The scattering of phonons by the strain and rotation fields of crystal defects

The scattering of long-wavelength phonons due to the spatial variation of elastic moduli that is produced by the inhomogeneous elastic strain and rotation fields of static crystal defects is calculated in terms of the second- and third-order elastic constants of the undeformed crystal. The present theory is distinguished from those of previous authors by its ability to deal with rotation angles that are not necessarily small, such as those associated with large-angle grain boundaries or macroscopically bent or twisted crystals. For small rotations the classical equations of motion and the second-quantised Hamiltonian obtained by previous authors are rederived and the modifications appropriate to large rotations are discussed. Approximate, but simple, expressions for scattering cross sections, etc., are obtained; these facilitate subsequent calculations of transport coefficients and lead to estimates of lattice thermal resistivities in dislocated crystals that are in good agreement with experiment. Previous theoretical studies of the strain-field scattering problem are reviewed.

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