Diffusion of Cadmium in Lead

Abstract

The diffusivity ${D}_{2}$ of cadmium in high-purity lead single crystals has been measured from 150\ifmmode^\circ\else\textdegree\fi{}C to the melting point, using tracer and sectioning techniques, and is described by ${D}_{2}=0.409\mathrm{exp}(\ensuremath{-}\frac{21230}{\mathrm{RT}})$ ${\mathrm{cm}}^{2}$/sec. Lead self-diffusivity is enhanced by the addition of cadmium in accordance with ${D}_{1}={{D}_{1}}^{0}\ifmmode\times\else\texttimes\fi{}(1+{b}_{1}X+{b}_{2}{X}^{2}+{b}_{3}{X}^{3})$, where ${b}_{i}$ are the linear and higher-order enhancement factors, and ${{D}_{1}}^{0}$ and ${D}_{1}$ are the self-diffusivity of lead in pure lead and in lead alloys containing $X$ atom fraction of cadmium, respectively. It is found that ${b}_{1}\ensuremath{\cong}\frac{{D}_{2}}{{{D}_{1}}^{0}}$, varying from 19 to 45 over the temperature range 300-198\ifmmode^\circ\else\textdegree\fi{}C. It is shown from the results of Howard and Manning that the minimum linear enhancement factor for the vacancy mechanism is ${b}_{min}=\ensuremath{-}18+1.9448(\frac{{D}_{2}}{{{D}_{1}}^{0}})$, substantially larger than that observed. The fast diffusion of cadmium cannot then be accounted for on the basis of the model proposed by Lidiard for the simple vacancy mechanism. It is suggested that cadmium, like the solutes Ag, Au, and Cu, dissolves both interstitially and substitutionally in lead, the enhancement of lead self-diffusion being associated with an interaction between vacancies and interstitial cadmium ions. A comparison of diffusion data for several impurities in lead shows that the dominant mechanism of solute diffusion is determined primarily by solute valence. Since the dominant diffusion mechanism of a solute is a natural consequence of its degree of interstitial dissolution, it is proposed that solute valence plays a major role in determining the energetics of interstitial dissolution.