Effect of Isotopes on Low-Temperature Thermal Conductivity

An analysis of the experimental results of the low-temperature thermal conductivity of single crystals of Si, Ge, and KCl indicates that their maximum conductivities are limited by isotope scattering of phonons rather than by umklapp processes. The isotope scattering in solid helium and sapphire is sufficiently low so that nearly pure umklapp scattering can be observed. The measured thermal conductivities of Si${\mathrm{O}}_{2}$, KBr, and diamond appear to still be limited by impurities. However, even in pure crystals of these three materials the isotope scattering precludes the appearance of pure umklapp scattering.