Compositional and temperature effects on sulfur speciation and solubility in silicate melts

Article history: Received 17 July 2018 Received in revised form 28 November 2018 Accepted 8 December 2018 Available online 19 December 2018 Editor: M. Bickle


Introduction
Sulfur plays an important role in many geological environments. It is a major volatile component in volcanic systems in the form of SO 2 and H 2 S gases; it is an essential nutrient in sulfate metabolism on the seafloor and it provides sulfide hosts for economically important elements such as Ni, Cu, Pt, and Au. This diverse range of properties is a result of the stabilities of several oxidation states of sulfur in natural environments. The relative stabilities of these different oxidation states control the distribution of sulfur between Earth's various geochemical reservoirs, core, mantle, crust, oceans and atmosphere. They also have profound influence on the distribution of many chalcophile (sulfur-loving) elements between these different reservoirs.
Although Earth's core has been estimated to contain about 1.7% S (Dreibus and Palme, 1995) the primitive mantle (bulk silicate Earth) contains only around 200 ppm S as FeS-rich sulfide (Palme and O'Neill, 2014). Despite this low abundance, however, the low solubility of sulfide in silicate melts (Li and Ripley, 2005;O'Neill and Mavrogenes, 2002;Smythe et al., 2017;Wendlant, 1982) means that mid-ocean ridge basalts (MORB), generated by partial melting of the mantle, are saturated in a liquid sulfide phase possibly throughout the entire liquid line of descent (Mathez, 1976). In this case, even very small amounts of sulfide control the concentrations of a number of nominally incompatible chalcophile elements such as Cu, Ag, Bi, Sb, Pb and the Pt-group metals in the equilibrium melts Wood, 2013, 2015). In contrast to MORB in which S is present almost entirely in the S 2− oxidation state, island arc rocks may exhibit saturation in either sulfide or sulfate (S 6+ ) the latter being stabilized at the higher oxygen fugacities ( f O 2 ) recorded above some subduction zones (Carmichael, 1991;Jugo et al., 2010). In such cases the stabilizing of higher oxidation states leads to degassing of SO 2 an important agent of climate cooling.
The presence of sulfur is also significant in the evolution of other terrestrial bodies. The silicate surface of Mercury exhibits high S and low FeO contents and the planet is believed to be highly reduced (Nittler et al., 2011). Consistent with these interpretations are the high concentrations of S (up to 11 wt%) and low FeO contents (<1 wt%) observed experimentally in FeS-saturated silicate melts under strongly reducing conditions (Wohlers and Wood, 2017). Based on the compositions of SNC meteorites, Dreibus and Wänke (1985) noted strong depletions of chalcophile Co, Ni, Cu, In and Tl in silicate Mars relative to silicate Earth and suggested dissolution of greater fractions of these elements in Mars' core, together with a higher concentration of S (14.2%) in this reservoir. More recently, measurements of the compositions of Martian surface rocks by the Spirit Rover shows basalts containing up to 2.37% SO 3 (McSween et al., 2006). As sulfate is much more soluble than sulfide in silicate melts (Jugo et al., 2010) these observations suggest that S exhibits multiple oxidation states on Mars as well as Earth and that S 6+ dominates in the near-surface environment.
Given the importance of both S 2− and S 6+ in natural silicate melts on both Earth and Mars, our aim here has been to examine the conditions of f O 2 and f S 2 under which S 2− is replaced by S 6+ as the stable oxidation state in silicate melts with high (Mars-like) and low (Earth-like) FeO contents. Fincham and Richardson (1954) showed that S 2− is the dominant S species in silicate melts at low f O 2 by demonstrating a linear relationship (with gradient 1/2) between log [S] (the sulfur content of the melt) and log ( f S 2 / f O 2 ). This relationship arises from dissolution of sulfide according to the following equilibrium:

Sulfur speciation in silicate melts
The equilibrium constant (K 1 ) for this reaction is given by, By combining O 2− activity, the activity constant of S 2− and the equilibrium constant, we can then define the 'sulfide capacity' C S 2− : The sulfide capacity is, for any given silicate melt, a function of its major element composition. From Equation (3) we see that for fixed melt composition, temperature and pressure log [S 2− ] should depend on the log ( f S 2 / f O 2 ) with a one-half slope. Deviations from this slope indicate that S 2− is not the dominant sulfur species in the melt. Under oxidizing conditions (i.e. f O 2 's above the fayalitemagnetite-quartz, FMQ, oxygen buffer), Fincham and Richardson (1954) observed an increase in log [S] with increasing f O 2 , indicating that sulfate becomes the dominant species under these conditions. This equilibrium can be expressed through the reaction: As with sulfide, a sulfate capacity parameter (C S 6+ ) can be defined and used to express the dependence of concentration on f O 2 and f S 2 . From Equation (4) we define the equilibrium constant (K 4 ) as, We can then define the sulfate capacity (C S 6+ ) by combining K 4 , aO 2− melt , and γ SO 2− 4 melt . Rearranging yields: The transition from sulfide to sulfate with increasing f O 2 can readily be understood by combining reactions (1) and (4) as follows: The stoichiometry of this equilibrium, specifically the large number of oxygen atoms required for oxidation, implies that the transition in stability between these species occurs over a narrow f O 2 range. This can be shown explicitly if the equilibrium is expressed in terms of the activities or concentrations of its components: In Equation (8) activities have been approximated by concentrations and equilibrium constant K 7 replaced by K (i.e. K = K 7 ·γ S 2− melt /γ SO 2− 4 melt ). The transition from S 2− to SO 2− 4 , occurring over the expected narrow f O 2 interval, has been observed using the XANES method between FMQ and FMQ+2 by Jugo et al. (2010) and at FMQ by Klimm et al. (2012b). Compositional and temperature effects on the transition are unknown. The principal goal of our study was, therefore, to isolate these effects on speciation for a broad range of melt compositions.

Approaches to determining sulfur speciation
X-ray Absorption Near-Edge Structure (XANES) spectroscopy has been employed in several studies to measure the relative proportions of S 6+ and S 2− in silicate glasses (Métrich et al., 2009;Botcharnikov et al., 2011;Brounce et al., 2017;Jugo et al., 2010). The large contrast in electron shielding between the S 2− and S 6+ species gives rise to a difference of ∼10 eV in K-edge energy  (Métrich et al., 2009) that is easily resolvable using XANES. Previous studies have demonstrated a positive correlation between the energy of the S K -edge and sulfur valence state (e.g. Paris et al., 2001;Fleet et al., 2005;Almkvist et al., 2010), making discrimination between intermediate species (e.g. S − , S 0 , S 4+ ) also possible. In our study, XANES was used to identify the sulfur species present in synthetic silicate glasses, and to determine their relative abundances by comparing the amplitudes of their characteristic absorption peaks. An alternative way of estimating sulfur speciation is to determine the dependence of total sulfur concentration on f O 2 and f S 2 . The observed relationships are then compared to the possible stoichiometries of the sulfur dissolution reactions such as (1) and (4) above. If the trends observed are consistent with a particular chemical equilibrium, the relevant sulfur species can be assumed to be dominant in the melt. This was the approach pursued by Fincham and Richardson (1954), and successfully extended to more geologically relevant melts by O'Neill and Mavrogenes (2002). Over the f O 2 range of the S 2− to S 6+ transition the log f S 2 which can be obtained with commercial available gases at 1 atm is on the order of only −2.5 to −4.5, resulting in S concentrations in silicate melts as low as 1 ppm, well below the detection limit of electron probe micro-analysis (EPMA). We have therefore employed secondary-ion mass spectrometry (SIMS) for which the detection limit of S is ∼0.1 ppm. Both the spectroscopic and 'indirect' approaches to investigating speciation have been used in the present study.

Experimental methods
The silicate melt compositions investigated are given in Table 1 and were chosen to represent a broad range of terrestrial and Martian igneous rocks. The Martian basalts "JFR" and "DWF" are derived from the experimental products of Bertka and Holloway's (1994) study of Martian mantle melting (their Table 8), and represent ∼10% and ∼50% melts of a hypothetical model composition for Mars' mantle (Dreibus and Wanke, 1985). These experimentally derived compositions were used in preference to natural compositions, whose genetic relations to Mars' mantle are uncertain. The primitive and iron-rich model terrestrial basalts, "PRI" and "EVO", were generated by addition of olivine to an average MORB (from Gale et al., 2013) until equilibrium with Fo90.5 olivine was achieved at 1 bar pressure (to yield PRI), and subtraction of olivine and plagioclase to generate the iron-rich EVO composition. The andesitic and dacitic melts ("AND" and "DAC") are representative natural rock compositions from Carmichael et al. (1974).
The starting compositions were prepared from powdered oxides and carbonates, which were combined under ethanol into fine homogeneous powders, and decarbonated in air at 1000 • C. All experiments were conducted in a 1-atmosphere gas-mixing furnace at a constant temperature of 1300 • C, over an f O 2 range between FMQ-2 and FMQ+2 (extrapolated from the calibration of O'Neill (1987). Each experimental charge consisted of ∼10 mg of starting material which was suspended in the furnace on a loop of thin (0.25 mm) wire, stuck to the loop using paraffin oil. Rhenium wire was used below FMQ+1, while more oxidizing experiments (which would oxidize the Re metal) employed platinum as the loop material. Platinum loops were pre-saturated with Fe to minimize absorption from each charge. Experimental run conditions are given in Table 2.
The oxygen and sulfur fugacities were controlled by continuously flowing appropriate CO-CO 2 -SO 2 gas mixtures through the furnace. The gas mixtures required at each f O 2 and f S 2 were calculated numerically from thermodynamic data for the various C-S and O-bearing species (Chase et al., 1985), following the procedure of White et al. (1958) and flow rates were controlled by standard mass-flow controllers. Based on numerous repeat measurements of f O 2 using an ytrria-stabilized zirconia electrolyte we estimate the uncertainty in f O 2 as ±0.1 log units. We chose the highest possible f S 2 at each f O 2 in order to maximize the sulfur concentration in the melt and obtain XANES spectra with high signal/noise ratios. To test whether sufficient time was allowed to reach equilibrium in our samples a set of experiments using the DAC composition were done under reducing conditions over a range of run durations. The concentration of sulfur was found to reach equilibrium between 8 and 12 h. All further experiments were run for a minimum of 12 h.
An important requirement of this study was the exposure of each melt composition to exactly the same conditions of temperature, pressure and f O 2 , so that the influence of melt chemistry on sulfur redox state could be isolated. To this end the six charges were equilibrated simultaneously at each set of conditions, suspended together on a chandelier inside the furnace. The chandelier was drop-quenched in water at the end of each experiment. The recovered run-products were then mounted in epoxy and inspected under a petrographic microscope to ensure absence of crystalline phases and to test for presence of immiscible sulfides. Occasional very small Re-Fe sulfides, not quantitatively analyzable by microprobe, were found in some experiments performed on Re wires.

Analysis of major-elements and sulfur
The major-element composition of each glass was determined by Wavelength Dispersive Spectroscopy using a Cameca SX5 electron microprobe at Oxford University. All analyses were conducted with a 15 kV accelerating voltage and a 10 μm, 30 nA electron beam. Standards used for silicate glass analysis were albite (Si, Na), synthetic periclase (Mg), pyrope (Al), sanidine (K), rutile (Ti), Mn metal, Cr metal, fayalite (Fe), and pyrite and barite (S). Peak count times of 20 s were used for Mg, Al, and Si, 30 s for Na, K, Ca, Ti, Cr, Mn, and Fe, and 90 s for S. A natural S-bearing basaltic glass (L17, Edinburgh ion probe facility) containing 48.5 wt% SiO 2 , 13.2 wt% FeO*, and 1320 ppm S was used as a secondary standard. The limit of detection for S was ∼65 ppm. The JFR-1.67 glass (Table 2) was used to center the S peak for reduced compositions while the DWF+1.60 glass employed for oxidized compositions.

XANES
Sulfur K -edge XANES spectra were collected on the I18 beamline at the Diamond Light Source synchrotron facility (UK). Spectra were obtained using the Si(111) monochromator, with the instrument in fluorescence mode. The take-off angle was 40 • . An energy step-size of 0.25 eV was used across the XANES region, which was broadened to 5 eV at the spectrum extremities to minimize acquisition time while collecting sufficient data for good spectrum normalization. Multiple spectra were collected for selected glasses to verify instrumental reproducibility.
To minimize potential modification of S 6+ /S 2− during XANES analysis as noted by Wilke et al. (2008) and Jugo et al. (2010), a defocused beam (50 × 50 μm square) was used with the lowest fluence available (∼10 12 photon/s). The sample, detector, and beam-source were enclosed by a He-filled bag to minimize X-ray absorption and maintain acceptable signal/noise ratios at these low fluences. This configuration was found to eliminate most modification of the sulfur redox state under exposure to the X-ray beam as can be seen by the two FeSO 4 spectra in Fig. 1. The upper spectrum, collected under low-fluence conditions, lacks the small peak at 2478 eV that is present in the high-fluence spectrum below. The latter is indicative of photo-reduction by the beam.

Interpretation of XANES spectra
Following the methodology of previous researchers (e.g. Jugo et al., 2010) we adopted an empirical approach to determining speciation by correlating spectral features with specific ionic species in the glasses. These associations are established using spectra of our standards as well as the findings of previous workers. Three standards (FeS, S, and FeSO 4 powders) were analyzed to define the edge positions of the different sulfur species, and to explore the potential for beam-induced damage. Fig. 1 presents the spectra of these standards, as well as samples JFR-1.67 and JFR+1.60.
The FeS spectrum exhibits a sharp peak at 2470.4 eV, and a much broader one at 2478 eV. The 2470.4 eV peak corresponds to 1s to 3p and 3d transitions  and its amplitude has been shown to depend on the cation that S 2− is bonded to; transition metal sulfides exhibit a large peak at the energy, and sulfides of Ca and Mg exhibit none at all (Fleet et al., 2005). The broader feature represents a combination of 1s and 3p transitions and multiple scattering resonances and is invariably associated with the sulfide ion . Sulfide-saturated basaltic glasses (both natural and synthetic) examined by Jugo et al. (2010) and Fleet et al. (2005) exhibit a similar broad feature at this energy, with subtle variations in edge shape that presumably depend on the local bonding environment. Each of the six glasses in this study display this feature when equilibrated under the most reducing conditions, consistent with the dominance of sulfide at low f O 2 .
The FeSO 4 standard exhibits a single sharp peak at 2482 eV, which is characteristic of excitations from the sulfur 1s to the sulfur 3p and oxygen 2p orbitals of the SO 2− 4 anion . XANES spectra for sulfate compounds analyzed by previous workers have consistently shown this feature (e.g. Jugo et al., 2010;Klimm et al., 2012a;Almkvist et al., 2010), and it dominates the spectra of all six melt compositions prepared at the highest f O 2 , indicating that S 6+ is the stable sulfur species under the most oxidizing conditions. A small peak at this energy is also evident in the spectrum for the FeS standard, suggesting that our FeS powder has undergone some minor oxidation.
Both the high-fluence FeSO 4 standard and each of the most oxidized silicate melts (e.g. JFR+1.60 shown in Fig. 1) exhibit a small peak at 2478 eV, characteristic of the sulfite (S 4+ ) ion (Métrich et al., 2002). The absence of this peak in the FeSO 4 spectrum collected at low-fluence indicates that it is a product of beam damage rather than a feature intrinsic to the standard as shown by Wilke et al. (2008) and Jugo et al. (2010).

Speciation trends in the experimental glasses
For each of the six melt compositions studied, the sequence of spectra representing equilibrium under progressively more oxidizing conditions display a diminution of the broad feature at 2476 eV, and its replacement by the sharper peak at 2482 eV. Each melt composition therefore undergoes the expected transition between sulfide and sulfate stability with increasing f O 2 . The sequences of spectra for all 6 melts are shown in Fig. 2. Note that the XANES spectra for JFR, PRI, EVO and DWF melts are particularly sensitive to presence of small amounts of sulfate at low f O 2 and that this makes the XANES method complementary to SIMS analysis. The latter is more accurate at high S 6+ /S 2− as discussed below. An increase in spectrum noise with increasing oxidation state is evident, consistent with an observed decrease in S concentration with increasing f O 2 (Table 2). From Fig. 2 we can also observe, at fixed f O 2 increasing S 2− /S 6+ with increasing FeO content of the silicate melt. This is consistent with the observed increase of sulfide capacity (C S 2− ) with increasing FeO content (O'Neill and Mavrogenes, 2002). One spectrum (PRI at FMQ+0.13, Fig. 2) was measured on an area of glass containing a Re-Fe sulfide inclusion.
Backgrounds for each spectrum were subtracted using a cubic spline function and spectra were normalized to a post edge intensity of 1. The fractions of S 2− and S 6+ in our glasses (Table 2) were then calculating from the area ratios of the S 2− and S 6+ peaks us- Fig. 2. The complete series of S K -edge XANES spectra for the synthetic glasses investigated in this study. Spectra positioned higher in each series represent experiments performed under more oxidizing conditions ( f O 2 conditions labeled relative to FMQ). The change in speciation between sulfide and sulfate is indicated by the progressive diminution of the peak at 2476 eV and the growth of the peak of 2482 eV. Signal/noise ratios generally decrease with increasing f O 2 due to decreasing S concentration. Horizontally adjacent spectra represent melts at identical f O 2 conditions, and comparisons between these -where permitted by an adequate signal/noise ratio -suggests that melts with higher FeO content stabilize sulfate at higher f O 2 . Note that primitive MORB at FMQ+0.13 contains Re-Fe sulfide inclusions.
ing the peak fitting software Fityk (Wojdyr, 2010). To correct for the greater X-ray absorbance of sulfate relative to sulfide (Jugo et al., 2010;Jalilehvand, 2006) we applied the "generic scaling factor" from Manceau and Nagy (2012) which gives an intensity ratio of 2.39 when S 6+ and S 2− are in exactly equal concentrations. The sulfide and sulfate peaks were each modeled using a single gaussian together with a sigmoid function to account for the edge step. Concentrations were then calculated from the area ratios of the gaussian peaks adjusted by the factor of 2.39 discussed above. Due to the presence of minor amounts of sulfite, a gaussian and sigmoid were also included for S 4+ and the corrected gaussian area was added to the S 6+ area. The energy positions and widths of each function were determined from the spectra for the most oxidized and reduced glasses (Fig. 2) which were then fixed for all of the spectral modeling. Uncertainties in S 6+ /Σ S were determined by propagating the standard errors associated with the gaussian peak heights and widths for the fit to each spectrum. A detailed description of the peak fitting method and the modeling results are provided in the Supplementary materials.
The calculated fractions of S 6+ for each melt at the different f O 2 conditions are shown in Table 2 and plotted against FMQ in Fig. 3. Also shown in Fig. 3 are the theoretical oxygen fugacity The smooth curves are best fits to the JFR (red, R 2 = 0.999), and AND (blue, R 2 = 0.958) assuming a sulfide-oxidation equilibrium of the form given in Equation (8) curves for addition of 2O 2 to S 2− (as in reaction 7) assuming that activity coefficients for S 2− and SO 2− 4 are constant and unaffected by f O 2 . The curves were fitted to the results for the JFR and AND compositions.
Based on the SIMS analyses discussed below we are confident that the conditions of crossover from S 2− to S 6+ are accurately represented by the XANES spectra for 5 of the 6 melts studied. The exception is the dacite melt which appears to contain significant sulfate even at the lowest f O 2 employed (Fig. 2). This result is inconsistent with SIMS results for the dacite (discussed below) which indicate that S 2− is dominant at all oxygen fugacities below FMQ+0.13 (Fig. 4). Although we do not have an unequivocal explanation for the aberrant result, we suspect that it arises from a combination of photo-oxidation of the glass during collection of the spectrum and the low concentrations of sulfur in these samples resulting in a low signal to noise ratio. Because of the inconsistency between XANES and SIMS results for dacite we have excluded the S 6+ /S 2− ratios measured by XANES for the DAC glass from data Tables and Fig. 3. The resulting difference in crossover position between melts containing ∼5 wt% FeO and those containing ∼20 wt% FeO is ∼0.5 log units.

Speciation calculated from sulfur concentration
Total sulfur concentrations measured by SIMS are presented in Table 2, and for the JFR and DAC melts are plotted on a log-log scale against f S 2 / f O 2 ratio in Fig. 4. The proportionality relation arising from the sulfide dissolution reaction (Equation (3)) should emerge as a straight line of gradient 1/2 in the data. Points lying above the line reflect increasing S 6+ in the melt. As observed in earlier studies at 1 atm (Fincham and Richardson, 1954;Katsura and Nagashima, 1974) the S concentration reaches a minimum on approaching the S 2− to S 6+ transition.
As can be seen from Fig. 4, both the DAC and JFR compositions fit the theoretical log [S] versus log ( f S 2 / f O 2 ) slope corresponding to dominance of S 2− at all f O 2 's below FMQ. The same applies for all six melt compositions studied including DAC despite the presence of S 6+ in the XANES spectrum of this sample, which we attribute to beam damage (Table 2). In order to calculate S 6+ /S 2− for compositions run on Pt loops, we needed to correct for Fe-loss which was significant in some cases (Table 2). To do this we calculated the average sulfide capacity C S 2− as defined in Equation (3) for the experiments performed below FMQ. We corrected these C S 2− values for observed Fe-loss using the Fe-dependence of sulfur solubility from Smythe et al. (2017) Table 3. We then calculated the expected amounts of S 2− at each of the higher f O 2 's based on the measured melt compositions at these f O 2 's. Additional measured S concentrations above these S 2− values were then assumed to be S 6+ (Table 2). Positive deviations from the predicted "sulfide slope" occur for every melt composition, confirming the presence of an oxidized sulfur species, which our spectroscopic measurements indicate to be S 6+ . The size of these deviations from the "sulfide slope" and the implied quantities of S 6+ , are indicated in Fig. 4 by the red arrows. The SIMS data show that the transition from S 6+ /Σ S of <0.05 to S 6+ /Σ S of >0.95 lies between FMQ+0.13 and FMQ+0.62 for all six melts, except for the andesite, which may undergo oxidation at conditions ∼0.3 log units more reduced in f O 2 . Note, however, that the method is insensitive to small amounts of S 6+ because of the requirement to fit the 1/2 slope through the data points under the most reducing conditions. Fig. 4. The logarithm of total sulfur concentration (determined by SIMS) plotted against the logarithm of the f S 2 / f O 2 ratio, for the JFR and terrestrial DAC compositions. The f O 2 conditions of each experiment are individually labeled in log units relative to the FMQ buffer. Experiments lying further towards the left represent more oxidizing conditions. The black lines are weighted linear best-fits to experiments equilibrated at FMQ+0.13 and below, with gradients fixed at 1/2, thereby representing the sulfidedissolution equilibrium (Equations (1)-(3)). Melts with constant sulfide capacity are expected to lie along this slope, and positive deviations are interpreted as indicative of sulfate. Values for log C S 2− correspond to the y-intercept (Equation (3)).

Fig. 5.
Fraction of S as S 6+ derived from SIMS analyses plotted against f O 2 . Sulfate mole fractions were determined by subtracting modeled sulfide concentrations from the SIMS analyses of total sulfur (i.e. from the deviations in log [S] from the "sulfide-slopes" in Fig. 4). S 6+ /Σ S of gray symbols were determined by XANES spectroscopy (shown in Fig. 3). The smooth curves are weighted best fits to the JFR (red, R 2 = 0.997), AND (blue, R 2 = 0.980), and DAC (orange, R 2 = 0.996) assuming a sulfide-oxidation equilibrium of the form given in Equation (8). Note that, based on the SIMS results of Fig. 4, the sulfide-sulfate transformation for the DAC composition occurs at similar f O 2 conditions to those of the other 5 melts.
This constraint makes the first ∼30% of S 6+ difficult to quantify.
The SIMS method is therefore most accurate under oxidizing conditions where the deviations from the 1/2 slope of Fig. 4 are large. This makes the SIMS method complementary to the XANES approach since the latter enables detection of small amounts of S 6+ but decreases in accuracy at high f O 2 because of the declining sulfur concentrations (Fig. 2). Fig. 5 shows measurements of sulfur speciation as a function of f O 2 as determined by the sulfur concentration of our samples. We excluded results where the propagated uncertainty exceeded 15% of the S 6+ /Σ S value. As can be seen in Figs. 3 and 5 there is very good agreement between the two methods and a continuous line of crossover from S 2− to S 6+ can readily be constructed. The spread as a function of melt composition is small and behavior of our dacite composition appears to be consistent with that of the other melts. Fig. 5 shows that S 6+ /Σ S measured in our experiments closely follows the relationship predicted from Equation (8). This is in contrast to measurements performed by electron microprobe (e.g. Carroll and Rutherford, 1988) which are likely affected by the beam-damage discussed earlier (Jugo et al., 2010). Besides sulfur, iron is the only redox-sensitive element present in appreciable concentrations in the glasses investigated. The chemical speciation of these two elements must, therefore, depending on their concentrations, be correlated with one another. The oxidation reactions for sulfur and iron can be combined to yield the following electron-exchange equilibrium:

Relationship between of iron and sulfur oxidation states
as discussed by Métrich et al. (2009) andJugo et al. (2010). This implies a linear relationship between the logarithms of the activities of S 6+ /S 2− and Fe 3+ /Fe 2+ with a gradient of 8, the number of Fe 3+ ions reduced in oxidizing one S 2− to one S 6+ . Note that Wallace and Carmichael (1992) estimated a much lower slope by Fig. 6. Variation of log S 6+ /S 2− with log Fe 3+/ Fe 2+ for our experimental products. Filled blue symbols represent instances for which S 6+ /S 2− was determined from SIMS data, and unfilled blue symbols represents those for which S 6+ /S 2− was derived from linear combination fitting of XANES spectra. The green and orange symbols represent experiments on basaltic and andesitic melts performed at 1050 • C by Jugo et al. (2010) and Botcharnikov et al. (2011) respectively. All Fe 3+ /Fe 2− ratios are calculated using the formulation of Kress and Carmichael (1991). The black line was fit by weighted linear regression assuming the theoretical electron-exchange relationship of Equation (9) (R 2 = 0.931). The gray line was calculated using Equation (11).
using the microprobe S-speciation data of Carroll and Rutherford (1988), but the latter are likely to have been affected by photooxidation (Jugo et al., 2010). Sulfur speciation data from both of the methods used in our study, expressed as the logarithm of the concentration ratio S 6+ /S 2− are plotted against calculated values of log (Fe 3+ /Fe 2+ ) in Fig. 6. The Fe 3+ /Fe 2+ ratio for each glass was calculated using the model of Kress and Carmichael (1991), which uses as its input the T , P , f O 2 and major-element composition of the melt.
The experimental results for S 6+ /S 2− shown in Fig. 6 define a line whose gradient approximates that expected from equilibrium (9). The solid line is a best fit with a gradient forced to the theoretical value of 8. The correlation between oxidation states of S and Fe is relatively insensitive to the choice of model for calculating the Fe 3+ /Fe 2+ ratio and S 2− concentration in each melt; models for Fe 3+ /Fe 2+ by Jayasuriya et al. (2004), Sack et al. (1980, and Kress and Carmichael (1991) yield the same trend with similar coefficients of determination, and the effects of using different published coefficients for calculating the compositional dependence of C S 2− are similarly minor.
Also shown in Fig. 6 are the data of Jugo et al. (2010) and Botcharnikov et al. (2011) from experiments performed on hydrous basalts and andesites, respectively. These represent equilibrium at a lower temperature (1050 • C) and higher pressure (200 MPa). The S 6+ /S 2− ratios reported by these authors were calculated from XANES spectra, based on a treatment similar to that employed in this study. We estimated Fe 3+ /Fe 2+ ratios at the known f O 2 's of the experiments by applying the model of Kress and Carmichael (1991), as was done with the glasses from our own experiments. The two studies clearly define linear trends parallel to our data but displaced to lower S 6+ /S 2− by ∼2 log units at a given Fe 3+ /Fe 2+ .
The differences shown in Fig. 6 between our data, at 1300 • C and 1 atm and those of Jugo et al. (2010) and Botcharnikov et al. (2011) at 1050 • C and 0.2 GPa plausibly arise predominantly from the temperature difference between the studies. This conclusion derives from observations that compositional effects on the S 6+ /S 2− -Fe 3+ /Fe 2+ relationship are minor (Fig. 6) and that between 1 bar and 200 MPa pressure effects on redox equilibria are small. The effect of 200 MPa pressure increase on f O 2 difference between the Ni-NiO (NNO) oxygen buffer and the FMQ buffer at 1300 • C is, for example, only 0.08 log units. In order to elucidate the temperature effect more precisely we formulated Equation (9) in terms of homogeneous equilibrium in the silicate melt using neutral components as follows: FeS + 8FeO 1.5 = 8FeO + FeSO 4 (10) We then modeled the thermodynamic properties of the melt components using the relevant solids (sulfide, sulfate and oxides) and took data from the JANAF tables (http://kinetics .nist .gov /janaf/) to calculate the temperature effect on reaction (10). We fixed the equilibrium constant at 1300 • C using our experimental data and the best-fit line shown in Fig. 6. The 1050 • C line of Fig. 6 was then calculated (not fitted) based on the displacement down temperature estimated from the thermodynamic data. As can be seen from Fig. 6, the thermodynamic data for the solids enable fair prediction of the temperature effect on equilibrium (10) and we are justified in our assertion that the temperature effect dominates the differences between our results and those of earlier studies. To test the effect of changing sulfide and sulfate components we replaced FeS and FeSO 4 in equilibrium (10) by CaS and CaSO 4 . The calculated temperature effect is in the same direction but slightly smaller, the shift between 1300 • C and 1050 • C being 1.3 instead of 1.8 log units. We get a smaller effect (1.1 log units) if we use FeS, CaO and FeO 1.5 to produce CaSO 4 and FeO. Every equilibrium we have considered gives a substantial temperature effect, however and equilibrium (10) appears to fit the observations well.
The final expression for the relationship between sulfur and iron redox equilibria is: Fig. 7 illustrates the sulfur-iron redox relationship at different temperatures calculated from Equation (11) and expressed as S 6+ /Σ S versus log f O 2 relative to the FMQ buffer. In order to construct Fig. 7 we assumed that Equation (11) is correct and converted Fe 3+ /Fe 2+ to f O 2 using the equation of Kress and Carmichael (1991). This approach produces, at any given temperature a range of S 2− − S 6+ transition curves because of the dependence of Fe 3+ /Fe 2+ on silicate composition. The effect can be seen clearly in Fig. 7a where the curve for andesite at 1050 • C is separated slightly from that for basalt under the same conditions. Our calculated curves are, nevertheless in remarkably good agreement with the experimental data at 1050 • C. They are also consistent with the results of Matjuschkin et al. (2016) (Fig. 7a) who showed that, in andesitic compositions at 950 • C all S is present as S 2− at 0.2-0.4 log units above FMQ and that CaSO 4 precipitates at f O 2 above FMQ+∼3.4 and +∼3.6 at 1.0 and 1.5 GPa, respectively. Using our model this pressure dependence in S 6+ /S 2− is corrected-for by the pressure-dependence of Fe 3+ /Fe 2+ given by Kress and Carmichael (1991) and shown as dotted (1.0 GPa) and solid (1.5 GPa) red curves in Fig. 7a. Fig. 7b illustrates the temperature-dependence of crossover behavior at fixed bulk composition and pressure by plotting curves for andesite at temperatures between 900 and 1400 • C. We also show a comparison with our data at 1300 • C.

The compositional dependence of sulfate capacity
Both the XANES and the SIMS data indicate that the experiments conducted under the most oxidizing conditions (FMQ+1.6) contain sulfur exclusively in the form of sulfate. In aggregate, these experiments therefore demonstrate the dependence of sulfate concentration on melt composition at constant f O 2 and f S 2 (the  (11)). The red curves are calculated from Equation (11) for the andesitic composition investigated by Matjuschkin et al. (2016) at 950 • C and 1.0 (dashed) and 1.5 GPa. The f O 2 conditions of all S as S 2− in the melt and of CaSO 4 saturation at 1.0 GPa and 1.5 GPa as determined by Matjuschkin et al. (2016) are shown. Panel (b) shows the expected temperature dependence of Equation (11) with a series of theoretical sulfide-sulfate transformation curves calculated at various temperatures (labeled). The andesite data from the panel above is superimposed, and the appropriate 1300 • C curve highlighted in blue.
'sulfate capacity' of Fincham and Richardson, 1954). A strong negative correlation (R 2 = 0.983) is observed between log [S 6+ ] and the mole fraction of SiO 2 + TiO 2 in the silicate melt calculated on a single cation basis (Fig. 8) at fixed f O 2 -f S 2 conditions. The implication is that there are major compositional controls over solubilities of sulfates, with solubility more than 10 times greater in primitive basalt than in evolved dacite. Hence tendency towards saturation in, for example, anhydrite and the degassing of SO 2 are enhanced by fractional crystallization as well as by increased f O 2 .

Oxygen fugacities recorded by quenched melts
The micro-XANES method has been used extensively in recent years to measure the oxidation state of Fe in silicate glasses Fig. 8. Covariation between log [S 6+ ] (ppm) and mole fraction of SiO 2 + TiO 2 (calculated on a single cation basis) for the six melts equilibrated under the most oxidizing conditions (for which the sulfate species occurs exclusively). As indicated by the black line, the two variables are very strongly correlated (R 2 = 0.983). Uncertainties in mole fraction of SiO 2 + TiO 2 are smaller than symbols. and to use these measured Fe 3+ /Fe 2+ ratios to estimate the f O 2 of the melt prior to eruption (Cottrell and Kelley, 2011;Kelley and Cottrell, 2009;Plank et al., 2010). We have shown here that there is the expected relationship between the oxidation states of sulfur and iron (Fig. 6) and that this relationship is temperature-dependent. The temperature-dependence translates to the possibility of electron exchange between sulfur and iron during slow cooling of melt. Although sulfur is present at relatively low concentrations (∼1500 ppm) in typical basalt, the fact that sulfur has 8 times the redox power of iron per mole (reaction (9)) means that the effects of electron transfer between the two elements can be significant.
For illustration of the effects of electron transfer, we consider glasses from Mauna Kea, Hawaii (Brounce et al., 2017). Brounce et al. (2017) measured the oxidation states of both S and Fe using micro-XANES spectroscopy and demonstrated a decrease in Fe 3+ /Σ Fe from 0.196 to 0.131 with decreasing S content from 1480 to 350 ppm. These changes correspond to decreases in S 6+ /Σ S from 0.08 to 0.00 and an f O 2 decrease from FMQ+1.0 to FMQ-0.45. The authors ascribed the changes in Fe and S oxidation states to reduction caused by degassing, at about 1200 • C, of a C-O-H-S volatile phase which resulted in loss of most of the initial sulfur content. The effects of temperature on the relationships between S 6+ /S 2− and Fe 3+ /Fe 2+ ratios which we observe indicate, however, that the effect of S degassing is less dramatic than was estimated by Brounce et al. (2017).
We took the measured S 6+ /S 2− and Fe 3+ /Fe 2+ ratios for Mauna Kea glasses from Brounce et al. (2017) and calculated the equilibrium temperature they record as given by Equation (11). For the 31 samples we obtain an average temperature of 993 • C with a standard deviation of 30 • C. Note that if we were to adopt the new Mössbauer calibration of Berry et al. (2018) for Fe 3+ and Fe 2+ in basaltic glasses, and re-fit equation (11) using their Fe 3+ /Σ Fe values the apparent equilibrium temperature of the Mauna Kea glasses would increase slightly to 1004 • C. In either case the result indicates that there has been electron exchange between Fe 2+ and S 6+ during quenching such that the measured Fe 3+ /Σ Fe and hence estimated f O 2 are now higher than they were at the liquidus temperature. Reconstructing the liquidus Fe 3+ /Σ Fe by assuming, following Brounce et al. (2017), equilibrium between S and Fe at 1200 • C leads to a reduction in Fe 3+ /Σ Fe of the most oxidized S-rich samples by ∼0.05, a change much greater than the measurement uncertainty. This shift indicates that the actual f O 2 of the melt was about 0.8 log units lower than implied by the current (quenched) Fe 3+ /Σ Fe values. It implies that the oxi-dation states of S-rich glasses must be interpreted with care and that S-contents must be measured in tandem with micro-XANES measurements of Fe 3+ /Σ Fe.

Conclusions
We developed sulfur analysis by SIMS as a method to measure the S 2− contents of silicate melts at known f S 2 / f O 2 . We used this method, together with XANES spectroscopy to determine the effects of f O 2 on the S 6+ /S 2− ratios of six silicate melts, ranging from Fe-rich basalt to dacite in composition at 1300 • C and 1 atm pressure. The two techniques are complementary, in that XANES provides good constraints on S 6+ contents at low S 6+ /S 2− while the SIMS method provides better results at high S 6+ /S 2− ratio.
We find that the S 6+ /S 2− ratio in silicate melts is, at fixed f O 2 , almost independent of melt composition. Despite the wellestablished correlation between S-solubility and FeO concentration (O'Neill and Mavrogenes, 2002) we have found that in basaltic melts containing up to 20 wt% FeO, the transition from S 2− to S 6+ takes place at an f O 2 only ∼0.5 log units higher than in dacitic melts containing 5 wt% FeO. Thus, the stabilizing effect of FeO on S 2− in silicate melt is not reflected in S 6+ /S 2− at given f O 2 . The principal reason likely derives from our observation that SO 2− 4 concentration is, at fixed, f O 2 , f S 2 conditions negatively correlated with tetrahedral (SiO 2 + TiO 2 ) concentration (Fig. 8).
Thus, S 2− stabilization in natural FeO-rich melts is counterbalanced by stabilization of SO 2− 4 in these correspondingly low-SiO 2 melts. Conversely, destabilization of S 2− in FeO-poor dacitic melts is counterbalanced by destabilization of SO 2− 4 in these high SiO 2 liquids.
Although melt composition has little effect on the f O 2 at which S 2− is oxidized to SO 2− 4 , the effect of temperature is dramatic. Thus, a decrease in temperature from 1300 to 1100 • C displaces the S 2− to S 6+ transition upwards by about 1 log unit in f O 2 relative to the FMQ buffer. S 6+/ S 2− ratios for the quenched melts also exhibit a linear relationship with Fe 3+/ Fe 2+ , indicating that the redox couples for iron and sulfur can be directly related to one another.
The interdependence of the oxidation states of S and Fe means that the application of measurements of Fe 3+ /Fe 2+ in quenched glasses to estimate the f O 2 of natural melts may lead to significant errors. Based on XANES measurements of Fe 3+ /Fe 2+ and S 6+ /S 2− in glasses from Mauna Kea, Hawaii we find that there was significant exchange of electrons between S and Fe during quenching. The effect is sufficient to cause significant overestimation of equilibrium Fe 3+ /Σ Fe in the glasses and corresponding overestimate of f O 2 by ∼0.8 log units.