Vacancy properties in 5d bcc transition metals: Ab initio study at finite electron temperature

The self-diffusion constants for the monovacancy mechanism in the 5d transition-metals with bcc structure (β-Hf, Ta and W) are investigated by first-principles pseudopotential calculations within the framework of the Local Density Functional Theory. The formation and migration energies, calculated for relaxed configurations using supercells containing 27 and 54 atomic sites, are in quite good agreement with experimental data in Ta and W, with a discrepancy lower than 10%. Preliminary results in β-Hf using smaller supercells suggest very large relaxation energies. The effect of finite electron-temperature is shown to be quite important, and very different from one element to the other: the electron contribution to the activation entropy is negative in Ta and positive in W, reaching respectively -2 k_B and 2 k_B at the melting temperature. Using simple estimates for the attempt frequencies and the vibrational formation entropies, the calculated self-diffusion coefficient is in exceptional agreement with experiments in W, and clearly reproduces an accelerated diffusivity in Ta.