Isotope Effect in Self-Diffusion in Palladium

Abstract

The diffusion of ${\mathrm{Pd}}^{103}$ in single crystals of palladium has been measured over the temperature range of 1050-1500\ifmmode^\circ\else\textdegree\fi{}C by the tracer-sectioning technique. The results are $D={{0.205}_{\ensuremath{-}0.04}}^{+0.05}\mathrm{exp}[\ensuremath{-}\frac{(63600\ifmmode\pm\else\textpm\fi{}650)}{\mathrm{RT}}]{\mathrm{cm}}^{2}/sec.$Four measurements of the isotope effect for diffusion of ${\mathrm{Pd}}^{103}$ and ${\mathrm{Pd}}^{112}$ in each of four single crystals of palladium have been made between 1450 and 1500\ifmmode^\circ\else\textdegree\fi{}C. The measured isotope effect ${E}_{\ensuremath{\beta}}$ as defined by the equation ${E}_{\ensuremath{\beta}}=\frac{(1\ensuremath{-}\frac{{D}_{\ensuremath{\beta}}}{{D}_{\ensuremath{\alpha}}})}{[1\ensuremath{-}{(\frac{{m}_{\ensuremath{\alpha}}}{{m}_{\ensuremath{\beta}}})}^{\frac{1}{2}}]}$, where $\frac{{D}_{\ensuremath{\beta}}}{{D}_{\ensuremath{\alpha}}}$ and $\frac{{m}_{\ensuremath{\alpha}}}{{m}_{\ensuremath{\beta}}}$ are the ratios of the diffusion coefficients and masses of the two isotopes $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ was found to be 0.8134\ifmmode\pm\else\textpm\fi{}0.0424. This value is consistent only with diffusion by the vacancy mechanism, and indicates that the translational kinetic energy of the activated state in the jump direction is possessed entirely by the jumping atom as it crosses the saddle point.