Mid-infrared Optical Constants of Clinopyroxene

We have determined the mid-IR optical constants of several pyroxene compositions in the range of 100-4000 cm-1. Measured reflectance spectra of oriented single crystals were iteratively fit to modeled spectra derived from dispersion analysis. We follow the method of Mayerhofer et al. 2010, which is based on the Berreman 4x4 matrix formulation. This approach provides a consistent way to calculate the reflectance coefficients in low-symmetry cases. Additionally, while many models assume normal incidence to simplify the dispersion relations, this more general model applies to reflectance spectra collected at non-normal incidence. This allows us to use our specular reflectance accessory which has incidence and emergence angles of 30° Within a non-conducting crystal, electrons are bound to groups of atoms. Displacements of electrons in a crystal lattice create moving atomic dipoles, which can be described as damped harmonic oscillators. An incident E-field acts as a driving force on the oscillators, which have resonant frequencies (νj). The other parameters describing the oscillators are the strength (ρj), dampening coefficient (γj) and infinite frequency dielectric constant (ɛ∞). Dispersion theory relates these oscillator parameters to the complex index of refraction (ñ=n+ik), where n and k are commonly referred to as optical constants. For minerals of orthorhombic and higher symmetry, we can assume that these oscillations occur parallel to the crystal axes. In this case, the method of Spitzer and Kleinman (1960) can be implemented to determine the optical constants by separately fitting reflectance spectra with radiation polarized parallel to each crystal axis. When a mineral is biaxial and the axes are not orthogonal, the oscillators cannot be assumed to be parallel with the crystal axes. For a monoclinic material, the oscillators in the a-c plane are coplanar to, but not parallel with crystal axes. This results in an additional oscillator parameter (θj), the orientation of the oscillator with respect to the a-axis. Within the monoclinic plane, it is necessary to make measurements at least two different angles (Ω) with respect to the crystal axes. These two reflectance spectra need to be fit simultaneously. Optical constants for E‖b can be determined separately in the same manner as the orthorhombic case. Due to the additional complexity, optical constants have been derived for only a handful of geologically relevant monoclinic materials, including gypsum and orthoclase. Two input parameters that go into radiative transfer models, the scattering phase function and the single scattering albedo, are functions of a material's optical constants. Pyroxene is a common rock-forming mineral group in terrestrial bodies as well meteorites and is also detected in cosmic dust. Hence, having a set of pyroxene optical constants will provide additional details about the composition of solar system bodies and circumstellar materials.