Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit$mdash$extension to arbitrary crystal symmetry

Abstract

A formalism based on Yeh's 4 × 4 matrix algebra is developed to model reflectance and transmittance spectra of randomly oriented polycrystalline materials (sintered ceramics or glass ceramics) with arbitrary crystal symmetry provided that the crystallites are larger than the resolution limit of light. It may be applicable to powders, if the particle sizes are large compared to wavelength or show a broad distribution. The formalism is used to model the spectrum of polycrystalline fresnoite (Ba2TiSi2O8, optically uniaxial). The modelled and the measured spectra show a good correspondence, especially regarding peak position and form. Furthermore, approximations are derived for uniaxial crystal symmetry, which are superior to other approximations known from the literature such as the magic-angle arrangement. As a consequence of the formalism, randomly oriented polycrystalline materials consisting of ordered regions larger than the resolution limit should exhibit a non-zero cross polarization, despite being optically isotropic, which is proved experimentally. For an adequate interpretation of spectra of polycrystalline materials with non-cubic crystal symmetry, the particle size effect arising from the anisotropic crystal structure is demonstrated to be non-negligible.