Lattice Thermal Conductivity of Crystals Containing Dislocations

Abstract

General method to treat the scattering of lattice waves by static strain fields in anisotropic solids was applied to the calculation of thermal conductivity of crystals containing dislocations. The scattering cross widths for edge and screw dislocations in cubic crystals with {111} ⟨110⟩ and {110} ⟨110⟩ slip systems were derived, and the thermal resistivity of the dislocations was calculated using the relaxation-time approximation. The contribution from conducting phonons with different modes was treated separately. Numerical calculation has been done for Cu, Si, and LiF crystals. It was argued that the slow transverse phonons had dominant contribution to the decrease of thermal conductivity due to dislocations. Then the calculated values of the thermal conductivity for Cu and Si were reasonably close to the experimental values, while the discrepancy between the two was still large in LiF.