Lowest-Order Nonvanishing Contribution to Lattice Viscosity

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Abstract
The lowest-order nonvanishing contribution to the viscosity of a crystal lattice is considered. This contribution depends on the cubic anharmonic momentum-flux operator previously derived by the author. An inhomogeneous transport equation, which describes both anharmonic and imperfection phonon scattering and whose solution determines the viscosity, is presented. The scattering operator is then replaced by a single-relaxation-time approximation where the effective relaxation time is found from lattice-thermal-conductivity experiments. With the aid of a Debye-like model, solutions are obtained for the coefficients of viscosity. From these solutions the attenuations of longitudinal and transverse sound waves are calculated and compared with experiment for Ge and Si, where qualitative agreement is found.

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