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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
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.
LAMMPS pair_style eam/alloy (2010--Fellinger-M-R--Nb--LAMMPS--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. 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."
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
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.
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.

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.
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)
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.
EAM tabulated functions
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)
Notes: This file was sent by M.I. Mendelev (Ames Laboratory) on 13 December 2016 and posted with his permission.
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.

LAMMPS pair_style adp (2017--Smirnova-D-E--Zr-Nb--LAMMPS--ipr1)
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.
Date Created: October 5, 2010 | Last updated: October 02, 2018