Phonon focusing and phonon conduction in orthorhombic and tetragonal crystals in the boundary-scattering regime. II

Abstract

Striking differences (up to a factor of 100) are predicted in the intensity of phonons propagating ballistically along different directions in certain orthorhombic and tetragonal crystals. The predicted results arise from phonon focusing due to elastic anisotropy, due to the fact that in elastically anisotropic crystals the phonon phase and group velocities are, in general, not collinear. Conditions for the existence of cuspidal edges in group-velocity surfaces are given in symmetry planes along all directions where the phase and group velocities are collinear. Approximate amplification factors have been calculated for phonons of each polarization along symmetry-plane collinear axes. An analytic expression is also given for the nonsymmetry collinear direction for the longitudinal and one of the transverse modes. Calculations have been performed for a number of crystals and demonstrate that the phonon-focusing property can cause differences in the phonon transport in the boundary-scattering regime by more than 80%.