Ultrasonic attenuation in molecular crystals

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Abstract
It is now well established from an experimental point of view that, concerning the ultrasonic attenuation, molecular crystals exhibit a specific behavior among dielectric crystals. This fact suggests the presence of a relaxation process. Liebermann, who has introduced this field, has proposed a way to analyze this problem and in particular has given an expression for the ultrasonic absorption coefficient in terms of a relaxation time and some thermodynamic quantities. In contrast to Liebermann's approach, a solid-state viewpoint is presented here, and it is shown that this ultrasonic relaxation can be taken into account in the framework of Akhieser's theory. A general expression of the ultrasonic absorption coefficient is calculated in terms of the phonon collision operator using the Boltzmann-equation approach of Woodruff and Ehrenreich. The collision-time approximation widely used in dielectric crystals fails in molecular crystals for which the presence of slow relaxation times in the collision operator prevents the thermalization of the whole set of phonons and gives rise to an ultrasonic relaxation. Thus a more suitable approximation is suggested here, which leads to a new expression of the ultrasonic attenuation valid in molecular crystals. Different forms of this expression are discussed, and comparison with Liebermann's expression used in most of the previous papers shows that the present treatment takes better account of the anisotropy of the solid state. The fit of experimental results obtained for some ionic-molecular crystals also shows that the expression derived here gives better agreement than does Liebermann's. Finally, it is shown that in the framework of the present treatment and under rather general conditions, the anisotropy affects primarily the magnitude of the ultrasonic absorption due to the molecular relaxation, but it does not affect its frequency dependence.

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