Dependence of the Thermal Conductivity of Dilute Solid Mixtures of Orthohydrogen and Parahydrogen on Orthohydrogen Concentration

Abstract

The dependence on orthohydrogen ($o\ensuremath{-}{\mathrm{H}}_{2}$) concentration $c$ of the thermal conductivity of solid mixtures of $o\ensuremath{-}{\mathrm{H}}_{2}$ and parahydrogen ($p\ensuremath{-}{\mathrm{H}}_{2}$) is calculated in the single-mode relaxation-time approximation. The contribution of the phonon-phonon and phonon-boundary scattering to the relaxation time is determined phenomenologically from the experimental data on pure $p\ensuremath{-}{\mathrm{H}}_{2}$ due to Bohn and Mate. The phonon-$o\ensuremath{-}{\mathrm{H}}_{2}$ scattering is calculated from the statistical model of $o\ensuremath{-}{\mathrm{H}}_{2}$ in $p\ensuremath{-}{\mathrm{H}}_{2}$. The effect of zero-point motion is found to enhance interaction between the $o\ensuremath{-}{\mathrm{H}}_{2}$ and phonons substantially. Our results are compared with experimental data, and qualitative agreement is obtained.