Towards the grain boundary phonon scattering problem: an evidence for a low-temperature crossover

The problem of phonon scattering by grain boundaries is studied within the wedge disclination dipole (WDD) model. It is shown that a specific q-dependence of the phonon mean free path for biaxial WDD results in a low-temperature crossover of the thermal conductivity, $\kappa$. The obtained results allow to explain the experimentally observed deviation of $\kappa$ from a $T^3$ dependence below $0.1K$ in $LiF$ and $NaCl$.