Correlation Factors for Impurity Diffusion. bcc, Diamond, and fcc Structures

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Abstract
A general equation for the impurity correlation factor is derived in terms of effective escape frequencies. This equation applies even when the vacancy-jump frequency for association of a vacancy-impurity complex differs from the frequency far from an impurity. Parameters in this equation are calculated for body-centered cubic, diamond, and face-centered cubic structures. In these calculations, it is assumed that vacancy jumps which do not involve a nearest neighbor of the impurity are unaffected by the impurity but that association and dissociation jumps, which do involve nearest neighbors of the impurity, are affected. Analytical expressions for the correlation factor in terms of vacancy-jump-frequency ratios are obtained. In the bcc and fcc structures, results are given for two cases: (A) where all dissociative jumps are equally likely, and (B) where a vacancy which makes a dissociative jump to a second-nearest-neighbor site is still partially bound to the impurity, but vacancies which make dissociative jumps to other sites are not. In the diamond structure, case A cannot be distinguished from case B. Results for the diamond structure and for case A in the fcc structure differ only slightly from previous more approximate results. A comparison is made between the present random-walk method of calculating correlation factors and the pair-association method.