Transport of Heat and Approach to Second Sound in Some Isotopically Pure Alkali-Halide Crystals

The propagation of short thermal pulses has been studied in very pure samples of NaF, ${\mathrm{Li}}^7$F, and NaI in various crystallographic directions. In each of these crystals the flow of heat at high temperatures is by diffusion, and at the lowest temperatures, by the direct flight of phonons from heater to detector. In the ballistic region, the elastic anisotropy gives rise to a channeling of mode energy into certain preferred directions. Over a limited intermediate temperature range, the effect of normal-process scattering on the propagated heat pulse has been observed in NaF and ${\mathrm{Li}}^7$F: In the best NaF crystals the pulse velocity approaches the expected second-sound velocity. The observations can be explained satisfactorily in terms of the hydrodynamics of a weakly interacting phonon gas. Computer solutions generated to fit the observed thermal pulse shapes suggest that in NaF, the mean free path for normal-process scattering can be represented by $l_N=1.42\mathrm{}\times {10}^3{T}^{-3.71\mathrm{}}$ cm in the temperature range 10-20 °K.