The attenuation of longitudinal ultrasonic waves originating from their interaction with the phonon gas and from other thermoelastic causes has been evaluated in CaF₂ and BaF₂ at 300^∘{}K in the $〈100〉$ and $〈110〉$ directions using thermodynamic and elastic-constant data. The results obtained are in good agreement with the experimentally observed ones.
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Kor et al. (1972) studied this question.