may have different proportions of fayalite ad magnetite because of the crystallization style but different FeII/FeIII bulk ratios (Frost, 1991). However, in some systems, it is possible that the melt fixed the redox potential of the system via iron oxidation state, with the FeII/FeIII ratio approaching unity (e.g. Moretti et al., 2013).
It is also important to recall that fO2 is just a thermodynamic parameter used to conveniently report the oxidation state of a system, particularly when O2 is not an existing gaseous species that could be detected if the system were accessible to measurements. This is clearly proved by the very low values reported in ordinates in Figure 1.6. Therefore, fO2 turns out to be by‐product of thermodynamic calculations applied to the analyses from natural samples, in which the true redox observables are the oxidation states of iron and other elements in minerals and liquids. The common practice is then to measure the concentration ratio of redox couples of multiple valence elements in melts (FeII/FeIII, but also S‐II/SVI, VIII/VV, etc.) or in gases (e.g., H2/H2O, CO/CO2, H2S/SO2) and relate them to fO2 via thermodynamic calculations using appropriate standard state thermochemical data. As fO2 is provided, its value is then anchored via Equation 1.54 to a given gas‐solid buffer of the Reaction type 1.1 or 1.48 to 1.51. This is quite easy for gases, in which governing equilibria are directly solved if the gas analysis is provided (e.g., Giggenbach, 1980, 1987; Aiuppa et al., 2011 and references therein) and also for solid–solid equilibria, such as in case of coexisting iron–titanium oxide solid solutions titanomagnetite (Fe3O4‐Fe2TiO4) and hemo‐ilmenite (Fe2O3–FeTiO3) (Buddington and Lindsley, 1964) or for peridotite assemblages in the mantle (e.g., Mattioli and Wood, 1988; Gudmundsson and Wood, 1995), in which the good thermodynamic characterization of solid solutions allows quite accurately treating component activities, based on mineral analyses.
On the contrary, it is much less straightforward for fO2 estimates by oxidation states of Fe and/or S measured in glasses, as the oxybarometers derived by the study of synthetic quenched melts still suffer from too many empiric approaches. Because of their polymerized nature, silicate melts do not allow a precise distinction between solute and solvent like in aqueous solutions, where complexes and solvation shells can be easily defined in which covalence forces exhaust (see also Moretti et al., 2014). In fact, melt composition largely affects the ligand constitution and then the speciation state of redox‐sensitive elements. In the case of the FeII/FeIII ratio, the most common redox indicator for melts/glasses, the choice of components in reaction:
over a large compositional range (e.g., from mafic to silicic) does not offer the possibility to find accurate and internally consistent expressions for the activity coefficients of oxide components γFeO and γFeO1.5 (with FeO1.5 conveniently replacing Fe2O3) that solve the reaction equilibrium constant:
in which the term within integral is the difference of partial molar volumes of iron components. Expansion of excess contribution to its Gibbs free energy of mixing is used to define γFeO and γFeO1.5 in melt mixtures. However, when these are adopted to solve Equation 1.56 for measured FeII/FeIII values, they show success only over limited compositional datasets (Moretti, 2020 and references therein). Armstrong et al. (2019) calibrated volumes and interaction parameters of activity coefficients entering equation (1.56) for an andesitic melt (easily quenchable as a glass) with fO2 buffered by the Ru‐Ru2O assemblage in the T‐range 1673K to 2473K and for pressures up 23 GPa. Data fitting showed that volume term in Equation 1.56 turns from negative to positive for P > 10 GPa, which yielding iron oxidation with increasing pressure. The calibrated Equation 1.56 was then used by the authors to demonstrate how the mantle oxidized after the Earth’s core started to form by a deep magma ocean with initial FeIII/Fetot = 0.04 from which FeO disproportionated to Fe2O3 plus metallic iron at high temperature. The separation of Fe0 to the core raised the oxidation state of the upper mantle and of exsolved gases that were forming the atmosphere (Armstrong et al., 2019).
The search for one general formulation for all melt compositions of interest in petrology and geochemistry led to empirical expressions, in which adjustable parameters are introduced without the formal rigor requested by Equation 1.56 (e.g. Kress and Carmichael, 1991). These formulations furnish quite accurate fO2 values from measured FeII/FeIII ratios within the compositional domain in which they have been calibrated. Besides, they often violate reaction stoichiometry and do not ensure internal consistency: if used to calculate activities they fail the application of the Gibbs‐Duhem principle relating all component activities within the same phase (e.g., Lewis and Randall, 1961). Such expressions then treat fO2 as a Maxwell’s demon, doing what we need it to do to fit the calibration data and with the consequence that outside the calibration domain, all the unpredictable non‐idealities are discharged on the fO2 terms, resulting in biased calculations of fluid speciation, or other phase equilibria constraints.
As extensively treated in Moretti (2020), unpredictable non‐idealities reflect counterintuitive behaviors that cannot be accounted for by activity coefficients used in the equilibrium constant of Reaction 1.55. It is well known that depending on melt composition alkali addition (i.e. decreasing pO2–) can either oxidize or reduce iron in the melt. This occurs because of the change of speciation due to the amphoteric behavior of FeIII, which depending on composition and then pO2– can behave as either network former or modifier (see the conceptualization provided by Ottonello et al., 2001; Moretti, 2005, 2020; Le Losq et al., 2020; see also Reaction 1.41). Models that define the melt (oxo)acidity (Reaction 1.27) hence pO2– (e.g; polymeric models based on the Toop and Samis mixing of bridging, non‐bridging and free oxygens; see Moretti, 2020, and references therein) allows solving speciation and set activity‐composition relations of ionic and molecular species, just as for aqueous solutions and molten salts.
The problem of unsolved compositional behaviors due to speciation, that are not accounted for by typical oxide‐based approaches to mixtures, is exacerbated when dealing with the mutual exchanges involving iron and another redox‐sensitive elements, such as sulfur. Sulfur‐bearing melt species play a special role since the oxidation of sulfide to sulfate involves eight electrons: for any increment of the FeIII/FeII redox ratio, there is an eight‐fold increment for sulfur species (S–II/SVI; e.g., Moretti and Ottonello, 2003; Nash et al., 2019; Cicconi et al., 2020b; Moretti and Stefansson, 2020). Sulfur in magmas partitions between different phases (gas, solids such as pyrrhotite and anhydrite, and liquid as well, such as immiscible Fe–O–S liquids; Baker and Moretti, 2011 and references therein). The large electron transfer makes S–II/SVI a highly sensitive
