High spatial resolution analysis of the iron oxidation state in silicate glasses using the electron probe

Oxygen fugacity is an important control on the chemical and physical properties of silicate melts, the stability of magmatic phases, and the multiphase rheology of magmas (e.g., Hamilton et al. 1964; Dingwell and Virgo 1987; Kress and Carmichael 1991; Vicenzi et al. 1994; Bouhifd et al. 2004; Wilke 2005). It also determines the valence state of multivalent elements, such as Fe, Mn, Cr, V, Ce, Eu, and S, and hence the ratio of oxidized to reduced species in the glasses quenched from melts provides a proxy for oxygen fugacity during natural processes and laboratory experiments (e.g., Carmichael 1991; Kress and Carmichael 1991; Herd 2008). Many petrological and volcanological applications, such as analysis of glassy melt inclusions in minerals from volcanic rocks or interstitial glass in natural and experimental vesiculated and/or partially crystalline samples, require measurements at high spatial resolutions.

There are various techniques for quantifying the Fe oxidation state of silicate glasses, with trade-offs between resolution, error, sample preparation requirements, necessity for standards, and instrument accessibility (see McCammon 1999). Wet chemistry is a destructive bulk technique, requiring a minimum of 5 mg of material (e.g., Schuessler et al. 2008), which does not require standards but some expertise. Synchrotron-based absorption techniques, such as μXANES (>2 × 2 μm, e.g., Cottrell et al. 2018) and μMössbauer (>10 × 5 μm, e.g., Potapkin et al. 2012) allow high spatial resolution analysis, but the need for access to synchrotron facilities limits their utility. Also, μXANES can oxidize Fe in hydrous glasses during analysis, producing erroneous Fe oxidation state values (Cottrell et al. 2018). Raman spectroscopy also has a high spatial resolution (1 μm diameter), but has lower sensitivity for basaltic compositions and problems related to background fluorescence (e.g., Di Muro et al. 2009; Di Genova et al. 2016). Electron energy loss spectroscopy (EELS) would offer a superior spatial resolution (nanometer), but standards are inhomogeneous at this scale and beam damage is significant (Burgess et al. 2016).

Conversely, the electron probe is widely available and has the potential for routine analysis of Fe oxidation state in geological materials (mainly garnet and amphibole) at high spatial resolution (Hofer et al. 1994; Enders et al. 2000; Hofer and Brey 2007; Creighton et al. 2009, 2010; Malaspina et al. 2010; Lamb et al. 2012; Matjuschkin et al. 2014) and also glasses (Fialin et al. 2001, 2004, 2011). Typically, the electron probe uses the intensity of emitted characteristic X-rays to quantify chemical composition, such as FeKα to quantify Fe concentration (Fig. 1a), however various other factors can affect the intensity of characteristic X-rays. The FeLα and FeLβ lines are sensitive to the Fe oxidation state as their X-ray generation involves outer shell electrons (3d) affected by chemical bonding (Fig. 1a) (Gopon et al. 2013). The energy of X-ray emission and absorption associated with the FeL lines is very similar, which leads to self-absorption. The FeLα and FeLβ peaks coincide with the L₃ and L₂ absorption edges, respectively, and hence are distorted by them, resulting in asymmetric peak shapes and peak shifts due to the differing amounts of absorption on each side of the absorption edges (Smith and O'Nions 1971). The wavelength of the energy of the absorption edges shifts due to changes in the coordination and oxidation state of Fe (de Groot 2001; Hofer and Brey 2007). The L₃ absorption edge shifts more than the L₂ absorption edge, resulting in greater changes to the FeLα peak than the FeLβ (Hofer and Brey 2007). Thus, for a given chemical system (e.g., garnet, olivine, silicate glass), the FeLα and FeLβ peak positions and intensities vary depending on Fe concentration, oxidation state, and coordination (Fig. 1b; Hofer and Brey 2007).

There are two EPMA methods that exploit variations in FeLα and FeLβ to quantify Fe oxidation state (Fig. 1b). The peak shift method uses the linear relationship between the wavelength of the FeLα peak with Fe oxidation state at a given FeO_T (Hofer et al. 1994; Fialin et al. 2004) (Fig. 1b). To measure the FeLα peak position, wavescans across the FeLα peak are collected and a peak-fitting algorithm is applied to locate its wavelength. This method has been applied to silicate glasses with a statistical error on Fe²⁺/Fe_T of ±0.05, although the error on individual analyses was greater (Fialin et al. 2004). Alternatively, the flank method uses changes in the wavelength and intensity of both the FeLα and FeLβ peaks by measuring the intensity ratio of positions on the low-wavelength flank of FeLα (FeLα_f) and high-wavelength flank of FeLβ (FeLβ_f), termed FeLβ_f/FeLα_f (Hofer et al. 1994; Hofer 2002; Hofer and Brey 2007) (Fig. 1b). These flank positions coincide with the L₂ and L₃ absorption edges and, as the Fe²⁺ content changes, the L₃ absorption edge shifts. The sensitivity of the flank method results from the opposite sense of intensity change at each of the flank positions, as FeLα_f is on the high-absorption side of the L₃ absorption edge, whereas FeLβ_f is on the low-absorption side of the L₂ absorption edge, which utilizes changes in both peak position and intensities (Hofer et al. 1994). Optimum flank positions can be found by collecting absorption spectra or using the maximum and minimum in the difference spectrum between samples with different Fe concentration and oxidation states (Fig. 1b, Hofer and Brey 2007). The FeLβ_f/FeLα_f intensity ratio depends primarily on total ferrous iron (Fe²⁺), with a secondary dependence on total Fe (Fe_T), hence

where A, B, C, and D are fitting coefficients (Hofer and Brey 2007). The flank method has greater sensitivity than the peak shift method and does not require wavescans becasue measurements are made at two specific, pre-defined wavelengths (Hofer et al. 1994; Zhang et al. 2018). This method has been applied to some mineral groups (e.g., garnet, spinel) with an error on Fe²⁺/Fe_T of ±0.02 (Hofer and Brey 2007) and silicate glasses to within ±0.1 (Zhang et al. 2018).

The FeL lines have low intensity and therefore high beam currents and/or long count times are required to record them. Silicate glasses are typically unstable under these conditions, leading to changes in Fe oxidation state during analysis (Fialin et al. 2004, 2011; Fialin and Wagner 2012; Zhang et al. 2018). Similar problems have also been observed for Fe in amphiboles (Wagner et al. 2008; Lamb et al. 2012) and S in silicate glasses and anhydrite (Wallace and Carmichael 1994; Rowe et al. 2007; Klimm et al. 2012). Fialin and Wagner (2012) observed two competing mechanisms of redox change during electron beam irradiation of alkali-bearing silicate glasses leading to either oxidation or reduction. As glasses are insulators, electrons are trapped within the subsurface during electron beam irradiation, causing a region of negative charge to buildup at depth in the sample, even with a conductive coat (e.g., Cazaux 1996). Alkali ions (predominantly Na⁺ but also K⁺) migrate toward the region of negative charge (e.g., Humphreys et al. 2006) leaving behind interstitial O^2– that migrates and either outgasses or combines with two FeO precipitating Fe₂O₃, thus causing oxidation (e.g., Lineweaver 1963). This is different from oxidation processes driven by changes in oxygen fugacity. For basaltic glasses, Fe³⁺ is stabilized by the migration of Na⁺ and K⁺ toward them preventing Fe₂O₃ precipitation (Cooper et al. 1996). Concurrently, during electron beam irradiation electrons move away from the negatively charged region from O to Fe³⁺ sites resulting in net reduction (Nishida 1995).

To minimize beam damage and prevent redox changes a sample can be moved during analysis, which reduces the electron dose per unit area (Metrich and Clocchiatti 1996; Rowe et al. 2007; Fialin et al. 2011; Zhang et al. 2018). Unfortunately, this requires large regions of glass for analysis making it unfeasible for analyzing small areas, such as melt inclusions and interstitial glasses. Therefore, we adapt the flank method for high spatial resolution analysis of silicate glasses due to its greater sensitivity and the ability to measure at single spectrometer positions (Hofer et al. 1994). This is important because it is easier to measure time-dependent changes at specific wavelengths rather than using wavescans, as required for the peak shift method. We measured FeLβ_f/FeLα_f over time, based on the time-dependent intensity (TDI) technique first developed for alkali migration during EPMA of glasses by Nielsen and Sigurdsson (1981). FeLβ_f/FeLα_f is extrapolated to time zero to correct for changes over time, which we refer to as the Time-Dependent Ratio (TDR) correction, comparable to TDI corrections for alkalis. Due to the small sample size of silicate glasses analyzed by Fialin and Wagner (2012) and Zhang et al. (2018), the controls on Fe redox processes during electron beam irradiation have not been explored and, crucially, few hydrous glasses have been analyzed. Therefore, we also investigate the compositional and analytical controls on Fe redox changes.

Silicate glasses of known (68 samples) and unknown (47 samples) Fe oxidation state from various studies were mounted in epoxy and carbon coated (∼15 nm thickness). The sample set covers a wide compositional range (anhydrous normalized SiO₂ 43–78 wt%, total alkalis (Na₂O+K₂O) 1–12 wt%, and H₂O 0–10 wt%; Fig. 2a and Table 1), which are used to investigate the effect of composition on Fe oxidation state changes during analysis. Silicate glasses of known Fe oxidation state (independently measured using wet chemistry, Mössbauer or μXANES), spanning 0.1–1.0 Fe²⁺/Fe_T and 2–18 wt% FeO_T (Fig. 2b), are used to calibrate the technique.

There are 16 suites of experimental silicate glasses that have different average glass compositions with variable Fe oxidation state and/or H₂O. The normalized (volatile-free) average glass compositions, which are either taken from the literature or measured using EPMA (see Supplementary Material¹ for details and individual sample compositions) are given in Table 1. AR samples are anhydrous, low-silica glasses with a range of glass compositions: KLA-1-6-22 (Fuchs et al. 2014), SC1 (Botcharnikov et al. 2008), 140ox (Almeev et al. 2007), LS (previously unpublished studies conducted at the Institut für Mineralogie, Leibniz Universität Hannover, Germany), PF22 (Wengorsch et al. 2012), and BezBA (Almeev et al. 2013). These glass compositions were re-synthesized at various oxygen fugacities and analyzed using wet chemistry by Zhang et al. (2018), where they have been analyzed by the flank method using a moving stage approach. Hydrous, low-silica glasses are GRN (Stamper et al. 2014); ETNA (this study); MAS.1.A, MAS.1.B, and St8.1.B (Lesne et al. 2011); and AMS (Di Genova et al. 2014). GRN samples may have suffered oxidation during μXANES (Cottrell et al. 2018), therefore their reported Fe oxidation state values are not considered further and the samples are only used to explore the effects of composition on redox changes during EPMA. The high-silica glasses range from peralkaline (FSP in Di Genova et al. 2016, and PSG in Di Genova et al. 2013) to calcalkaline (Y in Di Genova et al. 2017a, and PSB in Riker et al. 2015), with both anhydrous (FSP and Y) and hydrous (PSG and PSB) glasses.

Additional anhydrous, low-silica glasses analyzed are AII and LW (Cottrell et al. 2009), Smithsonian microbeam basaltic glass standards VG2 and VGA99 (Jarosewich et al. 1980) and PU (Ulmer 1989; Blundy et al. 2018). Compositions are given in the Supplementary Material¹.

Wavescans of the FeL peaks on glasses with varying FeO_T and Fe oxidation state (Table 2) were analyzed to examine the controls on peak position and intensity. Data were collected on the JEOL JXA 8530F Hyperprobe at the School of Earth Sciences, University of Bristol, U.K., using a 50 nA beam current, 10 μm beam diameter, and 15 or 30 kV accelerating voltage. Three spectrometers, with two TAP and one TAPH crystals, were moved 0.071 mm per step for 100 steps with 0.5 s dwell time over the FeL peaks while the stage moved at 1 μm/s to minimize beam damage. To improve signal to noise ratio, multiple wavescans (40–80, depending on the accelerating voltage and glass FeO_T) were collected, and the spectra from the three spectrometers were combined to produce a single wavescan per sample.

Selecting flank positions. To identify the optimum flank positions for FeLβ_f/FeLα_f, the method of Hofer and Brey (2007) (described in the Introduction, Fig. 1b) was used. Two spectra, representing the range of FeO_T and Fe oxidation state (AR14 and AR19, Fig. 3a), were normalized to the maximum intensity of their FeLα peak from which the difference spectrum was calculated (AR14–AR19, Fig. 3c). Optimum flank positions correspond to the maximum (low-wavelength flank of FeLα, FeLα_f) and minimum (high-wavelength flank of FeLβ, FeLβ_f) of the difference spectrum. To avoid collecting wavescans on these glasses every session, the flank positions were measured relative to the FKα peak measured on MgF₂ for each TAP/TAPH crystal. This reduced the time required to find the flank positions during future analytical sessions and minimized the area damaged by electron beam irradiation.

Electron probe setup. Each spectrometer measured a single wavelength and the spectrometer setup (referred to by crystal) was two TAP crystals to measure FeLα_f, TAPH for FeLβ_f, LLIF for FeKα, and PETH for KKα. At the wavelengths of interest, the TAPH crystal offers twice the peak intensity of the TAP crystals, and the FeLβ has roughly half the intensity of the FeLα peak, therefore we chose the above combination of spectrometers to maximize count rates. The full-width half-maximum wavelength resolution for FKα in MgF₂ here is 0.0813, 0.0835, and 0.1034 Å (0.8792, 1.1235, and 0.9079 mm spectrometer units) for the two TAP and TAPH crystals, respectively (Buse and Kearns 2018). Differential pulse height analysis (PHA) mode was used to remove interferences such as the ninth-order FeKα, and PHA scans were collected every session on each spectrometer on FKα in MgF₂. Na is typically the most mobile element measured during electron beam irradiation and therefore commonly used to monitor beam damage. However, in the absence of an additional TAP crystal, we measured K (also highly mobile) instead on a PETH crystal. For each analytical session, FeKα was peaked-up on BCR-2 (USGS basaltic glass standard), KKα on sanidine, and the peak position of FKα was measured on MgF₂ to calculate the wavelengths of the flank positions on each TAP/TAPH crystal. Spectrometers were static during analysis as backgrounds are not required for flank analyses (Hofer et al. 1994). As no other elements (or backgrounds) were measured, no matrix correction could be performed to quantify Fe or K, thus only their relative intensity over time is used. Analytical conditions were a 15 kV accelerating voltage, 50 nA beam current, and 4–15 μm beam diameter, which allows the analysis of small volumes of glass. Intensity measurements were collected over 5 s for a total duration of ∼150 s on the same spot of glass. Ten repeat analyses on fresh glass per sample were collected, resulting in a total analysis area of ∼20–60 μm diameter. Data were collected over five sessions. A summary of the analytical protocol is provided in the Supplementary Material¹.

Redox stability. To investigate the effect of analytical conditions on redox changes, additional measurements were made at different analytical conditions (Table 3) on four glasses chosen to represent the range of glass compositions studied (Table 4). AR10 and AR16 are anhydrous low-silica glasses, which are oxidized and reduced, respectively. MAS.1.B4 and PSB63 are hydrous glasses that are low- and high-silica, respectively.

Data processing. To check for sample homogeneity, FeKα was compared between repeat analyses. If the FeKα intensity was significantly outside the counting error for other repeats, the erroneous repeat analysis was removed from further processing and, if the sample was too inhomogeneous, the sample was not processed further. The analyses were then averaged at each time interval for FeLα_f (separately for each spectrometer), FeLβ_f, FeKα, and KKα. Using these averages at each time interval, FeLβ_f was divided by the sum of FeLα_f from the two spectrometers to calculate FeLβ_f/FeLα_f. Errors on FeKα, KKα, FeLβ_f/FeLα_f and time are the standard deviation of the repeat measurements. An exponential equation of the following form was fitted to each sample:

where I is the FeLβ_f/FeLα_f intensity ratio and t is time, subscripts refer to the values at t = 0 and ∞, and I′₀ is the rate of change of I with time at t = 0. When the minimization failed to converge, I_∞ was fixed to the last measured value for the sample. The error in both these cases is the standard error on the fit coefficients. In those cases where FeLβ_f/FeLα_f was constant with time, convergence is not possible, therefore the average of FeLβ_f/FeLα_f with time was used, where the error was the standard deviation of these data. Analyses with large errors (>±0.1 for I₀ and >±0.01 for I′₀), likely due to inhomogeneity, extremely rapid redox changes or analytical problems, are discarded. An R code for data processing is included in the Supplementary Material¹.

Raman spectroscopy was used to detect the presence of nanolites before and after electron beam irradiation as nanolites alter the Raman spectra of silicate glasses. Magnetite nanolites produce a peak at ∼670 cm^–1, which also decreases the intensity of the surrounding silicate peaks (Di Genova et al. 2017a, 2017b). Carbon coats were removed prior to analysis. Raman spectra were collected using the Thermo-Scientific DXRxi Raman Imaging Microscope at the School of Earth Sciences, University of Bristol, U.K., with a green (520 nm) laser, 50× (long distance) or 100× objective, and 3–5 mW power to avoid sample oxidation. An extended grating was used to also collect data on H₂O content. All samples, except AMS, FSP, PSG, and Y, which have been previously analyzed by Di Genova et al. (2017a, 2017b), were analyzed on non-irradiated areas of glass. Selected glasses that cover a range of compositions (ETNA08, MAS.1.A5, FSP1, FSP9, PSG6, and PSB63) were additionally analyzed following electron beam irradiation.

Wavelength and intensity changes of FeL lines in silicate glasses. For the same Fe oxidation state, peak intensity increases and peak positions shift to higher wavelengths with increasing FeO_T (Fig. 3a). For the same FeO_T oxidized samples have greater peak intensities and lower wavelength peak positions than reduced samples (Fig. 3a). At higher accelerating voltages (30 vs. 15 kV) the intensity of FeLα and FeLβ decrease, but there is no appreciable shift in peak positions (Fig. 3b). Therefore, there is no appreciable change in optimum flank positions, although the difference between the flank intensities decreases (Fig. 3c).

Time-dependent intensity changes during electron beam irradiation. During electron beam irradiation, the intensity of KKα remains stable (anhydrous glasses) or decreases (hydrous glasses) over time (Fig. 4), whereas for FeKα the intensity remains stable (anhydrous glasses) or increases (hydrous glasses) (Fig. 5). The ratio of FeLβ_f/FeLα_f increases (anhydrous low-silica), remains stable (anhydrous low-silica and hydrous high-silica), or decreases (hydrous low-silica) over time (Fig. 6). In those cases where intensity changes are observed, the rate typically increases with decreasing beam diameter, decreasing accelerating voltage, and increasing beam current. Data were collected during different sessions, therefore differences in the absolute intensity at different conditions are not meaningful.

Before electron beam irradiation. The majority of glasses analyzed are nanolite-free prior to electron beam irradiation (Figs. 7a and 7b). Exceptions are AR37 (composition LS) and ETNA(2) (samples ETNA 3, 6, 7, 8, 14, 16, and 30), with a peak at ∼670 cm^–1 indicating magnetite nanolites. Magnetite nanolites were detected in AMS4 and Y-L using Raman spectroscopy by Di Genova et al. (2017a, 2017b).

After electron beam irradiation. Most glasses analyzed following electron beam irradiation (MAS.1.A4, FSP1, FSP9, and PSG6) exhibit new magnetite nanolites (peak at ∼670 cm^–1 wavenumbers) when irradiated using a 4 μm beam diameter implying oxidation (Fig. 7c). Additionally, ETNA08, MAS.1.A4, and PSG6 have a new peak at ∼1350 cm^–1, which corresponds to hematite (RUFF Raman spectra database, http://rruff.info/, Lafuente et al. 2015), implying the formation of hematite nanolites following electron beam irradiation (Fig. 7c). PSB63 shows no evidence for the presence of Fe-bearing nanolites following electron beam irradiation. The H₂O peak (∼3600 cm^–1) shows a decrease in height after electron beam irradiation for hydrous samples (ETNA08, MAS.1.A4, PSG6, and PSB63), implying a loss of water.

The ratio of FeLβ_f/FeLα_f over time increased, remained stable, or decreased (Fig. 6), which could be due to various causes as FeLβ_f/FeLα_f depends on Fe concentration, oxidation state, and coordination. FeKα increases over time (Fig. 5), implying an increase in Fe_T. This is due to the process of “grow-in” (Morgan and London 2005), where the concentration of immobile elements (e.g., Si, Al, and Fe) increases due to the migration of alkalis (e.g., Na⁺ and K⁺, Fig. 4) and H⁺ (Fig. 7c) toward the buildup of negative charge at depth (e.g., Humphreys et al. 2006) and possible density changes. The increase in Fe_T implied by the increase in FeKα for hydrous silicate glasses (MAS.1.B4 and PSB63, Fig. 5) is small (∼0.13 wt% FeO_T). This is calculated to cause a negligible change on FeLβ_f/FeLα_f (∼0.004, within measurement error), and therefore changes due to Fe concentration are not considered further.

Additional carbon contamination can be deposited on the sample during electron beam irradiation (Bastin and Heijligers 1988). This can change X-ray intensities over time due to the reduction of the electron landing energy caused by energy loss within and X-ray absorption by the contaminant (Reed 1975). The former is negligible at the high voltages used here, whereas the latter should not affect FeLβ_f/FeLα_f as the mass absorption coefficients of FeLα and FeLβ by C are very similar (5762.34 and 5485.53 cm²/g, respectively, from the FFAST database). To change FeLβ_f/FeLα_f by 1% relative (within measurement error) would require >100 nm of C contamination (calculated using CalcZAF) during the 150 s analysis. This is far more than has been measured in previous studies (e.g., 8 ± 2 nm over 180 s; Buse et al. 2016), therefore the effect of contamination can be considered negligible.

These considerations imply that any changes observed in FeLβ_f/FeLα_f are due primarily to changes in Fe oxidation state over time. Increasing FeLβ_f/FeLα_f is caused by increasing Fe²⁺/Fe_T and hence Fe reduction (Fe³⁺ → Fe²⁺). Conversely, decreasing FeLβ_f/FeLα_f is caused by decreasing Fe²⁺/Fe_T and hence Fe oxidation (Fe²⁺ → Fe³⁺). Finally, no change in FeLβ_f/FeLα_f with time implies stable Fe²⁺/Fe_T during analysis. The presence of predominantly magnetite nanolites after electron beam irradiation implies that oxidation proceeds via precipitation of FeO·Fe₂O₃, not just Fe₂O₃, as has been previously suggested (Fialin and Wagner 2012).

To investigate the compositional controls on the rate and mechanism of redox changes during electron beam irradiation, we define the parameter Total Mobile Cations (TMC), which is the molar sum of (H₂O + Na₂O + K₂O) per gram of glass (units: mol/g). This provides a maximum estimate of the moles of available oxygen if all the H⁺, Na⁺, and K⁺ migrated due to the buildup of negative charge (Humphreys et al. 2006). TMC is typically dominated by H₂O due to the low atomic mass of H compared to Na and K. Figure 8 shows the rate of change of FeLβ_f/FeLα_f with time at time zero (I′₀) against TMC. Glasses with TMC <0.1 mol/g remain stable or reduce over time (I′₀ ≥ 0 s^–1), corresponding to anhydrous (H₂O < 0.38 wt%), alkali-poor (Na₂O+K₂O < 5.5 wt%) glasses. Conversely, glasses with TMC > 0.1 mol/g remain stable or oxidize over time (I′₀ ≥ 0 s^–1) corresponding to either hydrous (H₂O > 1.03 wt%) or alkali-rich (11.3 ± 0.2 wt% N₂O+K₂O) glasses. The mechanisms causing reduction are likely always to occur in the glass during electron beam irradiation, therefore it appears that at TMC ≥ 0.1 mol/g the rate of oxidation is greater than the rate of reduction, hence oxidation prevails.

Figure 9 shows I′₀ against initial Fe²⁺/Fe_T for anhydrous, low-silica (43–56 wt% SiO₂) glasses where, for a specific glass composition, Fe²⁺/Fe_T correlates negatively with rate of reduction. Glasses that are mostly reduced (Fe²⁺/Fe_T > 0.9) cannot reduce any further and remain stable, therefore reduction is confined to initially oxidized glasses. Between the suites of glass with different compositions, there is no obvious compositional control on I′₀.

H₂O content.Figure 10 shows the rate of change of FeLβ_f/FeLα_f over time at time zero (I′₀) against TMC for suites of low-silica glasses (43–56 wt% SiO₂) that have variable H₂O concentrations, but constant glass composition. Broadly, I′₀ becomes more negative with increasing TMC. For a fixed glass composition the increase in TMC is due to increasing H₂O content, therefore the rate of oxidation increases with increasing H₂O. The diffusivity of H₂O in basaltic glasses depends on the total H₂O content (Okumura and Nakashima 2006), thus the rate of oxidation increases with increasing H₂O diffusivity. These results show that the migration of H⁺, in addition to Na⁺ and K⁺ as previously suggested by Fialin and Wagner (2012), leads to oxidation of Fe during electron beam irradiation. In fact, when considering the mobile cation responsible for Fe oxidation, H⁺ plays a more important role than might be expected from its oxide wt% concentrations alone due to the low atomic mass of H.

SiO₂ content. High-silica (61–78 wt% SiO₂) glasses remain broadly stable during electron beam irradiation (Fig. 8), despite the Raman spectra of electron beam irradiated areas using a 4 μm beam diameter indicating the formation of magnetite nanolites (Fig. 7c). This implies extremely rapid oxidation at 4 μm, which is consistent with the rate of alkali migration, and probably H, being faster during electron beam irradiation of high-silica compared to low-silica glasses (e.g., Fig. 4; Hayward 2011). This may be due to the more polymerized structure of high-silica glasses (Mysen et al. 1982).

Fe content. PSB glasses do not oxidize (I′₀ ≈ 0 s^–1, Fig. 8), and there are no Fe-bearing nanolites observable in the Raman spectra prior to or following electron beam irradiation (Fig. 7c), despite TMC > 0.4 mol/g due to their high alkali and water contents. These glasses contain little Fe (FeO_T ≤ 3.2 wt%), which could hinder oxidation as FeO groups may need to lie close together to produce Fe₂O₃.

Presence of nanolites. Surprisingly, low-silica (47–58 wt% SiO₂) glasses with TMC > 0.35 mol/g, which corresponds to H₂O > 4 wt% (Fig. 10), appear stable (I′₀ ≈ 0 s^–1). It is possible that they oxidized very quickly and the change is not observable. Analyses using a 10 μm beam size are also stable (Fig. 8a), but there is evidence for the formation of hematite nanolites during electron beam irradiation (Fig. 7c). This either means the oxidation is extremely rapid, due to the very high H₂O contents, or not occurring due to the presence of magnetite nanolites before irradiation where the Fe may be stable, but further study is required to understand this process fully.

For all X-rays measured (KKα, FeKα, and FeLβ_f/FeLα_f), the rate of change of intensity increases with decreasing beam diameter, decreasing accelerating voltage, and increasing beam current (Figs. 4, 5, 6, and 8), as is commonly observed during electron beam irradiation (e.g., Morgan and London 2005). The analytical conditions control the electron density implanted into the sample and, therefore, the magnitude of sub-surface charging. Increasing the beam current increases the electron dosage to the sample. The interaction volume is reduced by decreasing both the accelerating voltage and beam diameter, which limits the depth these electrons penetrate and the irradiated area, respectively. Overall, the rate of intensity change increases with increasing implanted electron density (i.e., decreased interaction volume and/or increased electron dosage).

Hofer and Brey (2007) found that the ratio of FeLβ_f/FeLα_f correlated linearly with Fe²⁺ for garnets, with a small secondary dependence on Fe_T. Consequently, their coefficients (m and c) of Fe²⁺ = m·(FeLβ_f/FeLα_f) + c were dependent on Fe_T. Our data showed no improvement to the correlation between FeLβ_f/FeLα_f and Fe²⁺ by allowing the coefficients to depend on Fe_T, therefore m and c are fitted without Fe_T dependence using a weighted least-squares regression (weighted using error on independently constrained Fe²⁺). The lack of dependence on Fe_T is likely because the composition of natural silicate glasses investigated here covers a much narrower range of Fe_T compared to garnets (<18 vs. 64 wt% FeO_T, respectively). The calibration curve is not constant between sessions (Fig. 11 and Table 5, and additional sessions in the Supplementary Material¹), therefore a new calibration curve should be produced for each session.

It appears that low-silica and peralkaline glasses require different calibration curves (Fig. 11b), therefore these two sample groups were fitted separately. Using these different calibration curves, Fe²⁺/Fe_T is replicated well for both compositions (Figs. 12a and 12b). Fe coordination also effects the FeL lines but the coordination of silicate glasses is very similar (Cottrell et al. 2009). Instead, it may be that absorption within the glass of the FeL lines is different between these two broad compositional groups due to their different compositions, although this was not observed for garnets (Hofer and Brey 2007). Compositional differences within the low-silica glasses may also explain the scatter observed in the calibration curves, but it is not possible to explore this fully using the current data set. It may be that errors on Fe²⁺/Fe_T can be reduced by using compositionally matched glass standards. In practice such standards are unlikely to be available, therefore we recommend using standards with broadly similar compositions (i.e., low-silica or peralkaline) when using this technique.

A calibration curve could not be created for high-silica glasses PSB and Y as they cover a narrow range of Fe²⁺ (<2 wt% Fe²⁺). Their Fe²⁺/Fe_T ratio are poorly replicated by the low-silica calibration curve (Fig. 12c) to which they lie more closely than the peralkaline calibration curve (Fig. 11b). This is likely due to their low Fe content (FeO_T < 3.3 wt%, except Y-L with 6.2 wt%), therefore this technique is unsuitable for low-Fe glasses (i.e., FeO_T < 5 wt%).

The Fe²⁺/Fe_T precision, using a residual standard error of 0.5 wt% on Fe²⁺ and 1% relative error on FeO_T, depends on the Fe concentration and oxidation state

e.g., ±0.03 for 10 wt% FeO_T and 0.5 Fe²⁺/Fe_T. The average accuracy for low-silica (43–56 wt% SiO₂) and peralkaline (70–76 wt% SiO₂) glasses with 5–18 wt% FeO_T, and 0–4 wt% H₂O, when the appropriate analytical conditions and calibration curves are used, is ±0.1 (Figs. 12a and 12b).

Analytical conditions can be optimized according to the nature of any given sample as different conditions (beam diameter and current, total count time of a single analysis, and number of analyses averaged) can be used on the standards and unknowns, so long as the accelerating voltage and flank positions remain the same. Hofer and Brey (2007) showed that for garnets the optimum accelerating voltage is 15 kV; at lower and higher accelerating voltages the sensitivity of the flank method is reduced. For glasses, the sensitivity of the flank method also decreased at higher accelerating voltages (Figs. 3b and 3c). An accelerating voltage of 15 kV allows the composition of the sample to be analyzed, via conventional EPMA, without further calibration or beam focusing.

The error on the corrected FeLβ_f/FeLα_f is a function of counting statistics, the fit of an exponential function to the change in FeLβ_f/FeLα_f with time, and the number of analyses averaged. Counting statistics can be improved by using a higher beam current, but this can cause the rate of change to occur too quickly to be observed. Decreasing the beam diameter will also increase the rate of change, as seen here for high-silica glasses, but improves spatial resolution. Therefore, it is important to know the approximate composition of the target glass (e.g., by EDS analysis) to understand how quickly the change in Fe oxidation is likely to occur. If redox changes occur too quickly, the time-corrected FeLβ_f/FeLα_f will be wrong leading to erroneous Fe²⁺/Fe_T values. Our data at a 15 kV accelerating voltage, 50 nA beam current, 4 μm beam diameter, and averaging 10 analyses produced a relative error on the corrected FeLβ_f/FeLα_f of ∼3%, and gave the flexibility to analyze various glass morphologies for hydrous low-silica glasses. A larger beam size (10–15 μm diameter) is needed to analyze high-silica samples containing sufficient iron (i.e., peralkaline) due to the rapid rate of oxidation, which unfortunately sacrifices spatial resolution. This technique may not be appropriate if samples contain fine-scale heterogeneities (e.g., nanolites), as the Fe coordination in these phases may differ to that in the glass.

The TDR flank method presented here could be applied to other beam-sensitive samples. Electron probe induced dehydrogenation has been observed for kaersutitic amphibole, resulting in the underestimation of Fe²⁺/Fe_T due to oxidation (Wagner et al. 2008). Wagner et al. (2008) showed the severity of damage correlated with analytical conditions and H₂O content of the amphibole, in much the same way as shown here for silicate glasses. Therefore, applying the TDR flank method to amphiboles may provide robust Fe oxidation state estimates without sacrificing spatial resolution.

Oxidation and reduction of S have been observed during analysis of silicate glasses and anhydrite when using the SKα peak shift to measure S oxidation state (Wallace and Carmichael 1994; Rowe et al. 2007; Wilke et al. 2011). Sulfur oxidation in silicate glasses appeared to follow an exponential trend and, as observed here, the estimate of redox state at time zero was found to agree with XANES measurements of the same sample (Wilke et al. 2011). Sulfur redox changes are controlled by similar factors to Fe such as initial S oxidation state (Rowe et al. 2007) and H₂O content (Wilke et al. 2008). If a flank-type method was developed for S (Wilke et al. 2011), time-dependent measurements could also be applied, negating the need to move samples during analysis (Metrich and Clocchiatti 1996; Rowe et al. 2007), and thereby improving spatial resolution.

Measuring the Fe oxidation state of silicate glasses allows estimation of oxygen fugacity prevailing during natural processes and in experiments. The time-dependent ratio flank method presented here combines the ability to measure the Fe oxidation state at high resolution with the utility of the electron probe. This will allow routine measurement of Fe oxidation state of melt inclusions and interstitial glass, previously hampered by the need for synchrotron access. Melt inclusions provide a unique insight into the pre-eruptive magma but studies have shown that the Fe oxidation state can be altered by degassing (e.g., Moussallam et al. 2014) and cooling (e.g., Hartley et al. 2017) post-entrapment, complicating their use as a proxy for oxygen fugacity. Hence, larger data sets generated due to easier access will allow the importance of these processes to be further investigated, although for some applications smaller errors will be required. Also, a better understanding of the analytical and compositional controls on redox changes during electron beam irradiation of silicate glasses (summarized in Fig. 13) can aid our understanding of glass structure and improve analytical routines.

We thank Richard Hinton for his assistance at the NERC ion microprobe facility at the University of Edinburgh, U.K. (IMF560/0515). We thank Priscille Lesne, Charlotte Stamper, Peter Ulmer, and Liz Cottrell for providing samples. E.C.H. is supported by a NERC GW4+ DTP studentship from the Natural Environment Research Council (NE/L002434/1) and is thankful for the support and additional funding from CASE partner GNS Science, New Zealand. G.K. acknowledges support from the New Zealand Strategic Science Investment Fund. H.M.M., R.A.B., and D.D.G. were supported by the NSFGEO-NERC “Quantifying disequilibrium processes in basaltic volcanism” (NE/N018567/1). R.R.A. was supported by the German Science Foundation (DFG project AL 1189/6-1). We thank John Donovan and two anonymous reviewers for their helpful comments.