Modified Model of Diffusion by Interstitial-Vacancy Pairs

Abstract

In order to adequately describe the diffusion of mercury in lead, the interstitial-vacancy pair model is redeveloped in a form which only allows impurity jumps which create or annihilate the pair and nearest-neighbor exchanges with the vacancy by solvent atoms, but in which the correlation coefficients for these three jump types are calculated explicitly. These calculations are done numerically for a range of jump frequencies using the formalism of Howard. In this new model, expressions are developed for the diffusivity, correlation coefficient, and enhancement of the solvent diffusivity which show behavior similar to the older models except that now ${f}_{0}<\frac{{b}_{11}}{[\frac{{D}_{2}(0)}{{D}_{1}(0)}]}\ensuremath{\le}3.80$, a feature true of the diffusion of both mercury and cadmium in lead which is not explicable in terms of the older model. This model is also in adequate agreement with the other features of diffusion in these two systems. It is demonstrated, however, that a complete description of the defects' natures requires measurements of a nondiffusive sort, and some suggestions are made.