Spontaneous decay of long-wavelength acoustic phonons

The damping constant of acoustic phonons has been investigated in a frequency regime where dispersion can be largely neglected, and for temperatures sufficiently low compared with the phonon frequency that the intrinsic damping is governed by the spontaneous decay via cubic anharmonicity. The theory is outlined in some detail with emphasis on the connections between basic lattice dynamics, interacting phonon theory and nonlinear elasticity theory. Particular aspects of the intra-branch decay, depending on the curvatures of the slowness surface, are discussed. For the isotropic continuum, the analytical formulae given by Slonimskii are critically reviewed. Quantitative results of numerical calculations for various cubic substances show a strong dependence of the damping constant on the propagation direction, in particular for the transverse modes, as a consequence of the anisotropy of the second- and third-order elastic constants, the experimental values of which have been used as input parameters.