Thermal Conductivity of Ceramic Nanocomposites – The Phase Mixture Modeling Approach

In nanocrystalline materials the grain boundaries must be considered as regions of finite thickness with properties different from the crystalline bulk material present in the crystallite cores. Thus, dense (i.e. pore-free) single-phase nanocrystalline materials can be considered as quasi-twophase systems whose effective properties can be calculated when quantitative thickness information is available and the property value of the grain boundary phase can be reliably estimated. Similarly, dense two-phase nanocomposites may be considered as quasi-three-phase systems and their effective properties can be predicted using an analogous phase mixture modeling approach. In this contribution this is done for the thermal conductivity of alumina-zirconia nanocomposites. A twostage homogenization procedure is applied, consisting of a first step in which the alumina-zirconia composite is treated as a symmetric-cell material, and a second step in which the highly disordered grain boundary phase is treated as a matrix-phase, coating the crystallite cores. The individual averaging steps are discussed with respect to the two- and three-point bounds, and the resulting grain size dependence is compared with that of pure alumina and zirconia, and literature data.