Theory of impurity diffusion in metals

Abstract

In a previous paper (Le Claire 1962) a simple electrostatic model was proposed for calculating the difference ΔQ between the activation energy for diffusion of an impurity in a metal and that for self-diffusion in the pure metal. The model is extended in the present paper to deal with the diffusion of impurities having the same valency as the solvent (homovalent impurities). For such cases the impurity is represented by a square potential well of depth equal to the difference between the electron-ground state energies of solute and solvent. Values of the perturbation potential due to such an ‘impurity’, calculated in both a Thomas-Fermi approximation and from a first-order solution of the March and Murray equations, are used to calculate ΔQ. For all presently known cases of homovalent diffusion the calculations give values for ΔQ close to those observed and always of the correct sign.