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# The potential for Vanadium in molecular dynamic simulation

One of the most significant factors in molecular dynamic simulatin is to choose the proper potential. Recently, I did some searching jobs on Vanadium (V) potential and finally decided which potential I am going to use. Here is a simple summary:**A brief introduction of EAM, F-S and MEAM potentials for BCC transition metals**

Before EAM, the pair potential, which had been proved to fail in some metals, was the only way to attempt to simulate defects such as dislocations, grain boundaies and cracks. In 1983, Daw and Baskes [1] presented EAM potential, they then extended this theory to impurities, surfaces in some FCC metals [2]. In 1984, Finnis and Sinclair [3] presented F-S potential for some transition metals. Then Rebonato [4] did some adaptation of the F-S potential for some BCC transition metal alloys in 1989. The EAM potential is based on density fuctional theory, while the F-S potential derives from a second-moment approximation to tight-binding. Their difference is that in F-S potential, the density fuction is a functional specific to the atomic types of both atoms I and J, so that different elements can contribute differently to the total electron density at an atomic site depending on the identity of the element at that atomic style [5]. Thus, F-S potential is more flexible. In 1989, M. I. Baskes et. al. [6] developed the EAM into MEAM, and he later modified the original MEAM potentials for 26 elements [7]. In 2000, Lee et. al. [8] presented second nearest-neighbor MEAM for Fe, which seems to be more accurate.

A review about EAM, F-S and MEAM potential can be found in [9].**The potentials for V**

In [3], Finnis and Sinclair presented the F-S potential for V, which was remedied by Ackland and Thetford [10] in 1987. Johnson and Oh [11] gave out an EAM potential for V in 1989, while Baskes presented V potential in [7]. These three V potentials (in [7], [10], [11]) were tested and compared in [12], in which the authors fitted the V potential to finite temperature properties.

Besides these potentials, Adams and Foiles [13] presented EAM potential for V in 1990, Han et. al. [14] developed F-S potential for V in 2003 in order to predict the behavior of point defects in metals, Lee and Baskes gave out second nearest-neighbor MEAM potential for V in [15].

According to [12], several published potentials for vanadium were fitted to incorrect value of 0.304 nm for the lattice constant, while the correct one should be 0.30274 nm. This means that the V potentials in [3], [7], [10], [11], [13] are incorrect. What's more, I am interested in neither the properties of V of finite temperature ([12]), nor the behavior of point defects ([14]).

Taking the reasons above into account, I choose MEAM potential for V in [15] to do my simulation. Of course, I did some tests using this potential for some factors I focus before the final decision.**Bibliography**

[1] Murray S. Daw and M. I. Baskes, Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals, Phys. Rev. Lett. 1983

[2] Murray S. Daw and M. I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces and other defects in metals, Phys. Rev. B 1984

[3] M. W. Finnis and J. E. Sinclair, A simple empirical N-body potential for transition metals, Philos. Mag. A 1984

[4] R. Rebonato, Adaptation of the Finnis-Sinclair potentials for conditions of extension and for b.c.c. transition metal alloys, Philos. Mag. Part B 1989

[5] LAMMPS Manual: pair_style eam/fs command

[6] M. I. Baskes, J. S. Nelson and A. F. Wright, Semiempirical modified embedded-atom potentials for silicon and germanium, Phys. Rev. B 1989

[7] M. I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Phys. Rev. B 1992

[8] Byeong-Joo Lee and M. I. Baskes, Second nearest-neighbor modified embedded-atom-method potential, Phys. Rev. B 2000

[9] Seong-Gon Kim, M. F. Horstemeyer et. al., Semi-empirical potential methods for atomistic simulations of metals and their construction procedures, J. Eng. Mater. and Tech. 2009

[10] G. J. Ackland and R. Thetford, An improved N-body semi-empirical model for body-centred cubic transition metals, Philos. Mag. A 1987

[11] R. A. Johnson and D. J. Oh, Analytic embedded atom method model for bcc metals, J. Mater. Res. 1989

[12] Manabu Satou, Sidney Yip and Katsunori Abe, Molecular dynamics simulation of vanadium using an interatomic potential fitted to finite temperature properties, J. Nuc. Mater. 2002

[13] James B. Adams and Stephen M. Foiles, Development of an embedded-atom potential for a bcc metal: Vanadium, Phys. Rev. B 1990

[14] Seungwu Han, Luis A. Zepeda-Ruiz et. al., Interatomic potential for vanadium suitable for radiation damage simulations, J. Appl. Phys. 2003

[15] Byeong-Joo Lee, M. I. Baskes et. al., Second nearest-neighbor modified embedded atom method potentials for bcc transition metals, Phys. Rev. B 2001

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