Lattice Thermal Conductivity of Solid Helium. II. Isotopic Mixtures

We have analyzed the thermal-conductivity data of ${\mathrm{He}}^4$-rich isotopic mixtures of solid helium in the hcp phase and ${\mathrm{He}}^3$-rich mixtures in the bcc phase at the molar volume 20.2 ${\mathrm{cm}}^3$/mole measured by Bertman et al. It is found that the $T^3$ dependence of normal processes generally used in Callaway's model can explain the thermal-conductivity data in the temperature range 0.6 to 1.8°K. The concentration dependence of the lattice distortion scattering due to added isotopic impurity is seen to be the theoretically expected one, i.e., $x(1-x)\mathrm{}$, and the stronger concentration dependence noticed by Bertman is not observed.