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

), including 68 glasses with known Fe oxidation state. The Fe oxidation state (Fe 2+ /Fe T ) of hydrous (0–4 wt% H 2 O) basaltic (43 – 56 wt% SiO 2 ) and peralkaline (70–76 wt% SiO 2 ) glasses with FeO T > 5 wt% can be quantified with a precision of ±0.03 (10 wt% FeO T and 0.5 Fe 2+ /Fe T ) and accuracy of ±0.1. We find basaltic and peralkaline glasses each require a different calibration curve and analysis at different spatial resolutions (~20 and ~60 μm diameter regions, respectively). A further 49 synthetic glasses were used to investigate the compositional controls on redox changes during electron beam irradiation, where we found that the direction of redox change is sensitive to glass composition. Anhydrous alkali‑poor glasses become reduced during analysis, while hydrous and/or alkali-rich glasses become oxidized by the formation of magnetite nanolites identified using Raman spectroscopy. The rate of reduction is controlled by the initial oxidation state, whereas the rate of oxidation is controlled by SiO 2 , Fe, and H 2 O content.


introDuCtion
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. 2009Creighton et al. , 2010;;Malaspina et al. 2010;Lamb et al. 2012;Matjuschkin et al. 2014) and also glasses (Fialin et al. 2001(Fialin et al. , 2004(Fialin et al. , 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 L 3 and L 2 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 L 3 absorption edge shifts more than the L 2 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 Fe 2+ /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 L 2 and L 3 absorption edges and, as the Fe 2+ content changes, the L 3 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 L 3 absorption edge, whereas FeLβ f is on the low-absorption side of the L 2 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 (Fe 2+ ), 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 Energy level diagram of the electron transitions that generate characteristic Fe X-rays, and (b) wavelength spectra of the FeLα and FeLβ peaks for a reduced, high FeO T (solid, AR19) and oxidized, low FeO T (dashed, AR14) silicate glass (Tables 1 and 2) plotted using the left-hand axes, and the difference spectrum (dotted, calculated once the wavescans are normalized to their maximum FeLα peak intensity) plotted using the right-hand axes.The red box indicates the wavelengths measured for the peak shift method (FeLα wavescan).The blue vertical lines indicate optimum wavelength positions measured for the flank method, which correspond to the maximum and minimum of the difference spectrum.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 Fe 2+ /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(Fialin et al. , 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 Fe 2 O 3 , thus causing oxidation (e.g., Lineweaver 1963).This is different from oxidation processes driven by changes in oxygen fugacity.For basaltic glasses, Fe 3+ is stabilized by the migration of Na + and K + toward them preventing Fe 2 O 3 precipitation (Cooper et al. 1996).Concurrently, during electron beam irradiation electrons move away from the negatively charged region from O to Fe 3+ 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 inclu-sions 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.

saMpLEs
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 SiO 2 43-78 wt%, total alkalis (Na 2 O+K 2 O) 1-12 wt%, and H 2 O 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 0.1-1.0Fe 2+ /Fe T and 2-18 wt% FeO T (Fig. 2b), are used to calibrate the technique.
There  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), andBezBA (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, andPSG in Di Genova et al. 2013) to calcalkaline (Y in Di Genova et al. 2017a, andPSB in Riker et al. 2015), with both anhydrous (FSP and Y) and hydrous (PSG and PSB) glasses.

FeL wavescans
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.

Time-dependent ratio FeLβ f /FeLα f measurements
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 MgF 2 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 MgF 2 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 MgF 2 .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 MgF 2 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 Material 1 .
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 I 0 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 Material 1 .

Raman spectroscopy
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 H 2 O 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.

Electron probe microanalysis
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 lowsilica), remains stable (anhydrous low-silica and hydrous highsilica), 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.

During ELECtron BEaM irraDiation
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 cm 2 /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 Fe 2+ /Fe T and hence Fe reduction (Fe 3+ → Fe 2+ ).Conversely, decreasing FeLβ f /FeLα f is caused by decreasing Fe 2+ /Fe T and hence Fe oxidation (Fe 2+ → Fe 3+ ).Finally, no change in FeLβ f /FeLα f with time implies stable Fe 2+ /Fe T during analysis.The presence of predominantly magnetite nanolites after electron beam irradiation implies that oxidation proceeds via precipitation of FeO•Fe 2 O 3 , not just Fe 2 O 3 , as has been previously suggested (Fialin and Wagner 2012).

Direction of redox change: Total mobile cations
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 (H 2 O + Na 2 O + K 2 O) 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 H 2 O 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 ), correspond- ing to anhydrous (H 2 O < 0.38 wt%), alkali-poor (Na 2 O+K 2 O < 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 (H 2 O > 1.03 wt%) or alkali-rich (11.3 ± 0.2 wt% N 2 O+K 2 O) 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.

Rate of reduction: Initial Fe oxidation state
Figure 9 shows I′ 0 against initial Fe 2+ /Fe T for anhydrous, lowsilica (43-56 wt% SiO 2 ) glasses where, for a specific glass composition, Fe 2+ /Fe T correlates negatively with rate of reduction.Glasses that are mostly reduced (Fe 2+ /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 .

Rate of oxidation
H 2 O 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% SiO 2 ) that have variable H 2 O 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 H 2 O content, therefore the rate of oxidation increases with increasing H 2 O.The diffusivity of H 2 O in basaltic glasses depends on the total H 2 O content (Okumura and Nakashima 2006), thus the rate of oxidation increases with increasing H 2 O 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.
SiO 2 content.High-silica (61-78 wt% SiO 2 ) 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 Fe 2 O 3 .
Presence of nanolites.Surprisingly, low-silica (47-58 wt% SiO 2 ) glasses with TMC > 0.35 mol/g, which corresponds to H 2 O > 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 H 2 O 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.

Effect of analytical conditions
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).

Quantifying fE oxiDation statE: tiME-DEpEnDEnt ratio fLanK MEtHoD
Calibration and errors Hofer and Brey (2007) found that the ratio of FeLβ f /FeLα f correlated linearly with Fe 2+ for garnets, with a small secondary dependence on Fe T .Consequently, their coefficients (m and c) of Fe 2+ = 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 Fe 2+ 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 Fe 2+ ).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 Material 1 ), 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, Fe 2+ /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 Fe 2+ /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 Fe 2+ (<2 wt% Fe 2+ ).Their Fe 2+ /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%).

Recommended analytical conditions
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 Fe 2+ /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.

Further applications
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 Fe 2+ /Fe T due to oxidation (Wagner et al. 2008).Wagner et al. (2008) showed the severity of damage correlated with analytical conditions and H 2 O 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 H 2 O 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.EPMA against independently constrained Fe 2+ /Fe T collected during all sessions for (a) low-silica (43-56 wt% SiO 2 ), (b) peralkaline (FSP+PSG), and (c) high-silica (69-78 wt% SiO 2 , using low-silica glass derived calibration curves) glasses, where symbol shape indicates average glass composition (Table 1) and color indicates H 2 O. Analytical conditions were 15 kV accelerating voltage, 50 nA beam current, and 4-15 μm beam diameter.

iMpLiCations
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.

figurE 3 .
figurE 3. Wavescans of FeL for silicate glasses (see Table2for compositions).Analytical conditions were: 50 nA beam current and 10 μm beam diameter, while the stage moved at 1 μm/s.Spectrometer position (L) is shown along the top and equivalent wavelength along the bottom.(a) Different FeO T and Fe oxidation states at 15 kV accelerating voltage, (b) different accelerating voltages, (c) different accelerating voltages with the intensity normalized to the maximum FeLα intensity, and (d) difference spectra (AR14-AR19) at different accelerating voltages, calculated from the normalized spectra, with optimum flank positions shown (vertical lines).The FeLβ f /FeLα f ratio is 0.55 for AR14 and 0.92 for AR19 at 15 kV.

figurE 4 .
figurE 4. Intensity of KKα with time.Analytical conditions (accelerating voltage, beam current, and beam diameter) shown along the top and sample description on the left-hand side.Symbols and colors as Figure 2a except that open/closed symbol indicates initial Fe oxidation state: open symbols are oxidized (Fe 2+ /Fe T < 0.2); closed symbols are reduced (Fe 2+ /Fe T > 0.7).

figurE 5 .
figurE 5. Intensity of FeKα with time.Analytical conditions (accelerating voltage, beam current, and beam diameter) shown along the top and sample description on the left-hand side.Symbols and colors as Figure 4.

figurE 7 .figurE 8 .
figurE 6. Intensity ratio of FeLβ f /FeLα f with time.Analytical conditions (accelerating voltage, beam current, and beam diameter) shown along the top and sample description on the left-hand side.Symbols and colors as Figure 4.
Na 2 O, and K 2 O are normalized to the volatile-free total), and (b) Fe 2+ /Fe T against FeO T for samples with known Fe oxidation state.Symbol shape indicates glass composition (Table 1), color indicates H 2 O content, and a black outline indicates known Fe oxidation state; those without an outline have unknown Fe oxidation state.

Table 1 .
(Cottrell et al. 2018free), average glass composition for the suites of experimental silicate glasses Notes: Oxides (in wt%) are measured using EPMA (all Fe reported as FeO, FeO T ), except H 2 O, which is measured by a SIMS, b KFT, or 0 indicates assumed due to experimental conditions.Fe 2+ /Fe T is measured by c wet chemistry, d µXANES, or not determined (n.d.).e Fe oxidation state measurements may have suffered from oxidation during µXANES and are therefore not used in this study(Cottrell et al. 2018).

Table 2 .
Fe content and oxidation state of glasses analyzed using wavescans Glass compositions refer to Table1.FeO T (all Fe reported as FeO) measured using EPMA and Fe 2+ /Fe T using wet chemistry.Errors of one standard deviation (1σ) corresponding to the last significant figure are shown in parentheses.

Table 3 .
EPMA conditions for time-dependent ratio FeLβ f /FeLα f measurements Conditions 1-3 were used to quantify Fe oxidation state, and additional measurements were made at conditions 4-6 on AR10, AR16, MAS.1.B4, and PSB63 to investigate redox stability.

Table 4 .
Glass compositions of AR10, AR16, MAS.1.B4, and PSB63 Notes: Oxides (in wt%) are measured using EPMA (all Fe reported as FeO, FeO T ), except H 2 O, which is measured by SIMS or 0 indicates assumed due to experimental conditions.Fe 2+ /Fe T is measured by a wet chemistry or b µXANES.Errors of 1σ corresponding to the last significant figure are shown in parentheses.
The rate of change of FeLβ f /FeLα f with time at time zero (I′ 0 ) against Fe 2+ /Fe T for anhydrous low-silica glasses, where symbol color indicates average glass composition (Table1) and linear regressions are shown (solid lines).Analytical conditions were: 15 kV accelerating voltage, 50 nA beam current, and 4 μm beam diameter.The rate of change of FeLβ f /FeLα f with time at time zero (I′ 0 ) against Total Mobile Cations (TMC) for hydrous low-silica glasses, where symbol shape and color indicates average glass composition (Table1), and open symbols indicate the presence of nanolites.Analytical conditions were: 15 kV accelerating voltage, 50 nA beam current, and 4 μm beam diameter.

Table 5 .
Example of results for weighted linear regression for Fe 2+ calibration Data were collected in sessions 1 and 5 using analytical conditions of a 15 kV accelerating voltage and 50 nA beam current.n is the number of measurements included in the fit.m and c are the slope and intercept, respectively, for Fe 2+ = m•(FeLβ/FeLα) + c.Adj.R 2 is the adjusted R 2 .R.S.E. is the residual standard error on estimated Fe 2+ .Fits are for low-silica and a peralkaline glasses.Calibration curves derived for two sessions (1 and 5), where Fe 2+ is constrained using Fe 2+ /Fe T from independent techniques and Fe T from EPMA.Symbol shape indicates average glass composition (Table