Thermal conductivity of thermal barrier coatings

In thermal barrier coatings and other ceramic oxides, heat is conducted by lattice waves, and also by a radiative component which becomes significant at high temperatures. The theory of heat conduction by lattice waves is reviewed in the equipartition limit (above room temperature). The conductivity is composed of contributions from a spectrum of waves, determined by the frequency dependent attenuation length. Interaction between lattice waves (intrinsic processes), scattering by atomic scale point defects and scattering by extended imperfections such as grain boundaries, each limit the attenuation length in different parts of the spectrum. Intrinsic processes yield a spectral conductivity which is independent of frequency. Point defects reduce the contribution of the high frequency spectrum, grain boundaries and other extended defects that of the low frequencies. These reductions are usually independent of each other. Estimates will be given for zirconia containing 7wt% Y2O3, and for yttrium aluminum garnet. They will be compared to measurements. The effects of grain size, cracks and porosity will be discussed both for the lattice and the radiative components. While the lattice component of the thermal conductivity is reduced substantially by decreasing the grain size to nanometers, the radiative component requires pores or other inclusions of micrometer scale.