Focusing of Phonons in Crystalline Solids due to Elastic Anisotropy

Large differences (up to a factor of 100) have been observed in the intensity of phonons of different polarizations propagating ballistically in LiF, KCl, and Al₂{O}₃$. These observations were made by means of heat-pulse experiments carried out on single crystals, in the temperature range 1.5-3.5 ^∘{}K. The results are explained in terms of phonon focusing due to the fact that in elastically anisotropic crystals the phonon phase and group velocities are, in general, not collinear. Calculations of the focusing effect, to determine the relative intensities of phonons of each polarization in many crystal directions, have been carried out for a number of solids. The results of these calculations are in good agreement with the experimental results obtained in this study, as well as with those obtained by other investigators on Si, Ge, and NaF.