First-principles analysis of solute diffusion in dilute bcc Fe-X alloys

The diffusivities of substitutional impurity elements in iron have been computed with ab inito electronic density functional techniques, using exchange-correlation functional PW91. Excess entropies and the attempt frequency for a jump were determined by calculating phonon frequencies in the harmonic approximation. The influence of the degree of spontaneous magnetization on diffusivity is taken into account by means of the Girifalco model. The activation energy for diffusion has been determined by computing the vacancy formation energy, impurity-vacancy binding energies, migration barrier energies, and the effective energy associated with correlation of vacancy-mediated jump. For each type of impurity atom these contributions have been evaluated and analyzed up to and including the fifth nearest-neighbor shell of the impurity atom. It is found that impurities that have a low migration energy tend to have high effective energy associated with vacancy migration correlation, and vice versa, so that the total diffusion activation energies for all impurities are surprisingly close to each other. The strong effect of vacancy migration correlation is found to be associated with the high migration energy for iron self-diffusion, so that movement of vacancies through the iron bulk is in all cases, except cobalt, the limiting factor for impurity diffusion. The diffusivities calculated with the PW91 functional show good agreement with most of the experimental data for a wide range of elements.