Saddle-point configuration in impurity diffusion in face-centred cubic metals

Abstract

In order to calculate the changes in activation energies from self-diffusion values when impurities diffuse in simple matrix metals, we have considered the saddle-point configuration in a point-ion model using low-order perturbation theory. It is shown why, in this calculation, it is necessary to transcend the Sommerfeld model, for an essential feature is the difference in the electrostatic energy of interaction with the lattice for the impurity atom at a lattice site and at the saddle-point. A value for the change in the energy of movement is obtained and for Zn diffusing in copper the result is 0.079 ev, whereas a recent theory of Le Claire, who used a model of the saddle-point due to Huntington, gives 0.22 ev. The change in activation energy is therefore dominated by this term in Le Claire's treatment, whereas in the present theory the energy of formation contribution is almost as large as the change in the energy of movement. There remains a contribution from correlation in impurity diffusion jumps. Le Claire estimated this as 0.10 ev for Zn in Cu. However, Manning has shown recently that for Cd in Ag, the correlation correction is ∼0.05 ev. Adopting this value, we find an activation energy of 0.11 ev, to be compared with the experimental value of 0.17 ev. Considering the approximations involved, the agreement seems satisfactory.