Embedded - Atom - Method Interatomic Potentials for BCC - Iron
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nNTE•ATOMIC
EMBEDDED - ATOM - METHOD FOR
POTENTIPALS
BCC - IRON
G. Simonelli, R. Pasianot, E.J. Savino Departamento de Materiales, Comisi6n Nacional de Energfa At6mica, Av. Libertador 8250, (1429) Buenos Aires, Argentina. ABSTRACT An embedded-atom-method (EAM) interatomic potential [1] for bcc-iron is derived. It is fitted exactly to the lattice parameter, elastic constants, an approximation to the unrelaxed vacancy formation energy, and Rose's expression for the cohesive energy [2]. Formation energies and relaxation volumes of point defects are calculated. We find that the relative energies of the defect configurations depend on the functional fitting details of the potential considered, mainly its range: the experimental interstitial configuration of lowest energy can be reproduced by changing this parameter. This result is confirmed by calculating the same defect energies using other EAM potentials, based on the ones developed by Harrison et al. [3]. INTRODUCTION Atomistic simulation is a powerful tool for studying defect properties in materials. To deal with this kind of problems, which involve a great number of atoms, only semi-empirical potentials are feasible for representing the atomic interactions. The pair approximation, used almost exclusively during the 60's and 70's, is being quickly superseded by semi-empirical approaches to the many-body interaction problem, inherent to the solid state. Among these, the embedded-atom-method (EAM) [1], and the N-body potentials (FS) [4], are well known; they have removed some inadequacies of the pair potentials, and allowed to treat surfaces and cavities on a better physical basis. In the EAM approximation, the energy of the lattice is written as
E=E Ei •(1) i
where E, is the energy associated to each site i:
E,= 1/2k V(RP) + F(p,) joi
(2)
The first term V(Rv) represents the pair part of the interaction; it depends only on the distance R, between atoms i and j. The second term takes account of the many-body interactions. F(p1 ) is the energy to embed an atom into the local electron density p,, which is calculated as a linear superposition of atomic electron densities (3) pi =•O (Ry) Though it was shown that semi-empirical many-body potentials of this type cannot handle covalent bonding adequately, and some extensions of the method have been given [5,6], there are several developments to treat transition metals [3,4,7-9]. In this work we fit EAM potentials for bcc-iron modifying the scheme presented by Pasianot et al. [5], in order to obtain a more systematic procedure. The many-body Mat. Res. Soc. Symp. Proc. Vol. 291. @1993 Materials Research Society
568
contribution to the shear elastic constants in their eqs. (15-b) and (15-c) is eliminated, so as to recover the EAM approximation. Two different potentials are constructed. One of them includes up to third neighbors in the interaction and the other, up to second neighbors. We compute the formation energies and relaxation volumes of a vacancy and of various interstitial configurations using these potential
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