Relation between Thermal Ultrasonic Attenuation and Third-Order Elastic Moduli for Waves along the 〈110〉 Axis of a Crystal

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Abstract
When sound waves are transmitted along the 〈110〉 direction in a cubic crystal, the waves consist of combinations of longitudinal and shear waves when referred to the crystalographic axes. In previous publications, it has been shown that shear waves have a relaxation time equal to the thermal relaxation time, while longitudinal waves have a relaxation time about twice as large. Hence, in determining the ultrasonic attenuation due to conversion to thermal phonons, it is necessary to weight the conversion coefficients by this difference in the relaxation time. Tables for the Gruneisen numbers for the 39 pure modes are calculated for the longitudinal and shear waves along the 〈110〉 direction. These tables are applied to the recent measurements of the attenuation of sound waves for lithium fluoride, for which the third-order moduli have also been measured. The large anisotropy of the ultrasonic attenuation for shear waves is accounted for by the third-order moduli used in conjunction with these Tables.

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