Residual resistivity of defects in metals.

Abstract

A simple expression for the residual resistivity of defects in metals is derived which includes the Bloch-wave character of the electronic structure of the host metal lattice at its Fermi surface. This expression involves, apart from Friedel phase shifts of the defect, only the average Fermi velocity and the average s, p, d, etc. partial-wave character of the electron states of the host metal atom at its Fermi energy, both of which are easily obtained in the course of a standard band-structure calculation. The explicit dependence on the partial-wave character makes the expression somewhat different from the well-known formula for the jellium matrix (which is, however, recovered in the free-electron limit), and the expression derived earlier by Gupta and Benedek. Calculations for impurities in copper show good agreement with experiment. We also show that the residual resistivities are extremely sensitive to the values of the Friedel phase shifts. Very minor changes in their values alter the residual resistivities dramatically. This indicates the major role played by these phase shifts in determining the residual resistivities, and the need for their accurate determination.