Dynamic Properties and Focusing of Phonons in Metallic and Dielectric Crystals of Cubic Symmetry. Review 1

Abstract—The spectrum and polarization vectors of phonons in alkali and noble metals belonging to cubic crystals with positive anisotropy of elastic moduli are calculated. They are compared with the results for dielectric crystals. It is shown that the anisotropy of the spectrum in them is significantly higher than in dielectric crystals such as Ge and Si. The polarization vectors of the slow t₂ mode in them have an anomalously large longitudinal component compared to Ge and Si crystals. In Na, Li, and K crystals, it reaches 70, 60, and 30%, respectively. This leads to a significantly greater effect of the slow t₂ mode on electron–phonon relaxation and drag thermopower in alkali metals. Isoenergetic surfaces are calculated, and the features of phonon propagation in alkali and noble metals are analyzed. Their most interesting feature is the effect of focusing on the propagation of longitudinal phonons in alkali metals. For phonon wave vectors in the {100} planes, the directions of group velocities for all alkali metals are close to [101]. Estimates have shown that, for Na, Cs, and K crystals, more than 90, 86, and 79% of phonons, respectively, with wave vectors in the {100} plane propagate in the [101] directions. This effect can be used to obtain plane-parallel phonon beams from a point source of longitudinal vibrations, as well as for other technical applications. The effect of anisotropy of elastic energy on the density of phonon states in alkali metals is analyzed. The results for metallic and dielectric crystals of cubic symmetric are compared. The ranges of angles corresponding to phonon focusing and defocusing are determined. The phonon flux enhancement factors are calculated and compared for metallic and dielectric crystals. The dependences of the types of curvature of isoenergetic surfaces of acoustic modes in alkali and noble metals on the values of anisotropy parameters are analyzed.