Isotope Effect for the Diffusion of Cadmium in Lead

Abstract

This experiment to determine the isotope effect for diffusion of ${\mathrm{Cd}}^{109}$ and ${\mathrm{Cd}}^{115m}$ in pure lead was performed as a critical test of the proposed interstitial-vacancy pair mechanism of solute diffusion. The relative diffusivity of the two radioisotopes was determined, after sectioning, by counting with a thin NaI detector system, using energy discrimination. Stability and reproducibility of the count rates were tested and verified, an upper limit on the effect of crossover shown to be negligible, and a zero-isotope-effect experiment performed successfully. The isotope effect for the volume diffusion of cadmium in lead was determined to be $(\frac{D_{109}}{D_{115m}}-1)=0.0032\mathrm{}\pm 0.001$ at 248°C, corresponding to a solute correlation factor $f=0.12\mathrm{}$ for a mechanism involving single atomic jumps. It is then shown that this result, together with previous results for the solute and self-diffusivities $D_2^{}{}_{}{}^0$ and $D_1^{}{}_{}{}^0$ and the linear-enhancement factor $b_{11}$ for self-diffusion, are inconsistent with the simple vacancy, interstitial, interchange, and ring mechanisms of solute diffusion, but agree with predictions of the model for solute diffusion by means of interstitial solute-vacancy pairs. The migration of associated vacancies results in a strong correlation of successive atomic jumps of bound interstitial solute atoms.