Hydrogen hopping rates and hydrogen-hydrogen interactions in PdHx.

Abstract

Ultrasonic-attenuation measurements have been performed on single-crystal ${\mathrm{PdH}}_{\mathrm{x}}$ over the temperature range 80--300 K and for 0.64\ensuremath{\le}x\ensuremath{\le}0.76. The longitudinal and the two independent transverse modes that propagate along the [110] crystalline direction were investigated over a range of frequencies from 10 to 150 MHz. Evidence was found for more than one type of motion. The assumption of two simple relaxation processes was sufficient to give a reasonable fit to all of the data. The attempt frequencies for these two processes were found to depend somewhat on H concentration and acoustic mode, but the activation energies did not. The activation energies and approximate attempt frequencies were found to be 0.155 eV and 3\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, and 0.254 eV and ${10}^{14}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. These values are suggestive, respectively, of tunneling and classical barrier hopping. The relaxation strengths (\ensuremath{\delta}C's) derived from the fit do not satisfy the Cauchy relation, which means that central forces do not fully describe the H-H interactions. By restricting consideration to nearest- and next-nearest-neighbor H-H interactions, elements of the force-dipole tensor describing H-H interactions are found, including a noncentral force contribution.