Anisotropy of the Vacancy Migration in Ti, Zr and Hf Hexagonal Close-Packed Metals from First Principles

Abstract

The vacancy properties in group-IV hexagonal close-packed metals (Ti, Zr and Hf) have been investigated by Density Functional Theory (DFT) calculations performed with the SIESTA code. The migration energies are found to be systematically lower by »0.15 eV within the basal plane than out of the basal plane. The electronic origin of this significant contribution to diffusion anisotropy is evidenced by the analysis of the local electronic densities of states and by a comparison with and empirical potential. The average value of the migra- tion energy is in very good agreement with available experimental data in Zr. The activation energies for self-diffusion obtained assuming a vacancy mechanism are in good agreement with experiments in Zr and Hf, although slightly too small, but a significant discrepancy is observed in Ti.