in magmatic melts; Moretti, 2020 and references therein), whereas its effectiveness as a buffer of the redox potential is limited by the abundance of sulfur in magma, significantly lower than iron.
The modelling of joint Fe and S redox exchanges is still a major challenge which sees contrasting approaches (see Moretti, 2020). Formulations exist with various degrees of empiricism, but even those displaying better performances in exploring the fO2 – fS2 space of natural silicate melts (Moretti and Baker, 2008) should be carefully tested in reproducing phase diagrams involving multiple phases, including coexisting Fe–O–S melt, FeS(s), and Fe3O4(s). Introduction of sulfur equilibria in petrogenetic grids would be a major step forward for modelling in igneous petrology. Besides, it would provide the liaison with processes occurring in late‐ to post‐magmatic stages, prior to further cooling down to real hydrothermal conditions dominated by condensed water (see Figure 1.4). For late‐ to post‐magmatic stages, such as in the case of porphyry‐copper ore formation, logfO2‐logfS2 diagrams. Figure 7 reliably summarizes phase relations in the Fe–S–O system, in a way similar to Figure 1.2 and 1.4. It is worth noting that the diagram in Figure 1.7 can also be seen as resulting from reactivity of a sub‐solidus mixed iron molten oxide–sulfide, in which the two main ligands are O2– and S2– (half‐reactions 1.6, 1.11, and 1.12).
Figure 1.7 Two‐redox potential fO2‐fS2 diagram. The conformation of stability fields in the Fe–O–S space is essentially the same also for large fO2 and fS2 variations with temperature
(redrawn from Nadoll et al., 2011).
A natural assemblage of pyrite + magnetite + pyrrhotite corresponds then to the triple point marked by a star in Figure 1.7, which at a given T is invariant for fO2 and fS2 values given by the simultaneous occurrence of Reaction 1.10 and:
(1.57)
that allow identifying the stable phase as a function of temperature and fugacities (or activities) of reference gas species. It is worth noting that in absence of water (no H in the system represented in Figure 1.7) the boundary between FeS2 and FeS is a function of fS2 only (see Reaction 1.10) but not of fO2, as instead reported in Figure 1.4.
1.3. CONCLUDING REMARKS AND PERSPECTIVES
In this short compendium we show the redox features in aqueous‐hydrothermal and igneous Earth. This allows the summarizing of the main redox features of a system, to show what we know of its equilibrium properties, but also what we do not know, especially for melts and magmas. We make a parallel between redox in magmas and redox in aqueous‐hydrothermal solutions and show that what really changes is the way redox variables are reported. It is better described in aqueous solutions, via E‐pH relations, because of the sound knowledge of acid–base properties, which allows good prediction of system reactivity with compositional changes and fosters applications in water‐based geochemistry and industrial practice (e.g. corrosion and hydrometallurgy).
Just as the measurement of pH is the key to studies of acid–base reactions, those of reactions involving the O2– ion in silicate melts naturally go through the measurement of pO2–, a magnitude similar to pH and playing an identical role. Same as a pH indicator electrode, a pO2– indicator electrode is the essential instrument to study acid–base properties of silicate melts. Technical challenges exist about this electrode as an instrument of analytical control operating directly in melts at high temperature and also as working assembly for anode reaction (inverse of Reaction 1.6). Besides, the low flux of oxide ion compared to cations is limited in melts and the lack of physical and chemical information about the molecular entities involved in the transport processes at each electrode and in the bulk of the electrolyte presents a conceptual difficulty for engineering the electrodes (Allanore et al., 2015).
Contrary to waters, in which E‐pH pairs can be measured in the field by probe electrodes and then directly compared to theoretical assessments, magma‐related samples do not offer the possibility to probe the conditions (temperature, pressure, gas composition, and also phase proportion) under which they equilibrated before becoming accessible to our observations. These conditions cannot be restored and must be calculated under strong assumptions, for example that glasses have preserved the same oxidation state of the melt from which they quenched. The impossibility to restore and measure the original system has surely contributed to overlooking the role played by acid–base properties and resulted in oxide‐based redox descriptions of melts and magmas centred around the thermodynamic concept of fO2, whose sole adoption was boosted by experimental petrology and the thermodynamic approach based on Ellingham’s diagrams in extractive metallurgy. The acid–base concept was progressively relegated to qualitative assessments (e.g., silicic for acidic and mafic for basic).
With the exception of volcanic gases, where fO2 (or related quantities such as fH2) can be directly measured with solid‐state O2 electrodes (Aiuppa et al., 2011 and references therein), the common practice, recently boosted by advancements in microbeam spectroscopic techniques (e.g., XANES) is to measure masses of elements in their different oxidation state and then relate such ratios to fO2 via approaches either based on thermodynamics or having a thermodynamic flavour to solve for the role of composition. Nevertheless, such approaches are valid only in limited compositional ranges and discharges on calculated fO2 the non‐ideal behaviours that are determined by speciation, hence by pO2–, and which cannot be reproduced by interaction parameters of oxide components (see Moretti, 2020).
These unpredictable non‐ideal behaviours are reflected by the shape of the excess Gibbs free energy of mixing, which is correctly reproduced only by ionic‐polymeric approaches to silicate melts mixing properties (e.g., Mao et al., 2006; Hillert et al., 1985; Ottonello and Moretti, 2004), which formalize the role of composition in establishing the relationships between polymerization and redox state in the melt. These approaches could be in perspective used to generate pO2– based phase diagrams, particularly logfO2‐pO2– diagrams analogous to logfO2‐pH ones reported in Figure 1.4 for aqueous‐hydrothermal solutions.
The joint description of acid–base properties and redox exchanges via predominance and stability diagrams
