Thermal Resistance due to Point Defects at High Temperatures

An expression is obtained for the lattice thermal conductivity at high temperatures in the limit when the scattering of phonons by point defects is stronger than by umklapp processes. The latter limit the phonon mean free path at low frequencies and most of the heat is transported at frequencies such that the point defect and umklapp mean free paths are equal. The conductivity varies as ${\mathrm{}\left(\mathrm{AT}\right)\mathrm{}}^{-\frac{1}{2}}$, where $A$ is proportional to the strength of the point defect scattering, $T$ is the temperature. The theory is in rough agreement with the thermal conductivity of Ge-Si alloys, measured by Steele and Rosi.