Low-Temperature Heat Transport in Solid HD

The thermal conductivity of solid HD has been measured and compared with theory over the temperature range 4-0.2 K. Since the sample remained frozen over the entire period in which the measurements were made, the ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ impurities, as well as the other crystal defects, were assumed fixed in the lattice. However, the concentration of the $J=1\mathrm{}$ orthohydrogen ($o-{\mathrm{H}}_2$) and paradeuterium impurities in the sample changed through the slow $J=1\mathrm{}$ to $J=0\mathrm{}$ conversion taking place in the solid. The rate of conversion and consequently the $J=1\mathrm{}$ concentration was determined by measuring, as a function of time, the heat of conversion resulting from $J=1\mathrm{}$ to $J=0\mathrm{}$ transitions. Because of the variation in the $J=1\mathrm{}$ concentration, it was possible to separate the thermal resistivity into a ($J=1\mathrm{}$)-dependent part and a part independent of $J=1\mathrm{}$ concentration. The resistivity resulting from phonon scattering by $J=1\mathrm{}$ molecules was compared to existing theory for two-phonon Raman scattering by $o-{\mathrm{H}}_2$ molecules in a parahydrogen solid. At the lowest temperatures, the temperature dependence of this resistivity was too large to be accounted for by a two-phonon process. It is suggested that a one-phonon process is responsible for the increase in the resistivity at low temperatures. The results of a calculation are given to demonstrate the palusibility of this argument. Below 1 K, the ($J=1\mathrm{}$)-independent conductivity can be adequately fitted by a $T^3$ temperature dependence. From this dependence it was inferred that the sample was polycrystalline. Above 1 K, the ($J=1\mathrm{}$)-independent conductivity is dominated by the presence of the ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ isotopic impurities. The techniques used to measure these impurity concentrations are described in detail.