Abstract
The scattering of phonons from a substitutional impurity is studied in a simplified model of face-centred cubic and body-centred cubic lattices. The scattering amplitudes are expressed in terms of partial waves and the total cross sections are found by using the optical theorem. In the long wavelength limit the total cross sections are found to be proportional to ω4, showing Rayleigh-type scattering. The mean free paths of phonons due to scattering by impurities are also given in this limit. The condition for resonances in each partial wave is investigated. In an appendix the method of evaluation of the Green functions, together with tables of their numerical values for the body-centred cubic lattice, are given.
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