Prediction of radiative transport through translucent thermal barrier coatings (TBCs) can only be performed if the scattering and absorption coefficients and index of refraction of the TBC are known. To date, very limited information on these coefficients, which depend on both the coating composition and the microstructure, has been available for the very commonly utilized plasma-sprayed 8 wt% yttria-stabilized zirconia (8YSZ) TBCs. In this work, the scattering and absorption coefficients of freestanding plasma-sprayed 8YSZ coatings were determined from room-temperature normal-incidence directionalhemispherical reflectance and transmittance spectra over the wavelength range from 0.8 to 7.5 lm. Spectra were collected over a wide range of coating thickness from 60 to almost 900 lm. From the reflectance and transmittance spectra, the scattering and absorption coefficients as a function of wavelength were obtained by fitting the reflectance and transmittance values predicted by a four flux model to the experimentally measured values at all measured 8YSZ thicknesses. While the combined effects of absorption and scattering were shown in general to exhibit a nonexponential dependence of transmittance on specimen thickness, it was shown that for sufficiently high absorption and optical thickness, an exponential dependence becomes a good approximation. In addition, the implications of the wavelength dependence of the plasma-sprayed 8YSZ scattering and absorption coefficients on (1) obtaining accurate surfacetemperature pyrometer measurements and on (2) applying midinfrared reflectance to monitor TBC delamination are discussed.

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The temperature dependence of the scattering and absorption coefficients for a set of freestanding plasma‐sprayed 8 wt% yttria‐stabilized zirconia (8YSZ) thermal barrier coatings (TBCs) was determined at temperatures up to 1360°C in a wavelength range from 1.2 μm up to the 8YSZ absorption edge. The scattering and absorption coefficients were determined by fitting the directional‐hemispherical reflectance and transmittance values calculated by a four‐flux Kubelka–Munk method to the experimentally measured hemispherical‐directional reflectance and transmittance values obtained for five 8YSZ thicknesses. The scattering coefficient exhibited a continuous decrease with increasing wavelength and showed no significant temperature dependence. The scattering is primarily attributed to the relatively temperature‐insensitive refractive index mismatch between the 8YSZ and its internal voids. The absorption coefficient was very low (<1 cm−1) at wavelengths between 2 μm and the absorption edge and showed a definite temperature dependence that consisted of a shift of the absorption edge to shorter wavelengths and an increase in the weak absorption below the absorption edge with increasing temperature. The shift in the absorption edge with temperature is attributed to strongly temperature‐dependent multiphonon absorption. While TBC hemispherical transmittance beyond the absorption edge can be predicted by a simple exponential decrease with thickness, below the absorption edge, typical TBC thicknesses are well below the thickness range where a simple exponential decrease in hemispherical transmittance with TBC thickness is expected. [Correction added after online publication August 11, 2009: “edge to a shorter wavelengths” has been updated as “edge to shorter wavelengths.”]

Abstract--Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating al the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximalion for spectral behavior in laminated multiple layers if the overall oplical thickness is larger than about ten. A hybrid spectral rnodcl is developed using Ihe two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.