Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

Abstract

The interaction Hamiltonian of lattice vibrations and “impurity” ortho-hydrogen molecules of solid para-hydrogen has been derived from the potential of the anisotropic valence and dispersion forces. Below the thermal conductivity peak, along with boundary scattering, inelastic scattering of phonons by isolated ortho-hydrogen molecules has been shown to provide the principal contribution to the thermal resistivity at ortho concentrations c < 0.01. For c > 0.01 the heat flux in the lattice varies mainly through the resonant absorption and emission of phonons between rotational states of ortho-hydrogen molecular pairs. The thermal conductivity is calculated in the relaxation-time approximation for the equilibrium distribution of ortho-hydrogen molecules. The calculated dependences of the thermal conductivity on temperature and concentration are compared with those measured at temperatures up to 3.2 K and with c ≤ 0.05. The derived values are of the right order of magnitude and show good qualitative agreement with experiment.