Revisiting the anisotropic complex refractive indices of sodium nitrate for interpretation of the reflectance spectra of pressed pellets

Abstract

Reflectance spectroscopy is notoriously confounding in that the spectral response is highly dependent upon morphology. Fortunately, all such perturbations are neatly encoded by the complex refractive index. Herein, we quantitatively model the infrared reflectance spectrum of a specularly flat pressed pellet sample of the birefringent compound, sodium nitrate. Single crystals of sodium nitrate were synthesized and spectroscopically analyzed using polarization-dependent single-angle reflectance spectroscopy. Once measured and validated, the optical constants were applied to model the pressed pellet reflectance spectrum. It was evident that an average of the anisotropic refractive indices was insufficient to account for the measured pellet reflectance. The Python package pyElli was used to calculate a basis set of orientation-dependent reflection spectra spanning the distinct φ and θ Euler rotations of the uniaxial crystal. When the population of orientations was allowed to vary freely in a spectral fit analysis, the fit-deduced orientations were tightly clustered along φ = 45°, hinting at residual anisotropy in the pressed pellet sample. Conversely, an equally valid spectral fit (with marginally worse fit metric) was obtained when the population was constrained to an isotropic distribution of orientations. Subsequent non-zero cross-polarization reflectance measurements likewise suggested anisotropy in the pellet. However, both grazing-incidence wide-angle x-ray scattering and scanning electron microscopy measurements revealed that the microcrystal orientations at the surface of the pressed pellet sample were isotropically distributed. Application of the measured complex refractive indices for modeling the reflectance spectrum of the pressed pellet, and rectification of these seemingly contradictory observations will be discussed.