Effect of Boundaries and Isotopes on the Thermal Conductivity of LiF

In order to test thermal-transport theories with data involving readily calculable phonon scattering rates, the thermal conductivity of LiF has been measured between 1 and 100°K, first for a series of isotopically pure crystals with sandblasted surfaces ranging in mean width from 1 to 7 mm, and then for a series of crystals ranging in isotopic content of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ from 99.99 to 51%. These data are used to investigate Casimir's theory, the boundary scattering mechanism, and the importance of normal processes in LiF. Sandblasted crystals at the lowest temperatures are found to exhibit a boundary-limited conductivity proportional to crystal width and the cube of the temperature, in agreement with Casimir's theory. However, the proportionality constant is strongly influenced not only by the sandblasting procedure but also by dislocations in the crystal interior. Further measurements, coupled with annealing studies and etch-pit counts, show that dislocations introduced near the crystal surface during sandblasting play a major role in the frequency-independent surface scattering of phonons assumed in Casimir's theory. The importance of normal processes is assessed by comparing both the boundary and isotope data with conductivities calculated from Callaway's model with normal processes neglected. Berman and Brock have already fitted similar isotope data with Callaway's theory, and normal processes played a crucial part in the fit. The present fits demonstrate the necessity of considering normal processes in LiF by showing that, though boundary data can be matched, even a determined effort to match the isotope data does not succeed when normal processes are neglected. Furthermore, normal processes are shown to provide the only mechanism for improving the fit.