The experimental setup for the confocal Fe K-edge μ-XANES was established at the microprobe end station of the P06 beamline of the PETRA III synchrotron radiation source at DESY, Hamburg, Germany. The microprobe end station provides a beam size down to 0.35×0.35 µm2 at a photon flux of 1010 photons per second in the spot. For the measurements in this study, the spot size was about 0.8×1.2 µm2. The radiation from a 2 m U32 undulator was monochromatized by a Si(111) double-crystal monochromator providing an energy resolution of ca. 1.4×10-4 eV. Higher harmonics were rejected using a pair of mirrors with a bare silica stripe after the monochromator. The final focus was achieved by a KB-mirror system. The intensity of the incoming beam was monitored in front of and behind the KB mirror for normalization of the fluorescence signal. A polycapillary half lens designed by X-Ray Optical Systems (XOS^®) with a focal spot at a distance of 2.5 mm was mounted on a Si-drift detector, which was set at a 90∘ angle to the incoming beam to detect the fluorescence signal from the sample.

The sample was placed in the sample holder so that the sample surface was oriented at 45∘ to the incoming beam and hence at 45∘ to the detector capillary (Fig. 2). The positioning of the sample could be visualized by a microscope and controlled by high-precision x–y–z driving motors of the sample stage. Using a 7.5 µm thin Fe-metal foil as a reference sample, the two foci of the beam and the detector capillary were adjusted to each other as shown in Fig. 2a, so that they define a restricted excitation volume. The depth of the confocal volume was measured by scanning this Fe foil through the excitation volume, and a value for FWHM (full width at half maximum) of 30 µm was determined, which represents the true value convoluted with the thickness of the Fe foil. In this study, the excitation volume defined by the beam and detector optics is used to restrict the measured volume to that close to the surface in order to minimize contributions from deeper parts of the sample. To achieve this, a depth scan in the z direction (Fig. 2b) was performed after adjustment on a given melt inclusion in the focal spot in order to set the optimum depth position.

The adjustment of the x–y position was achieved by scanning the sample in the x (horizontal) and y (vertical) directions (Fig. 2b). Since the signal intensity depends on the amount of Fe in the sample, the signal contrast resembles contribution from the host mineral with high Fe content (e.g., olivine) and from the MI with lower Fe content. The adjustment of the measurement spot is schematically illustrated in Fig. 3. After localization of the optimal x–y position on the surface of the MI, it was scanned along the z axis (at 90∘ to the MI surface, but 45∘ to the incoming beam; see Fig. 2b) to identify the optimal depth of the confocal volume with respect to the surface. The maximum signal of the z scan corresponds to the region just beneath the sample surface, and to further minimize any contamination from the host mineral, the sample was moved along the z axis so that the excitation volume was slightly “above” the sample surface.

Two beam time sessions were used to develop and apply this setup. During the first one, XANES spectra were recorded in step-scan mode; i.e., the monochromator and undulator were moved to a given energy point, and then the signal was integrated over 1 or 2 s for the pre-edge region (between 7105 and 7125 eV). This resulted in a considerable amount of overhead time for moving and settling of the monochromator and undulator, so that 9 min was needed in total for a single scan, where the total integration time of the sample signal was only 210 s. To improve this technique, in the second session, continuous scanning of the monochromator and undulator was used, which was already proven to provide high-quality X-ray absorption spectroscopy (XAS) spectra (Chernikov et al., 2016) and was set up to work with the electronics of the XRF detector.

In order to optimize the acquisition time and sampling rate in terms of eV steps, the spectra were taken in two scans: one covering only the pre-edge region and edge jump (7105–7125 eV), resulting in a high sampling rate and small steps (0.11 eV) across the pre-edge region, and a second scan over the entire range from 7080 to 7250 eV with 0.4 eV step. Each of these scans took about 1 min. The fluorescence signal was normalized to the intensity of the incoming beam, the two scans were merged, and then the spectra were normalized to the edge jump and analyzed. The pre-edge intensity and centroid position were determined using the fitting procedure developed by Wilke et al. (2004) using 7111.08 eV as the reference energy position of metallic Fe.

The Fe oxidation state in the glasses was determined using the variogram for the pre-edge centroid and intensity proposed by Wilke et al. (2001, 2004). The polynomial of Fe3+ / ΣFe vs. centroid (red line in Fig. 4) proposed by Wilke et al. (2004) describes well the data for reference basaltic glasses (red squares in Fig. 4), where the centroid was determined by confocal XANES and Fe3+ / ΣFe was analyzed by the Mössbauer method (Botcharnikov et al., 2005). However, some of the measured melt inclusions in our study have rhyolitic composition, and, thus, application of the calibration made on basaltic glass may potentially lead to an overestimation of the ferric content. This is due to a potentially higher amount of tetrahedral Fe3+ in this type of highly polymerized glass. Tetrahedral Fe in general leads to stronger pre-edge intensities due to stronger p character of the unoccupied electronic d states that hybridize with p orbitals of the oxygen (e.g., Wilke et al., 2007; Cottrell et al., 2009; Fiege et al., 2017). Data on haplogranitic and haplotonalitic glasses have shown that Fe2+ in these glasses produces similar pre-edge intensities to those of basaltic and alkali-silicate glasses (Wilke et al., 2006, 2007). To account for the difference for Fe3+ between basaltic and silica-rich compositions, we used the centroid variation of Fe between the reduced silica-rich glass and the tetrahedral Fe3+ in the variogram for the pre-edge centroid and intensity (Wilke et al., 2001, 2004). This calibration is represented by the black line in Fig. 4.

In order to test this calibration, we used literature data on Fe-bearing haplotonalitic compositions (Wilke et al., 2002, 2006); own unpublished data for a haplogranitic sample, used as a starting material in Wilke et al. (2007); and new data determined on a rhyolitic composition (see Supplement Table for details). For the three latter samples, the Fe3+ / ∑Fe ratio in the glass was determined by the wet-chemical and spectroscopic technique of Schüssler et al. (2008). The constructed trend (black line in Fig. 4) fits well to the data points of the silica-rich samples (black squares in Fig. 4). Thus, the Fe3+ / ∑Fe of silica-rich glasses can be determined from the pre-edge centroid [eV] as follows (black line in Fig. 4): Fe3+/ΣFe=0.27×(centroid-7112)-0.02+(centroid-7112)2+0.123×(centroid-7112)4. Figure 4 shows that the trends for basaltic and silica-rich glasses differ considerably for reduced samples but merge for samples with Fe3+ / ∑Fe >0.6. Both calibrations were used for the processing of analytical data obtained in this study.

The confocal capability of the method was tested using slices of oxidized basaltic glass (SC1-oxi) with thickness of 30, 50, 80, 100, 200 and 300 µm mounted on a piece of San Carlos olivine. The calibrated and optimized setup was applied to analyze melt inclusions in forsteritic to fayalitic olivines from the Hekla volcano, Iceland.

Intense X-ray beams, as provided by an undulator source, may easily alter the oxidation state of elements in a given sample. These effects scale with the photon dose, and they are well known in organic and biological tissue and usually become more severe at low energy. Strong oxidation state alteration in silicate glasses was reported for S (Wilke et al., 2008), but also the Fe oxidation state in glasses may be altered at high photon flux and particularly in water-bearing samples (Cottrell et al., 2018). Defocusing and attenuation of the beam were proposed as necessary requirements to minimize the beam damage at high photon flux (Cottrell et al., 2018). However, since the high spatial resolution was a prerequisite in our methodology, any defocusing of the beam was not applicable. Hence, to avoid beam damage, the incoming beam had been attenuated by Al filters before focusing. The level of attenuation was optimized by test measurements on the ferrobasaltic glass in sample B11 after Botcharnikov et al. (2005), which contains about 5 wt % H2O and has an Fe3+ / ΣFe ratio of about 0.25. We performed repeated XANES scans on the same spot. Beam damage was immediately visible by a shift of the main edge position and changes in the pre-edge region. Further, we monitored the signal at 7117 eV (main edge) over time. A constant signal was indicative of damage-free beam conditions, and it was achieved only at 98 % attenuation on the B11 sample, which corresponds to 108 photons per second in the focus of 0.8×1.2 µm2 of the incident beam. Furthermore, since several (depending on Fe content of the MI) scans were summed up to achieve good counting statistics, after each scan the sample was moved by 1 µm to avoid long exposure on a single spot (see Fig. 3). These measures resulted in negligible beam damage on all investigated reference materials and samples (see below).

Figure 5 shows examples of XRF-intensity scans in all x–y–z directions for the location of the measurement spot (Fig. 5a–c and e–f) as well as the resulting XANES spectra for two melt inclusions in an olivine matrix (Fig. 5d and g). In the first example, no. MI1 (sample from mid-ocean ridge basalt, MORB), a comparison between XANES data taken in step-scan mode (black and red lines in Fig. 5d) and continuous mode (green line in Fig. 5d) is shown. In both cases, counting statistics in the pre-edge region are sufficient for the analysis. However, data taken in continuous mode provide better sampling statistics over the entire scan range (compare green line with red and black lines in Fig. 5d). Further, the step-scan data demonstrate slightly higher Fe3+ contents (Fe3+ / ∑Fe = 0.145 after the first scan and Fe3+ / ∑Fe = 0.151 after the second scan) when compared with data from the continuous scan mode (Fe3+ / ∑Fe = 0.123). This effect might result from a longer dwell time on the given spot and potential beam damage. Continuous-scan data are the result of 20 individual scans on the position always shifted by 1 µm (see Fig. 3). The second example illustrates the limits of spatial resolution on no. MI44 (sample from arc basalt) that is relatively wide in the y direction but thin in the z direction as indicated by the small maximum in the center of the y scan, presumably resembling contribution from the underlying olivine host. Further, no. MI44 is only 30 µm wide in the x direction. The resulting XANES shows clear contamination by the signal from the host olivine as evident from the sharp signal peak at the K-edge position and from the prominent signal shoulder at the ca. 7140 eV characteristic for crystalline materials. The spatial resolution in the x direction is particularly limited by the fact that the sample surface is set up at 45∘ towards the incoming beam. Thus, inclusions that are too thin may still easily show contaminating signal by the host mineral. Possible complex geometry or chemical heterogeneity of the inclusion may also potentially affect the quality of the analysis and should be taken into account.

In order to test the limits of the confocal approach, a set of glass chips was prepared and fixed on the polished cylinders of San Carlos olivine. The glass chips were made of double-polished oxidized ferrobasaltic glass (the same composition as in Botcharnikov et al., 2005) with a thickness of 30, 50, 80, 100, 200 and 300 µm. The glass chips were hot-pressed onto the olivine crystal surface using a thin layer of wax. The thickness of the wax layer was estimated to be ca. 1–2 µm. Because the glass is very oxidized (66 % Fe3+, SC1-oxi sample from this study and A39 sample after Zhang et al., 2018) and amorphous, whereas the olivine is crystalline and contains only Fe2+, potential contamination of the Fe-XANES glass signal by the olivine signal should be easily visible. The results of this test are illustrated in Fig. 6a. The Fe3+ / ΣFe ratio is identical for all glass chips independent of thickness, within error. This is particularly emphasized by the zoom on the pre-edge region prior to background subtraction (Fig. 6b). The small variability found in the final results is thus only related to the background subtraction procedure. The determined values also agree with wet-chemistry data for this glass (grey field in Fig. 6a). Any contamination by olivine should shift the Fe3+ / ΣFe to lower values, which is not observed. Further, none of spectra shows extra features at the main edge region that may stem from olivine. This simple test implies that the confocal method is applicable for the melt inclusions with a thickness down to at least 30–40 µm.

The optimized confocal technique was tested on reference glasses with known Fe3+ / ΣFe ratio (Supplement Table). A set of ferrobasaltic glass samples from the study of Botcharnikov et al. (2005) was analyzed. The Fe3+ / ΣFe of these samples was determined previously by Mössbauer and XANES in the study of Botcharnikov et al. (2005) and used later to investigate the sensitivity of glasses to beam damage (Cottrell et al., 2018). The proportion of Fe3+ in these glasses varies from <10 % to 60 %. Additional reference material (SC1-oxi) is the oxidized (Fe3+ / ΣFe = 66%) ferrobasaltic glass synthesized at 1600 ∘C and ambient pressure in air (identical to the sample A39 in Zhang et al., 2018). Two synthetic rhyolite glasses (unpublished data) were analyzed using wet chemistry (method of Schuessler et al., 2008). Figure 7 shows that reference values of plotted samples are consistent with Fe oxidation state values derived using the pre-edge region (see polynomials in Fig. 4). Thus, it demonstrates that the Fe3+ / ΣFe is reproduced within analytical uncertainty by the new confocal technique in all reference glasses, indicating that the analytical setup is robust and that beam damage is avoided.

The new method was applied for the analysis of melt inclusions in olivine from the Hekla volcano, Iceland. The magmas erupted from Hekla show not only a high variability in melt composition from basaltic to rhyolitic but also a rare case of olivine crystals with forsterite number (Fo = Mg / (Mg + Fe) in moles) varying from ca. Fo84 in basalts to Fo3 in rhyolites (e.g., Moune et al., 2007; Portnyagin et al., 2012; Lucic et al., 2016; Geist et al., 2021). The most recent studies concluded that erupted rocks of Hekla represent a series of magmas originated predominantly by extensive (up to 90 %) fractional crystallization with little crustal interaction in a tabular vertically oriented macro-dike extending from the lower to the upper crust (Geist et al., 2021). The parental mafic magmas contained about 0.6 wt % H2O and were generated at relatively reducing conditions close to FMQ (FMQ is fayalite–magnetite–quartz redox equilibrium) (Moune et al., 2007; Portnyagin et al., 2012). Evolving magmas show increasing H2O and K2O concentrations up to ∼6.2 wt % and ∼3 wt %, respectively, with an almost constant mass ratio H2O / K2O of 2–2.3 in melt inclusions, which trapped the least degassed melts or lost minimal amounts of hydrogen by diffusion through the olivine host (Portnyagin et al., 2012; Lucic et al., 2016; Geist et al., 2021). Variations in redox conditions of the Hekla magmas fall within ±0.5 log units of the FMQ buffer as estimated from the compositions of coexisting magnetites and ilmenites enclosed in olivine and pyroxene phenocrysts (Portnyagin et al., 2012; Schattel et al., 2014; Geist et al., 2021). Such a narrow range of redox conditions and absence of any correlation with H2O content in magmas were interpreted as a decoupling between water activity and oxygen fugacity in the Hekla magmatic system and as an inheritance of redox signature from the mantle source (Portnyagin et al., 2012; Schattel et al., 2014). In other words, it was suggested that magma differentiation occurred at conditions open to oxygen, and, thus, it may reflect redox conditions in the off-rift Icelandic crust (Schattel et al., 2014).

However, although the data for H2O content and magma composition were obtained for melt inclusions, the estimates on the redox conditions were derived indirectly by analyzing mineral inclusions of Mt and Ilm in phenocrysts. Although it was claimed that ilmenite–magnetite pairs can preserve redox signature from depths of rhyolitic magma chambers and that this signature is not affected by water degassing (Waters and Lange, 2016), kinetic experiments showed that redox equilibria of Fe–Ti oxides can be significantly modified by changes in the external T–fO2 conditions within hours (Venezky and Rutherford, 1999; Hou et al., 2021). Only the assumption of complete chemical isolation of mineral inclusions within the host olivine during magmatic evolution would allow an assessment of the redox signature from depth. Furthermore, recently Humphreys et al. (2022) suggested that basaltic melt inclusions can record late-stage redox evolution of degassing magmas and that this process is decoupled from diffusive re-equilibration of the H2O content in the inclusions. These examples clearly demonstrate a controversy of redox record interpretations in natural magmatic systems and a need for better understanding of redox proxies.

The unique wide range of Hekla melt and olivine compositions allows for an important test of our confocal μ-XANES method as well as for possible volcanological implications. We have selected several olivine grains, covering the whole compositional range, from the studies of Moune et al. (2007) and Portnyagin et al. (2012). One additional MI of intermediate composition (I12-8-1-39) from the H2 Hekla eruption (1855 BC) was selected and analyzed in this study. A brief summary for the selected melt inclusions is presented in Table 1, and the compositions of melt inclusions are shown in Fig. 8.

The compositions of MIs, analyzed by EMPA, demonstrate strong correlation with the composition of host olivine (Fo number) as shown in Fig. 8a (SiO2) and in Fig. 8b (FeO). The correlation is also clearly visible for the concentration of dissolved H2O (determined by SIMS) in MIs (Fig. 8c). The melt water content shows a linear relationship with the concentrations of SiO2 and K2O, demonstrating a crystal fractionation trend of the magma from basalt to rhyolite with accumulation of incompatible elements and volatiles, as discussed by Portnyagin et al. (2012). Figure 8d shows the relationship between olivine composition and temperature of the magma calculated using the thermometer of olivine–melt equilibria in the presence of H2O after Putirka (2008).

The analyzed Fe3+ / ΣFe ratios (%) in the MIs are shown in Fig. 9 as a function of Fo number of the olivine host (Fig. 9a) and the water content of the inclusions (Fig. 9b). The results show a dramatic increase in the Fe3+ proportion from 17 % to 46 % with decreasing Fo and increasing H2O concentration. It must be noted that this increase is not linear and visible mostly for glass compositions from dacites to rhyolites, whereas andesites to basalts show almost constant Fe oxidation state.