On the ultrasonic attenuation of transverse waves in the (1,1,0) direction in cubic crystals

Abstract

Previous work (see abstr. A25442 of 1975) concerning the attenuation of transverse waves in the (1,0,0) direction is extended to an investigation of the (1,1,0) direction in cubic crystals. In order to compare the strength of Landau and Rumer processes of temperature dependence T4 with near collinear energetically disallowed processes of expected temperature dependence T7 or T9, finite thermal phonon lifetimes have been used throughout the calculations. This has been done by numerical techniques and full account of crystal anisotropy and the three-phonon anharmonic coupling has been taken. An extensive comparison is made with experimental data, good agreement being obtained in most cases. It is found that in the case of the slow transverse mode in germanium and silicon, the experimentally observed temperature-dependent attenuation of approximately T2 can be explained in terms of interactions with fast transverse thermal phonons. The crystal calcium fluoride is treated in some detail and it is found that sixty per cent of the attenuation of the slow transverse mode is due to 'same branch' energetically allowed interactions with slow transverse thermal phonons in the temperature range 30-40K.