Phonon focusing and phonon conduction in hexagonal crystals in the boundary-scattering regime

Striking differences (up to factors of several hundred) are predicted in the intensity of phonons propagating ballistically along different directions to the $c$ axis in certain hexagonal crystals. The predicted results arise from phonon focusing, due to the fact that in elastically anisotropic crystals the phonon phase and group velocities are, in general, not collinear. Analytic expressions have been derived for the amplification factor for phonons of each polarization along all directions where the phase and group velocities are collinear. Calculations have been performed for a number of hexagonal crystals and demonstrate that the phonon-focusing property can effect differences in the phonon transport in the boundary-scattering regime by as much as 300%.