LITMIR.BIZ

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and Osborn (1959) established the link between fO₂ and the course of igneous differentiation. Crystallization under high fO₂ leads to the calc‐alkaline magmatic series common on the continents, while crystallization under low fO₂ results in the tholeiitic magma series common in ocean basins. In order to connect these laboratory‐based insights to natural rocks, petrologists began to develop proxies for fO₂, and to apply them in earnest. Through seminal contributions such as Eugster (1959), Haggerty (1976), Christie et al. (1986), Carmichael (1991), Wood et al. (1990), Frost and Lindsley (1992), Ballhaus (1993), Canil (1997), and innumerable others, petrologists began to quantify and map the link between tectonic environment and oxygen fugacity.

      3.1.1. Theoretical Background

      Oxygen fugacity, or fO₂, describes the potential for an element to occur in an oxidized or reduced state – that is, with a higher or lower charge. If oxygen were an ideal gas, its chemical potential (μ) would simply be related to its partial pressure (P) via

      (3.1)

      Where is the standard state chemical potential of O₂, R is the gas constant, T is the temperature in Kelvin, and P₀ is the standard state pressure of pure O₂. Because no gas, and certainly no rock, behaves as an ideal gas, we substitute fugacity (f) for partial pressure, which corrects pressure for non‐ideality, much as chemical activity corrects concentration for non‐ideality. The chemical potential of oxygen is then

      (3.2)

      when = 1 (the fugacity of pure O₂ at 1 bar and T of interest). In this way, we can relate the free energy of any equilibria of pure phases involving O₂ to oxygen fugacity via the change in Gibbs free energy (

(3.3)

      where K_eq is the equilibrium constant. When P and T are specified, such equilibria of pure phases fix the activity of O₂, or “buffer” the fO₂.

      3.1.2. Fe‐Based Oxybarometry

      Equilibria involving iron are useful because iron is the most abundant multivalent element in the solid Earth and is present in the common rock‐forming minerals. For example, the oxygen fugacity of the equilibrium reaction of the pure phases fayalite goes to ferrosilite plus magnetite:

      (3.4)

can be calculated from the free energy change of the reaction using Equation 3.3. The equilibrium constant can be written:

      (3.5)

      where represents the activity of the end‐member component (e.g., ferrosilite) within the mineral phase (e.g., orthopyroxene). In the case of pure phases, the activity is equal to unity, and so the following relationship holds true:

      (3.6)

      In experimental systems, oxygen fugacity can be imposed by an invariant buffer reaction involving pure phases (activities equal to unity, for example nickel [Ni] and nickel oxide [NiO]). In natural systems, oxygen fugacity is determined by equilibria involving multi‐component silicate minerals, melts, and gases; mineral phases are rarely found as pure end‐member compositions. This requires us to relate mineral compositions to component activities. Accurate activity‐composition models are therefore important when comparing the fO₂ recorded by a single equilibrium reaction across a wide range of compositions, and even more so when comparing the fO₂ recorded by different fO₂ equilibria – when the accuracy, and not just the precision, of each equilibrium reaction is paramount. We relate the measured compositions of natural phases to the activities of end‐member components (e.g., the activity of pure magnetite in spinel, ) via equations like

(3.7)

Equation 3.7 describes the spinel oxybarometer (Ballhaus et al., 1991; O’Neill & Wall, 1987; Wood & Virgo, 1989) and its form prompts a review of several important points.

Any calculation of fO₂ assumes that all phases that fix the activity of oxygen are present and in equilibrium. For example, fO₂ is not constrained by the spinel oxybarometer if orthopyroxene is absent from the assemblage (unless the activity of silica can be constrained by some other means). Likewise, the composition of magnetite records fO₂ only in the presence of ilmenite (Buddington & Lindsley, 1964). We can also see from the above equations that the activity of oxygen will rise with temperature such that it is convenient to refer to a reference buffer. In this contribution we reference the quartz‐fayalite‐magnetite (QFM) buffer (Frost, 1991) because its pressure‐dependence parallels adiabatic melt ascent (Kress and Carmichael, 1991), facilitating comparison of magmas equilibrated at different pressures and temperatures.

      It also follows from the thermodynamic treatment above that the bulk rock ratio of ferric to total iron (Fe³⁺/∑Fe = Fe³⁺/[Fe³⁺ + Fe²⁺]) in crystalline rocks cannot be equated to oxygen fugacity, because the former varies with mineral mode (extensive property) whereas the latter varies with component activity (intensive property). In melts (and glasses), steric effects are greatly reduced, such that melt (glass) Fe³⁺/∑Fe ratios can be related to fO₂; however, this does not mean that the Fe³⁺/∑Fe ratios of melts vary systematically with fO₂ independent of composition. With melts too, Fe³⁺/∑Fe ratios must be related to fO₂ after considering composition because oxide components in the melt can stabilize or destabilize Fe³⁺ relative to Fe²⁺ at given fO₂ (e.g., Borisov et al., 2018; Kress & Carmichael, 1991; O’Neill et al., 2018).

      Based on iron’s role in both setting and monitoring fO₂ (Frost, 1991; D. J. Frost & McCammon, 2008), prior Fe‐based compilations of fO₂ as a function of tectonic setting have relied on either spinel oxybarometry (e.g., Ballhaus, 1993; Wood et al., 1990), magnetite‐ilmenite equilibria (e.g., Frost & Lindsley, 1992), or bulk rock and/or sediment Fe³⁺/∑Fe ratios (e.g., Carmichael, 1991; Lecuyer & Ricard, 1999). In this chapter, we do not compile fO₂ calculated for bulk “glass” Fe³⁺/∑Fe ratios because in most cases the metadata provided in publications are absent or insufficient to ensure that the samples have not suffered post‐eruptive oxidation or are free of phenocrysts, both of which have been shown to compromise the fidelity of fO₂ proxies (Bezos & Humler, 2005; Brounce et al., 2017; Cottrell & Kelley, 2011; Grocke et al., 2016; Stolper & Bucholz, 2019; Bezos et al., 2021). Further, while very convenient for generating large datasets and informing box models

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