Oxygen diffusion along the [0001] axis in Zr(0001)

Abstract

Auger electron spectroscopy has been used to measure the diffusion of oxygen away from the surface of single-crystal zirconium (0001). The experimental data have been modeled by an infinitely thin oxygen layer (ITOL) and thicker layers. The ITOL model best describes the diffusion behavior under the experimental conditions used. The measurements contain no interference from the presence of oxide on the surface. The resulting Arrhenius expression for diffusion has ${\mathit{D}}_{0}$=(4.14\ifmmode\pm\else\textpm\fi{}1.92)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ ${\mathrm{cm}}^{2}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\mathit{E}}_{\mathit{a}}$=199.1\ifmmode\pm\else\textpm\fi{}2.6 kJ ${\mathrm{mol}}^{\mathrm{\ensuremath{-}}1}$ and is a direct measure of diffusion along the c axis. The fundamental vibrational frequency \ensuremath{\nu} for the \ensuremath{\alpha}-Zr lattice was also calculated and found to be (6.3\ifmmode\pm\else\textpm\fi{}2.9)\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, which is in good agreement with the Debye frequency for zirconium.