The electrical resistivity due to structural defects

Abstract

Starting from the Greene-Kohn (1965) solution of the Boltzmann equation, a general expression for the electrical resistivity of a structural defect is obtained. The defects are described in terms of atomic positions and the scattering properties of the individual atoms comprising the defect are treated in terms of the pseudopotential theory developed by Ziman (1964) and Harrison (1966). It is found that, in a way similar to the factorization of the potential matrix element into a structure factor and a form factor, the expression for the resistivity contains factors depending only on the defect structure, and some simple resistivity matrices which require evaluating only once for any given metal. Applications to two- and three-centre scattering problems, and to the resistivity of the strain field around a point defect, are given in order to illustrate the suitability of the new expression both for deriving formal properties of defect resistivity, and for computation in particular cases.