Experimental and Theoretical Study of the Scattering of Phonons byUCenters in Alkali Halide Crystals

Abstract

The thermal conductivity of KCl, KBr, and KI containing ${\mathrm{H}}^{-}$ and ${\mathrm{D}}^{-}$ ions has been measured in the temperature range 0.35°K-100°K. The thermal conductivity of RbCl containing ${\mathrm{H}}^{-}$ ions has been measured between 1.2°K and 100°K. Depressions of the thermal conductivity from the pure-crystal value on the low-temperature side of the maximum, which were present in all samples, appear to be due to KH or RbH precipitates, or "bubbles" of hydrogen gas. On the high-temperature side only KI containing ${\mathrm{H}}^{-}$ or ${\mathrm{D}}^{-}$ ions exhibited a resonant dip in the conductivity curve, and this resonance was mass-independent. The theoretical calculations of Krumhansl on the scattering of phonons by vacancy-type defects could not account for the experimental resonances of the doped KI crystals. A nearest-neighbor central and noncentral force-constant model was used for the calculation of the thermal-conductivity relaxation rates of the $A_{1g}$, $E_g$ $F_{1g}$, $F_{2g}$, $F_{1u}$, and $F_{2u}$ configurations of the cubic group for KCl, KBr, and KI with $U$ centers. These calculations show the $E_g$ and $F_{1u}$ modes to be strong scatterers of phonons at low frequencies, with the resonant relaxation rate for KI being the only rate that dominates the intrinsic scattering rates of the three systems studied. This result is in good agreement with the observed thermal-conductivity data. In addition, the results suggest a correlation between resonances observed in thermal-conductivity studies and infrared-sideband studies.