Phonon-Phonon Interaction

Abstract

Upon increase in frequency of ultrasonic waves in solids—i.e., for an increase in energy of coherent phonons and increase in ultrasonic intensity—the interaction of phonons and phonons, electrons, photons, and magnons becomes more and more important. Interactions between coherent phonons are discussed. This type of interaction is a purely acoustical aspect of the problem—nonlinear interactions between elastic waves or the nonlinear acoustics of a solid in the narrow sense. The selective rules, which define the possible conditions for three-phonon interactions consist of the conservation of energy and quasimomentum of the interacting phonons. These conditions follow both from the nonlinear equations of elasticity theory and from quantum-mechanical consideration with account of the anharmonicity of the lattice. Experimental work in the investigation of three-phonon interactions—the generation of harmonics of a longitudinal wave, the formation of the second harmonic of a transverse wave due to the presence of dislocations, the scattering of sound by sound in the intersection of waves of different polarizations. Experiments on the nonlinear interaction of elastic waves allow us to find certain third-order elastic moduli. Interactions of thermal phonons with coherent phonons, which lead to ultrasonic absorption in solids are considered. These are connected both with the disruption of the equilibrium distribution of thermal phonons, and also with the direct interaction of ultrasonic and thermal phonons.