Transport in Materials with Disclination Dipoles: Applications to Polycrystals and Amorphous Dielectrics

The problem of both electron and phonon scattering by wedge disclination dipoles (WDD) is studied in the framework of the deformation potential approach. The exact analytical results for the mean free path are obtained within the Born approximation. The WDD-induced contribution to the residual resistivity in nanocrystalline metals is estimated. Using the WDD-based model of a grain boundary, the thermal conductivity, kappa, of polycrystals and amorphous dielectrics is studied. It is shown that the low-temperature crossover of kappa experimentally observed in LiF, NaCl, and sapphire can be explained by the grain-boundary phonon scattering. A combination of two scattering processes, the phonon scattering due to biaxial WDD and the Rayleigh-type scattering, is suggested to be of importance in amorphous dielectrics. Our results are in a good agreement with the experimentally observed kappa in a-SiO_2, a-GeO_2 a-Se, and polystyrene over a wide temperature range.