N-body interatomic potentials for hexagonal close-packed metals

Abstract

Finnis-Sinclair (F-S) type many-body potentials have been constructed for eight hexagonal metals: Co, Zr, Ti, Ru, Hf, Zn, Mg and Be. The potentials are parameterized using cubic splines and fitted to the cohesive energy, unrelaxed vacancy formation energy, five independent second-order elastic constants and two eauilibrium conditions. Hence, each of the constructed potentials represents a stable hexagonal close-packed lattice with a particular non-ideal c/a ratio. In the F-S scheme the many-body part is represented by a sauare root function and this form implies that C₁₂ – C₆₆>0. However, C ₁₂ –C₆₆ is negative for Zn, Be and Ru at Iow temperatures. For this reason a modified many-body function has been employed for these metals. To ensure the applicability of the potentials in modelling of extended lattice defects, the mechanical stability of the corresponding hexagonal close-packed lattice with respect to large homogeneous deformations has been tested. For all the metals considered, the h.c.p. lattice is shown to be energetically most stable when compared with f.c.c, b.c.c, body-centred-tetragonal and simple hexagonal lattices. In the context of the testing of the potentials, the stacking fault energies on the basal piane have also been calculated. They are in the experimentally-expected range for most metals considered. These tests demonstrate that there is no indication of unphysical instabilities even for very large deviations from the eauilibrium structure, and the potentials are thus suitable for studies of extended lattice defects in both divalent and transition hexagonal metals. As an application, phonon dispersion relations have been calculated. They are in a good agreement with experiments, with the exception of the optical branch in the [001] direction where electronic effects play a dominant role. Finally, the self-interstitial formation energies have been evaluated for seven possible sites. This calculation suggests that in all hexagonal metals the crowdion and the octahedral site are the most favourable interstitial configurations.