Correlation factor and isotope effect for dissociative impurity diffusion in f.c.c. metals

Abstract

A model of dissociative (interstitial-substitutional) impurity diffusion in f.o.c. lattices is discussed, in which the binding energy (E ₁ ∞^B) between interstitial impurity atoms and lattice vacancies is assumed to go to zero at third nearest interstitial sites. Taking E ₁ ∞^B as a variable parameter, the correlation factor (f) and the isotope effect (E) are formulated in terms of various jump frequency ratios, including the ratio of interstitial to vacancy mobilities. It is shown that f and E can have drastically different values due to the possible separate mobility of the impurity interstitials and the lattice vacancies. In the limiting case of the vacancy being static relative to the interstitial, E=1, whereas f can be very small. Values of E and f are calculated for the specific case of diffusion in Pb, and it is shown that small values of E(≃ 0·2) can occur, even at small values of E ₁∞^B(<0·2 eV), in realistic ranges of the various jump frequencies.

It is suggested that using the general dissociative diffusion model presented here, it may be possible to explain the small values of E measured recently for Ag diffusion in Pb.