Vacancy formation energies and volumes in simple metals

Abstract

The most popular theories of vacancy formation energy have been of two apparently independent kinds. The first is based on the jellium model, in which the vacancy is represented by a spherical hole in the uniform positive background. The second approach, originated by Harrison [5], is to apply second order perturbation theory to the free electron gas. Practitioners of both methods, e.g. [l-4] for the first and [S-l I] for the second, have often obtained good agreement with experiment but it has not previously been clear to what extent this is fortuitous. In the present paper we clarify the relative merits of the two approaches. The vacancy formation volume s2’ has often been calculated with pair potentials [ 12,131. Although pair potentials follow naturally from second order perturbation theory they only represent a small fraction of the total energy E so it is important to know how SLf depends on the rest of E. We reformulate the problem and find that indeed pair potentials alone are quite inadequate.