Some effects of structural disorder on phonon lifetimes

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Abstract
A calculation in the long-wavelength limit of the damping of a plane wave due to structural disorder is presented. Two contributions are found to be important: the first is incoherent and leads to a mean free path proportional to the fourth power of the phonon wave vector. The strength of the scattering, when estimated using available parameters, is sufficient to account for the thermal conductivity of glasses in the region of the plateau. The second contribution comes from coherent scattering and appears to be unique to strongly scattering systems such as amorphous substances. An estimate of its strength is very difficult because it depends on the magnitude of fourth-order elastic constants. However, it appears to be more than sufficient to account for a substantial part of the phonon mean free path at very long wavelengths.

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