Abstract
The lattice viscosity of anharmonic crystals, containing randomly dstributed isotopic impurities, is investigated theoretically, using the correlation formula due to McLennan. The effect of mass and force constant changes, due to substitutional defects, along with the cubic- and quartic-anharmonic interactions in the phonon spectrum, has been taken into account, in analyzing the phonon viscous effects in such crystals. It has been shown that, even in the diagonal approximation for the momentum flux operator, the viscosity can be separated into diagonal and non-diagonal contributions. The former, giving major contribution to lattice viscosity, reduces to the form given by Rice, in case of small half-widths. The non-diagonal contribution, which is small but finite, depends on the mass change parameter and hence vanishes in the absence of isotopic impurities. The present results differ from those obtained by others, inasmuch as our expression for lattice viscosity include phonon-relaxation time, not assumed to obey the inverse summation rule which remains only approximately valid. In the present results for viscosity, it has been replaced by the inverse of actual phonon-width, involving the cross-terms of defect and anharmonic parameters, thus, giving an important contribution.
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