By the use of an iterative method the linearized phonon-Boltzmann equation for a dielectric solid subjected to a thermal gradient is solved in the frame of three-phonon interactions. In this way it is possible to calculate the thermal conductivity of rare-gas solids starting from the pair potential and accounting for the real Brillouin zone of the lattice. The numerical results are in full agreement with experiment and represent a considerable improvement with respect to those previously deduced for an isotropic solid.
The picture of a grain boundary as a periodic array of dislocations implies the occurrence of phonon scattering processes that the Klemens theory of thermal conductivity does not account for. A grain boundary works similar to a diffraction grating, producing diffraction spectra of various orders: each order number n is associated with a class of scattering processes contributing to thermal resistance. The Klemens theory corresponds to nϭ0: it is shown that processes with n 0 are essential to explain the heat transport properties of a specimen containing grain boundaries. The theory is used to explain the behavior of thermal conductivity, both in the range below 5 K and in the region of the conductivity peak, as observed in crystals of lithium fluoride, alumina, and quartz. It is also applied to the conductivity curve of fused silica, in the frame of a model where a glass is pictured as a solid with a high-density distribution of grain boundaries.
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