Thermal Conductivity, Second Sound, and Phonon-Phonon Interactions in NaF

Abstract

The thermal conductivity of several NaF crystals of varying purity has been measured between 2 and 100 °K. The full Callaway formalism is employed to derive phonon-phonon scattering rates from the thermal-conductivity data. The data can be fitted above 37 °K only by assuming a change from the low-temperature scattering rates. Heat-pulse data and the observation of second sound are reported for a crystal less pure than that studied by Jackson et al. The temperature region of second-sound propagation observed for several NaF crystals of varying purity along with the derived phonon-phonon scattering rates are used to give quantitative meaning to the criteria for the observation of second sound. The thermal-conductivity measurements and the second-sound observations are consistent with a scattering rate for normal processes between 10 and 25 °K of ${\tau }_N^{-1\mathrm{}}=1\mathrm{}\times {10}^{-10\mathrm{}} \omega T^4$ ${\sec }^{-1\mathrm{}}$.