Anisotropic attenuation of transverse ultrasound in cubic crystals of Ge, Si, and diamond with various isotopic compositions

The attenuation of transverse ultrasound in germanium, silicon, and diamond crystals is considered with allowance for competing isotopic and anharmonic scattering processes. The dependence of the attenuation of transverse ultrasound on the direction of the wave vector of quasi-transverse phonons is analyzed within an anisotropic continuum model. The Landau-Rumer mechanism is considered for anharmonic scattering processes. Given the second-and third-order elastic moduli, the parameters are found determining ultrasonic absorption in the above crystals with various degrees of isotopic disorder. The attenuation coefficients of transverse ultrasound associated with isotopic and anharmonic scattering processes are shown to have qualitatively different angular dependences. Therefore, from studying the anisotropic attenuation of ultrasound in cubic crystals, one can determine the dominant mechanism of ultrasonic absorption in isotopically modified crystals.