Surface conductance and the diffusion of H and D in Pd

Abstract

The absorption of H and D into a palladium sphere of precise radius and density is examined experimentally with use of pressure-volume-temperature measurements and control techniques to achieve the stepwise boundary condition and constant pressure assumed in the common solutions to Fick's second law. Measurements were made at temperatures over the range of 298 to 1373 K after preparing the Pd by cyclic baking of the sphere in vacuum and in very pure ${\mathrm{H}}_{2}$ or ${\mathrm{D}}_{2}$. Near 473 K and higher temperatures, excellent agreement with Fick's-second-law solutions were obtained. Below 473 K, deviations from simple diffusion in the metal were observed and explained by postulating a surface conductance. From known solutions for diffusion in a sphere with a surface conductance, the diffusion coefficients (D) and the minimum achievable surface conductances (h) were determined to be ${\mathit{D}}_{\mathrm{H}}$=3.512\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$${\mathit{e}}^{\mathrm{\ensuremath{-}}(2759.9}$ K)/T ${\mathrm{m}}^{2}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, ${\mathit{D}}_{\mathrm{D}}$=2.219\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$${\mathit{e}}^{\mathrm{\ensuremath{-}}(2538.0}$ K)/T ${\mathrm{m}}^{2}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, and ${\mathit{h}}_{\mathrm{H}}$=${\mathit{h}}_{\mathrm{D}}$=4.05${\mathit{e}}^{\mathrm{\ensuremath{-}}(4995.3}$ K)/T m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$.