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 \ifmmode^\circ\else\textdegree\fi{}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 \ifmmode^\circ\else\textdegree\fi{}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 \ifmmode^\circ\else\textdegree\fi{}K of ${\ensuremath{\tau}}_{N}^{\ensuremath{-}1}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} \ensuremath{\omega}{T}^{4}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.