the equilibrium oxygen partial pressure or the corresponding PH2/PH2O or PCO/PCO2 ratios between metal and its oxide can be read off directly at a given temperature by drawing the line connecting point O for PO2, C for PCO/PCO2, or H for PH2/PH2O 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 PO2, 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 FeII/FeIII, 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 FeII and FeIII. 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)
(1.49)
(1.50)
(1.51)
All these equilibria have the interesting feature of displaying unitary activities for oxide component appearing as pure phases, such that their equilibrium constants simply describe the variations of O2 activity (aO2) with temperature:
(1.52)
or, by defining fugacity, with temperature and pressure:
(1.53)
with A, B, and C constants. The pressure term, C, allows computing directly fO2 rather than aO2 at the pressure of interest. Mineral assemblages making up Reactions 1.1 and 1.44 to 1.47 are not necessarily occurring in deep Earth and igneous environments, whereas the actual multi‐component space of phases fix the aO2 via multiple equilibria in which solid solutions and/or the presence of relatively mobile liquid (silicate melts) and/or supercritical fluids play a fundamental role.
Figure 1.6 Common solid oxygen buffers used in petrology and geochemistry. The lines represent the fugacity‐temperature conditions where the phases coexist stably. FMQ: fayalite, magnetite, quartz; IW: iron–wüstite; WM: wüstite–magnetite; HM magnetite–hematite. Oxygen fugacity values were computed for a total pressure of 1 bar. Also reported is the value of logfO2 in air (PO2 ~0.21 bar).
However, when one of these mineral “buffers” is selected as a reference, the acting logfO2 can be given as a relative value, without temperature:
A relative fO2 scale embodying temperature effects bears just a practical implication (tracking fO2 variations with respect to a reference) but not a real meaning about logfO2 evolution in igneous systems and related environments (e.g., Moretti and Steffansson, 2020). In particular, a common misconception was that in a system a given value of Δbuffer (e.g., ΔQFM = 0.5) could represent some kind of “magic number” characteristic of the whole “rock system” throughout its thermal and chemical evolution. In natural environments oxygen activity (hence fugacity) in fact varies to accommodate the compositional variations and the speciation state of the mineral/melt/fluid phases, and also when highly mobile volatile components are involved, such that fO2 can thus be fixed by factors that are external to the system object of the thermodynamic description.
Similarly, the rock system evolution cannot be approximated by a unique FeII/FeIII ratio, that the system had when completely molten. Indeed,
