Theory of impurity scattering in dilute metal alloys based on the muffin-tin model

Abstract

The exact electronic eigenstates of a single substitutional impurity in an otherwise perfect lattice of muffin-tin potentials are developed for the purpose of investigating impurity scattering in dilute metal alloys. The impurity eigenfunctions are determined by an extension of the Green's-function method of band-structure calculation. Expressions are derived for the transition and scattering matrices describing impurity-induced elastic scattering between two Bloch states. These results are then related to a number of experimental situations; namely to measurements of residual resistivity, Dingle temperatures, Knight-shift satellites, and spin-lattice relaxation in conduction-electron spin resonance. The formal expressions depend upon the impurity and host atomic scattering phase shifts and upon the band structure of the host lattice through Bloch-wave amplitude coefficients and Brillouin-zone integrals of the inverse of the Green's-function secular matrix. The atomic scattering phase shifts can be determined from ab initio calculations of the muffin-tin potentials or can be inferred from semiempirical analysis of experimental data.