Analytlcal and numerical calculations of the thermal conductivity of Al₂O₃ - ZrO₂ composite ceramics

Thermal conductivity is one of the essential properties of ceramic materials with respect to their application as insulation materials, refractories or materials for electronics. The topic of this contribution is the estimation and calculation of the thermal conductivity of Al₂O₃-ZrO₂ composite ceramics using analytical and numerical approaches. Both the dependence of thermal conductivity on the composition and on the grain size is taken into account for two-phase composite models. In the first part, an analytical solution of the dependence on the composition based upon the micromechanical bounds (Hashin-Shtrikman bounds) and on the grain size based upon the phase mixture approach is presented with the use of a relatively new relation (sigmoidal average). For the estimation of the latter a model of grain boundary as a separate phase of thickness 1 nm and thermal conductivity close to that of glasses and amorphous dielectrics, viz. 1.1 W/mK is assumed. The second part presents numerical calculations of thermal conductivity via the finite element method (COMSOL Multiphysics software) applied on the model geometry used in the analytical solution and on randomly generated microstructures. The results of both calculation methods are compared with one another and also with experimental data. The presented analytical and numerical approaches are not only designed for the Al₂O₃ - ZrO₂ system, but are of general use for any isotropic particulate composite material. (author)