Attenuation of Longitudinal Ultrasonic Waves in Insulators at Room Temperature

Abstract

It is possible to distinguish between two intrinsic loss mechanisms for longitudinal ultrasonic waves propagating in dielectric single crystals, viz., the thermoelastic loss mechanism and the Akhiezer mechanism. In the normal derivation of the theoretical expressions of the attenuation coefficients for these mechanisms, the former involves the thermal conductivity and the thermal expansion coefficients, while the latter involves the thermal conductivity and the Grüneisen numbers of the thermal phonon modes. These Grüneisen numbers can only be deduced from a knowledge of the third-order elastic constants. We have found experimentally that, for the 15 materials for which sufficient data are available, the attenuation from the Akhiezer mechanism exceeds that from the thermoelastic mechanism by a factor of about 40. This result is shown to be a consequence of the distribution of the Grüneisen numbers of the thermal phonon modes about the mean value. It is suggested that our conclusions can be used to predict the total ultrasonic attenuation in other materials from a knowledge of a few macroscopic properties, even if the third-order elastic constants are unknown. Such predictions are made for GaAs, InSb, and diamond. The third-order elastic constants of GaAs, InSb, and LiF have also been used to compute the ultrasonic attenuation in these materials, and to compute the volume Grüneisen constants. The latter are found to be in good agreement with experimental values except for InSb.