Atomic self-diffusion anisotropy of HCP metals from first-principles calculations

A plane wave pseudo-potential method based on density functional theory is employed to calculate the migration energy barrier for the atomic self-diffusion in HCP metals including Mg, Zn, Ti, Zr, and Hf. The influences of some key factors (plane-wave cutoff energy, k-mesh, supercell size, and geometric optimization scheme) on the calculated migration energy barrier and its anisotropy are systematically investigated. We show that the supercell size affects heavily the migration energy barrier and its anisotropy for the metals with valence d electrons (Ti, Zr, and Hf) but not for the ones with only valence s metals (Mg). In general, the anisotropy of the migration energy barrier reduces with increasing size of the supercell especially for Ti, Zr, and Hf. The optimization of the shape and volume of the supercell matters for the migration energy barrier calculated with the small size supercell but not for that calculated with the large supercell. With the calculated migration energy barrier, the self-diffusion coefficients are evaluated based on the transition state theory and compared with other first-principles calculations and the experimental measurements.