Theory of Phonon Contribution to Internal Friction of Solids

The theory of the internal friction, or viscosity, in insulating solids is discussed with the aid of the correlation-function expressions for viscosity. It is assumed that the displacements are sufficiently small that a phonon description can be used; consequently, the theory does not apply to such phenomena as plastic flow. There are a number of similarities with the theory of thermal conductivity, but also several interesting differences. In particular the microscopic momentum is not transported with the phonon group velocity; it follows that the Boltzmann equation cannot be used to treat the momentum transport, or viscosity. In addition it is found that, in contrast to the theory of thermal conductivity, one can expect to find a finite viscosity when umklapp processes are neglected.