LITMIR.BIZ

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SiO₂ TiO₂ FeO Na₂O Al₂O₃ CaO MgO K₂O MnO P₂O₅ “terrestrial” 42–78 0–4 0.1–18 1–6 11–23 0.1–15 1–14 0–6 0–0.5 0–2 N=98 MORB‐like 45–55 0.5–4 6–16 1.5–4 12–18 8–14 4–12 0–3 0–0.4 0–1 N=33 Major element ranges equal or exceed (Basaltic Volcanism Study Project, 1981) and (Ewart, 1979)

       c. Application of Kress and Carmichael (1991)

A subset of the data we compiled for this review reports glass Fe³⁺/∑Fe ratios. Unlike mineral equilibria, we must relate glass Fe³⁺/∑Fe ratios to fO₂ via an empirical model that accounts for composition. Several studies parameterize the relationship between Fe³⁺/∑Fe ratio and fO₂ and a detailed comparison can be found in Borisov et al. (2018). For this compilation, we investigated those of Borisov et al. (2018), O’Neill et al. (2018), and Kress and Carmichael (1991). [During preparation of this manuscript, a typo in O’Neill et al. (2018) came to light; the coefficient for P₂O₅ in Eqn. 9b in the text of O'Neill et al. (2018) should be –0.018 not –0.18 as written. We use the correct equation here.]

      The Borisov et al. (2018) and Kress and Carmichael (1991) models are both empirical parameterizations of hundreds of wet‐chemical determinations of Fe³⁺/∑Fe ratios of glasses of diverse compositions equilibrated in controlled‐atmosphere experiments. O’Neill et al. (2018) heavily weights (“anchors”) their calibration with the Mössbauer determinations of Fe³⁺/∑Fe ratios of basalts (one basalt composition from Berry et al. (2018), two basalt compositions from Cottrell et al. (2009), but with the Fe³⁺/∑Fe ratios “corrected” to be consistent with Berry et al. (2018), one low‐Fe basalt composition from Jayasuriya et al. (2004), and one high‐Fe sherggotite from Righter et al. (2013), but without that study’s correction for recoilless fraction). They then derive the compositional terms from approximately the same database of wet‐chemical results used in the Borisov et al. (2018) and Kress and Carmichael (1991) models, though O’Neill et al. (2018) uses only compositions with < 60 wt.% SiO2. Not included was the Mössbauer study of Zhang et al. (2018), which determined recoilless fraction using cryogenic Mössbauer. Correction for recoilless fraction reduces the Fe³⁺/∑Fe ratios of Cottrell et al. (2009) by a few percent absolute, though this decrease is not equivalent to the “correction” applied by O’Neill et al. (2018). The Mössbauer studies of Zhang et al. (2018) and Berry et al. (2018) obtain fundamentally different results. We prefer the Mössbauer treatment of Zhang et al. (2018) because the methods applied in Berry et al. (2018) depend on assumptions we believe are flawed, including that highly reduced basalt is free of ferric iron (even under the most reducing conditions, Fe⁰ coexists with substantial Fe³⁺ (Allen & Snow, 1955; Bowen & Schairer, 1932); that hyperfine parameters remain constant as Fe³⁺/∑Fe ratio varies (there is ample evidence to the contrary, e.g., Mysen, 2006); and that center shifts > 0.6, at low quadrupole splitting, should be assigned to ferrous iron (this assertion is unsupported, see Zhang et al., 2018 for a discussion). Of course, when exploring the accuracy of a technique, it is advantageous to cross‐calibrate. We note that the calibration of Zhang et al. (2018) yields an fO₂‐ Fe³⁺/∑Fe ratio relationship that is the same within uncertainty as Kress and Carmichael (1991) model and Borisov et al. (2018) model, based on independent wet‐chemical measurements (see also Partzsch et al., 2004), and spinel oxybarometry (Davis & Cottrell, 2018). Debate on these points must play out in the peer‐reviewed literature and so for the purpose of this compilation, we take a different, agnostic, approach.

      For our assessment, we take advantage of the fact that electrochemical sensors, the devices that monitor the fO₂ within gas‐mixing furnaces, are accurate to better than ±0.1 log units in fO₂ and yield oxybarometric results consistent with independent calorimetric data, even accounting for potential interlaboratory biases due to poor calibration of the furnace hotspot (O’Neill & Pownceby, 1993). Taking advantage of this precision and accuracy, we use Borisov et al. (2018)’s recent compilation of 435 controlled‐atmosphere experiments to assess the parameterizations; the same experimental database that provides the compositional terms in all three parameterizations. The 435 experiments have wet‐chemical determinations of Fe³⁺/∑Fe ratios, and so are independent of the aforementioned debate concerning Mössbauer spectroscopy. We calculated the furnace fO₂ predicted by each parameterization for 435 compositions from QFM ‐3.3 to +7.3, and for 98 “terrestrial” compositions (Table A1) in the Earth‐relevant fO₂ range of QFM ‐3 to +4.1.

Because our inputs are the experimental temperatures, reported major elements, and reported wet‐chemical determinations of Fe³⁺/∑Fe ratios of the experiments, this analysis makes no assumptions about the accuracy of the data that underlie O’Neill et al. (2018), Borisov et al. (2018), or Kress and Carmichael (1991). This analysis only asks how well the three parameterizations predict the known furnace fO₂ of those 435 experiments given their independently‐determined compositions. For the indicated terrestrial range, O’Neill et al. (2018)’s parameterization returns furnace fO₂s that are, on average, 0.56 (±0.55) log units higher than measured, Kress and Carmichael (1991)’s returns furnace fO₂s that are 0.09 (±0.58) lower than measured, and Borisov et al., (2018)’s returns 0.05 (±0.52) lower than measured. Standard errors on the estimates are reported in Table A2. We could therefore move forward confidently with either Kress and Carmichael (1991) or Borisov et al. (2018) but use the former simply because we had completed our analysis before Borisov et al. (2018) was published. Table A2 reports the standard error of each parameterization for the entire compilation and compositional subsets as defined in Table A1. Our analysis assumes that there is no systematic inaccuracy amongst the wet‐chemical studies compiled by Borisov et al., (2018). O’Neill et al. (2018) raise the possibility that some wet‐chemical determinations could be erroneous, and cite four suspect studies. Of these four, only two are included in the compilation of Borisov et al. (2018), and of these, 80% are from the study of Thornber et al. (1980). We therefore assessed whether inclusion/exclusion of the Thornber et al. (1980) data would significantly impact our analysis. It does not. For example, excluding data from Thornber et al. (1980) from the terrestrial data set (n = 55 without

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