The Scattering of Low-Frequency Lattice Waves by Static Imperfections

TLDR

Scattering of lattice waves by static imperfections is analyzed using second‑order perturbation theory. The transition matrix includes terms from mass differences, elastic‑constant variations, and elastic strain. Point imperfections scatter as the fourth power of frequency, dislocations as the first power, and grain boundaries independently of frequency, with scattering cross‑section magnitudes estimated for various defects in alkali halides and the results related to low‑temperature lattice thermal conduction.

Abstract

The scattering of lattice waves by static imperfections is treated by second-order perturbation theory. The transition matrix is composed of contributions due to the mass difference of lattice points, changes in the elastic constants of linkages between lattice points, and elastic strain. Point imperfections are shown to scatter as the fourth power of frequency, dislocations as the first power, and grain boundaries independently of frequency. The magnitude of the scattering cross section is estimated for a variety of lattice defects in alkali halides, for screw and edge dislocations and for grain boundaries. These results are discussed in relation to thermal conduction by the lattice at low temperatures.