Diffusion of Copper and Gallium in Single Crystals of Zinc

Abstract

The sectioning technique was used to study the diffusion of radioactive tracers in high-purity zinc single crystals. Diffusion both parallel and perpendicular to the hexagonal axis was measured. The diffusion of ${\mathrm{Cu}}^{64}$ was measured over the temperature range from about 338\ifmmode^\circ\else\textdegree\fi{}C to 415\ifmmode^\circ\else\textdegree\fi{}C with the results ${D}_{\mathrm{II}}=(2.22\ifmmode\pm\else\textpm\fi{}0.57)\mathrm{exp}[\ensuremath{-}(29.53\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}] \frac{{\mathrm{cm}}^{2}}{sec},$ ${D}_{\ensuremath{\perp}}=(2.00\ifmmode\pm\else\textpm\fi{}0.54)\mathrm{exp}[\ensuremath{-}(29.92\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ The diffusion of ${\mathrm{Ga}}^{72}$ was measured over the range from about 240\ifmmode^\circ\else\textdegree\fi{}C to 403\ifmmode^\circ\else\textdegree\fi{}C with the results ${D}_{\mathrm{II}}=(0.016\ifmmode\pm\else\textpm\fi{}0.001)\mathrm{exp}[\ensuremath{-}(18.40\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ ${D}_{\ensuremath{\perp}}=(0.018\ifmmode\pm\else\textpm\fi{}0.001)\mathrm{exp}[\ensuremath{-}(18.15\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ Copper diffused at a rate faster than gold but slower than silver. As in silver and gold, ${D}_{\mathrm{II}}g{D}_{\ensuremath{\perp}}$; but the anisotropy was much smaller in Cu than in Ag or Au. The measured values of gallium fall somewhat below those for indium and show ${D}_{\ensuremath{\perp}}g{D}_{\mathrm{II}}$. The relative diffusion rates are qualitatively in accord with the predictions of LeClaire's theory of homovalent diffusion. The sign of anisotropy is explained in terms of the electrostatic interaction between the diffusing ion and the vacancy, and the reduced anisotropy of copper diffusion is interpreted as evidence of a size effect.