Diffusion of Interstitial Solute-Vacancy Pairs in a Dilute Alloy

It has been proposed that the diffusion of cadmium in lead, which is inconsistent with the vacancy mechanism of solute diffusion, occurs by means of an interstitial migration which is strongly correlated because of an attraction between interstitial cadmium ions and vacancies. It is plausible that cadmium, like the noble-metal solutes, should dissolve in lead by the dissociative mechanism, but interact strongly with vacancies by a screened electrostatic interaction. A thermodynamic model of a dilute dissociative solid solution is developed, and expressions for the equilibrium fractions of substitutional, interstitial, and interstitial solute—vacancy close-pair solute states are derived. Following the method of Lidiard, the solute diffusivity and linear enhancement of self-diffusion in this dissociative fcc alloy are calculated. It is shown that in the limit of tightly bound close pairs, the linear-enhancement factor is $b_{11}=f_0\left(\frac{D_2^{}{}_{}{}^0}{D_1^{}{}_{}{}^0}\right)$, in close agreement with the observed linear enhancement of lead self-diffusivity by cadmium additions. It is, therefore, inferred that cadmium diffuses in lead by means of this bound-close-pair mechanism. It is also shown that the solute correlation factor, and therefore the isotope effect for solute diffusion must be very small for this mechanism of diffusion.