Abstract
X-ray absorption near-edge structure (XANES) spectroscopy enables in situ direct measurements of microscale Fe2+/Fe3+ ratios in minerals and has greatly contributed to the understanding of the redox states during rock formation. Traditionally, the Fe2+/Fe3+ has been quantified based on 1s→3d/4p pre-edge peak features. However, optically anisotropic minerals show significant differences in absorption of polarized X-rays for measurements in different crystallographic orientations, introducing considerable errors in estimates of Fe2+/Fe3+. Multivariate analysis (MVA) utilizing entire X-ray absorption fine structure (XAFS) spectral features combined with appropriate training data, preprocessing, and hyperparameter optimization, offers a potential solution to this issue. This study examines the X-ray absorption anisotropy of clinopyroxene for six distinct crystallographic orientations relative to X-ray propagation and polarization directions using eleven natural single crystals with a wide range of Fe3+/ΣFe (0–0.88) and compositions (diopside, augite, aegirine). We used the full XAFS spectra of the oriened clinopyroxenes to construt MVA models that can accurately estimate Fe3+/ΣFe in unknown orientations. Our measurements reveal that most of the XANES absorption-edge peak features display a clear dependence on the polarization direction of the incident X-ray, and suggest their absorption anisotropy can mainly be ascribed to dipole-allowed 1s→4p transition process. On the other hand, the pre-edge peaks exhibit a complex absorption anisotropy that depends on both the propagation and polarization directions, suggesting a complicated nature of quadrupole-allowed 1s→3d transitions enhanced by dipole transitions to mixed 3d–4p orbitals. We found that the conventional pre-edge-based determinations of Fe3+/ΣFe involve large uncertainties of ±13.5–15.3%Fe3+ mainly due to the substantial X-ray absorption anisotropy. Our optimal MVA model using least absolute shrinkage and selection operator (Lasso), trained with autoscaled XANES spectra of oriented clinopyroxenes, can sucessfully predict %Fe3+ in clinopyroxenes from within the test dataset without prior knowledge of the with a root-mean-squared error of ±7.8%Fe3+. In addition, our results show a good agreement between weighted energy channels of the MVA models and XANES peak features resolved by the polarization-dependent experiment. The MVA coefficients provided in this study give an effective method of deriving reliable Fe3+/ΣFe from XAFS measurements of clinopyroxene irrespective of orientation, emphasizing the advantages of employing a combination of features from the pre-edge, main-edge, and post-edge domains of the spectra in deriving the relationships.