An atomistic study of formation and migration of vacancies in (1121) twin boundaries in Ti and Zr

Abstract

Abstract The formation and migration of vacancies in (1121) twin boundaries in α-Ti and α-Zr are studied by computer modelling. Three empirical central force potentials constructed within the embedded-atom method are used to represent atomic interactions. Minimum-energy structures for the grain boundary are found first and the vacancy is then introduced by removing an atom and allowing further relaxation of the structure. Formation energies, entropies and relaxation volumes are calculated for different positions of vacancies. In order to analyse the vacancy migration, and thus the boundary self-diffusion, various vacancy jumps have been investigated and the corresponding migration energies and entropies calculated. The most probable paths composed of these simple jumps are then proposed. Both the formation and the migration free energies are significantly lower than in the bulk which demonstrates the role of the grain boundary as a vacancy sink and a fast diffusion channel. These free energies are then employed in evaluation of the diffusion coefficient tensor, the effective activation energies Qjj and the pre-exponential factors D 0jj when the jj component of this tensor is assumed to follow an Arrhenius relationship Djj = D 0jj exp (-Qjj /k B T). The boundary diffusion is then contrasted with the bulk diffusion and the calculated diffusion coefficients compared with available experimental data.