Vacancy formation and migration enthalpies were calculated by using ab initio pseudopotential techniques. The results (3.0 and 0.8eV, respectively) which were obtained by relaxing super-cells that contained 54 atomic sites were in excellent agreement with experimental data (3.1 and 0.7eV, respectively). The electronic entropy had a slight effect upon their temperature dependence. The effects of structural relaxation, which reduced the formation enthalpy by 14%, were significantly larger than for group-VI elements and were typical of the normal behavior for a body-centered cubic structure. The experimental tracer self-diffusion coefficient was well-predicted by rate theory; using estimates of the vibrational formation entropy and the attempt frequency.

First-Principles Study of Vacancy Formation and Migration Energies in Tantalum. A.Satta, F.Willaime, S.De Gironcoli: Physical Review B, 1999, 60[10], 7001-5