Diffusion of Single Vacancies and Divacancies in Quenched Gold

Abstract

An effective diffusion coefficient ${D}_{\mathrm{eff}}$, and an effective energy of migration ${E}_{m}$ are derived which describe the combined diffusion of single vacancies and divacancies which are in thermal equilibrium. ${D}_{\mathrm{eff}}$ is the appropriate diffusion "constant" to be used in Fick's law, if one wishes to describe the flow of voids, and expresses the fact that each vacancy during its random walk spends part of its lifetime as a single vacancy and part of its lifetime as a divacancy. ${E}_{m}$ can be expressed in terms of ${{E}_{m}}^{1}$ and ${{E}_{m}}^{2}$ (the energies of migration of a single vacancy and a divacancy, respectively), and is concentration- and temperature-dependent. Its minimum is ${{E}_{m}}^{2}\ensuremath{-}{B}_{2}$, where ${B}_{2}$ is the binding energy of a divacancy. From analysis of measurements of ${E}_{m}$ on Au specimens quenched from above 800\ifmmode^\circ\else\textdegree\fi{}C, one finds that ${{E}_{m}}^{2}\ensuremath{-}{B}_{2}\ensuremath{\sim}0.56$ eV, or more directly that ${{E}_{m}}^{1}+{B}_{2}\ensuremath{-}{{E}_{m}}^{2}=0.26\ifmmode\pm\else\textpm\fi{}0.03$ eV. The same value for this latter parameter was derived from another independent experiment, namely from the critical concentration of vacancies for which clustering will just occur.The binding energy of a divacancy in Au was observed to be: ${B}_{2}=0.10\ifmmode\pm\else\textpm\fi{}0.03$ eV, and its energy of migration: ${{E}_{m}}^{2}=0.66\ifmmode\pm\else\textpm\fi{}0.06$ eV. ${B}_{2}$ was obtained from an analysis of the decrease in resistivity observed during the transient process in which single vacancies and divacancies come into equilibrium with one another. In addition it was found that the resistivity of a divacancy is (4.6\ifmmode\pm\else\textpm\fi{}3)% less than that of two well-separated single vacancies.