Resonant Scattering of Phonons. I. CN-Doped Alkali Halides

The resonant scattering of phonons in KCl:CN and KBr:CN has been investigated. It is found that the ${\omega }^4$ dependence for the resonant scattering of phonons as obtained by Griffin and Carruthers for a similar resonance process in $n-\mathrm{Ge}$ does not explain published phonon-conductivity results in CN-doped alkali halides in the temperature range where the resonant-scattering dips occur. The results can, however, be described very well by the formula $\tau _r^{}{}_{}{}^{-1\mathrm{}}\propto \frac{{\omega }^2}{{({\omega }^2-\omega _0^{}{}_{}{}^2)}^2}$, which has been obtained by Kwok for $n-\mathrm{Ge}$ using a Green's-function approach. This approach is well known to be more suitable for frequencies close to the resonant frequencies where the usual perturbation techniques fail because of divergence difficulties.