4:25 PM - 4:40 PM
[MZZ42-09] Accurate micro-XAFS determination of Fe2+/Fe3+ in optically anisotropic minerals by multivariate statistical approach
Keywords:X-ray absorption fine structure spectroscopy, Orientation effect, Fe2+/Fe3+, Multivariate analysis, Clinopyroxene
X-ray absorption near-edge structure (XANES) spectroscopy is a unique speciation technique that provides non-destructive and direct measurements of chemical states of elements in (sub-)microareas regardless of the form of samples. It significantly contributes to our understanding of redox environments and evolutionary processes of the Earth and planetary materials. Iron (Fe) is particularly significant as a redox proxy, being ubiquitously present in terrestrial planetary and asteroidal materials. Its chemical states have been widely quantified by taking advantage of the unique characteristics of XANES spectroscopy.
However, conventional XANES-based determinations of chemical states in geological materials have been associated with large uncertainties, primarily due to absorption anisotropy of X-rays relative to sample orientations. Since photoelectric transitions depend on both crystallographic orientations and polarization properties of incident electromagnetic radiation, optically anisotropic media and highly ordered samples exhibit angular dependencies in absorption. This anisotropy introduces considerable errors in common Fe3+/ΣFe measurements (ΣFe=Fe2++Fe3+) based on energy shifts of the 1s→3d/4p pre-edge peak centroid, for example, ±20% for pyroxenes and amphiboles, and ±10–15% for micas[1].
Recently, multivariate statistical approaches utilizing full XAFS spectra (XANES+EXAFS) have been proposed as effective methods for accurately determining Fe3+/ΣFe and oxygen fugacity (fO2)[2]. By learning spectral data of multiple orientations and various compositions, more accurate measurements of Fe3+/ΣFe may be possible even for optically anisotropic minerals irrespective of crystallographic orientations[3].
This study focused on clinopyroxene, a crucial ferromagnesian silicate mineral in petrogenetic contexts, and applied multivariate analysis (MVA) to accurately determine Fe3+/ΣFe in pyroxene crystals using full Fe K-edge XAFS. First, we prepared eleven fresh and homogenous clinopyroxene single crystals (diopside, augite, aegirine). Major element compositions, crystallographic orientations, and Fe2+/Fe3+ ratios were measured using EPMA, EBSD, and Mössbauer spectroscopy, respectively. We then conducted polarization-dependent XAFS experiments using linearly polarized X-rays at the BL-4A, Photon Factory, KEK, to examine the XAFS anisotropy for six mutually perpendicular crystallographic orientations.
We found that the absorption-edge and rising-edge peaks show anisotropy that depends on the polarization direction of incident X-rays, indicating 1s→4p dipole transitions. In contrast, pre-edge peaks show anisotropy that depends on not only the polarization direction but also the propagation direction of X-rays, suggesting contributions of 1s→3d quadrupole transitions.
We then applied three MVA methods (PLS, Lasso, Ridge), which are effective for spectroscopic data characterized by multicollinearity between explanatory variables and p>>N conditions, using the six oriented spectra as training data. Constructed MVA models can successfully predict Fe3+/ΣFe in randomly oriented clinopyroxenes of a test dataset with RMSE errors of ±7.2–8.5 %Fe3+. For clinopyroxene with the same orientation as the training data, Fe3+/ΣFe can be estimated more accurately (±5.1 %Fe3+). On the other hand, conventional pre-edge-based determinations have larger prediction errors of ±13.5–15.3 %Fe3+ due to the strong orientation effect. Additionally, regression coefficients of the MVA models well correlate with absorption peak energies resolved from polarization-dependent spectra as well as some of EXAFS features, demonstrating that absorbance at these energies is highly informative in predicting Fe3+/ΣFe.
Our MVA models allow for more accurate non-destructive micro-XAFS determinations of Fe2+/Fe3+ in clinopyroxene crystals irrespective of orientations, which is particularly beneficial in petrographic thin sections. When applied to clinopyroxene grains in thin sections of eclogite, the MVA models consistently estimate Fe3+/ΣFe as 54–61 %Fe3+, whereas the conventional pre-edge-based method yields large errors of 41–71 %Fe3+ depending on orientations. This analytical advancement leads to a significant improvement by about 200℃ in temperature estimates using garnet–clinopyroxene Mg–Fe2+ geothermometry. Future applications of this method are expected to provide better constraints on the thermal structure and redox environment of terrestrial planets.
However, conventional XANES-based determinations of chemical states in geological materials have been associated with large uncertainties, primarily due to absorption anisotropy of X-rays relative to sample orientations. Since photoelectric transitions depend on both crystallographic orientations and polarization properties of incident electromagnetic radiation, optically anisotropic media and highly ordered samples exhibit angular dependencies in absorption. This anisotropy introduces considerable errors in common Fe3+/ΣFe measurements (ΣFe=Fe2++Fe3+) based on energy shifts of the 1s→3d/4p pre-edge peak centroid, for example, ±20% for pyroxenes and amphiboles, and ±10–15% for micas[1].
Recently, multivariate statistical approaches utilizing full XAFS spectra (XANES+EXAFS) have been proposed as effective methods for accurately determining Fe3+/ΣFe and oxygen fugacity (fO2)[2]. By learning spectral data of multiple orientations and various compositions, more accurate measurements of Fe3+/ΣFe may be possible even for optically anisotropic minerals irrespective of crystallographic orientations[3].
This study focused on clinopyroxene, a crucial ferromagnesian silicate mineral in petrogenetic contexts, and applied multivariate analysis (MVA) to accurately determine Fe3+/ΣFe in pyroxene crystals using full Fe K-edge XAFS. First, we prepared eleven fresh and homogenous clinopyroxene single crystals (diopside, augite, aegirine). Major element compositions, crystallographic orientations, and Fe2+/Fe3+ ratios were measured using EPMA, EBSD, and Mössbauer spectroscopy, respectively. We then conducted polarization-dependent XAFS experiments using linearly polarized X-rays at the BL-4A, Photon Factory, KEK, to examine the XAFS anisotropy for six mutually perpendicular crystallographic orientations.
We found that the absorption-edge and rising-edge peaks show anisotropy that depends on the polarization direction of incident X-rays, indicating 1s→4p dipole transitions. In contrast, pre-edge peaks show anisotropy that depends on not only the polarization direction but also the propagation direction of X-rays, suggesting contributions of 1s→3d quadrupole transitions.
We then applied three MVA methods (PLS, Lasso, Ridge), which are effective for spectroscopic data characterized by multicollinearity between explanatory variables and p>>N conditions, using the six oriented spectra as training data. Constructed MVA models can successfully predict Fe3+/ΣFe in randomly oriented clinopyroxenes of a test dataset with RMSE errors of ±7.2–8.5 %Fe3+. For clinopyroxene with the same orientation as the training data, Fe3+/ΣFe can be estimated more accurately (±5.1 %Fe3+). On the other hand, conventional pre-edge-based determinations have larger prediction errors of ±13.5–15.3 %Fe3+ due to the strong orientation effect. Additionally, regression coefficients of the MVA models well correlate with absorption peak energies resolved from polarization-dependent spectra as well as some of EXAFS features, demonstrating that absorbance at these energies is highly informative in predicting Fe3+/ΣFe.
Our MVA models allow for more accurate non-destructive micro-XAFS determinations of Fe2+/Fe3+ in clinopyroxene crystals irrespective of orientations, which is particularly beneficial in petrographic thin sections. When applied to clinopyroxene grains in thin sections of eclogite, the MVA models consistently estimate Fe3+/ΣFe as 54–61 %Fe3+, whereas the conventional pre-edge-based method yields large errors of 41–71 %Fe3+ depending on orientations. This analytical advancement leads to a significant improvement by about 200℃ in temperature estimates using garnet–clinopyroxene Mg–Fe2+ geothermometry. Future applications of this method are expected to provide better constraints on the thermal structure and redox environment of terrestrial planets.