On the theory of impurity diffusion in metals

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Abstract
The theory of diffusion proposed by Lazarus (1954), in which attention was directed to the effects on diffusion properties of the electrostatic interaction between an impurity and a vacancy, is re-examined and a model proposed which, in particular, allows a more direct estimation of the difference in the activation energies for jumps of an impurity atom and a solvent atom. This difference is simply related to the electrostatic interaction between the excess charge Ze of the impurity and the two half-vacancies which flank it at the saddle point. Calculated values of the difference between an observed activation energy for impurity diffusion and that for self-diffusion of the (noble metal) solvent turn out to be in good agreement with experiment. As in the original treatment by Lazarus, the effective charge difference between solute and solvent ions is a central parameter of the model and magnetic properties are invoked to suggest values for this in cases where the solute is a transition metal. The contribution from the temperature dependence of the correlation factors, which is also estimated from the model, appears to be considerable and may be connected with the difference often observed between activation energies for diffusion directly measured and those obtained indirectly, for example, by internal friction measurements. Estimates also are made, with satisfactory results, of the correlation factors and the effects of a solute on the solvent diffusion rates. The ratios of the vibrational frequencies of solute and solvent are inferred from the model and their order of magnitude shown to be consistent with the expected effect of the electrostatic interaction between vacancy and solute.