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both Me and Me^ν+_2/νO in Reaction 1.45 are in their standard states, the equilibrium constant, K₄₅, corresponding to this reaction can be expressed as:

(1.47)

where fO₂⁰ is the pure gas component gas fugacity at standard state (in this case 1 bar and T of interest). If, at any temperature, the acting oxygen fugacity is greater than the calculated value from Equation 1.47, spontaneous oxidation of metal M occurs, while oxide Me^ν+_2/νO_(s) decomposes to metal Me and gaseous oxygen at the oxygen partial pressure less than the equilibrium value. In other words, an element is unstable, and its oxide is stable at higher oxygen potentials than its ΔG_f⁰–T line on the Ellingham diagram. Therefore, the larger negative value for ΔG_f⁰ an oxide has, the more stable it is. In the Ellingham diagram of Figure 1.4, it can be seen, for example, that the reduction of Cr₂O₃ by carbon is possible (from the thermodynamic standpoint) at temperature above 1250°C and at each reported temperature by aluminum. It is worth noting that the Ellingham line for the formation of carbon monoxide (CO) has a negative slope, while those of all other oxides have positive slopes. As a result, at sufficiently high temperatures, carbon will reduce even the most stable oxides.

      

Figure 1.5 (a) Ellingham diagram for the main components of the melt/slag (solid lines) and possible reducing agents (dotted lines). The slopes of the lines representing ΔG_f⁰–T relations change at the temperature in which the phase transformations of reactants or products occur. Modified from Zhang et al. (2014). (b) Full Ellingham diagram for some relevant oxides including CO₂ equilibria and normographic scales for oxygen fugacity and related quantities via CO/CO₂ and H₂/H₂O ratios at P_tot = 1 bar. The scale of /_O ratio is used in the same manner as that of P_CO/P_CO2 ratio, except that the point H on the ordinate at T= 0 K is used instead of point C.

      Modified from Hasegawa (2014). All reactions’ components are considered in their pure stable phase t 1 bar and T of interest.

      Reaction 1.45 illustrates in fact how pairs of metals and their oxides, both having unitary activity, can be used as redox buffers, such that fO₂ values can be easily fixed at any temperature. Even in the presence of a third phase, such as silicate melts or any other liquid, gas–solid assemblages allow a straightforward application of Equation 1.47 to impose fO₂, unless solid phases are not refractory, and dissolve other components exchanges with the coexisting liquid. Reaction 1.1, involving metal iron and wustite, is a typical example (so‐called IW buffer) of one of these gas–solid equilibria fixing fO₂.

      In order to illustrate the effect of the fluid phase, refined versions of the Ellingham diagrams included normographic scales, which are designed so that the equilibrium oxygen partial pressure or the corresponding P_H2/P_H2O or P_CO/P_CO2 ratios between metal and its oxide can be read off directly at a given temperature by drawing the line connecting point O for P_O2, C for P_CO/P_CO2, or H for P_H2/P_H2O in Figure 1.5 and the condition of interest (Reaction 1.45 at T of interest) and then extending it to the corresponding normographic scale.

      It is now quite obvious to see how both metallurgists and petrologists could then develop techniques to constrain fO₂ to investigate melting and sub‐solidus conditions of oxides and silicates. After the seminal studies of Bowen and Schairer (1932, 1935) on FeO–SiO₂ and MgO–FeO–SiO₂ systems and in which the authors used iron crucibles in an inert (O₂‐free) atmosphere to equilibrate the phases with metallic iron at very low but also unknown P_O2, early fO₂ control techniques were applied by Darken and Gurry (1945, 1946), who detailed the Fe–O system based on the use of CO and CO₂, or CO₂ and H₂, conveyed in a gas‐mixer supplying a continuous mixture in definite constant volume proportions.

      Later Eugster, in his early experiments to determine the phase relations of annite had to prevent its oxidation and formation of magnetite (Eugster 1957, 1959; Eugster and Wones 1962). He then developed the double capsule technique, with a Pt capsule containing the starting material, surrounded by a larger gold capsule. A metal–oxide or oxide–oxide pair plus H₂O was then placed between the two metal containers. In these experiments, reaction involving OH‐bearing minerals and H₂O provides a fixed and known hydrogen fugacity (Eugster 1977), so through the dissociation Reaction 1.14 measurement of fH₂ allows calculating both fO₂ given the fH₂O at the experimental pressure (aH₂O = 1)of the internal capsule.

      Since Eugster, many metal–oxide and oxide–oxide assemblages have been used in experimental petrology that have been called “redox buffers.” These buffers have contributed to our understanding of the role of fO₂ on melt phase equilibria and mineral composition on Earth, also under volatile saturated conditions due to the possibility of evaluating fluid phase speciation at the experimental P and T conditions (e.g., Pichavant et al., 2007; Frost and McCammon, 2008. Mallmann and O’Neill, 2009; Feig et al., 2010). The results of experimental petrology made it possible to systematically collect glasses (quenched melts) to measure ratios of metals in their different oxidation states, particularly Fe^II/Fe^III, and relate such ratios to experimental P, T, and fO₂, glass composition, or other spectroscopic observations about glass/melt structure and the local coordination of targeted metals (Neuville, 2020 and references therein).

Obviously on Earth iron is the most abundant multivalent element and because of its speciation behaviour it gives rise to many reactions involving minerals and liquid (i.e., natural melts, particularly silicate ones). Reactions such as Reaction 1.1 are then useful for providing a scale with geological significance for fO₂ conditions that are recorded in rock and minerals formed in past and present Earth environments, from the core (in which Fe⁰ dominates) up to shallow crust and through all igneous environments where it exists, and Fe^II and Fe^III. To provide systematics for the aO₂ conditions the following gas–solid reactions, other than Reaction 1.1, were then assessed (Figure 1.6):

      (1.48) Скачать книгу