PHONON FOCUSING AND 2ND SOUND IN SOLIDS

The article gives a survey of the elastic wave surfaces for crystals, the phenomenon of phonon focusing, the heat pulse experiments and second sound in solids. Because of the elastic anisotropy of crystals, the group velocity of the acoustic wave is generally not coincident with the wave velocity and consequently, the phonons are focused in certain directions of the crystal. The nature of the constant frequency surfaces for the slow shear (ST), fast shear (ET) and longitudinal (L) modes and their singularities are discussed, Illustrations are given for the sections of these surfaces by the principal planes, as well as the three dimensional view of the inverse velocity and intensity surfaces. The phonon magnification factor (PMF) is defined as the ratio of the solid angle in the wave vector space to the solid single in the group velocity space. Phonons are highly focused along directions for which the PMF ii high or alternatively along segments of the inverse velocity surface for which the gaussian curvature vanishes. Methods are described to evaluate the PMF numerically. The Schmidt figures show that phonons are highly focused in certain regions of the group velocity space and besides there are regions bereft of phonons too. In the heat pulse experiments, phonons are generated, by passing electrical or laser pulses of short duration over a thin metallic film coated on one side of the crystal. The longitudinal, fast transverse and slow transverse phonons propagate ballistically at low temperatures with the group velocity of the phonons and they are observed on the other side of the crystal through similar bolometers. The results of the experiments by various workers as well as the phonon imaging technique are reviewed. As a result of phonon focusing heat conductivity is anisotropic in crystals. The heat pulse experiments have also demonstrated that the electron hole droplets in semiconductors can be propelled by a flux of non-equilibrium phonons. The force on an e-h droplet arising from the absorption of a phonon is maximum when the wave vector of the phonon is oriented along the major axis of the Fermi surface, and besides the absorption of the phonons is highly anisotropic. Second sound is a form of heat conductivity as a temperature wave. The hydrodynamic equations for the flow of the phonon gas are derived, and from this the dispersion equation for SS is obtained. When the window conditions are satisfied, SS propagates without damping; otherwise, it gets damped when resistive processes start gaining in strength. SS has been observed in NaF, 3He, He-4 and Bismuth among the solids. In the heat pulse experiments, SS emerges as a new mode at a time instant later than that of the slow transverse mode.