LITMIR.BIZ

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in determining the speciation state (e.g., anionic or cationic) following the definition at Reaction 1.27. The effect of the solvent also includes the amphoteric behaviour of some dissolved oxides such as Fe₂O₃ or Eu₂O₃, which can behave either as acids, yielding FeO₂^– (i.e., FeO₄^5– tetrahedral units) and EuO₂^– (i.e., EuO₄^5–) or bases, yielding Fe³⁺ and Eu³⁺ cations (Fraser, 1975; Ottonello et al., 2001; Moretti, 2005; Le Losq et al., 2020). The multiple speciation behaviours determined by pO^2– can be summarized by the following reaction mechanism (e.g., Moretti, 2005; Pinet et al., 2006):

(1.41)

      Predominance and stability diagrams (e.g., E‐pH, E‐pO^2–, E‐logfO₂, or logfO₂ vs. the log‐fugacity of pH or other gaseous species in the system such as SO₂, CO₂) depend on the availability of good thermodynamic data and especially a well‐established testament of acid‐base properties of the investigated system and its solvent(s). For silicate melts and glasses, such a testament is represented by the oxobasicity scale from the Lux definition (Reaction 1.27). Electrochemical experiments should then be envisioned to complete and validate the database in order to ensure predictions about forming species and measure their activities.

1.2. OXYGEN FUGACITY: THE CENTRALITY OF AN ELUSIVE PARAMETER

      Voltage E and oxygen fugacity (fO₂) are both measures of oxidation state. The relation between fO₂ and E for a given electrolytic medium can be established by the anode reaction where oxygen is produced. In the case of aqueous solutions, conversion is provided by half‐reaction 1.15 and Equation 1.18. We can then replace E‐pH diagrams with analogous logfO₂‐pH diagrams. In this treatment, the actual speciation state of solutions is still the key to investigate the system, but half‐reactions are not considered, and the equilibrium values of overall reactions are used, same as for activity plots. As for E‐pH plots, boundaries will shift by varying the total amount of soluble elements in the electrolytic solution, hence the activity of dissolved ionic species or the corresponding gas fugacity (e.g. when carbonates or sulfides and sulfates are present).

Figure 1.4 shows that in logfO₂‐pH diagrams phase, boundaries that in E‐pH diagrams were dependent on pH only (and not on the concentration of dissolved ions) are horizontal. Moreover, a quick comparison between figures 2 (Eh‐pH diagram) and 4 (logfO₂‐pH diagram) also shows that on the logfO₂ vs. pH representation the pyrite–magnetite boundary, which appears only for pH > 7, maintains the positive slope. At the T conditions of Figure 1.4 this boundary is represented by the overall reaction:

      (1.42)

      Besides, at 145°C (water saturated conditions) the pyrite–pyrrhotine boundary is defined at pH > 7 and is positive because:

      (1.43)

whereas for pH < 7 the boundary is horizontal, given by the proton‐free reaction:

(1.44)

      As we have already seen, when considering high‐temperature non‐aqueous (oxide) systems in the inner Earth geospheres, there is no acid–base framework and anchoring fO₂ or E to pH makes no sense in absence of the solvent liquid water.

      To measure the chemical potential of redox exchanges in higher temperature geological systems, geoscientists turned their attention to molecular oxygen transfer among molecular components such as oxides or mineral‐like macromolecular entities.

      The practice between geoscientists becomes to assess criteria for fO₂ (or aO₂) estimations disconnected from the formal description of the acid–base character of magmas. In particular, techniques were established involving mineral phases coexisting in igneous rock to establish thermodynamic or empiric laws and trends from quenched glasses via indirect measurements, most often of spectroscopic nature (e.g., Neuville et al., 2020). This change of perspective reflects the obvious consideration that geoscientists deal with samples (solidified rocks) made accessible at Earth’s surface and which represent the final snapshots at the end of a long thermal and chemical evolution, whose a posteriori reconstruction is the objective of the geochemical (lato sensu) investigation.

      We may then say that for practical reasons geoscientists remained anchored to the original Lavoisier‐like definition of oxidation occurring in combustion processes, related to the exchange of oxygen molecules. The fact that most of the chemical analyses were from techniques in which oxygen was not directly determined but allowed to give oxides has also further favored these approaches.

      In this framework, a mutual exchange of knowledge has always characterized the field of geochemistry and petrology on one side and that of metal extraction in metallurgy in the other. Relations of the type

(1.45)

with v the charge (positive) of the cation of the metal M in the corresponding oxide. Reaction 1.45 is the main target of extractive metallurgy (see also Reaction 1.34), but also sketches the ensemble of processes that occurred since early Earth’s evolution to segregate the metallic core.

Ellingham diagrams (Ellingham 1944; Figure 1.5) are used in metallurgy to evaluate the ease of reduction of metal oxides, as well as chlorides, sulfides, and sulfates. The diagram shows the variation of the standard Gibbs free energy of formation, ΔG⁰, with temperature for selected oxides and is used to predict the equilibrium temperature for reactions of the type of Reaction 1.45 and particularly the oxygen fugacity under which ore will be reduced to its metal. The standard Gibbs energy change of formation of a compound (the Gibbs energy change when one mole of a compound is formed from elements at P = 1 bar) is given by:

      (1.46)

      with R the universal gas constant and A and B constants.

      To compare the relative stabilities of the various oxides, the Ellingham diagram is prepared for oxidation reactions involving one mole of oxygen. For the oxidation of a metal, ΔG⁰ represents the chemical affinity of the metal for oxygen. When the magnitude of ΔG⁰ is negative, the oxide phase is stable over the metal and oxygen gas. Furthermore, the more negative the value, the more stable the oxide is. The Ellingham diagram also indicates which element will reduce which metal oxide. The similarity between the electromotive force series (E⁰) and the Ellingham diagram, which rates the tendency of metals to oxidize, should be easily recognized.

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