Scattering of phonons from a substitutional impurity

Abstract

The scattering of phonons from a substitutional impurity in a simple cubic lattice is studied in detail. The scattering amplitude is expressed in terms of partial waves characterized by the irreducible representations of the point group of the lattice, and the total scattering cross section is found by using the optical theorem. The condition for occurrence of resonances in each partial wave amplitude is investigated. In an appendix, a table of the Green's function integrals for a simple cubic lattice is given.