Optical constants of minerals derived from emission spectroscopy: Application to quartz

The objective of this study was to develop a method for determining the optical constants (i.e., the real (n) and imaginary (k) indices of refraction) of single-crystal, uniaxial minerals using emission, rather than reflection, observations as a step toward deriving n and k from particulate minerals. The vibrational, midinfrared, emissivity spectra of polished quartz crystals were obtained by measuring the thermal radiance from planar surfaces, parallel and perpendicular to the optic axis. From these oriented spectra the ordinary ray was directly measured, and the extraordinary ray was mathematically derived. The n and k values for quartz were obtained by application of the Fresnel laws of reflection to the ordinary- and extraordinary-ray spectra of the polished surfaces. Comparison of theoretical spectra, obtained through classical Lorentz-Lorenz dispersion theory, to experimental spectra enabled new oscillator parameters for quartz to be determined. Construction of the ordinary-ray spectrum required seven oscillators defined by frequencies (ν, converted to wavenumbers) of 1215 cm^-1, 1161 cm^-1, 1067 cm^-1, 795 cm^-1, 694 cm^-1, 449 cm^-1, and 393 cm^-1; strengths (4πρ) of 0.03, 0.007, 0.67, 0.11, 0.01, 0.815, and 0.4; and damping terms (γ) of 0.4, 0.007, 0.008, 0.0115, 0.01, 0.012, and 0.012, respectively. Construction of the extraordinary-ray spectrum required six oscillators defined by frequencies (converted to wavenumbers) of 1222 cm^-1, 1074 cm^-1, 776 cm^-1, 509 cm^-1, 494 cm^-1, and 364 cm^-1; strengths of 0.011, 0.67, 0.10, 0.015, 0.7, and 0.68; and damping terms of 0.15, 0.008, 0.011, 0.016, 0.014, and 0.019, respectively. These results were compared to the previously published results of Spitzer and Kleinman that required an additional oscillator (seven total) to define the extraordinary-ray spectrum. Regardless of the difference in number of required oscillators, the spectra of n and k for the two studies agree within the experimental error. The results confirm that emission spectroscopy is a viable means for determining the optical constants of uniaxial minerals using the technique described in this study.