Determination of Optical Constants of Ceria By Combined Analytical and Experimental Approaches KRITHIGA GANESAN, 1 LEONID A. DOMBROVSKY, 2 TAE-SIK OH, 3,4 and WOJCIECH LIPIN ´ SKI 1,5 1.—Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455, USA. 2.—Joint Institute for High Temperatures, NCHMT, Kra- snokazarmennaya 17A, Moscow, Russia 111116. 3.—Materials Science, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA. 4.—Present address: Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadel- phia, PA 19104, USA. 5.—e-mail: lipinski@umn.edu Optical constants of ceria are determined in the visible and near-infrared spectral ranges. Two techniques are employed to obtain the index of refrac- tion. The first technique is a direct procedure which involves analysis of wave interference in the transmission spectrum of a ceria thin film. The second technique is an indirect procedure that involves analysis of transmission and reflection spectrum of ceria with sintered morphology. The index of absorption is obtained in the spectral range of weak absorption using the indirect pro- cedure. The identified index of absorption is in turn used in an alternative approach based on the subtractive Kramers–Kro ¨nig relation to estimate the spectral dependence of the index of refraction. The index of refraction iden- tified from the measured transmittance of the thin film is qualitatively con- sistent with that found in the literature. The subtractive Kramers–Kro ¨nig analysis indicates that the spectral dependence of the index of refraction in the transparency range is highly sensitive to the absorption spectrum in the neighboring spectral range of strong absorption, and it is insensitive to the absorption spectrum in the spectral range of weak absorption. INTRODUCTION Cerium dioxide (ceria) has been widely employed in technical applications such as multilayer coat- ings, 1,2 electrolytes in fuel cells, 3–5 photonic crys- tals in solar cells, 6–8 and reactive structures in solar thermochemical reactors. 9–13 These applica- tions have motivated optical and radiative charac- terization of various forms of ceria, such as single- crystal ceria 14 and polycrystalline ceria prepared by different techniques such as chemical vapor deposition, electron/ion beam deposition, 15–20 pulsed laser deposition, 21,22 and sol–gel deposi- tion. 23,24 Spectral optical constants of ceria are particularly critical for predicting optical and radiative characteristics of nonscattering 25,26 and scattering ceria media 27 in the limit of macroscopic electrodynamics. 28 . Optical constants are typically obtained by empirical fitting applied to the trans- mittance and reflectance spectra, 16,17,22 Kramers– Kro ¨nig analysis, 29 interferometry applied to trans- mittance spectra, 21 Kubelka–Munk function ap- plied to reflectance spectra, 30 and using ab initio calculations. 31 A considerable spread of data of optical constants of ceria is found in the literature due to different preparation and characterization conditions and methods of ceria and substrates, resulting in different morphological characteris- tics. 21,32,33 The identification of index of absorption in the range of weak absorption of semitransparent materials including ceria is challenging because identification techniques such as those based on Kubelka–Munk and Kramers–Kro ¨nig relations re- quire quantities such as the reflectance or the index of refraction to obtain the index of absorp- tion. However, even small uncertainties in these quantities, on the order of 0.5%, affect the deter- mination of the index of absorption because the index of absorption is low, on the order of 0.1% in the spectral range of weak absorption. JOM, Vol. 65, No. 12, 2013 DOI: 10.1007/s11837-013-0708-y Ó 2013 TMS 1694 (Published online August 8, 2013)