Bulk sensitive determination of the Fe3+/FeTot-ratio in minerals by Fe L2/3-edge X-ray Raman scattering

We present the ﬁ rst measurements of the iron L 2/3 -edge of the compounds FeO, Fe 2 O 3 , and Fe 3 O 4 at ambient pressure and of FeCO 3 at high pressures of 2.4 and 40 GPa using a diamond anvil cell by X-ray Raman scattering spectroscopy, a bulk sensitive probe of soft X-ray absorption edges making use of hard X-rays. We show that the spectral shape of the Fe L 2/3 -edge can be analyzed quantitatively to reveal the oxidation state of iron in matter. Consequently, in situ X-ray Raman scattering spectroscopy at the iron L-edge at high pressure and temperature opens exciting perspectives to characterize the local coordination, oxidation, and spin state of iron at high pressure and temperature, conditions that are of relevance for e.g. geological sciences or chemical processing.


Introduction
Iron is one of the most common elements of the inner Earth, strongly affecting the macroscopic properties of related minerals, melts, and glasses. 1,2Under pressure-temperature conditions of the deep Earth, the local chemical and physical properties of iron, e.g.4][5] Quantitative information about these parameters is used in order to understand the structural changes during geochemical and geophysical processes such as Fe-Mg partitioning, iron melting and density variations for instance associated with the spin crossover in iron.In situ experiments under the relevant thermodynamic conditions provide unique insights into geochemical and geophysical processes. 6,71][12][13] The related pre-edge features, which contain information on the Fe 3d states, are difficult to resolve and a high-resolution monochromator setup is needed.So far, XAS studies of the near edge structure in situ at high pressure are rare, and analysis of the main edge is used. 14Moreover, the 3d state can be probed directly by resonant X-ray emission. 15Information on the orbital and spin magnetic moment is obtained using X-ray magnetic circular dichroism 16 and X-ray linear magnetic dichroism. 17e L 2/3 -edge spectroscopy (2p / 3d) is also a sensitive method in order to study the local properties of iron and is performed either using so X-rays [18][19][20] or by electron-energy loss spectroscopy (EELS) [21][22][23] with a transmission electron microscope.Compared to pre-edge studies of the redox state at the Fe K-edge, the variation of the corresponding intensity parameter determined on the Fe L-edge is large, thus offering a potentially higher precision for determining the oxidation state.In other words, if there would be no experimental constraints for measuring either one of the edges, the L-edge should provide results with better precision.Therefore, measurements of the Ledge, if feasible, may be a valuable alternative where changes in the pre-edge of the K-edge are too small to be resolved.XAS and EELS at the L-edges at X-ray energies below 1 keV are used for applications in e.g.geology, 3,21,24 physics, 19,[25][26][27][28][29] biology, 30,31 catalysis, [32][33][34][35] and materials science. 18,36However, these techniques cannot be applied for in situ high pressure experiments owing to the highly absorbing sample environment, e.g.resistively or laser heated diamond anvil cells.
8][39][40][41][42][43] Recently, in situ high pressure measurements of the Fe M 2/3 -edge demonstrated the ability to track the pressure induced spin cross-over in FeS and to extract quantitative information about the crystal eld splitting of the 3d states in iron. 44The Fe M 2/3 -edge is signicantly modied by weak changes of the oxidation and spin state, but it is less sensitive to the local coordination. 45ecently, magnetic circular dichroism of X-ray Raman scattering was observed at the iron L 2/3 -edge of pure iron. 46In general, measurements of the Fe L 2/3 -edge by X-ray Raman scattering spectroscopy are a very good alternative for studies of the oxidation state, the local coordination, and the spin state of iron in compounds under geologically relevant conditions.In this paper we focus on the capability of X-ray Raman scattering spectroscopy to analyze the oxidation state of a sample both at ambient and at high pressure.

X-ray Raman scattering
8][49][50][51] Consequently, the local atomic and electronic structure can be probed bulk sensitively yielding information about e.g.oxidation state, spin state and local coordination.By scanning the energy loss in the vicinity of an electron binding energy, core level excitations can be studied both in the dipole and non-dipole limits. 48The intensity of the scattered radiation is proportional to the dynamic structure factor, which is given for transition metals and rare-earth elements due to the strong interaction between the 3d electron and the hole wave functions by with the sum over all nal states f.The transition matrix elements are given by the initial state radial wave function c(r) with the energy E c , the nal state wave function f(r) with the energy E f , and the k-th order Bessel function j k (qr) scaled by the corresponding transition probability D k . 52The dynamic structure factor in eqn (1) is presented in the limit of polycrystalline and powder samples, for which the angular dependence of the matrix element is averaged.With respect to the symmetry properties of the initial and nal state wave functions only transitions with k ¼ 1 (dipole) and k ¼ 3 (octupole) are allowed for the particular p to d transition of the Fe L 2/3 -edge. 52,53The weight of each transition channel is governed by the magnitude ħq of the momentum transfer vector, that can be tuned in an experiment by changing the scattering angle.

Experimental details
The XRS experiment was performed at beamline PNC/XSD 20-ID of the Advanced Photon Source employing the LERIX spectrometer. 54Here, 19 Si(444) analyzer crystals are arranged in a semicircle (radius of 1 m) covering an angular range from 9 to 171 , which results in a momentum transfer range from 0.7 ÅÀ1 to 8.7 ÅÀ1 .The energy of the incident X-rays with an overall resolution of 1.0 eV was tuned by using a Si(111) monochromator.In order to measure the Fe L 2/3 -edge, the energy of incident X-rays was scanned from 8.582 keV to 8.682 keV resulting in an energy loss interval from 670 eV to 770 eV, respectively.Polycrystalline FeO ( [6] Fe 2+ , space group Fm3m, corresponding to the geologically relevant mineral wustite), Fe 2 O 3 ( [6] Fe 3+ , space group R 3c, corresponding to hematite), and Fe 3 O 4 (corresponding to magnetite with a composition of 1/3 [6] Fe 2+ , 1/3 [6] Fe 3+ , and 1/3 [4] Fe 3+ ) powders with a trace metal basis of 99.9%, 99.995%, and 99.99%, respectively, were measured without further treatment.The samples were characterized by X-ray diffraction at beamline BL9 of the DELTA synchrotron source. 55Phase purity was found for Fe 2 O 3 and Fe 3 O 4 whereas FeO contained a small amount (<3%) of iron.The spectra were collected in 1.5 hours (FeO) and 4 hours (Fe 2 O 3 and Fe 3 O 4 ).Due to the small momentum transfer dependence of the shape of the Fe L 2/3 -edge, the spectra were summed up over the entire q-range.Subsequently, a background described by a polynomial function was tted to the energy loss values below 700 eV and subtracted from the data.This background subtraction procedure is similar to that typically applied to EELS data. 21Finally, background corrected spectra were normalized to the integrated intensity in the energy loss region from 700 eV to 728 eV.For a general description of the XRS data analysis see ref.

Results and discussion
The results of the XRS measurements of the Fe L 2/3 -edges on FeO, Fe 2 O 3 , and Fe 3 O 4 are presented in Fig. 1.The spin-orbit splitting for FeO given by the distance between the inection points of the Fe L 3 -and Fe L 2 -edges can be estimated to be 12.8 AE 0.2 eV, which is in very good agreement with earlier results. 58ignicant spectral differences can be observed, if the Fe L 2/3edge of FeO is compared to that of Fe 2 O 3 .The energy shi between the inection points of the Fe L 3 -(707.1 eV) and Fe L 2edges (720.3 eV) of Fe 2 O 3 results in a spin-orbit coupling of 13.2 AE 0.2 eV, which agrees very well with values obtained by EELS. 21,58The shape of the Fe L 2/3 -edge of Fe 3 O 4 shows a very broad, asymmetric, and featureless maximum due to the contribution of both FeO-and Fe 2 O 3 -like Fe L 2/3 -edge spectra.
A comparison of the XRS results with XAS and EELS data, e.g.published in ref. 19, 20 and 59, shows a very good agreement concerning the relative energy position and shape of the Fe L 2/3edges, which is a surprising result considering the origin of the excitation mechanism of the experimental techniques.While only dipole transitions are probed by XAS, a certain momentum transfer contribution can be found in EELS.However, typical EELS measurements are performed at low scattering angles, which restrict electronic excitations to dipole-like transitions.In contrast, XRS spectra are in general strongly dominated by higher order transitions at high scattering angles.Although the momentum transfer dependence of the multiplet spectra is very strong for transition metals, 45,52,60 it is hardly observed at the Fe L 2/3 -edge of FeO, Fe 2 O 3 and Fe 3 O 4 .The ability to access nondipole excitations is governed by the absolute value of the momentum transfer as well as the length scale of the effective radial overlap between the initial and nal state wave functions, which is small for the 2p and 3d wave functions of iron.Thus, the momentum transfer range examined in this study is too small to get signicant higher order contributions and the statistical accuracy of the spectra can be signicantly enhanced due to the fact that the signal collected at different scattering angles by using multi-element spectrometers can be summed up.
The collected spectra can be employed to extract quantitative information about the Fe 3+ /Fe Tot -ratio.Therefore, the position and spectral shape of the Fe L 2/3 -edge can be used as an indicator of the oxidation state and several extraction algorithms are discussed in the literature (see e.g.ref. 23).In order to obtain the Fe 3+ /Fe Tot -ratio, Garvie and Buseck 61 propose to t Fe 2+ and Fe 3+ references to a spectrum taken on a mixed oxidation state sample.This algorithm is only applicable for materials with identical end-members and coordination of iron, which is not the case for Fe 3 O 4 .Alternatively, a series of analytical functions, e.g.Gaussian-or Lorentzian-type, can be tted instead of reference spectra.The position and relative intensities of the series of analytical functions contain information about the Fe 3+ /Fe Tot -ratio and local coordination of iron.However, several proles with a large number of free parameters must be used in order to obtain accurate results. 22,62Another alternative proposed by van Aken et al. 21exploits the intensity ratio between the Fe L 3 -edge and the Fe L 2 -edge, which strongly depends on the Fe 3+ /Fe Tot -ratio contained in the material.The applicability of this algorithm was demonstrated for different examples of high-spin iron species with a variable oxidation state.Keeping in mind that this procedure can only be applied for high-spin iron species with conserved site symmetry, 20 the algorithm will be discussed in detail and applied to the XRS data in order to demonstrate the potential of XRS measurements to obtain quantitative information about the Fe 3+ /Fe Tot -ratio in the following.
The Fe L 2/3 -edge measurements presented in Fig. 1 are further analyzed in order to remove the contribution of the excitations into the continuum states by subtracting a double arc-tangent function with the xed inexion points at 708.65 eV and 721.65 eV, respectively. 21The resulting arc-tangent background for FeO, Fe 2 O 3 , and Fe 3 O 4 is shown in Fig. 1.Subsequently, background corrected spectra shown in Fig. 2 are integrated in the energy loss ranges from 708.5 eV to 710.5 eV (I(L 3 )) and from 719.5 eV to 721.5 eV (I(L 2 )), as suggested by van Aken et al. 21The intensity ratio I(L 3 )/I(L 2 ) is then correlated with the Fe 3+ /Fe Tot -ratio x of well characterized samples via with a ¼ 0.183 AE 0.011, b ¼ À0.455 AE 0.015 and c ¼ 0.368 AE 0.005.Eqn (2) can be used as a calibration curve to determine the Fe 3+ /Fe Tot -ratio in unknown minerals by calculating their relative intensity I(L 3 )/I(L 2 ).van Aken et al. suggest that EELS would provide access to the Fe oxidation state on the particle length scale of 10 to 100 nm with a precision of 0.03 to 0.04 in terms of Fe 3+ /Fe Tot , which is similar to Mössbauer spectroscopy.In order to prove the applicability of this algorithm to the XRS results, I(L 3 )/I(L 2 ) was calculated for FeO (Fe 3+ /Fe Tot ¼ 0), Fe 2 O 3    In order to demonstrate the potential of this method to determine the iron oxidation state in situ under extreme conditions we performed a high pressure XRS measurement at beamline ID20 of ESRF (European Synchrotron Radiation Facility) using a multiple analyzer spectrometer. 57An FeCO 3 single crystal ( [6] Fe 2+ , space group R 3c corresponding to siderite) was loaded in a Böhler-Almax diamond anvil cell using a rhenium gasket and helium as the pressure medium to guarantee quasi-hydrostatic conditions at high pressure.The sample with dimensions of about 15 mm Â 25 mm Â 25 mm was measured for 12 hours at 2.4 GPa and 8 hours at 40 GPa.The pressure was determined via the ruby uorescence method. 63he analyzer energy was 12.92 keV and the incident energy was scanned from 13.623 keV to 13.663 keV with an overall energy resolution of 2.1 eV at a momentum transfer of 3.2 AE 0.9 ÅÀ1 .The spectra were analyzed as discussed above.The results obtained at 2.4 GPa are presented in Fig. 1 and show a good agreement with the FeO spectral shape despite the different energy resolution.Following the analysis procedure of van Aken et al. 21(see Fig. 2) the extracted Fe 3+ /Fe Tot ratio ts to the universal curve within the accuracy of the experiment.The deviation between the L-edge's shape measured at 40 GPa and thus the change of the I(L 3 )/I(L 2 ) ratio compared to 2.4 GPa is due to the fact that the high spin to low spin transition already started. 64This clearly conrms that the analysis by van Aken is strictly limited to iron compounds in the high spin state.The different energy resolution achieved with XRS and EELS does not affect the results of this analytical procedure.However, both the energy resolution and statistical accuracy can be improved in future experiments, which clearly demonstrates the feasibility of in situ measurements of the Fe L 2/3 edge at high pressure to evaluate the redox state.

Conclusion
In this paper, bulk sensitive measurements of the Fe L 2/3 -edge by XRS spectroscopy are presented and their sensitivity to the oxidation state of iron is discussed for the examples of FeO, Fe 2 O 3 , and Fe 3 O 4 .Relative intensities of the spectral features of the Fe L 2/3 -edge are used to extract quantitative information about the Fe 3+ /Fe Tot -ratio using the calibration curve by van Aken et al. 21This approach is a prospective method to study the oxidation and spin state of iron bulk sensitively in situ under high pressure and high temperature conditions beyond the limits of other experimental techniques.The feasibility of in situ measurements under high pressure conditions using a diamond anvil cell was successfully demonstrated with the example of FeCO 3 probed at 2.4 GPa and 40 GPa.

Fig. 1
Fig. 1 Results of the Fe L 2/3 -edge measurements of FeO (black), a-Fe 2 O 3 (blue), and Fe 3 O 4 (green) at ambient pressure.Moreover, the spectrum of FeCO 3 measured in situ at 2.4 GPa (grey) and 40 GPa (red) using a diamond anvil cell is presented.The gray dashed line represents a background modeled by a double arc-tangent function.The spectra are vertically shifted for a better overview.

Fig. 2
Fig.2Background corrected XRS spectra with indicated integration ranges; inset: calculated I(L 3 )/I(L 2 ) fractions as a function of the Fe 3+ / Fe Tot ratio in comparison with the calibration curve proposed by van Aken et al.21 (Fe 3+ /Fe Tot ¼ 1) and Fe 3 O 4 (Fe 3+ /Fe Tot ¼ 0.67).A comparison between evaluated intensity ratios on the basis of XRS measurements with the calibration curve determined by van Aken et al. is shown in the inset of Fig.2.Our data indicate that this technique may be transferred to XRS and thus has the potential of gaining precise redox information using a bulk sensitive probe for samples with a larger grain size where XAS and EELS are not appropriate.Particularly, for in situ high pressure experiments the XRS technique may provide new ways of studying Fe redox equilibria.