A novel methodology to determine spectral radiative properties of ceria ceramics

Radiative properties of optically thick ceria ceramics encountered in solar-driven thermochemical cycles are determined in the spectral range 0.352 μm by employing a novel methodology. The methodology consists of an analytical solution based on the modified twoflux approximation and the Monte Carlo ray-tracing method. The analytical solution is used to identify transport scattering albedo from normal-hemispherical reflectance of optically thick samples. The Monte Carlo ray-tracing method is used to obtain transport scattering coefficient in the spectral range 0.9–1.4 μm from bi-normal narrow-cone transmittance. Mie theory is employed to obtain transport scattering coefficient in an extended spectral range. Further, the index of absorption of bulk ceria is estimated by the additive relation for optically soft materials in the spectral range of weak absorption. The proposed methodology is suitable for problems where traditional identification procedures have limited applicability because of highly scattering, optically thick materials and unknown index of absorption in the spectral range of weak absorption. The results indicate that Mie theory for independently scattering spherical pores and grains is appropriate for describing the radiative properties of ceria ceramics in the range of semi-transparency. Nomenclature a radius (μm) A size-distribution parameter (μm -1 ) B size-distribution parameter F gamma distribution (μm -1 ) N number of rays n index of refraction p porosity R reflectance; random number R1 reflectivity s attenuation path length (m) T transmittance Greek symbols α absorption coefficient (mm -1 ) β extinction coefficient (mm -1 ) γ coefficient in boundary condition, equation (1) κ index of absorption λ wavelength (μm) μ directional cosine σ scattering coefficient (mm -1 ) χ eigenvalue ω scattering albedo Subscripts d-d bi-normal d-h directional-hemispherical m maximum tr transport property trans transmitted x diffraction (size) parameter