Application of the Callaway theory to analysis of thermal transport by phonons in ceramic and biomorphic composites

• Evidence that Callaway's theory can applied to thermal conductivity of such composites as Si3N4/BN and SiC/Si.
• Estimations of temperature intervals in which thermal conductivity of Si3N4/BN and SiC/Si is dominated by transfer of phonons.
• Finding of basic phonon scattering mechanisms due application of Callaway's theory.
• Estimations of mean free phonon paths as a result of application of Callaway's theory.

By applying the Klemens–Callaway expression for the thermal conductivity in the framework of the Debye's model of phonons we present an analysis of the thermal transport by phonons in ceramic composites Si3N4/BN of various fibre structure (including plaited fibre configurations denoted [0/45] and [0/90]) and biomorphic composites (or ecocomposites) SiC/Si based on beech matrices filled with Si of two different volume percentage (2% and 26%). We obtained a good agreement with the Debye–Klemens–Callaway theory of the thermal conductivity at low temperatures for the ceramic composites Si3N4/BN with the plaited fibre configurations. A good fitting of the Callaway expression for the thermal conductivity coefficient in the whole temperature range can be made to our experimental results for the biomorphic composites SiC/Si. The latter fitting allowed us to assess the magnitude of the mean free path of phonons scattered by the boundaries of grains. We also estimated that the contribution of the conduction electrons to the heat transfer at low temperatures is 5–7% of the effective thermal conductivity in case of SiC/Si.