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Microanalysis of Fe3+/ΣFe in geological samples using synchrotron-based X-ray absorption spectroscopy has become routine since the introduction of standards and model compounds. Existing calibrations commonly use least-squares linear combinations of pre-edge data from standard reference spectra with known coordination number and valence state acquired on powdered samples to avoid preferred orientation. However, application of these methods to single mineral grains is appropriate only for isometric minerals and limits their application to analysis of in situ grains in thin sections. In this work, a calibration suite developed by acquiring X-ray absorption near-edge spectroscopy (XANES) data from amphibole single crystals with the beam polarized along the major optical directions (X, Y, and Z) is employed. Seven different methods for predicting %Fe3+ were employed based on (1) areanormalized pre-edge peak centroid, (2) the energy of the main absorption edge at the location where the normalized edge intensity has the highest R2 correlation with Fe3+/ΣFe, (3) the ratio of spectral intensities at two energies determined by highest R2 correlation with Fe3+/ΣFe, (4) use of the slope (first derivative) at every channel to select the best predictor channel, (5 and 6) partial least-squares models with variable and constant numbers of components, and (7) least absolute shrinkage and selection operator models. The latter three sophisticated multivariate analysis techniques for predicting Fe3+/ΣFe show significant improvements in accuracy over the former four types of univariate models. Fe3+/ΣFe can be measured in randomly oriented amphibole single crystals with an accuracy of ±5.5-6.2% absolute. Multivariate approaches demonstrate that for amphiboles main edge and EXAFS regions contain important features for predicting valence state. This suggests that in this mineral group, local structural changes accommodating site occupancy by Fe3+ vs. Fe2+ have a pronounced (and diagnostic) effect on the XAS spectra that can be reliably used to precisely constrain Fe3+/ΣFe. [ABSTRACT FROM AUTHOR]

Measurements of Fe3+/ΣFe in geological materials have been intractable because of lack of access to appropriate facilities, the time-consuming nature of most analyses, and the lack of precision and reproducibility in most techniques. Accurate use of bulk Mössbauer spectroscopy is limited by largely unconstrained recoilless fraction (f), which is used to convert spectral peak area ratios into valid estimates of species concentrations and is unique to different mineral groups and compositions. Use of petrographic-scale synchrotron micro-XANES has been handicapped by the lack of a consistent model to relate spectral features to Fe3+/ΣFe. This paper addresses these two deficiencies, focusing specifically on a set of garnet group minerals. Variable-temperature Mössbauer spectra of the Fe2+-bearing almandine and Fe3+-bearing andradite end-members are used to characterize f in garnets, allowing Fe3+/ΣFe to be measured accurately. Mössbauer spectra of 19 garnets with varying composition were acquired and fit, producing a set of garnet-specific standards for Fe3+ analyses. High-resolution XANES data were then acquired from these and 15 additional previously studied samples to create a calibration suite representing a broad range of Fe3+ and garnet composition. Several previously proposed techniques for using simple linear regression methods to predict Fe3+/ΣFe were evaluated, along with the multivariate analysis technique of partial least-squares regression (PLS). Results show that PLS analysis of the entire XANES spectral region yields the most accurate predictions of Fe3+ in garnets with both robustness and generalizability. Together, these two techniques present reliable choices for bulk and microanalysis of garnet group minerals. [ABSTRACT FROM AUTHOR]