Electrostatic fields round localized defects in metals

Abstract

A procedure for dealing with localized defects in metals is proposed, based on three main assumptions. First, the validity of the Thomas-Fermi approximation is assumed, secondly departures of the perturbing potentials from spherical symmetry are neglected, and thirdly, no account is taken of any relaxation of the lattice which may occur on the introduction of localized defects. However, the framework outlined is sufficiently general to enable the second assumption to be avoided, should this turn out to be necessary. It is expected that the method will be useful for foreign atoms entering the lattice substitutionally, provided the atomic size is such that no serious distortion of the lattice is produced, and also for vacancies, although in this latter case it will no doubt eventually prove necessary to consider relaxation effects. The method proposed is illustrated by studying numerically the case of a vacancy in copper, and an approximate self-consistent field is established for the perturbed lattice, based on the method of Slater and Krutter for the unperturbed crystal. A partial wave analysis using the free-electron approximation has then been carried out. The resistivity comes out considerably larger than that obtained by previous workers and possible reasons for this are discussed.