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The effect of phonon focusing on the temperature dependence of thermal conductivity κfalse(Tfalse) of single crystalline silicon is studied at temperatures from 3 to 40 K in the frame of generalized Callaway theory. Thermal conductivity has been calculated for silicon samples in the form of finite length rectangular rods with different orientations of long axis and side faces. To evaluate the phonon scattering rate due to diffuse boundary scattering, the analytical expressions derived recently by us were utilized. Theoretical results representing the dependence of κfalse(Tfalse) on temperature and sample orientation are in agreement with experimental data. Contributions of different phonon polarizations to the thermal conductivity have been analyzed. The transverse phonon branches are most important as expected, the slow transverse mode being the most prominent in the formation of conductivity anisotropy. The phonon dispersion was found to have a weak effect on the calculated κfalse(Tfalse) at these temperatures.

The quasi-transverse ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli is analyzed. The scattering of the ultrasound by point defects and during anharmonic scattering processes is considered. The quasi-transverse ultrasound absorption is analyzed as a function of the wavevector direction in terms of the anisotropic continuum model. The Landau-Rumer mechanism is considered for anharmonic scattering processes. Known values of the second- and third-order elastic moduli are used to calculate parameters determining the ultrasound absorption. It is shown that the angular dependences of the quasi-transverse ultrasound absorption differ qualitatively if the anharmonic scattering processes dominate in cubic crystals with positive and negative anisotropies of the second-order elastic moduli. For the scattering by point defects and the anharmonic scattering processes, the angular dependences of the quasi-transverse ultrasound absorption exhibit the inverse behavior, making it possible to determine the dominating mechanism of the ultrasound relaxation in the crystals under study.