Introduction

One of the most important intensive variables that petrologists, geochemists, and geophysicists are interested in quantifying is the oxygen fugacity (ƒO2) in different environments and how it has changed over time. This topic has generated tremendous interest due to the role that ƒO2 and redox chemistry play in the chemical evolution of planetary bodies and atmospheres, which has implications for determining the conditions required for life to thrive at (or near) the planetary surface. A widely used indicator of ƒO2

in magmas is based on the Fe³⁺/Fe²⁺ ratio of quenched glasses; the Fe oxybarometer. This approach is calibrated using experiments where beads of silicate melts of various compositions are exposed to mixed-gas atmospheres at 1 atm in a tube furnace, allowing the ƒO2 to be precisely controlled and varied, and then measuring the resulting Fe³⁺/Fe²⁺

of the recovered experimental glasses. Such experiments provide a calibration whereby one can parameterize the dependence of Fe³⁺/Fe²⁺ on ƒO2, which can then be used to determine the ƒO2 experienced by natural glasses (quenched silicate melts) based on measurements

of their major and minor element compositions and Fe³⁺/Fe²⁺ ratios. Most natural glasses contain sulfur, which is multivalent (-2 to +6 oxidation state) and is an important participant in redox chemistry, and can therefore influence the Fe³⁺/Fe²⁺ as well as its dependence on T and ƒO2. However, all of existing models that relate the Fe³⁺/Fe2+ and composition of melts to T and ƒO2 were calibrated on sulfur-free liquid (e.g., Sack et al. 1980; Kilinc et al.

1983; Borisov & Shapkin 1990; Kress & Carmichael 1991; Jayasuriya et al. 2004;

Nikolaev et al. 1996; Borisov et al. 2018, O’Neill et al. 2018).

Although 1 atm gas-mixing experiments using S-bearing gases can be done, they typically only access a narrow range of sulfur fugacity (ƒS2) such that the S contents of the coexisting silicate melts are lower than those observed in many natural samples at comparable ƒO2 (e.g., Nash et al. 2019). Traditional high-pressure experiments result in higher solubilites of sulfur in silicate melt, but are limited by relatively coarse controls of ƒO2 and ƒS2. The failure to utilize experiments on melts with S contents comparable to those of undegassed silicate melts results in two major flaws in efforts to relate measured Fe³⁺/Fe²⁺ ratios in natural glasses to ƒO2: (1) the presence of S itself may have effects on ƒO2 that have yet to be characterized; and (2) therefore, while measurements of Fe³⁺/Fe²⁺

may be accurate, the conversion to ƒO2 may be inaccurate for natural S-bearing melts because the calibrations are based on sulfur-free experiments.

Experimental studies on olivine-hosted melt inclusions have demonstrated that olivine acts a semi-permeable membrane with respect to volatile elements (e.g., Roedder 1979; Sobolev and Danyushevsky 1994; Hauri 2002; Gaetani et al. 2012; Bucholz et al.

2013; Mironov et al. 2015; Portnyagin et al. 2019; Saper & Stolper 2020), which means that during experimental treatment melt inclusions are closed to sulfur escape but are

capable of equilibrating with the external ƒO2 imposed by the furnace atmosphere. Because gas-mixing furnaces have exquisite ƒO2 control, this offers a highly promising technique to explore the properties of the S-bearing melts inside melt inclusions at variable ƒO2. Data from an initial set of experiments (Saper & Stolper 2020) show that the Fe³⁺/Fe²⁺ ratios measured by XANES in experimentally equilibrated olivine-hosted inclusion glasses equilibrated at FMQ-1 are systematically lower than the those predicted by the S-free models that relate ƒO2 to the Fe³⁺/Fe²⁺ of basaltic liquids. A similar magnitude and direction of the effect of S on Fe³⁺/Fe²⁺ was also documented in high-pressure experiments described in an AGU abstract (Graz et al. 2006), which were never published. These preliminary data raise the very real possibility that previous calculations of the ƒO2 of natural sulfur-bearing melts may need to be reevaluated and recalculated by taking into account the effect of sulfur.

The same experimental approach can be used to explore the possibility that Fe³⁺/Fe²⁺ ratios in natural glasses may change during cooling, and are only “frozen in” at the glass transition temperature. If this is the case, it greatly complicates the use of room T measurements of the Fe³⁺/Fe²⁺ ratios in glasses to extract information, such as ƒO2, about high-T magmatic liquids. The same uncertainty arises for the ratios of redox species of other multivalent elements in silicate melts, including Cr³⁺/Cr²⁺ (Berry et al. 2003), S⁶⁺/S^2- (e.g., Metrich et al. 2009), and V⁵⁺/V⁴⁺/V³⁺/V²⁺ (e.g., Mallman & O’Neill 2009). In its simplest form the relationship between the oxidation states of iron and sulfur in silicate melts can be modeled by the redox reaction:

S^2- + 8Fe³⁺ ⇌ 8Fe²⁺ + S⁶⁺ (1)

A consequence of the eight electrons exchanged in this reaction is that, although sulfur concentrations are generally much lower than iron in natural melts, sulfur can play a disproportionately important role in redox chemistry. The sulfur-iron electron exchange reaction has been suggested to be strongly temperature-dependent (e.g., Metrich et al.

2009; Nash et al. 2019), which would mean that both the Fe³⁺/Fe²⁺ and S⁶⁺/S^2- measured at room temperature in S-bearing glasses are dependent on cooling rate and so may differ from theratios present in the melt at high temperature. Curiously, although both Metrich et al. 2009 and Nash et al. 2019 agree that the effect of temperature on equation (1) is strong, they disagree on which direction the reaction will proceed with decreasing T. Very little is known about the kinetics of reaction (1), in part due to the experimental challenges described above. If reaction (1) proceeds sufficiently rapidly, which is expected at least at T above the solidus based on in-situ measurements of Fe-Cr electron exchange in melts (Berry et al. 2003), then the additional constraint of cooling rate is required in order to evaluate the fidelity of room T measurements of Fe³⁺/Fe²⁺ and S⁶⁺/S^2- as proxies for the same ratios at high T in both experimental and natural melts.

This chapter describes preliminary experiments using olivine-hosted melt inclusions as S-bearing experimental vessels where ƒO2 is precisely controlled by H2-CO2

gases in a 1 atm tube furnace atmosphere. In addition to isothermal experiments that are quenched directly from the hotspot, which achieves the highest cooling rates permissible for the experimental setup (Xu & Zhang 2002), a protocol is described for running a series of cooling experiments which can be used to evaluate the cooling rate at which the high- temperature Fe³⁺/Fe²⁺ and S⁶⁺/S^2- ratios begin to be modified by electron exchange with sulfur (or whether the high T ratio can be quenched at all), while keeping melt composition

roughly constant. This information can be used to provide guidance on which natural glasses may have had their Fe³⁺/Fe²⁺ and S⁶⁺/S^2- modified during cooling, and to assess the magnitude and direction of this effect.

The results reported in this chapter represent only the second set of experimentally treated basaltic glasses to have had both Fe³⁺/Fe²⁺ and S⁶⁺/S^2- measured by synchrotron micro X-ray absorption near edge spectroscopy (XANES). Head et al. (2018) rehomogenized basanitic olivine-hosted melt inclusions from Nyamuragira, East African Rift for 10 minutes in a 1 atm furnace at 1130-1140°C and an ƒO2 on the fayalite-quartz- magnetite buffer (FMQ buffer), and then used XANES to measure the valences of sulfur and iron (and vanadium) in the quenched inclusion glasses (n=5). The Head et al. (2018) experiments were designed to be short duration specifically to mitigate exchange with the furnace atmosphere. Therefore, the melt inclusion experiments described hereafter represent the first co-determined measurements of S and Fe valences in experimental basaltic glasses that were left to equilibrate at high-T for >10 minutes in a 1 atm furnace with precisely known ƒO2 and thus to have constraints on nearly all of the relevant variables: ƒO2, T, cooling rate, melt composition, Fe³⁺/Fe²⁺, and S⁶⁺/S^2-. Note that Beerman et al. (2011) is the only other experimental study (IHPV) with co-determined Fe and S valences in quenched glasses, Fe³⁺/Fe²⁺ was determined by Mössbauer spectroscopy and S by electron microprobe Kα shifts (Wallace & Carmichael 1994; Carroll & Rutherford 1998). The accuracy of the latter technique has been questioned (Jugo et al. 2010). In addition to these experiments, Fe and S XANES results from two natural melt inclusions from Papakōlea, Mauna Loa, Hawai‘i with drastically different cooling rates provide a case study to explore the cooling-rate and temperature dependences of equation (1).

Because most natural igneous melts contain some sulfur, the results of this project can inform more accurate interpretations of the redox and thermal histories of volcanic, plutonic, and mantle rocks on the Earth and other terrestrial planets. For example, constraints on the temperature-dependence of equation (1) and accurate placement of the transitions of S^2- to S⁶⁺ and Fe²⁺ to Fe³⁺ as a function of ƒO2 are critical for evaluating the role of S in modulating the ƒO2 in the mantle wedge proximal to subducting and devolatilizing slabs of oceanic crust (e.g., Klimm et al. 2012), the effect of S degassing on the ƒO2 of magmas (e.g., Gaillard and Scaillet 2009, Gaillard et el. 2011, Moussallam et al. 2016, Edmonds & Woods 2018), and the genesis of porphyry ore deposits (e.g., Tang et al. 2020).