Application of Pseudopotentials to the Theory of Self-Diffusion in Metals

Abstract

A pseudopotential theory for the energetics of vacancy migration is formulated by a total-energy comparison of two vacancy-lattice configurations. Band-structure and electrostatic energy contributions are found to be significant. Energy of motion is determined as a function of diffusing atom and vacancy positions for the three common metal geometries. When combined with a prior theory for formation energy, activation energies for self-diffusion are obtained. Reasonable agreement with experiment is noted for the close-packed geometries using phenomenological pseudopotentials obtained from previous studies. For example, the observed anisotropy in hcp diffusion is accurately described for magnesium. The neglect of lattice relaxation in our simple model becomes a more significant effect in the case of the bcc alkali metals. Here the calculated formation energies are considerably larger than experiment, leading to overestimation of the activation energies for the self-diffusion of vacancies. When our approach is used to test various pseudopotential form factors, the model potentials which best fit the phonon dispersion curves produce the most reasonable values of activation energy.