Thermal conductivity of highly disordered semiconductor alloys

Hot-pressed silicon-germanium alloys exhibit a reduced thermal conductivity compared to their single-crystal counterparts. Of considerable practical importance is the relationship between the reduction in thermal conductivity and the grain size of the alloy. Previous work indicated that the boundary scattering mean free path was about an order of magnitude less than the alloy grain size (Meddins and Parrott, J. Phys. C, vol.9, p.1263). A partial explanation of this discrepancy between the physical and 'effective' grain size is obtained by taking into consideration details of the phonon dispersion relations.