtleties in applying and using these tools with recommendations for practitioners and IP developers. read less Q. Yang and P. Olsson, “Full energy range primary radiation damage model,” Physical Review Materials. 2021. link Times cited: 9 Abstract: A full energy range primary radiation damage model is presen… read more Abstract: A full energy range primary radiation damage model is presented here. It is based on the athermal recombination corrected displacements per atom (arc-dpa) model but includes a proper treatment of the near threshold conditions for metallic materials. Both ab initio (AIMD) and classical molecular dynamics (MD) simulations are used here for various metals with body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp) structures to validate the model. For bcc and hcp metals, the simulation results fit very well with the model. For fcc metals, although there are slight deviations between the model and direct simulation results, it is still a clear improvement on the arc-dpa model. The deviations are due to qualitative differences in the threshold energy surfaces of fcc metals with respect to bcc and hcp metals according to our classical MD simulations. We introduce the minimum threshold displacement energy (TDE) as a term in our damage model. We calculated minimum TDEs for various metal materials using AIMD. In general, the calculated minimum TDEs are in very good agreement with experimental results. Moreover, we noticed a discrepancy in the literature for fcc Ni and estimated the average TDE of Ni using both classical MD and AIMD. It was found that the average TDE of Ni should be \ensuremath{\sim}70 eV based on simulation and experimental data, not the commonly used literature value of 40 eV. The most significant implications of introducing this full energy range damage model will be for estimating the effect of weak particle-matter interactions, such as for \ensuremath{\gamma}- and electron-radiation-induced damage. read less C. Taylor and H. Ke, “Investigations of the intrinsic corrosion and hydrogen susceptibility of metals and alloys using density functional theory,” Corrosion Reviews. 2021. link Times cited: 8 Abstract: Mechanisms for materials degradation are usually inferred fr… read more Abstract: Mechanisms for materials degradation are usually inferred from electrochemical measurements and characterization performed before, during, and after exposure testing and/or failure analysis of service materials. Predicting corrosion and other materials degradation modes, such as hydrogen-assisted cracking, from first-principles has generally been limited to thermodynamic predictions from Pourbaix or Ellingham diagrams and the Galvanic series. Using electronic structure calculations, modern first-principles methods can predict ab initio the key rate-controlling processes for corrosion and hydrogen susceptibility as a function of pH, potential, and solution chemistry, and materials composition and microstructure. Herein we review density functional theory (DFT) approaches for studying the electrochemical reactions occurring on fresh metal and alloy surfaces related to environmentally assisted cracking and localized corrosion/pitting. Predicted changes in surface chemistry as a function of the environment were correlated against experimental crack growth rate data obtained for alloys 718, 725, and pipeline steel under electrochemical control. We also review the application of the method to study the effects of alloying on the chloride susceptibility of stainless steels and Ni–Cr-based corrosion-resistant alloys. Perspectives for improving the model are given, and extending it to future fields of application in corrosion science and engineering. read less B. Lin, J. Wang, J. Li, and Z. Wang, “A neural-network based framework of developing cross interaction in alloy embedded-atom method potentials: application to Zr–Nb alloy,” Journal of Physics: Condensed Matter. 2020. link Times cited: 2 Abstract: Interaction potentials are critical to molecular dynamics si… read more Abstract: Interaction potentials are critical to molecular dynamics simulations on fundamental mechanisms at atomic scales. Combination of well-developed single-element empirical potentials via cross interaction (CI) is an important and effective way to develop alloy embedded-atom method (EAM) potentials. In this work, based on neural-network (NN) models, firstly we proposed a framework to construct CI potential functions via utilizing single-element potentials. The framework contained four steps: (1) extracting characteristic points from single-element potential functions, (2) constructing CI functions by cubic spline interpolation, (3) evaluating the accuracy of CI functions by referring to first-principle (FP) data, and (4) searching for reasonable CI functions via NN models. Then with this framework, we developed a Zr–Nb alloy CI potential utilizing the MA-III (pure Zr potential developed by Mendelev and Ackland in 2007) and the Fellinger, Park and Wilkins (FPW) (pure Nb potential developed by FPW in 2010) potentials as single-element parts. The calculated results with this Zr–Nb alloy potential showed that: (1) the newly developed CI potential functions could simultaneously present the potential-function features of Zr and Nb; (2) the normalized energy–volume curves of L12 Zr3Nb, B2 ZrNb and L12 ZrNb3 calculated by this CI potential reasonably agreed with FP results; (3) the referred MA-III Zr and FPW Nb potentials can satisfactorily reproduce the priority of prismatic slip in Zr and the tension–compression asymmetry of 〈111〉{112} slip in Nb, while other ab initio developed Zr–Nb alloy potentials cannot. Our study indicates that, this NN based framework can take full advantage of single-element potentials, and is very convenient to develop EAM potentials of alloys; moreover, the new-developed Zr–Nb alloy EAM potential can reasonably describe the complicated deformation behaviors in Zr–Nb systems. read less K. Kowalczyk-Gajewska and M. Ma’zdziarz, “Elastic properties of nanocrystalline materials of hexagonal symmetry: The core-shell model and atomistic estimates,” International Journal of Engineering Science. 2020. link Times cited: 5 J. Byggmastar, K. Nordlund, and F. Djurabekova, “Gaussian approximation potentials for body-centered-cubic transition metals,” Physical Review Materials. 2020. link Times cited: 22 Abstract: We develop a set of machine-learning interatomic potentials … read more Abstract: We develop a set of machine-learning interatomic potentials for elemental V, Nb, Mo, Ta, and W using the Gaussian approximation potential framework. The potentials show good accuracy and transferability for elastic, thermal, liquid, defect, and surface properties. All potentials are augmented with accurate repulsive potentials, making them applicable to radiation damage simulations involving high-energy collisions. We study melting and liquid properties in detail and use the potentials to provide melting curves up to 400 GPa for all five elements. read less S. Kramynin and É. Akhmedov, “Change in Thermophysical Properties and Melting Temperature of Niobium with Increasing Pressure,” Physics of Metals and Metallography. 2019. link Times cited: 1 D. Vizoso, C. Deo, and R. Dingreville, “Scaling laws and stability of nano-sized defect clusters in niobium via atomistic simulations and statistical analysis,” Journal of Materials Science. 2019. link Times cited: 4 Z. Chen et al., “Interatomic Potential in the Nonequilibrium Warm Dense Matter Regime.,” Physical review letters. 2018. link Times cited: 18 Abstract: We present a new measurement of lattice disassembly times in… read more Abstract: We present a new measurement of lattice disassembly times in femtosecond-laser-heated polycrystalline Au nanofoils. The results are compared with molecular dynamics simulations incorporating a highly optimized, embedded-atom-method interatomic potential. For absorbed energy densities of 0.9-4.3 MJ/kg, the agreement between the experiment and simulation reveals a single-crystal-like behavior of homogeneous melting and corroborates the applicability of the interatomic potential in the nonequilibrium warm dense matter regime. For energy densities below 0.9 MJ/kg, the measurement is consistent with nanocrystal behavior where melting is initiated at the grain boundaries. read less K. Zhang, M. Fan, Y. Liu, J. Schroers, M. Shattuck, and C. O’Hern, “Beyond packing of hard spheres: The effects of core softness, non-additivity, intermediate-range repulsion, and many-body interactions on the glass-forming ability of bulk metallic glasses.,” The Journal of chemical physics. 2015. link Times cited: 16 Abstract: When a liquid is cooled well below its melting temperature a… read more Abstract: When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10(-2) K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 10(10) K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness. read less E. Metsanurk, A. Caro, A. Tamm, A. Aabloo, and M. Klintenberg, “First-principles study of point defects at a semicoherent interface,” Scientific Reports. 2014. link Times cited: 11 Y.-S. Lin, M. Mrovec, and V. Vitek, “A new method for development of bond-order potentials for transition bcc metals,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 22 Abstract: A new development of numerical bond-order potentials (BOPs) … read more Abstract: A new development of numerical bond-order potentials (BOPs) for the non-magnetic transition metals V, Nb, Ta, Cr, Mo and W is presented. The principles on which the BOPs have been set up are the same as in earlier developments (Aoki et al 2007 Prog. Mater. Sci. 52 154). However, the bond integrals are based on the recently advanced method of parametrization of tight-binding from DFT calculations (Madsen et al 2011 Phys. Rev. B 83 4119, Urban et al 2011 Phys. Rev. B 84 155119) and do not require any screening. At the same time, the functional form of the environmentally dependent repulsion is identified with the functional form of the repulsion arising from the overlap of s and p electrons in argon as proposed in Aoki and Kurokawa (2007 J. Phys.: Condens. Matter 19 136228). This is justified by the same physical origin of the environment dependent repulsion, which in transition metals arises from the overlap of s electrons that are being squeezed into the ion core regions under the influence of the strong covalent d bonds. The testing of the developed BOPs involves investigation of alternative higher energy structures, transformation paths connecting the bcc structure with other structures via continuously distorted configurations, evaluation of the vacancy formation energy and calculation of phonon spectra. In all cases, the BOP calculations are in more than satisfactory agreement with either DFT calculations and/or available experimental data. The calculated γ-surfaces for {1 0 1} planes all suggest that the core of 1/2〈1 1 1〉 screw dislocations is non-degenerate in the transition metals. This is also in full agreement with available calculations that account fully for the quantum-mechanical nature of the d electrons that provide the bulk of the bonding in transition metals. The testing of developed BOPs clearly demonstrates that they are transferable to structures well outside the regime of the ideal bcc lattice and are suitable for investigating the atomic structure and behaviour of extended crystal defects. read less D. Belashchenko, “Computer simulation of liquid metals,” Physics—Uspekhi. 2013. link Times cited: 84 Abstract: Methods for and the results of the computer simulation of li… read more Abstract: Methods for and the results of the computer simulation of liquid metals are reviewed. Two basic methods, classical molecular dynamics with known interparticle potentials and the ab initio method, are considered. Most attention is given to the simulated results obtained using the embedded atom model (EAM). The thermodynamic, structural, and diffusion properties of liquid metal models under normal and extreme (shock) pressure conditions are considered. Liquid-metal simulated results for the Groups I–IV elements, a number of transition metals, and some binary systems (Fe–C, Fe–S) are examined. Possibilities for the simulation to account for the thermal contribution of delocalized electrons to energy and pressure are considered. Solidification features of supercooled metals are also discussed. read less P. Zhang and D. Trinkle, “Database optimization for empirical interatomic potential models,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 8 Abstract: Weighted least squares fitting to a database of quantum mech… read more Abstract: Weighted least squares fitting to a database of quantum mechanical calculations can determine the optimal parameters of empirical potential models. While algorithms exist to provide optimal potential parameters for a given fitting database of structures with corresponding energy-related predictions and to estimate prediction errors using Bayesian sampling, defining an optimal fitting database based on potential predictions remains elusive. A testing set of structures and energy-related predictions provides an empirical measure of potential transferability. Here, we propose an objective function for fitting databases based on testing set errors. The objective function allows the optimization of the weights in a fitting database, the assessment of the adding or removing of structures in the fitting database, or the comparison of two different fitting databases. To showcase this technique, we consider an example Lennard-Jones potential for Ti, where modeling multiple complicated crystal structures is difficult for a radial pair potential. The algorithm finds different optimal fitting databases, depending on the objective function of potential prediction error for a testing set. read less D. Smirnova et al., “A ternary EAM interatomic potential for U–Mo alloys with xenon,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 71 Abstract: A new interatomic potential for a uranium–molybdenum system … read more Abstract: A new interatomic potential for a uranium–molybdenum system with xenon is developed in the framework of an embedded atom model using a force-matching technique and a dataset of ab initio atomic forces. The verification of the potential proves that it is suitable for the investigation of various compounds existing in the system as well as for simulation of pure elements: U, Mo and Xe. Computed lattice constants, thermal expansion coefficients, elastic properties and melting temperatures of U, Mo and Xe are consistent with the experimentally measured values. The energies of the point defect formation in pure U and Mo are proved to be comparable to the density-functional theory calculations. We compare this new U–Mo–Xe potential with the previously developed U and Mo–Xe potentials. A comparative study between the different potential functions is provided. The key purpose of the new model is to study the atomistic processes of defect evolution taking place in the U–Mo nuclear fuel. Here we use the potential to simulate bcc alloys containing 10 wt% of intermetallic Mo and U2Mo. read less X.-J. Yuan, N. Chen, and J. Shen, “Construction of embedded-atom-method interatomic potentials for alkaline metals (Li, Na, and K) by lattice inversion,” Chinese Physics B. 2012. link Times cited: 1 Abstract: The lattice-inversion embedded-atom-method interatomic poten… read more Abstract: The lattice-inversion embedded-atom-method interatomic potential developed previously by us is extended to alkaline metals including Li, Na, and K. It is found that considering interatomic interactions between neighboring atoms of an appropriate distance is a matter of great significance in constructing accurate embedded-atom-method interatomic potentials, especially for the prediction of surface energy. The lattice-inversion embedded-atom-method interatomic potentials for Li, Na, and K are successfully constructed by taking the fourth-neighbor atoms into consideration. These angular-independent potentials markedly promote the accuracy of predicted surface energies, which agree well with experimental results. In addition, the predicted structural stability, elastic constants, formation and migration energies of vacancy, and activation energy of vacancy diffusion are in good agreement with available experimental data and first-principles calculations, and the equilibrium condition is satisfied. read less A. Gufan, O. V. Kukin, and I. A. Osipenko, “An invariant form of the potential energy function used to simulate properties of condensed matter,” Bulletin of the Russian Academy of Sciences: Physics. 2012. link Times cited: 3 L. Wang and A. van de Walle, “Ab initio calculations of the melting temperatures of refractory bcc metals.,” Physical chemistry chemical physics : PCCP. 2012. link Times cited: 13 Abstract: We present ab initio calculations of the melting temperature… read more Abstract: We present ab initio calculations of the melting temperatures for bcc metals Nb, Ta and W. The calculations combine phase coexistence molecular dynamics (MD) simulations using classical embedded-atom method potentials and ab initio density functional theory free energy corrections. The calculated melting temperatures for Nb, Ta and W are, respectively, within 3%, 4%, and 7% of the experimental values. We compare the melting temperatures to those obtained from direct ab initio molecular dynamics simulations and see if they are in excellent agreement with each other. The small remaining discrepancies with experiment are thus likely due to inherent limitations associated with exchange-correlation energy approximations within density-functional theory. read less X.-J. Yuan, N. Chen, and J. Shen, “Lattice-Inversion Embedded-Atom-Method Interatomic Potentials for Group-VA Transition Metals,” Chinese Physics Letters. 2011. link Times cited: 1 Abstract: The lattice-inversion embedded-atom-method (LI-EAM) interato… read more Abstract: The lattice-inversion embedded-atom-method (LI-EAM) interatomic potential we developed previously [J. Phys.: Condens. Matter 22 (2010) 375503] is extended to group-VA transition metals (V, Nb and Ta). It is found that considering interatomic interactions up to appropriate-distance-neighbor atoms is crucial to constructing accurate EAM potentials, especially for the prediction of surface energy. The LI-EAM interatomic potentials for group-VA transition metals are successfully built by considering interatomic interactions up to the fifth neighbor atoms. These angular-independent potentials drastically promote the accuracy of the predicted surface energies, which match the experimental results well. read less R. F. Zhang, J. Wang, I. Beyerlein, and T. Germann, “Twinning in bcc metals under shock loading: a challenge to empirical potentials,” Philosophical Magazine Letters. 2011. link Times cited: 53 Abstract: Using density functional theory (DFT), we found that high pr… read more Abstract: Using density functional theory (DFT), we found that high pressures intrinsically favor twinning in niobium by reducing the thickness of a stable twin. Five empirical interatomic potentials for niobium were considered in molecular dynamics (MD) shock simulations. The results show that two potentials exhibit the experimentally observed twinning behavior. Comparing with DFT under high pressure, we found that these two potentials are capable of reproducing the generalized stacking fault (GSF) curve, but the others predict several artificial metastable states along the GSF curve resulting in an artificial structural transformation. read less H. Sheng, M. Kramer, A. Cadien, T. Fujita, and M. Chen, “Highly optimized embedded-atom-method potentials for fourteen fcc metals,” Physical Review B. 2011. link Times cited: 387 Abstract: Highly optimized embedded-atom-method (EAM) potentials have … read more Abstract: Highly optimized embedded-atom-method (EAM) potentials have been developed for 14 face-centered-cubic (fcc) elements across the periodic table. The potentials were developed by fitting the potential-energy surface (PES) of each element derived from high-precision first-principles calculations. The as-derived potential-energy surfaces were shifted and scaled to match experimental reference data. In constructing the PES, a variety of properties of the elements were considered, including lattice dynamics, mechanical properties, thermal behavior, energetics of competing crystal structures, defects, deformation paths, liquid structures, and so forth. For each element, the constructed EAM potentials were tested against the experiment data pertaining to thermal expansion, melting, and liquid dynamics via molecular dynamics computer simulation. The as-developed potentials demonstrate high fidelity and robustness. Owing to their improved accuracy and wide applicability, the potentials are suitable for high-quality atomistic computer simulation of practical applications. read less E. Pechenik, I. Kelson, and G. Makov, “Formulation of wide-ranging embedded-atom-type potentials: the role of mechanical stability,” Modelling and Simulation in Materials Science and Engineering. 2012. link Times cited: 1 Abstract: Wide-ranging inter-atomic potentials are necessary for model… read more Abstract: Wide-ranging inter-atomic potentials are necessary for modeling many problems in material physics that involve multiple atomic environments and phases. The domains of thermodynamic and mechanical stability of embedded-atom-type potentials are examined for the cubic phases. It is shown that the choice of the pair potential is critical in determining the domain of stability of embedded-atom-type potentials. In particular, the Lennard-Jones embedded-atom potential is shown not to stabilize the bcc phase. A simple four-parameter universal equation of state-based embedded-atom potential is shown to have a domain of stability for all the cubic phases and to reproduce the high-pressure equation of state. A model phase diagram for the three cubic phases is presented. This potential is fitted to 17 elemental systems and found to be able to reproduce both the elastic constants and the ground state crystalline structure. For elements with a low degree of elastic anisotropy, this potential can also reproduce the high-pressure behavior. read less Q.-nan Wang, J. Wang, J. Li, Z. Zhang, and S. Mao, “Consecutive crystallographic reorientations and superplasticity in body-centered cubic niobium nanowires,” Science Advances. 2018. link Times cited: 38 Abstract: Niobium nanowires show superplasticity through the close syn… read more Abstract: Niobium nanowires show superplasticity through the close synergy of multiple deformation modes with consecutive reorientations. Plasticity of metallic nanowires is often controlled by the activities of single deformation mode. It remains largely unclear whether multiple deformation modes can be activated in an individual metallic nanowire and how much plasticity they can contribute. In situ nanomechanical testing reveals a superior plastic deformation ability of body-centered cubic (BCC) niobium nanowires, in which a remarkable elongation of more than 269% is achieved before fracture. This superplastic deformation originates from a synergy of consecutively nucleated multiple reorientation processes that occur for more than five times via three distinct mechanisms, that is, stress-activated phase transformation, deformation twinning, and slip-induced crystal rotation. These three coupled mechanisms work concurrently, resulting in sequential reorientations and therefore superplastic deformation of Nb nanowires. Our findings reveal a superior mechanical property of BCC Nb nanowires through the close coordination of multiple deformation modes, which may have some implications in other metallic nanowire systems. read less U. Pudasaini, G. Eremeev, C. Reece, J. Tuggle, and M. Kelley, “Initial growth of tin on niobium for vapor diffusion coating of Nb3Sn,” Superconductor Science and Technology. 2018. link Times cited: 28 Abstract: Nb3Sn offers significant potential to exceed the performance… read more Abstract: Nb3Sn offers significant potential to exceed the performance of niobium for superconducting radio frequency accelerator cavities. The most promising path toward deployment is by tin vapor diffusion coating of Nb cavity interiors via a two step nucleation-then-growth sequence. Reported here is a materials science study of the nucleation process. We manipulated the accessible range of process variables and determined the effect on composition and microstructure using an array of materials characterization tools. Broadly, nucleation deposits tin as a thin surface phase and, under some conditions, as near-micron sized particles as well, resembling Stranski–Krastanov growth. Conditions that impair nucleation promote the formation of defects, such as patches, in subsequent coating growth. Otherwise no significant effect on the subsequently grown coating was found for structures produced during nucleation. read less P. Brommer, A. Kiselev, D. Schopf, P. Beck, J. Roth, and H. Trebin, “Classical interaction potentials for diverse materials from ab initio data: a review of potfit,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 76 Abstract: Force matching is an established technique to generate effec… read more Abstract: Force matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit. Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_102133002179_005
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.	EAM_Dynamo_FellingerParkWilkins_2010_Nb__MO_102133002179_005
DOI	10.25950/befb2eea https://doi.org/10.25950/befb2eea https://commons.datacite.org/doi.org/10.25950/befb2eea
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 EAM_Dynamo__MD_120291908751_005
Driver	EAM_Dynamo__MD_120291908751_005
KIM API Version	2.0
Potential Type	eam

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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 5.55002e-09 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
F The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous 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
N/A Unable to perform verification check due to an error.	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
P Unit conversion successful	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: 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: 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

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

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: 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: Nb

Cubic Crystal Basic Properties Table

Species: Nb

Tests

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 Nb v004	view	6296
Cohesive energy versus lattice constant curve for diamond Nb v004	view	7362
Cohesive energy versus lattice constant curve for fcc Nb v004	view	6226
Cohesive energy versus lattice constant curve for sc Nb v004	view	6773

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 Nb at zero temperature v006	view	5662
Elastic constants for fcc Nb at zero temperature v006	view	3967
Elastic constants for sc Nb at zero temperature v006	view	1727

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2019
DOI: https://doi.org/10.25950/d794c746

Computes the elastic constants for hcp crystals 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	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)
Elastic constants for hcp Nb at zero temperature v004		view	1242

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	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)
Equilibrium crystal structure and energy for Nb in AFLOW crystal prototype A_cF4_225_a v003		view	172315
Equilibrium crystal structure and energy for Nb in AFLOW crystal prototype A_cI2_229_a v003		view	173592

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 Nb v007	view	2591
Equilibrium zero-temperature lattice constant for diamond Nb v007	view	3839
Equilibrium zero-temperature lattice constant for fcc Nb v007	view	3903
Equilibrium zero-temperature lattice constant for sc Nb v007	view	2655

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	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)
Equilibrium lattice constants for hcp Nb v005		view	12862

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	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)
Broken-bond fit of high-symmetry surface energies in bcc Nb v004		view	27607

VacancyFormationEnergyRelaxationVolume__TD_647413317626_001

Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/fca89cea

Computes the monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals.

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)
Monovacancy formation energy and relaxation volume for bcc Nb		view	226530

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	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)
Vacancy formation and migration energy for bcc Nb		view	3832978

Errors

ElasticConstantsCubic__TD_011862047401_006

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

LatticeConstantCubicEnergy__TD_475411767977_006

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for bcc Nb	other	view
Equilibrium zero-temperature lattice constant for diamond Nb	other	view

LatticeConstantHexagonalEnergy__TD_942334626465_004

Test	Error Categories	Link to Error page
Equilibrium lattice constants for hcp Nb	other	view

Files

CMakeLists.txt
LICENSE.CDDL
Nb.eam.alloy
kimprovenance.edn
kimspec.edn

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EAM_Dynamo_FellingerParkWilkins_2010_Nb__MO_102133002179_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo_FellingerParkWilkins_2010_Nb__MO_102133002179_005.zip	Zip	Windows archive

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This Model requires a Model Driver. Archives for the Model Driver EAM_Dynamo__MD_120291908751_005 appear below.

EAM_Dynamo__MD_120291908751_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo__MD_120291908751_005.zip	Zip	Windows archive

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EAM_Dynamo_FellingerParkWilkins_2010_Nb__MO_102133002179_005

Verification Check Dashboard

Visualizers (in-page)

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

Tests

Errors

Files

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