Anisotropic Isotope Effect for Diffusion of Zinc and Cadmium in Zinc

The sectioning technique and the half-life method of isotope discrimination were used to study the relative rates of diffusion of ${\mathrm{Zn}}^{65}$ and ${\mathrm{Zn}}^{69m}$, and of ${\mathrm{Cd}}^{109}$ and ${\mathrm{Cd}}^{115}$ in high-purity zinc single crystals. The isotope effect, $E_{\beta }^{}{}_{}{}^{\alpha }=\frac{\left(\frac{1-D^{\alpha }}{D^{\beta }}\right)}{[1-{\left(\frac{m^{\beta }}{m^{\alpha }}\right)}^{\frac{1}{2}}]}$, was measured; $\frac{D^{\alpha }}{D^{\beta }}$ and $\frac{m^{\alpha }}{m^{\beta }}$ are the ratios of the diffusion coefficients and of the masses of the two isotopes $\alpha$ and $\beta$, respectively. The average of the values of $E_{69}^{}{}_{}{}^{65}$ at 411.6 and 382.8°C for diffusion of zinc isotopes in zinc, parallel to the hexagonal axis, is 0.669±0.024, whereas the corresponding value perpendicular to the hexagonal axis is 0.687±0.022. These results are consistent with diffusion by vacancy (basal and nonbasal) mechanisms and appear to rule out the interstitial, ring, interstitialcy, and crowdion as the dominant mechanism. The observed isotope effect, both for parallel and perpendicular diffusions, is thus about 13% less than the value predicted on the basis of the inverse-square-root mass dependence of the atomic jump frequency, i.e., the correlation factor for self-diffusion. This deviation is apparently due to many-body aspects of diffusion, and on these considerations it is concluded that a small fraction (about 13%) of the translational kinetic energy of the activated state is possessed by atoms other than the jumping atom. At 410.1°C, the values of $E_{115}^{}{}_{}{}^{109}$ for diffusion of cadmium isotopes in zinc, parallel and perpendicular to the hexagonal axis, are 0.507±0.034 and 0.317±0.032, respectively. These values indicate an attractive interaction between the cadmium impurity and the vacancy, the interaction being larger when both of them are in the same basal plane. Under the assumption that the many-body consideration is essentially the same as for self-diffusion, and by making some reasonable simplifying approximations as to how the presence of the impurity influences the vacancy jump, the enhancement of cadmium diffusion over zinc diffusion is examined. It is found that the rapid interchange of the cadmium impurity with the vacancy and the greater density of the vacancies next to the cadmium impurity are both responsible for the enhancement in the diffusivity of cadmium in zinc.