Revisiting Quantitative Infrared Analysis of Absorbing Species in Anisotropic Media

The abundance of volatiles profoundly impacts the interior evolution and surface habitability of Earth and other terrestrial planets. Infrared spectroscopy, with exceptional sensitivity, holds a central responsibility for such detection and quantification. Here, we revisit the physical principles and measurement methodologies of quantitative infrared analysis, and find that a commonly used mathematical formulation of absorption in arbitrarily oriented crystalline samples is subject to significant errors in non-principal planes. A new description of infrared absorption in crystals is derived from the concepts of electric dipole, optical indicatrix, and crystal symmetry. The model’s validity is examined through a case study of O-H stretching bands in a non-principal plane of olivine, using both polarized and unpolarized infrared analysis. Building on this foundation and performing Monte Carlo simulations, we evaluate the performance of four analytical strategies that employ unoriented sample grains under polarized or unpolarized radiation, highlighting their robustness, limitations, and uncertainties. We show that (1) measurements of maximum and minimum polarized absorbances in three perpendicular planes are equivalent to measuring principal polarized absorbances, regardless of crystal symmetry or refractive indices; (2) measuring three mutually perpendicular polarization directions, on the other hand, may introduce substantial systematic errors; (3) averaging unpolarized spectra consistently underestimates the total absorbance; and (4) the latter two approaches yield greater potential errors for low-symmetry systems or for bands that are highly anisotropic or intense, whereas increasing the number of absorption peaks may mitigate these errors. Our model holds for both high- and low-symmetry crystal systems and can provide guidance for accurately quantifying infrared-absorbing species in minerals.