Magma Redox Geochemistry. Группа авторов

      which results from acid–base exchanges of the type:

      (1.31)

      (1.32)

      coupled to half‐reaction 1.6.

Both Reactions 1.29 and 1.30 yield the E‐pO^2– relationship:

      (1.33)

      The lower stability limit of the solvent can be given by either the reduction of alkaline cation in the corresponding metal:

(1.34)

      whose potential is independent of pO^2–, or the reduction of CO₃^2– and SO₄^2– anions given by:

      (1.35)

Figure 1.4 Log fO₂ ‐ Ph diagrams for 290°C (left panel) and 145°C (right panel) at saturated vapor pressure, showing predominance fields for aqueous sulfur species (dashed lines), stability fields for Fe–O–S minerals and bornite–chalcopyrite (solid grey lines). The solubility contours (left panel: 1, 10, 100 ppm; right panel: 0.1, 1 ppm) are for gold in the form Au(HS)₂^–.

      Modified from Raymond et al. (2005).

      (1.36)

      and to which the following E‐pO^2– relationships correspond (CO₃^2– and SO₄^2– anions having unitary activity):

      (1.37)

      (1.38)

      Figure 1.3 shows the results on carbonate and sulfate melts (modified from Trémillon, 1974, and references therein). The utilizable regions appear as quadrilaterals on the E‐pO² graph. If in sulfates, the region is a parallelogram similar to the E‐pH region in aqueous solution, the theoretical range of potential in molten carbonates appears more restricted in an oxoacidic medium than in an oxobasic medium, because the lower limit varies versus pO^2‐ with a slope greater than that of the upper limit (Trémillon, 1974).

      Silicate melts have been so far an underestimated electrolytic medium acting as a solvent for oxides. This is mainly because E‐pO^2– diagrams cannot be based on predictive thermodynamics and physical chemistry assessments such as the dilute electrolyte concept and its developments in the case of previous solvents, aqueous solutions particularly (Allanore, 2015). In silicate melts, and more generally molten oxides, oxygen tout‐court cannot be identified as the solvent, despite its abundance. Silicate melts are in fact a high‐temperature highly interconnected (polymerized) matrix in which solvation units cannot be easily defined and both ionic and covalent bonds rule the reactive entities that make up the melt network. Because of this, some approaches have been formalized in terms of the Lewis acid–base definition (network formers and their oxides, such as SiO₂ and Al₂O₃ are acids; network modifiers and their oxides such as MgO, CaO, Na₂O are bases) by using electronegativity and optical basicity that allow distinguishing and calculating three types of oxygen (bridging, non‐bridging, and so‐called free oxygen) whose mixing determines the polymerization and the thermodynamic properties of the melt mixture as a function of composition (Toop and Samis, 1962a,b; Allanore, 2013, 2015 and references therein; Moretti, 2020 and references therein). Nevertheless, silicate melts still lack a fully developed acid–base framework formalizing the thermodynamic properties of reactive species formed during the solvolysis, as the solvent itself changes its polymerization properties upon introduction of other oxide components, which are highly soluble contrary to what observed for salts in aqueous solutions. The most general thermodynamic approaches postulate mineral‐like molecular structures to interpolate existing data.

In molten silicates the electric charge is primarily transported by cations, whose contribution increases with concentration of network modifiers, hence basicity. The major element, oxygen in its three forms and particularly O^2– and O‐based anionic complexes do not contribute substantially to the charge transport (Dickson and Dismukes, 1962; Dancy and Derge, 1966; Cook and Cooper, 1990, 2000; Cooper et al., 1996a,b; Magnien et al., 2006, 2008; Cochain et al., 2012, 2013; Le Losq et al. 2020). This is a striking difference when comparing silicate melts to previously described electrolytes, particularly with the aqueous electrolytes, in which the concentration of hydroxide ions or water is always large enough to sustain high current densities (Allanore, 2013). From a practical standpoint the anode reaction producing oxygen (the inverse of Reaction 1.6) is strongly impacted by the low transport of free oxide ions, that is free oxygen, which is at very low concentration. Besides, the anode design and technical performance would greatly benefit of the precise knowledge of oxygen physical chemistry in silicate melts, which for the moment is still too limited to narrow compositional ranges that have been investigated spectroscopically (Allanore, 2015).

      Nevertheless, because of their nature, silicate melts can dissolve important amounts of metals. Besides, they exhibit a large range of thermal stability, with high temperature conditions that favor fast kinetics of redox exchanges. Upper temperature limits for electrochemical applications are given by the formation of gaseous silicon monoxide or by alkali oxide thermal decomposition in alkaline systems or by high vapor pressure for Mn‐bearing systems (Allanore, 2015). In terms of transport properties, silicate melts are a solvent with high viscosity, a fact that is however compensated by the high diffusivity of the metal cation (Allanore, 2013), i.e., the cathode reactant.

      Many measurements have however been carried out on melts of geological interest, also fostered by the interest in silicate electrolysis to produce on site metals and particularly molecular oxygen for terraformation of extraterrestrial planets (e.g., Haskin et al., 1992). Electrochemical series were then established in binary SiO₂‐MO systems (e.g., Schreiber, 1987) but also in ternary joins such as the diopside one (Semkow and Haskin 1985; Colson et al., 1990) for redox exchanges of the type:

      (1.39)

      in which half‐reactions of the type

      (1.40)

      combine with Half‐reaction 1.7. Nevertheless, such series do