× Updated! Potentials that share interactions are now listed as related models.
 
Citation: C. Yang, and L. Qi (2019), "Modified embedded-atom method potential of niobium for studies on mechanical properties", Computational Materials Science, 161, 351-363. DOI: 10.1016/j.commatsci.2019.01.047.
Abstract: Niobium (Nb) as a refractory metal has appealing mechanical properties due to high ductility at room temperature. Density functional theory (DFT) calculations confirmed its intrinsic ductility by showing its perfect lattice generates an elastic shear deformation preceding its cleavage fracture under <100> ideal tensile deformation. Based on DFT calculations of simple atomic configurations, we applied an evolution strategy method to build a modified embedded-atom method (MEAM) spline-interpolation potential that can reproduce the intrinsic ductility of Nb during ideal tensile deformation. Further examinations show that simulations based on this MEAM potential can exhibit other essential characteristics of deformation behavior, such as ideal shear strengths, generalized stacking fault energies, twin boundary energies, phonon spectrum, etc., that are consistent with DFT calculations. This potential also outputs the structures, energetic stability and glide mechanism of 1/2<111> screw dislocations, such as dislocation core structures, core energies, migration barriers and dislocation core trajectories, consistent with DFT calculations. Therefore, this MEAM potential is suitable to study the mechanical behaviors of Nb, especially those under extreme loading conditions and considering non-Schmid effects.

LAMMPS pair_style meam/spline (2019--Yang-C--Nb--LAMMPS--ipr1)
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Notes: This file was provided by Liang Qi on July 7, 2022.
File(s):
Citation: R.S. Elliott, and A. Akerson (2015), "Efficient "universal" shifted Lennard-Jones model for all KIM API supported species".

Notes: This is the Nb interaction from the "Universal" parameterization for the openKIM LennardJones612 model driver.The parameterization uses a shifted cutoff so that all interactions have a continuous energy function at the cutoff radius. This model was automatically fit using Lorentz-Berthelotmixing rules. It reproduces the dimer equilibrium separation (covalent radii) and the bond dissociation energies. It has not been fitted to other physical properties and its ability to model structures other than dimers is unknown. See the README and params files on the KIM model page for more details.

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Notes: Listing found at https://openkim.org.
Link(s):
Citation: M.R. Fellinger, H. Park, and J.W. Wilkins (2010), "Force-matched embedded-atom method potential for niobium", Physical Review B, 81(14), 144119. DOI: 10.1103/physrevb.81.144119.
Abstract: Large-scale simulations of plastic deformation and phase transformations in alloys require reliable classical interatomic potentials. We construct an embedded-atom method potential for niobium as the first step in alloy potential development. Optimization of the potential parameters to a well-converged set of density-functional theory (DFT) forces, energies, and stresses produces a reliable and transferable potential for molecular-dynamics simulations. The potential accurately describes properties related to the fitting data and also produces excellent results for quantities outside the fitting range. Structural and elastic properties, defect energetics, and thermal behavior compare well with DFT results and experimental data, e.g., DFT surface energies are reproduced with less than 4% error, generalized stacking-fault energies differ from DFT values by less than 15%, and the melting temperature is within 2% of the experimental value.

IMD option EAM (2010--Fellinger-M-R--Nb--IMD--ipr1)
Notes: These files were provided by Michael Fellinger, Hyoungki Park, and John Wilkins (The Ohio State University) and posted with their permission on 14 July 2010. Details of the fitting procedure and testing can be found in the reference listed above.
File(s):
LAMMPS pair_style eam/alloy (2010--Fellinger-M-R--Nb--LAMMPS--ipr1)
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Notes: These files were provided by Michael Fellinger, Hyoungki Park, and John Wilkins (The Ohio State University) and posted with their permission on 14 July 2010. Mike Fellinger also provided the additional note: "The Nb.eam.alloy file is in the setfl format suitable for the LAMMPS MD code. This format requires r*phi and rho to be tabulated from r = 0 to r = r_cut. The domain of phi and rho in the published potential is 1.738 ≤ r ≤ 4.75 A. For phi, we extend the cubic polynomial for 1.738 ≤ r ≤ 2.073 A to r = 0. For rho, we linearly extrapolate from r = 1.738 A to r = 0. The potential in the IMD format is tabulated with 5,001 points for each function. The potential in the LAMMPS setfl format is tabulated with 10,001 points for each function. Comparisons of the two tabulations show very slight differences in some defect energies, probably due to the different numbers of tabulation points."
File(s):
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Notes: Listing found at https://openkim.org. This KIM potential is based on the files from 2010--Fellinger-M-R--Nb--LAMMPS--ipr1.
Link(s):
Citation: P.M. Derlet, D. Nguyen-Manh, and S.L. Dudarev (2007), "Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals", Physical Review B, 76(5), 054107. DOI: 10.1103/physrevb.76.054107.
Abstract: We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the “local” d band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

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Notes: Listing found at https://openkim.org.
Link(s):
Citation: S. Han, L.A. Zepeda-Ruiz, G.J. Ackland, R. Car, and D.J. Srolovitz (2003), "Interatomic potential for vanadium suitable for radiation damage simulations", Journal of Applied Physics, 93(6), 3328-3335. DOI: 10.1063/1.1555275.
Abstract: The ability to predict the behavior of point defects in metals, particularly interstitial defects, is central to accurate modeling of the microstructural evolution in environments with high radiation fluxes. Existing interatomic potentials of embedded atom method type predict disparate stable interstitial defect configurations in vanadium. This is not surprising since accurate first-principles interstitial data were not available when these potentials were fitted. In order to provide the input information required to fit a vanadium potential appropriate for radiation damage studies, we perform a series of first-principles calculations on six different interstitial geometries and vacancies. These calculations identify the 〈111〉 dumbbell as the most stable interstitial with a formation energy of approximately 3.1 eV, at variance with predictions based upon existing potentials. Our potential is of Finnis–Sinclair type and is fitted exactly to the experimental equilibrium lattice parameter, cohesive energy, elastic constants and a calculated unrelaxed vacancy formation energy. Two additional potential parameters were used to obtain the best fit to the set of interstitial formation energies determined from the first-principles calculations. The resulting potential was found to accurately predict both the magnitude and ordering of the formation energies of six interstitial configurations and the unrelaxed vacancy ground state, in addition to accurately describing the migration characteristics of the stable interstitial and vacancy. This vanadium potential is capable of describing the point defect properties appropriate for radiation damage simulations as well as for simulations of more common crystal and simple defect properties.

Moldy FS (2003--Han-S--Nb--MOLDY--ipr1)
Notes: The parameters in Nb.moldy were obtained from http://homepages.ed.ac.uk/graeme/moldy/moldy.html and posted with the permission of G.J. Ackland.
File(s):
Citation: B.-J. Lee, M.I. Baskes, H. Kim, and Y.K. Cho (2001), "Second nearest-neighbor modified embedded atom method potentials for bcc transition metals", Physical Review B, 64(18), 184102. DOI: 10.1103/physrevb.64.184102.
Abstract: The second nearest-neighbor modified embedded atom method (MEAM) [Phys. Rev. B 62, 8564 (2000)], developed in order to solve problems of the original first nearest-neighbor MEAM on bcc metals, has now been applied to all bcc transition metals, Fe, Cr, Mo, W, V, Nb, and Ta. The potential parameters could be determined empirically by fitting to (∂B/∂P), elastic constants, structural energy differences among bcc, fcc and hcp structures, vacancy-formation energy, and surface energy. Various physical properties of individual elements, including elastic constants, structural properties, point-defect properties, surface properties, and thermal properties were calculated and compared with experiments or high level calculations so that the reliability of the present empirical atomic-potential formalism can be evaluated. It is shown that the present potentials reasonably reproduce nonfitted properties of the bcc transition metals, as well as the fitted properties. The effect of the size of radial cutoff distance on the calculation and the compatibility with the original first nearest-neighbor MEAM that has been successful for fcc, hcp, and other structures are also discussed.

LAMMPS pair_style meam (2001--Lee-B-J--Nb--LAMMPS--ipr1)
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Notes: These potential files were obtained from http://cmse.postech.ac.kr/home_2nnmeam, accessed Nov 9, 2020.
File(s):
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Notes: Listing found at https://openkim.org.
Link(s):
Citation: G.J. Ackland, and R. Thetford (1987), "An improved N-body semi-empirical model for body-centred cubic transition metals", Philosophical Magazine A, 56(1), 15-30. DOI: 10.1080/01418618708204464.
Abstract: The recently published semi-empirical potentials of Finnis and Sinclair for the metals V, Nb, Ta, Mo and W appear to give unphysical results for properties involving small interatomic separation. This is remedied by adding to the potentials cores fitted to electron gas calculations on dimers. The adjusted potentials are shown to predict a more realistic pressure-volume relationship. Interstitial formation energies are calculated for various configurations, using quenched molecular dynamics and static relaxation. Some preliminary results on interstitial migration are presented.

Equations (1987--Ackland-G-J--Nb--parameters--ipr1)
Notes: The file AckThet.pdf was obtained from http://homepages.ed.ac.uk/graeme/moldy/moldy.html and posted with the permission of G.J. Ackland.
File(s):
 
Citation: R. Fereidonnejad, A.O. Moghaddam, and M. Moaddeli (2022), "Modified embedded-atom method interatomic potentials for Al-Ti, Al-Ta, Al-Zr, Al-Nb and Al-Hf binary intermetallic systems", Computational Materials Science, 213, 111685. DOI: 10.1016/j.commatsci.2022.111685.
Abstract: Interatomic potentials for the Al-Ti, Al-Ta, Al-Zr, Al-Nb and Al-Hf binary systems have been developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The fundamental materials properties (structural, thermodynamic and elastic behaviors of different intermetallics) could be readily described with the potentials using molecular dynamic simulation (MD), in rational agreements with experimental or first principles data. The potentials are further utilized to develop an interatomic potential for the (TiZrNbHfTa)Al3 high entropy intermetallic compound (HEIC), which open the door to understand atomic scale behavior of HEICs.

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Notes: These files were provided by Rahele Fereidonnejad on August 24, 2022.
File(s):
 
Citation: D. Farkas, and C. Jones (1996), "Interatomic potentials for ternary Nb - Ti - Al alloys", Modelling and Simulation in Materials Science and Engineering, 4(1), 23-32. DOI: 10.1088/0965-0393/4/1/004.
Abstract: Interatomic potentials of the embedded-atom type were developed for the Nb - Al system via an empirical fitting to the properties of A15 Nb3Al. The cohesive energy and lattice parameters are fitted by the potentials, which also give good agreement with experimental values for the same properties in the D022 NbAl3 phase. A second interatomic potential was developed for the Nb - Ti system via a fitting to the lattice parameters and thermodynamic properties of the disordered BCC phase. The Al and Ti potentials used here are the same as those used in our previous work to derive Ti - Al potentials based on TiAl. This allows the use of the present potentials in conjunction with those previously derived interactions to study ternary Nb - Ti - Al alloys. The potentials were used to calculate the heats of solution of Al and Ti in Nb, and to simulate the Ti2NbAl orthorhombic phase.

LAMMPS pair_style eam/alloy (1996--Farkas-D--Nb-Ti-Al--LAMMPS--ipr1)
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Notes: This file was generated and tested by Ganga Purja Pun and Yuri Mishin (George Mason Univ.) using the files below that were supplied by Diana Farkas (Virginia Tech.). Testing information is in Test_report_AlTiNb.pdf. These files were approved by Dr. Purja Pun and Profs. Farkas and Mishin and posted on 1 Jul 2014.
File(s):
EAM tabulated functions (1996--Farkas-D--Nb-Ti-Al--table--ipr1)
Notes: These files were provided by Diana Farkas and approved by her on 1 Jul 2014.
File(s):
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Notes: Listing found at https://openkim.org. This KIM potential is based on the files from 1996--Farkas-D--Nb-Ti-Al--LAMMPS--ipr1.
Link(s):
 
Citation: H.-K. Kim, W.-S. Jung, and B.-J. Lee (2010), "Modified embedded-atom method interatomic potentials for the Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems", Journal of Materials Research, 25(7), 1288-1297. DOI: 10.1557/jmr.2010.0182.
Abstract: Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed.

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Notes: These potential files were obtained from http://cmse.postech.ac.kr/home_2nnmeam, accessed Nov 9, 2020.
File(s):
See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
 
Citation: H.-K. Kim, W.-S. Jung, and B.-J. Lee (2010), "Modified embedded-atom method interatomic potentials for the Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems", Journal of Materials Research, 25(7), 1288-1297. DOI: 10.1557/jmr.2010.0182.
Abstract: Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed.

LAMMPS pair_style meam (2010--Kim-H-K--Nb-C--LAMMPS--ipr1)
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Notes: These files are based on files obtained from http://cmse.postech.ac.kr/home_2nnmeam.
File(s):
See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
 
Citation: I. Sa, and B. Lee (2008), "Modified embedded-atom method interatomic potentials for the Fe–Nb and Fe–Ti binary systems", Scripta Materialia, 59(6), 595-598. DOI: 10.1016/j.scriptamat.2008.05.007.
Abstract: A semi-empirical interatomic potential formalism, the second-nearest-neighbor modified embedded-atom method (2NN MEAM), has been applied to obtain interatomic potentials for Fe–Nb and Fe–Ti systems based on the previously developed potentials for pure Fe, Nb and Ti. The present potentials generally reproduce the fundamental physical properties of the Fe–Nb and Fe–Ti systems accurately. The potentials can be easily combined with already-developed MEAM potentials for binary carbide or nitride systems and can be used to describe Fe–(Ti,Nb)–(C,N) multicomponent systems.

LAMMPS pair_style meam (2008--Sa-I--Fe-Nb--LAMMPS--ipr1)
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Notes: These potential files were obtained from http://cmse.postech.ac.kr/home_2nnmeam, accessed Nov 9, 2020.
File(s):
See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
 
Citation: X. Huang, L. Liu, X. Duan, W. Liao, J. Huang, H. Sun, and C. Yu (2021), "Atomistic simulation of chemical short-range order in HfNbTaZr high entropy alloy based on a newly-developed interatomic potential", Materials & Design, 202, 109560. DOI: 10.1016/j.matdes.2021.109560.
Abstract: Chemical short-range order (CSRO) in high entropy alloys (HEAs) has attracted interests recently and is believed to be capable for tuning their mechanical properties. However, the characterization of CSRO in HEAs through experimental methods remains challenging. In this work, a modified embedded-atom method interatomic potential with good accuracy for studying CSRO in HfNbTaTiZr alloy system was developed. By employing the potential, molecular dynamic/Monte Carlo simulation was performed to investigate the CSRO in HfNbTaZr HEA. The results indicated that Hf-Zr and Nb-Ta atom pairs were preferred in the BCC solid solution of HfNbTaZr, and a new type of CSRO with topological B2 order was predicted, which can help to understand the mechanical properties of HfNbTaZr HEA. It was also found that forming of CSRO was an incubation process for the precipitation in HfNbTaZr, implying the significance of CSRO on the phase stability or precipitation behavior of HEAs. The findings in the present work can help in understanding CSRO and establishing its relationship with precipitates in HEAs, and more topics related to CSRO and phase stability in HfNbTaTiZr alloy system can be further investigated by atomistic simulation.

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Notes: These files were provided by Xiusong Huang (Shenzhen University) on May 5, 2021 and posted with his permission.
File(s):
 
Citation: X.-G. Li, C. Chen, H. Zheng, Y. Zuo, and S.P. Ong (2020), "Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy", npj Computational Materials, 6(1), 70. DOI: 10.1038/s41524-020-0339-0.
Abstract: Refractory multi-principal element alloys (MPEAs) have exceptional mechanical properties, including high strength-to-weight ratio and fracture toughness, at high temperatures. Here we elucidate the complex interplay between segregation, short-range order, and strengthening in the NbMoTaW MPEA through atomistic simulations with a highly accurate machine learning interatomic potential. In the single crystal MPEA, we find greatly reduced anisotropy in the critically resolved shear stress between screw and edge dislocations compared to the elemental metals. In the polycrystalline MPEA, we demonstrate that thermodynamically driven Nb segregation to the grain boundaries (GBs) and W enrichment within the grains intensifies the observed short-range order (SRO). The increased GB stability due to Nb enrichment reduces the von Mises strain, resulting in higher strength than a random solid solution MPEA. These results highlight the need to simultaneously tune GB composition and bulk SRO to tailor the mechanical properties of MPEAs.

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Notes: Listing found at https://openkim.org.
Link(s):
 
Citation: M.I. Mendelev (2022), "to be published".

Notes: Mikhail Mendelev notes that "this is an improved version of 2016--Zhang-Y-Ashcraft-R-Mendelev-M-I-et-al--Ni-Nb where the crystal phase formation energies were taken into account."

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Notes: This file was provided by Mikhail Mendelev on Feb 11, 2021 and posted with his permission.
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Citation: Y. Zhang, R. Ashcraft, M.I. Mendelev, C.Z. Wang, and K.F. Kelton (2016), "Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy", The Journal of Chemical Physics, 145(20), 204505. DOI: 10.1063/1.4968212.
Abstract: The state-of-the-art experimental and atomistic simulation techniques were utilized to study the structure of the liquid and amorphous Ni62Nb38 alloy. First, the ab initio molecular dynamics (AIMD) simulation was performed at rather high temperature where the time limitations of the AIMD do not prevent to reach the equilibrium liquid structure. A semi-empirical potential of the Finnis-Sinclair (FS) type was developed to almost exactly reproduce the AIMD partial pair correlation functions (PPCFs) in a classical molecular dynamics simulation. This simulation also showed that the FS potential well reproduces the bond angle distributions. The FS potential was then employed to elongate the AIMD PPCFs and determine the total structure factor (TSF) which was found to be in excellent agreement with X-ray TSF obtained within the present study demonstrating the reliability of the AIMD for the simulation of the structure of the liquid Ni–Nb alloys as well as the reliability of the developed FS potential. The glass structure obtained with the developed potential was also found to be in excellent agreement with the X-ray data. The analysis of the structure revealed that a network of the icosahedra clusters centered on Ni atoms is forming during cooling the liquid alloy down to Tg and the Nb Z14, Z15, and Z16 clusters are attached to this network. This network is the main feature of the Ni62Nb38 alloy and further investigations of the properties of this alloy should be based on study of the behavior of this network.

LAMMPS pair_style eam/fs (2016--Zhang-Y--Ni-Nb--LAMMPS--ipr1)
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Notes: This file was sent by M.I. Mendelev (Ames Laboratory) on 13 December 2016 and posted with his permission. Update 19 July 2021: The contact email in the file's header has been changed.
File(s):
See Computed Properties
Notes: Listing found at https://openkim.org. This KIM potential is based on the files from 2016--Zhang-Y--Ni-Nb--LAMMPS--ipr1.
Link(s):
 
Citation: S. Starikov, and D. Smirnova (2021), "Optimized interatomic potential for atomistic simulation of Zr-Nb alloy", Computational Materials Science, 197, 110581. DOI: 10.1016/j.commatsci.2021.110581.
Abstract: We present a new classical interatomic potential for a study of the binary Zr-Nb system, taking into account a wide range of the components concentrations. The potential was developed by virtue of the force-matching method that is capable of ensuring a high accuracy at the description of the complex systems containing diverse crystal phases. At simulation of pure Zr, the potential correctly describes a relative stability of Zr phases (α-Zr, β-Zr and ω-Zr) and qualitatively reproduces the right arrangement of these phases in the phase diagram. It is remarkable that β-Zr phase is found to have a dynamically unstable structure at the low temperature, in agreement with the ab initio calculations. The potential can also play a role in considering the tasks related to the crystal defects in the Zr-Nb system. In support of this statement, we show the simulation results proving adequate representation of a number of key properties of the crystal defects in Zr-Nb system. In particular, the offered potential reproduces formation/solution energies of point defects with well accuracy. To illustrate wide application possibilities for the model, we made a prediction of atomic self-diffusion and impurity diffusion in Zr and Nb. Also, the potential ensures correct description of a screw dislocation in niobium, which is a crucial point for the investigation of plasticity.

Notes: This is an updated parameterization of 2017--Smirnova-D-E-Starikov-S-V--Zr-Nb. Most notably, this new version predicts the correct representation of the relative phase stability of zirconium phases.

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Notes: This file was provided by Sergei Starikov (Ruhr-University) on May 25, 2021 and posted with his permission.
File(s):
Citation: D.E. Smirnova, and S.V. Starikov (2017), "An interatomic potential for simulation of Zr-Nb system", Computational Materials Science, 129, 259-272. DOI: 10.1016/j.commatsci.2016.12.016.
Abstract: We report a new attempt to study properties of Zr-Nb structural alloys. For this purpose we constructed an angular-dependent many-body interatomic potential. The potential functions were fitted towards the ab initio data computed for a large set of reference structures. The fitting procedure is described, and its accuracy is discussed. We show that the structure and properties of all Nb and Zr phases existing in the Zr-Nb binary system are reproduced with good accuracy. The interatomic potential is appropriate for study of the high-pressure hexagonal ω-phase of Zr. We also estimated characteristics of the point defects in α-Zr, β-Zr and Nb; results are proven to correlate with the existing experimental and theoretical data. In case of α-Zr the model reveals anisotropy of the vacancy diffusion, in agreement with previous calculations and experiments. The potential provides an opportunity for simulation of Zr-Nb alloys based on α-Zr and β-Zr. This conclusion is illustrated by the results obtained for the alloys with different niobium concentrations: up to 7% in case of hcp alloys and up to 50% for bcc alloys.

Notes: The reference was updated on 17 January 2017. Update: This potential is known to have issues with pure zirconium phases. See 2021--Starikov-S-Smirnova-D--Zr-Nb for an updated parameterization.

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Notes: These files were sent by D. Smirnova (Joint Institute for High Temperatures, Russian Academy of Sciences) on 15 December 2016 and posted with her permission.
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Date Created: October 5, 2010 | Last updated: August 26, 2022