Correlation Effects in Impurity Diffusion

Abstract

Expressions are developed giving the correlation factor for an impurity diffusing in an otherwise pure lattice. These expressions will apply in general since, in the derivation, there is no requirement that there must be a large binding energy tending to create vacancy-impurity complexes. When this requirement is eliminated, accurate expressions can be obtained even for the nonclose-packed lattices. Both vacancy and interstitialcy mechanisms are treated. A matrix method developed by LeClaire and Lidiard for the face-centered cubic lattice is applied to various lattices to obtain approximate expressions for the correlation factor. Then a correction is applied giving the effect of those dissociating vacancies (or interstitialcies) which return to the impurity. It is found that the effect is the same as if only a fraction of the dissociative jumps actually occurred. If it is assumed that the effect of an impurity is quite localized, the probability of return can be calculated in a very straightforward manner. It is shown that the effect of returning vacancies (or interstitialcies) can be quite important. The resulting expressions are used to estimate the correlation factor in nondilute alloys.