Development of anN-body interatomic potential for hcp and bcc zirconium

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Abstract
An interatomic potential based on the second-moment approximation of the tight-binding scheme is developed for zirconium, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of the hcp phase. In this work we attempt to model realistically two different crystallographic phases of a solid with the same potential. The reliability of our potential is tested in both the hcp and the bcc phases with regard to defect properties, thermal expansion, phonon properties, and mean-square displacements. For this purpose, we perform quenched molecular-dynamics relaxations, quasiharmonic lattice-dynamics calculations, and molecular-dynamics simulations. The low vacancy-formation and migration energies found in the bcc phase are consistent with the fast diffusivity experimentally observed. Unlike some other N-body potentials recently proposed to model bcc transition metals, our potential is not affected by the flaw of unphysical or even negative thermal expansion. We obtain thermal expansions that agree well with experiments in both phases, although they turned out to be slightly too large. The phonon-dispersion curves and, in particular, the anomalies in the bcc phase are well reproduced. We emphasize the stabilization with temperature of the T1 N-point phonon of the bcc phase, which is related to the bcc- to hcp-phase transition. We obtain a temperature dependence of this mode much weaker than in the experimental case. This influences the temperature behavior of the vibrational properties: In particular the mean-square displacement is markedly higher than the one extracted from experiments in the bcc phase at high temperatures. On the other hand, mean-square displacements in the hcp phase are in excellent agreement with experiment. The results are quite satisfactory in view of the small number of fitting parameters and the difficulties commonly encountered in matching the properties of bcc metals.