Impurity Diffusion in Cadmium

Abstract

Diffusion of impurities in single crystals of cadmium has been studied by tracer-sectioning techniques. For heterovalent diffusion the diffusion coefficients, in ${\mathrm{cm}}^2$ / sec, are given by $D_{\parallel }\left(\mathrm{In}\right)=\exp (-2.29\mathrm{}\pm 0.20)\exp [-\frac{(17.45\mathrm{}\pm 0.19)1000}{\mathrm{RT}}]$, $D_{\perp }\left(\mathrm{In}\right)=\exp (-2.41\mathrm{}\pm 0.16)\exp [-\frac{(16.94\mathrm{}\pm 0.15)1000}{\mathrm{RT}}]$, $D_{\parallel }\left(\mathrm{Ag}\right)=\exp (0.34\mathrm{}\pm 0.47)\exp [-\frac{(24.64\mathrm{}\pm 0.48)1000}{\mathrm{RT}}]$, $D_{\perp }\left(\mathrm{Ag}\right)=\exp (-0.39\mathrm{}\pm 0.62)\exp [-\frac{(25.07\mathrm{}\pm 0.65)1000}{\mathrm{RT}}]$, $D_{\parallel }\left(\mathrm{Au}\right)=\exp (0.34\mathrm{}\pm 0.08)\exp [-\frac{(25.47\mathrm{}\pm 0.08)1000}{\mathrm{RT}}]$, and $D_{\perp }\left(\mathrm{Au}\right)=\exp (1.15\mathrm{}\pm 0.22)\exp [-\frac{(26.43\mathrm{}\pm 0.22)1000}{\mathrm{RT}}]$. The activation energies obtained in this study could be interpreted with LeClaire's screening model. Good agreement between experimental results and theoretical estimates was obtained. For homovalent diffusion (including self-diffusion), the results are $D_{\parallel }\left(\mathrm{Zn}\right)=\exp (-2.04\mathrm{}\pm 0.26)\exp [-\frac{(18.03\mathrm{}\pm 0.25)1000}{\mathrm{RT}}]$, $D \left(\mathrm{Zn}\right)=\exp (-2.48\mathrm{}\pm 0.24)\exp [-\frac{(18.02\mathrm{}\pm 0.24)1000}{\mathrm{RT}}]$, $D_{\parallel }\left(\mathrm{Cd}\right)=\exp (-2.14\mathrm{}\pm 0.13)\exp [-\frac{(18.61\mathrm{}\pm 0.12)1000}{\mathrm{RT}}]$, $D_{\perp }\left(\mathrm{Cd}\right)=\exp (-1.70\mathrm{}\pm 0.19)\exp [-\frac{(19.59\mathrm{}\pm 0.19)1000}{\mathrm{RT}}]$, $D_{\parallel }\left(\mathrm{Hg}\right)=\exp (-1.55\mathrm{}\pm 0.07)\exp [-\frac{(18.78\mathrm{}\pm 0.06)1000}{\mathrm{RT}}]$, and $D_{\perp }\left(\mathrm{Hg}\right)=D_{\parallel }\left(\mathrm{Hg}\right)$. It is felt that valence and size effects are in competition for homovalent diffusion. The size effect appears dominant in the case of Cd as the base metal, whereas for Zn as the base metal the valence effect seems to dominate. A preliminary study of the isotope effect of Zn in Cd was also conducted. The resulting values of $E$ for diffusion parallel and perpendicular to the $c$ axis were 0.4388 ± 0.0495 and 0.6829 ± 0.1023 at 199.3°C. These results seems to rule out the interstitial mechanism as the dominant mechanism in agreement with the usual assumption that the vacancy mechanisms (basal and nonbasal) prevail for the hexagonal metals.