Temperature dependence of magmatic iron redox speciation to 2100 °C

S.P. Aithala, C.A. Macris, M.M. Hirschmann; S.P. Aithala; M.M. Hirschmann; C.A. Macris

by admin | May 19, 2026 | mainpost, vol40

TY  - JOUR
T1  - Temperature dependence of magmatic iron redox speciation to 2100 °C
JO  - Geochemical Perspectives Letters
VL  - 40
SP  - 18
EP  - 23
PY  - 2026
AU  - S.P. AithalaAU  - C.A. MacrisAU  - M.M. HirschmannDO  - https://doi.org/10.7185/geochemlet.2617
UR  - https://www.geochemicalperspectivesletters.org/article2617
AB  - The iron redox speciation of silicate melts, quantified by Fe3+/Fe2+ ratios, is of significance to redox evolution during magmatism and is temperature dependent, but exploration of temperature effects has been limited by the narrow range of investigable super-liquidus conditions accessible in gas mixing furnaces (∼1200–1600 °C). This study combines gas mixing and aerodynamic-laser-levitation furnace experiments to quench glasses from a single martian basaltic melt composition at fixed fO2 and 100 kPa from 1250–2100 °C. This 850 °C span allows improved quantification of temperature dependence on Fe3+/Fe2+ ratios. Fe3+/Fe2+ ratios, measured by XANES, are used to calibrate thermodynamic parameterisations. Results indicate that models calibrated from smaller intervals have variable success quantifying the influence of temperature on magmatic Fe3+/Fe2+ ratios. A survey of experimental results suggests that the temperature dependence of Fe3+/Fe2+ does not vary appreciably with melt composition. The new data improve constraints on iron redox systematics during igneous differentiation of martian magmas by quantifying the effect of cooling on magma Fe3+/Fe2+ and, in extrapolation, refine predictions of Fe3+/Fe2+ ratios established in magma oceans at extreme temperatures, by constraining the temperature dependence of Fe3+/Fe2+ at a fixed fO2 relative to melt-alloy equilibrium.

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Temperature dependence of magmatic iron redox speciation to 2100 °C

S.P. Aithala¹,

¹Dept. of Earth and Environmental Sciences, University of Minnesota, Minneapolis, MN 55455, USA

C.A. Macris²,

²Earth and Environmental Sciences, Indiana University-Indianapolis, Indianapolis, IN 46202, USA

M.M. Hirschmann¹

¹Dept. of Earth and Environmental Sciences, University of Minnesota, Minneapolis, MN 55455, USA

Affiliations | Corresponding Author | Cite as | Funding information

Geochemical Perspectives Letters v40 | https://doi.org/10.7185/geochemlet.2617
Received 17 July 2025 | Accepted 4 March 2026 | Published 19 May 2026

Published by the European Association of Geochemistry
under Creative Commons License CC BY-NC-ND 4.0

Keywords: iron redox, oxygen fugacity, aerodynamic-laser-levitation furnace, XANES, Mössbauer, martian magmatism, magma ocean



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Abstract

The iron redox speciation of silicate melts, quantified by Fe³⁺/Fe²⁺ ratios, is of significance to redox evolution during magmatism and is temperature dependent, but exploration of temperature effects has been limited by the narrow range of investigable super-liquidus conditions accessible in gas mixing furnaces (∼1200–1600 °C). This study combines gas mixing and aerodynamic-laser-levitation furnace experiments to quench glasses from a single martian basaltic melt composition at fixed f_O2 and 100 kPa from 1250–2100 °C. This 850 °C span allows improved quantification of temperature dependence on Fe³⁺/Fe²⁺ ratios. Fe³⁺/Fe²⁺ ratios, measured by XANES, are used to calibrate thermodynamic parameterisations. Results indicate that models calibrated from smaller intervals have variable success quantifying the influence of temperature on magmatic Fe³⁺/Fe²⁺ ratios. A survey of experimental results suggests that the temperature dependence of Fe³⁺/Fe²⁺ does not vary appreciably with melt composition. The new data improve constraints on iron redox systematics during igneous differentiation of martian magmas by quantifying the effect of cooling on magma Fe³⁺/Fe²⁺ and, in extrapolation, refine predictions of Fe³⁺/Fe²⁺ ratios established in magma oceans at extreme temperatures, by constraining the temperature dependence of Fe³⁺/Fe²⁺ at a fixed f_O2 relative to melt-alloy equilibrium.

Figures

Figure 1 Raw and recalculated ratios from VF (1250–1500 °C) and ALLF (1800–2100 °C) experimental series versus reciprocal temperature (error bars represent 2σ). Adjustments are made to compare experiments at a common oxygen fugacity and composition (see SI). Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).	Figure 2 The slope of versus inverse temperature (h-coefficients) for either series of ≥2 experiments conducted at variable temperature and constant composition and f_O2, or from the h-coefficient’s empirical models, as a function of composition ((a) SiO₂ and (b) FeO). Experimental series (data points) are from the present study and others (Table S-5). Models (dashed lines) are from previous studies (see Fig. 1 caption for model source key). Hollow symbols represent the h-coefficients for series comprising two experiments. The solid lines are linear weighted-least squares regressions of h-values vs. wt. % SiO₂ (left) (h = 5.095 ± 5.120 X wt. % SiO₂ + 4472 ± 302.5; r² = 0.027) or wt. % FeO (right) (h = −45.20 ± 17.21 X wt. % FeO + 5141 ± 147.7; r² = 0.161) to experimental series containing more than two experiments.	Figure 3 Comparison of predicted f_O2 change during unbuffered, isochemical cooling of shergottite liquids Tissint, NWA 6234, and NWA 1068/1100 from liquidus to 1100 °C as calculated by different models (see Fig. 1) following Aithala et al. (2026). Equation 8, the preferred model derived from the present study’s temperature series is shown as a solid black line with shaded area representing 2σ uncertainties (see Fig. S-3 to compare with Eqs. 7 and 9). Gray and red stars indicate f_O2s of early and late crystallised assemblages measured in shergottites, respectively.	Figure 4 Fe³⁺/Fe^T ratios predicted for Humphrey silicate liquid at 100 kPa, logf_O2 = IW-2 (Hirschmann, 2021) at temperatures ranging from 1500–4000 K calculated from thermodynamic models that incorporate non-zero values of ΔC_P (see Fig. 1). Gray and red stars indicate Fe³⁺/Fe^T ratios for Equation 8 at 2500 and 4000 K (Fe³⁺/Fe^T = 0.020 and 0.046, respectively). Shaded region reflects 2σ uncertainty on the h-coefficient of Equation 8.
Figure 1	Figure 2	Figure 3	Figure 4

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Introduction

The redox speciation of multivalent cations, especially iron, has a significant influence on igneous mass transfer and phase equilibria (Cottrell et al., 2021

Cottrell, E., Birner, S.K., Brounce, M., Davis, F.A., Waters, L.E., Kelley, K.A. (2021) Oxygen fugacity across tectonic settings. In: Moretti, R., Neuville, D.R. (Eds.) Magma Redox Geochemistry. American Geophysical Union Geophysical Monograph Series 266, John Wiley & Sons, Inc., Hoboken, NJ, 33–61. https://doi.org/10.1002/9781119473206.ch3

and references therein). The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

; Jayasuriya et al., 2004

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

; Righter et al., 2013

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

; Borisov et al., 2018

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

; Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017

Zhang, H.L., Hirschmann, M.M., Cottrell, E., Withers, A.C. (2017) Effect of pressure on Fe3+/ΣFe ratio in a mafic magma and consequences for magma ocean redox gradients. Geochimica et Cosmochimica Acta 204, 83–103. https://doi.org/10.1016/j.gca.2017.01.023

, 2024

Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

; Armstrong et al., 2019

Armstrong, K., Frost, D.J., McCammon, C.A., Rubie, D.C., Boffa Ballaran, T. (2019) Deep magma ocean formation set the oxidation state of Earth’s mantle. Science 365, 903–906. https://doi.org/10.1126/science.aax8376

; Deng et al., 2020

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

; Kuwahara et al., 2023

Kuwahara, H., Nakada, R., Kadoya, S., Yoshino, T., Irifune, T. (2023) Hadean mantle oxidation inferred from melting of peridotite under lower-mantle conditions. Nature Geoscience 16, 461–465. https://doi.org/10.1038/s41561-023-01169-4

). Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

; Righter et al., 2013

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

; Borisov et al., 2018

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

; Deng et al., 2020

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

; Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

). In addition, the few experimental studies designed to isolate the effects of temperature (e.g., Kress and Carmichael, 1988

Kress, V.C., Carmichael, I.S.E. (1988) Stoichiometry of the iron oxidation reaction in silicate melts. American Mineralogist 73, 1267–1274.

; Moore et al., 1995

Moore, G., Righter, K., Carmichael, I.S.E. The effect of dissolved water on the oxidation state of iron in natural silicate liquids. Contributions to Mineralogy and Petrology 120, 170–179 (1995) https://doi.org/10.1007/BF00287114

; Borisov and McCammon, 2010

Borisov, A., McCammon, C. (2010) The effect of silica on ferric/ferrous ratio in silicate melts: An experimental study using Mossbauer spectroscopy. American Mineralogist 95, 545–555. https://doi.org/10.2138/am.2010.3217

; Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

) have spanned relatively narrow intervals (≤350 K).

Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021

Cottrell, E., Birner, S.K., Brounce, M., Davis, F.A., Waters, L.E., Kelley, K.A. (2021) Oxygen fugacity across tectonic settings. In: Moretti, R., Neuville, D.R. (Eds.) Magma Redox Geochemistry. American Geophysical Union Geophysical Monograph Series 266, John Wiley & Sons, Inc., Hoboken, NJ, 33–61. https://doi.org/10.1002/9781119473206.ch3

) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012

Hirschmann, M.M. (2012) Magma ocean influence on early atmosphere mass and composition. Earth and Planetary Science Letters 341–344, 48–57. https://doi.org/10.1016/j.epsl.2012.06.015

, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Deng et al., 2020

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

; Henningsen et al., 2025

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

). For the former, one case of interest is redox variations during petrologic evolution of martian basalts, which are more pronounced than their terrestrial equivalents (Herd, 2019

Herd, C.D.K. (2019) Reconciling redox: Making spatial and temporal sense of oxygen fugacity variations in martian igneous rocks. 50th Lunar and Planetary Institute Science Conference, Abstract #2746.

; Aithala et al. 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

). Experimental studies of Fe redox systematics of Fe-rich, martian-relevant magmas from Righter et al. (2013)

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

and Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

found that Fe³⁺/Fe²⁺ ratios of these magmas are more sensitive to temperature than Fe-poor silicate liquids. Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

concluded that this increased temperature sensitivity could drive significant f_O2 increases relative to standard redox buffers during magmatic cooling and hypothesised that this effect could account for a significant fraction of the f_O2 increases measured within and across martian basalts.

Recent studies pertaining to magma oceans have considered redox conditions in melts equilibrating with core-destined Fe alloy and found, at these extreme conditions (>2500 K), temperature may have a pronounced effect on Fe³⁺/Fe²⁺ ratios (Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Henningsen et al., 2025

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

) and may contribute significantly to the relatively oxidised conditions established during Earth’s mantle solidification. However, large differences in Fe³⁺/Fe²⁺ ratios calculated from different models (Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

) arise because of uncertainties in extrapolation to high temperature from experimental constraints, which are limited to <1650 °C.

To better constrain the temperature-Fe redox systematics of silicate melts, we investigated Fe³⁺/Fe²⁺ variations from 1250–2100 °C for an Fe-rich martian-relevant basaltic melt. These experiments span 850 °C, a greater range for a nearly isochemical system than any previous investigation of Fe³⁺/Fe²⁺ ratios in silicate melts and therefore provide fundamental constraints on the thermodynamics of iron redox in silicate melts. They are applicable to understanding redox processes during martian igneous evolution and can improve understanding of Fe³⁺/Fe²⁺ ratios at magma ocean conditions.

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Thermodynamic Background

Magmatic Fe³⁺/Fe²⁺ratio is governed by the reaction,

At standard pressure, P₀ (100 kPa), the energetics of this reaction are given by

where X_i represents the mole fraction of component, i, ΔG_T,P₀ is the change in free energy at temperature T (K), R is the gas constant (8.314 J/mol K), and γ_i are the activity coefficients for melt components, i.

Estimates of ΔG_T,P₀ can be derived empirically from experiments on iron-bearing molten silicates by the simplified expression,

where a and b are regressed coefficients (Sack et al. 1981

Sack, R.O., Carmichael, I.S.E., Rivers, M., Ghiorso, M.S. (1981) Ferric-ferrous equilibria in natural silicate liquids at 1 bar. Contributions to Mineralogy and Petrology 75, 369–376. https://doi.org/10.1007/bf00374720

; Kilinc et al. 1983

Kilinc, A., Carmichael, I.S.E., Rivers, M.L., Sack, R.O. (1983) The ferric-ferrous ratio of natural silicate liquids equilibrated in air. Contributions to Mineralogy and Petrology 83, 136–140. https://doi.org/10.1007/bf00373086

; Borisov et al. 2018

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

). An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

; Jayasuriya et al., 2004

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

; Deng et al., 2020

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

; Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

):

where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984

Stebbins, J.F., Carmichael, I.S.E., Moret, L.K. (1984) Heat capacities and entropies of silicate liquids and glasses. Contributions to Mineralogy and Petrology 86, 131–148. https://doi.org/10.1007/bf00381840

; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992

Lange, R.A., Navrotsky, A. (1992) Heat capacities of Fe₂O₃-bearing silicate liquids. Contributions to Mineralogy and Petrology 110, 311–320. https://doi.org/10.1007/BF00310746

). The influence of the ΔC_P term on calculated Fe³⁺/Fe²⁺ ratios is small at temperatures <1650 °C, but as noted by Hirschmann (2022)

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

can significantly enhance predicted Fe³⁺/Fe²⁺ ratios in extrapolations above 2000 K.

Following previous work (e.g., Sack et al., 1981

Sack, R.O., Carmichael, I.S.E., Rivers, M., Ghiorso, M.S. (1981) Ferric-ferrous equilibria in natural silicate liquids at 1 bar. Contributions to Mineralogy and Petrology 75, 369–376. https://doi.org/10.1007/bf00374720

; Kress and Carmichael, 1991

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

; Jayasuriya et al., 2004

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

; Righter et al., 2013

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

, Borisov et al., 2018

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

; Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the

term with a simple compositional term, ∑d_iX_i, to yield the expression,

For experimentally quenched glasses synthesised at a single f_O2 and identical composition, the effect of temperature simplifies to

where C is the sum of c, ∑d_{iX_i}, and klogf_O2.

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Temperature Dependence on Fe³⁺/Fe^T from 1250–2100 °C

Starting mixes similar to martian basalt Humphrey (McSween et al., 2006

McSween, H.Y., Ruff, S.W., Morris, R.V., Bell, J.F., Herkenhoff, K., Gellert, R., Stockstill, K.R., Tornabene, L.L., Squyres, S.W., Crisp, J.A., Christensen, P.R., McCoy, T.J., Mittlefehldt, D.W., Schmidt, M. (2006) Alkaline volcanic rocks from the Columbia Hills, Gusev crater, Mars. Journal of Geophysical Research: Planets 111, E09S91. https://doi.org/10.1029/2006je002698

; Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

) were synthesised from high purity reagents for super-liquidus 100 kPa experiments in vertical gas mixing (VF) and aerodynamic-laser-levitation furnace (ALLF) experiments (Table S-1). VF experiments, previously reported by Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

, were equilibrated in air and ALLF experiments were levitated in O₂ gas. Experiments were quenched rapidly (SI), with all but one sample (VF271) yielding 100 % glass. Major element compositions of all glasses were determined by EPMA (Table S-2) and Fe³⁺/Fe²⁺ ratios were determined by XANES (Table S-3). VF glass Fe³⁺/Fe²⁺ was also determined with Mössbauer spectroscopy (Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

), but the ALLF glass was not, as their small masses precluded conventional Mössbauer spectroscopic analyses. Compositions of glasses from the partially crystallised experiment and the ALLF experiments differ from the starting composition owing, respectively, to partial crystallisation and volatilisation of Na, K, and P (Fig. S-1; Supplementary Information (SI)).

top

Discussion

After adjusting experimental Fe³⁺/Fe²⁺ of VF271 and the ALLF experiments to represent a single average composition (SI), we evaluate the temperature coefficient, h, and the significance of the ΔC_p term by regressing versions of Equation 6. At constant composition and f_O2, we regress 3 weighted-least squares equations: one with a regressed h-coefficient where ΔC_p ≡ 0, (Eq. 7), one with a regressed h-coefficient and fixed ΔC_p (adopted from Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

) (Eq. 8), and finally fitting both h- and ΔC_p terms (Eq. 9):

According to the unreduced χ² goodness of fit

, all regressions are similarly accurate and precise (Table S-4), and their curves overlap throughout the investigated temperature interval (Fig. 1). The ΔC_p terms in Equations 8 and 9 having opposite signs indicates divergent deviations from linearity.

**Figure 1** Raw and recalculated ratios from VF (1250–1500 °C) and ALLF (1800–2100 °C) experimental series *versus* reciprocal temperature (error bars represent 2σ). Adjustments are made to compare experiments at a common oxygen fugacity and composition (see SI). Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991)
Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. *Contributions to Mineralogy and Petrology* 108, 82–92. https://doi.org/10.1007/Bf00307328
, J04_10 and J04_12 = Jayasuriya *et al.*, (2004)
Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. *American Mineralogist* 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203
, Eqs. 10 and 12; R13 = Righter *et al.*, (2013)
Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. *American Mineralogist* 98, 616–628. https://doi.org/10.2138/am.2013.4251
, D20 = Deng *et al.*, (2020)
Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. *Nature Communications* 11, 2007. https://doi.org/10.1038/s41467-020-15757-0
, H22 = Hirschmann (2022)
Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. *Geochimica et Cosmochimica Acta,* 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005
, A26 = Aithala *et al.*, (2026)
Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. *Journal of Geophysical Research: Planets* 131, e2025JE009148. https://doi.org/10.1029/2025JE009148
.

Previous models, parameterised from smaller temperature intervals and not optimised for a martian composition, do not reproduce the

s as well as Eqs. 7–9, which are calibrated from the present experiments. However, parameterisations from Kress and Carmichael (1991)

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

, Jayasuriya et al. (2004

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

; Eq. 12), and Borisov et al. (2018)

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

match experimental

values within experimental uncertainties. The Hirschmann (2022)

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

model reproduces VF series

well but overestimate ALLF

. The Jayasuriya et al. (2004

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

; Eq. 10), Righter et al. (2013)

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

, and Deng et al. (2020)

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

models yield systematic discrepancies. The Hirschmann (2022)

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

model overestimates are likely the result of low temperature Fe³⁺/Fe²⁺ data points being fit with a small h-coefficient combined with superimposition of an independently derived, positive ΔC_p term, resulting in positive deviations at elevated temperatures. The new experiments at 1800–2100 °C demonstrate that a larger h-coefficient is warranted.

Examining models regressed here, Equation 7 better fits the experiments compared to Equation 8 as demonstrated by its smaller χ² (Table S-4), despite the unlikely assumption of ΔC_p ≡ 0. The effect of a positive ΔC_p, causing positive

deviations at elevated temperature relative to linear models, is not evident in the experimental interval 1250–2100 °C. In fact, the measured

trend to slightly lower values at elevated temperatures, as evident from the possibly negative value of ΔC_p (−23.74 J/K ± 51.05 J/K; p value = 0.66) regressed in Equation 9. A negative value of ΔC_p conflicts with calorimetric studies of Fe-bearing silicate liquids (Stebbins et al., 1984

Stebbins, J.F., Carmichael, I.S.E., Moret, L.K. (1984) Heat capacities and entropies of silicate liquids and glasses. Contributions to Mineralogy and Petrology 86, 131–148. https://doi.org/10.1007/bf00381840

; Lange and Navrotsky, 1992

Lange, R.A., Navrotsky, A. (1992) Heat capacities of Fe₂O₃-bearing silicate liquids. Contributions to Mineralogy and Petrology 110, 311–320. https://doi.org/10.1007/BF00310746

) and this specific value is not statistically significant, nor does its inclusion improve the fit from the linear Equation 7 model from the perspective of reduced chi square (Table S-4). Ultimately, a well defined value of ΔC_p may not be resolvable from the present data; i.e. Hirschman (2022)

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

noted that the effects of ΔC_p should be pronounced at temperatures well above 2000 K. Potentially, the assumption of a constant ΔC_p value is not appropriate, as the effects of anharmonicity may be important at very high temperatures (Fiquet et al., 1992

Fiquet, G., Gillet, P., Richet, P. (1992) Anharmonicity and high-temperature heat capacity of crystals: the examples of Ca₂GeO₄, Mg₂GeO₄ and CaMgGeO₄ olivines. Physics and Chemistry of Minerals 18, 469–479. https://doi.org/10.1007/BF00200970

) Although all Equations 7–9 are similarly accurate and precise, we favour Equation 8 for modelling Fe³⁺/Fe²⁺ and f_O2 systematics at all temperatures as it accounts for a non-zero ΔC_p, established from independent calorimetric measurements. Notably, this model is very similar in both form and values to Kress and Carmichael (1991

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

; h-coefficient = 5235 vs. 4991, ΔC_p = 33.25 vs. 27.9 J/K) suggesting that their model extrapolates well to temperatures beyond its calibration dataset.

Are martian magmas’ Fe³⁺/Fe²⁺ and f_O2 more sensitive to temperature variations? The new experiments allow improved resolution of redox variation induced by cooling of martian basalts. Previous work by Righter et al. (2013)

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

and Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

found enhanced temperature sensitivity (i.e. smaller h-coefficient) for martian magmas as compared to models calibrated from terrestrial or simplified-composition silicate liquids. The newly regressed h-coefficient of 4894 K from Equation 7 from experiments at 1250–2100 °C is greater than h-coefficient of 3775 K found by Aithala et al.(2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

for the same composition (1250–1500 °C) and significantly exceeds the 1650 K value determined for a shergottitic composition (1300–1500 °C; Righter et al., 2013

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

). Compared to a wider range of model parameterisations and to experimental series in which a fixed starting composition was equilibrated in air over a range of temperatures, the h-coefficient of 4894 K is consistent with previous estimates (Fig. 2).

**Figure 2** The slope of *versus* inverse temperature (h-coefficients) for either series of ≥2 experiments conducted at variable temperature and constant composition and f_O2, or from the h-coefficient’s empirical models, as a function of composition (**(a)** SiO₂ and **(b)** FeO*). Experimental series (data points) are from the present study and others (Table S-5). Models (dashed lines) are from previous studies (see Fig. 1 caption for model source key). Hollow symbols represent the h-coefficients for series comprising two experiments. The solid lines are linear weighted-least squares regressions of h-values vs. wt. % SiO₂ (left) (h = 5.095 ± 5.120 X wt. % SiO₂ + 4472 ± 302.5; r² = 0.027) or wt. % FeO* (right) (h = −45.20 ± 17.21 X wt. % FeO + 5141 ± 147.7; r² = 0.161) to experimental series containing more than two experiments.

The survey of temperature effects on

from previous studies (Fig. 2) allows evaluation of the hypothesis that h-coefficients are compositionally dependent; h-coefficients from experimental series with >2 experiments show no resolvable correlation with SiO₂ and a weakly negative correlation with FeO* (Fig. 2). In addition, the h-coefficient derived from the present study is also consistent with previously investigated compositions despite elevated FeO*, suggesting that compositional influence on the h-coefficient is not supported, despite previous conclusions from Righter et al. (2013)

Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

and Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

.

With improved constraints for the temperature dependence of Fe³⁺/Fe²⁺ ratios in magmas, we apply Equation 8 to evaluate the isolated effect of magmatic cooling in generating f_O2 variations in martian basalt (SI). We consider the redox evolution of shergottites that have undergone significant f_O2 increase during differentiation, as recorded by oxybarometry of early and late crystallised mineral assemblages (Tissint — Castle and Herd, 2017

Castle, N., Herd, C.D.K. (2017) Experimental petrology of the Tissint meteorite: Redox estimates, crystallization curves, and evaluation of petrogenetic models. Meteoritics & Planetary Science 52, 125–146. https://doi.org/10.1111/maps.12739

; Northwestern Africa (NWA) 6234 — Gross et al., 2013

Gross, J., Filiberto, J., Herd, C.D.K., Daswani, M.M., Schwenzer, S.P., Treiman, A.H. (2013) Petrography, mineral chemistry, and crystallization history of olivine‐phyric shergottite NWA 6234: A new melt composition. Meteoritics & Planetary Science 48, 854–871. https://doi.org/10.1111/maps.12092

; Northwestern Africa (NWA) 1068/1100 — Herd 2006

Herd, C.D.K. (2006) Insights into the redox history of the NWA 1068/1110 martian basalt from mineral equilibria and vanadium oxybarometry. American Mineralogist 91, 1616–1627. https://doi.org/10.2138/am.2006.2104

), and calculate their f_O2 evolution from unbuffered, isochemical cooling following the scenario presented in Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

. Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

, using their martian-magma specific model, found that cooling contributed significant f_O2 increases relative to the quartz-fayalite-magnetite (QFM) buffer, accounting for a significant fraction of observed oxidation, minimising the necessary extent of potentially oxidative pressure variation and/or processes affecting magma chemistry including crystallisation, degassing, or assimilation. However, application of Equation 8 to model magmatic cooling from liquidus temperature (Aithala et al., 2026

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

) to 1100 °C results in decreases in f_O2 relative to QFM of 0.37, 0.39, and 0.37 log units f_O2 for Tissint, NWA 6234, and NWA 1068/1100 (Fig. 3). This contrasts the Aithala et al. (2026)

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

model and suggests that observed shergottite f_O2 increases are entirely a product of pressure variation, crystallisation, and/or other open system processes.

**Figure 3** Comparison of predicted f_O2 change during unbuffered, isochemical cooling of shergottite liquids Tissint, NWA 6234, and NWA 1068/1100 from liquidus to 1100 °C as calculated by different models (see Fig. 1) following Aithala *et al.* (2026)
Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. *Journal of Geophysical Research: Planets* 131, e2025JE009148. https://doi.org/10.1029/2025JE009148
. Equation 8, the preferred model derived from the present study’s temperature series is shown as a solid black line with shaded area representing 2σ uncertainties (see Fig. S-3 to compare with Eqs. 7 and 9). Gray and red stars indicate f_O2s of early and late crystallised assemblages measured in shergottites, respectively.

Differences in Fe³⁺/Fe^T ratios extrapolated to magma ocean conditions. Redox conditions in deep magma oceans may be established at extreme temperatures (>3500 K, Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Henningsen et al., 2025

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

) or yet higher on Super-Earths (Young et al., 2024

Young, E.D., Stixrude, L., Rogers, J.G., Schlichting, H.E., Marcum, S.P. (2024) Phase Equilibria of Sub-Neptunes and Super-Earths. The Planetary Science Journal 5, 268. https://doi.org/10.3847/psj/ad8c40

), and so the effect of elevated temperature on silicate melt Fe³⁺/Fe^T at these conditions may be substantial. Previous models applied to magma ocean redox (e.g., Deng et al. 2020

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

; Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Zhang et al. 2024

Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

, and references therein) reproduce Fe³⁺/Fe^T ratios from experiments at lower temperatures (1250–1500 °C), but when extrapolated to magma ocean temperatures, predict dramatically different Fe³⁺/Fe^T (Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

). Accurate extrapolation of magmatic Fe³⁺/Fe^T is crucial to understanding stabilisation of ferric iron in magma oceans. Without it, models calibrated from very high temperature, high pressure — e.g., experiments from Zhang et al. (2024)

Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

at 38–71 GPa and 3600–4400 K — could mis-attribute the effects of temperature and pressure. Further, if the temperature dependence of Fe³⁺/Fe^T is strong, then the potential temperature of magma ocean may strongly influence the Fe³⁺/Fe^T of the resulting solidified mantle (Henningsen et al., 2025

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

).

Although no experimentally derived model extends to the extreme temperatures of magma oceans, Equation 8 is calibrated on a greater range of temperatures than previous parameterisations, and so extrapolation to high temperature may have less uncertainty. Applied at 100 kPa, 2500–4000 K at 2 logf_O2 units below iron-wüstite (IW-2) (logf_O2-2500 K = −6.34, logf_O2-4000 K = −2.41; Hirschmann, 2021

Hirschmann, M.M. (2021) Iron-wüstite revisited: A revised calibration accounting for variable stoichiometry and the effects of pressure. Geochimica et Cosmochimica Acta 313, 74–84. https://doi.org/10.1016/j.gca.2021.08.039

), it predicts Fe³⁺/Fe^T ratios of 0.020–0.046 (Fig. 4), similar to that predicted by Kress and Carmichael (1991)

Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

(0.019–0.041) and greater than the models of Jayasuriya et al. (2004)

Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

Equation 10 (0.0046–0.0050) and Deng et al. (2020)

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

(0.007–0.032). However, the Hirschmann (2022)

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

model predicts significantly greater ratios (0.039–0.116), which are likely not realistic. A modest effect of extreme temperature on magmatic Fe³⁺/Fe^T indicates that the increase in Fe³⁺/Fe^T ratios found in high temperature-pressure experiments (Armstrong et al., 2019

Armstrong, K., Frost, D.J., McCammon, C.A., Rubie, D.C., Boffa Ballaran, T. (2019) Deep magma ocean formation set the oxidation state of Earth’s mantle. Science 365, 903–906. https://doi.org/10.1126/science.aax8376

; Kuwahara et al., 2023

Kuwahara, H., Nakada, R., Kadoya, S., Yoshino, T., Irifune, T. (2023) Hadean mantle oxidation inferred from melting of peridotite under lower-mantle conditions. Nature Geoscience 16, 461–465. https://doi.org/10.1038/s41561-023-01169-4

; Zhang et al., 2024

Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

) are owed primarily to the effect of pressure and that models incorporating strong temperature dependent effects on the Fe³⁺/Fe^T of the crystallised mantle (Hirschmann, 2022

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

; Zhang et al. 2024

Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

) will require re-examination. Recently, Henningsen et al. (2025)

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

argued that melt-alloy equilibration during alloy rain-out (at super-liquidus conditions) produces significantly greater Fe³⁺/Fe^T ratios than equilibration at the base of a MO, at near-liquidus conditions, but this conclusion is based on a strongly temperature dependent model that may not be accurate.

**Figure 4** Fe³⁺/Fe^T ratios predicted for Humphrey silicate liquid at 100 kPa, logf_O2 = IW-2 (Hirschmann, 2021
Hirschmann, M.M. (2021) Iron-wüstite revisited: A revised calibration accounting for variable stoichiometry and the effects of pressure. *Geochimica et Cosmochimica Acta* 313, 74–84. https://doi.org/10.1016/j.gca.2021.08.039
) at temperatures ranging from 1500–4000 K calculated from thermodynamic models that incorporate non-zero values of ΔC_P (see Fig. 1). Gray and red stars indicate Fe³⁺/Fe^T ratios for Equation 8 at 2500 and 4000 K (Fe³⁺/Fe^T = 0.020 and 0.046, respectively). Shaded region reflects 2σ uncertainty on the h-coefficient of Equation 8.

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Acknowledgements

This work was supported by NASA grant 80NSSC21K1826 to UMN, NSF grant EAR-231702 to UMN and IU Indianapolis, and NSF grant EAR-1851684 to IU Indianapolis. XANES analyses were conducted at beamline 4-BM (XFM) at the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704. The authors thank Ryan Tappero for assistance with XANES analyses at 4-BM, and Jennifer Mitchell for assistance with EPMA analyses. This work benefitted from many conversations with Daoheng Wang and from thoughtful reviews by Liz Cottrell and two anonymous referees.

Editor: Francis M. McCubbin

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References

Aithala, S.P., Lange, R.A., Hirschmann, M.M. (2026) Controls on iron-redox state in martian magmas quantified by Mössbauer spectroscopy, colorimetric wet chemistry, and XANES spectroscopy. Journal of Geophysical Research: Planets 131, e2025JE009148. https://doi.org/10.1029/2025JE009148

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
View in article
In addition, the few experimental studies designed to isolate the effects of temperature (e.g., Kress and Carmichael, 1988; Moore et al., 1995; Borisov and McCammon, 2010; Aithala et al., 2026) have spanned relatively narrow intervals (≤350 K).
View in article
For the former, one case of interest is redox variations during petrologic evolution of martian basalts, which are more pronounced than their terrestrial equivalents (Herd, 2019; Aithala et al. 2026).
View in article
Experimental studies of Fe redox systematics of Fe-rich, martian-relevant magmas from Righter et al. (2013) and Aithala et al. (2026) found that Fe³⁺/Fe²⁺ ratios of these magmas are more sensitive to temperature than Fe-poor silicate liquids. Aithala et al. (2026) concluded that this increased temperature sensitivity could drive significant f_O2 increases relative to standard redox buffers during magmatic cooling and hypothesised that this effect could account for a significant fraction of the f_O2 increases measured within and across martian basalts.
View in article
Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
Eq. 5.

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Starting mixes similar to martian basalt Humphrey (McSween et al., 2006; Aithala et al., 2026) were synthesised from high purity reagents for super-liquidus 100 kPa experiments in vertical gas mixing (VF) and aerodynamic-laser-levitation furnace (ALLF) experiments (Table S-1).
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VF experiments, previously reported by Aithala et al. (2026), were equilibrated in air and ALLF experiments were levitated in O₂ gas. Experiments were quenched rapidly (SI), with all but one sample (VF271) yielding 100 % glass. Major element compositions of all glasses were determined by EPMA (Table S-2) and Fe³⁺/Fe²⁺ ratios were determined by XANES (Table S-3).
View in article
VF glass Fe³⁺/Fe²⁺ was also determined with Mössbauer spectroscopy (Aithala et al., 2026), but the ALLF glass was not, as their small masses precluded conventional Mössbauer spectroscopic analyses.
View in article
Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
View in article
Previous work by Righter et al. (2013) and Aithala et al. (2026) found enhanced temperature sensitivity (i.e. smaller h-coefficient) for martian magmas as compared to models calibrated from terrestrial or simplified-composition silicate liquids.
View in article
The newly regressed h-coefficient of 4894 K from Equation 7 from experiments at 1250–2100 °C is greater than h-coefficient of 3775 K found by Aithala et al.(2026) for the same composition (1250–1500 °C) and significantly exceeds the 1650 K value determined for a shergottitic composition (1300–1500 °C; Righter et al., 2013).
View in article
In addition, the h-coefficient derived from the present study is also consistent with previously investigated compositions despite elevated FeO*, suggesting that compositional influence on the h-coefficient is not supported, despite previous conclusions from Righter et al. (2013) and Aithala et al. (2026).
View in article
We consider the redox evolution of shergottites that have undergone significant f_O2 increase during differentiation, as recorded by oxybarometry of early and late crystallised mineral assemblages (Tissint — Castle and Herd, 2017; Northwestern Africa (NWA) 6234 — Gross et al., 2013 ; Northwestern Africa (NWA) 1068/1100 — Herd 2006), and calculate their f_O2 evolution from unbuffered, isochemical cooling following the scenario presented in Aithala et al. (2026).
View in article
Aithala et al. (2026), using their martian-magma specific model, found that cooling contributed significant f_O2 increases relative to the quartz-fayalite-magnetite (QFM) buffer, accounting for a significant fraction of observed oxidation, minimising the necessary extent of potentially oxidative pressure variation and/or processes affecting magma chemistry including crystallisation, degassing, or assimilation.
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However, application of Equation 8 to model magmatic cooling from liquidus temperature (Aithala et al., 2026) to 1100 °C results in decreases in f_O2 relative to QFM of 0.37, 0.39, and 0.37 log units f_O2 for Tissint, NWA 6234, and NWA 1068/1100 (Fig. 3).
View in article
This contrasts the Aithala et al. (2026) model and suggests that observed shergottite f_O2 increases are entirely a product of pressure variation, crystallisation, and/or other open system processes.
View in article
Comparison of predicted f_O2 change during unbuffered, isochemical cooling of shergottite liquids Tissint, NWA 6234, and NWA 1068/1100 from liquidus to 1100 °C as calculated by different models (see Fig. 1) following Aithala et al. (2026).
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Armstrong, K., Frost, D.J., McCammon, C.A., Rubie, D.C., Boffa Ballaran, T. (2019) Deep magma ocean formation set the oxidation state of Earth’s mantle. Science 365, 903–906. https://doi.org/10.1126/science.aax8376

Show in context

The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
A modest effect of extreme temperature on magmatic Fe³⁺/Fe^T indicates that the increase in Fe³⁺/Fe^T ratios found in high temperature-pressure experiments (Armstrong et al., 2019; Kuwahara et al., 2023; Zhang et al., 2024) are owed primarily to the effect of pressure and that models incorporating strong temperature dependent effects on the Fe³⁺/Fe^T of the crystallised mantle (Hirschmann, 2022; Zhang et al. 2024) will require re-examination.
View in article

Borisov, A., McCammon, C. (2010) The effect of silica on ferric/ferrous ratio in silicate melts: An experimental study using Mossbauer spectroscopy. American Mineralogist 95, 545–555. https://doi.org/10.2138/am.2010.3217

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In addition, the few experimental studies designed to isolate the effects of temperature (e.g., Kress and Carmichael, 1988; Moore et al., 1995; Borisov and McCammon, 2010; Aithala et al., 2026) have spanned relatively narrow intervals (≤350 K).
View in article

Borisov, A., Behrens, H., Holtz, F. (2018) Ferric/ferrous ratio in silicate melts: A new model for 1 atm data with special emphasis on the effects of melt composition. Contributions to Mineralogy and Petrology 173, 98. https://doi.org/10.1007/s00410-018-1524-8

Show in context

The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
View in article
Estimates of ΔG_T,P₀ can be derived empirically from experiments on iron-bearing molten silicates by the simplified expression,
Eq. 3.
where a and b are regressed coefficients (Sack et al. 1981; Kilinc et al. 1983; Borisov et al. 2018).
View in article
Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
Eq. 5.

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Previous models, parameterised from smaller temperature intervals and not optimised for a martian composition, do not reproduce the s as well as Eqs. 7–9, which are calibrated from the present experiments. However, parameterisations from Kress and Carmichael (1991), Jayasuriya et al. (2004; Eq. 12), and Borisov et al. (2018) match experimental values within experimental uncertainties.
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Castle, N., Herd, C.D.K. (2017) Experimental petrology of the Tissint meteorite: Redox estimates, crystallization curves, and evaluation of petrogenetic models. Meteoritics & Planetary Science 52, 125–146. https://doi.org/10.1111/maps.12739

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We consider the redox evolution of shergottites that have undergone significant f_O2 increase during differentiation, as recorded by oxybarometry of early and late crystallised mineral assemblages (Tissint — Castle and Herd, 2017; Northwestern Africa (NWA) 6234 — Gross et al., 2013 ; Northwestern Africa (NWA) 1068/1100 — Herd 2006), and calculate their f_O2 evolution from unbuffered, isochemical cooling following the scenario presented in Aithala et al. (2026).
View in article

Cottrell, E., Birner, S.K., Brounce, M., Davis, F.A., Waters, L.E., Kelley, K.A. (2021) Oxygen fugacity across tectonic settings. In: Moretti, R., Neuville, D.R. (Eds.) Magma Redox Geochemistry. American Geophysical Union Geophysical Monograph Series 266, John Wiley & Sons, Inc., Hoboken, NJ, 33–61. https://doi.org/10.1002/9781119473206.ch3

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The redox speciation of multivalent cations, especially iron, has a significant influence on igneous mass transfer and phase equilibria (Cottrell et al., 2021 and references therein).
View in article
Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012, 2022; Deng et al., 2020; Henningsen et al., 2025).
View in article

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M. (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Communications 11, 2007. https://doi.org/10.1038/s41467-020-15757-0

Show in context

The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
View in article
Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012, 2022; Deng et al., 2020; Henningsen et al., 2025).
View in article
An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
View in article
Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
View in article
The Jayasuriya et al. (2004; Eq. 10), Righter et al. (2013), and Deng et al. (2020) models yield systematic discrepancies.
View in article
Previous models applied to magma ocean redox (e.g., Deng et al. 2020; Hirschmann, 2022; Zhang et al. 2024, and references therein) reproduce Fe³⁺/Fe^T ratios from experiments at lower temperatures (1250–1500 °C), but when extrapolated to magma ocean temperatures, predict dramatically different Fe³⁺/Fe^T (Hirschmann, 2022).
View in article
Applied at 100 kPa, 2500–4000 K at 2 logf_O2 units below iron-wüstite (IW-2) (logf_O2-2500 K = −6.34, logf_O2-4000 K = −2.41; Hirschmann, 2021), it predicts Fe³⁺/Fe^T ratios of 0.020–0.046 (Fig. 4), similar to that predicted by Kress and Carmichael (1991) (0.019–0.041) and greater than the models of Jayasuriya et al. (2004) Equation 10 (0.0046–0.0050) and Deng et al. (2020) (0.007–0.032).
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Fiquet, G., Gillet, P., Richet, P. (1992) Anharmonicity and high-temperature heat capacity of crystals: the examples of Ca₂GeO₄, Mg₂GeO₄ and CaMgGeO₄ olivines. Physics and Chemistry of Minerals 18, 469–479. https://doi.org/10.1007/BF00200970

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Potentially, the assumption of a constant ΔC_p value is not appropriate, as the effects of anharmonicity may be important at very high temperatures (Fiquet et al., 1992) Although all Equations 7–9 are similarly accurate and precise, we favour Equation 8 for modelling Fe³⁺/Fe²⁺ and f_O2 systematics at all temperatures as it accounts for a non-zero ΔC_p, established from independent calorimetric measurements.
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Gross, J., Filiberto, J., Herd, C.D.K., Daswani, M.M., Schwenzer, S.P., Treiman, A.H. (2013) Petrography, mineral chemistry, and crystallization history of olivine‐phyric shergottite NWA 6234: A new melt composition. Meteoritics & Planetary Science 48, 854–871. https://doi.org/10.1111/maps.12092

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We consider the redox evolution of shergottites that have undergone significant f_O2 increase during differentiation, as recorded by oxybarometry of early and late crystallised mineral assemblages (Tissint — Castle and Herd, 2017; Northwestern Africa (NWA) 6234 — Gross et al., 2013 ; Northwestern Africa (NWA) 1068/1100 — Herd 2006), and calculate their f_O2 evolution from unbuffered, isochemical cooling following the scenario presented in Aithala et al. (2026).
View in article

Herd, C.D.K. (2006) Insights into the redox history of the NWA 1068/1110 martian basalt from mineral equilibria and vanadium oxybarometry. American Mineralogist 91, 1616–1627. https://doi.org/10.2138/am.2006.2104

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We consider the redox evolution of shergottites that have undergone significant f_O2 increase during differentiation, as recorded by oxybarometry of early and late crystallised mineral assemblages (Tissint — Castle and Herd, 2017; Northwestern Africa (NWA) 6234 — Gross et al., 2013 ; Northwestern Africa (NWA) 1068/1100 — Herd 2006), and calculate their f_O2 evolution from unbuffered, isochemical cooling following the scenario presented in Aithala et al. (2026).
View in article

Herd, C.D.K. (2019) Reconciling redox: Making spatial and temporal sense of oxygen fugacity variations in martian igneous rocks. 50th Lunar and Planetary Institute Science Conference, Abstract #2746.

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For the former, one case of interest is redox variations during petrologic evolution of martian basalts, which are more pronounced than their terrestrial equivalents (Herd, 2019; Aithala et al. 2026).
View in article

Hirschmann, M.M. (2012) Magma ocean influence on early atmosphere mass and composition. Earth and Planetary Science Letters 341–344, 48–57. https://doi.org/10.1016/j.epsl.2012.06.015

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Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012, 2022; Deng et al., 2020; Henningsen et al., 2025).
View in article

Hirschmann, M.M. (2021) Iron-wüstite revisited: A revised calibration accounting for variable stoichiometry and the effects of pressure. Geochimica et Cosmochimica Acta 313, 74–84. https://doi.org/10.1016/j.gca.2021.08.039

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Applied at 100 kPa, 2500–4000 K at 2 logf_O2 units below iron-wüstite (IW-2) (logf_O2-2500 K = −6.34, logf_O2-4000 K = −2.41; Hirschmann, 2021), it predicts Fe³⁺/Fe^T ratios of 0.020–0.046 (Fig. 4), similar to that predicted by Kress and Carmichael (1991) (0.019–0.041) and greater than the models of Jayasuriya et al. (2004) Equation 10 (0.0046–0.0050) and Deng et al. (2020) (0.007–0.032).
View in article
Fe³⁺/Fe^T ratios predicted for Humphrey silicate liquid at 100 kPa, logf_O2 = IW-2 (Hirschmann, 2021) at temperatures ranging from 1500–4000 K calculated from thermodynamic models that incorporate non-zero values of ΔC_P (see Fig. 1).
View in article

Hirschmann, M.M. (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochimica et Cosmochimica Acta, 328, 221–241. https://doi.org/10.1016/j.gca.2022.04.005

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Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
View in article
Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012, 2022; Deng et al., 2020; Henningsen et al., 2025).
View in article
Recent studies pertaining to magma oceans have considered redox conditions in melts equilibrating with core-destined Fe alloy and found, at these extreme conditions (>2500 K), temperature may have a pronounced effect on Fe³⁺/Fe²⁺ ratios (Hirschmann, 2022; Henningsen et al., 2025) and may contribute significantly to the relatively oxidised conditions established during Earth’s mantle solidification.
View in article
However, large differences in Fe³⁺/Fe²⁺ ratios calculated from different models (Hirschmann, 2022) arise because of uncertainties in extrapolation to high temperature from experimental constraints, which are limited to <1650 °C.
View in article
An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
                                                                                                            Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
View in article
The influence of the ΔC_P term on calculated Fe³⁺/Fe²⁺ ratios is small at temperatures <1650 °C, but as noted by Hirschmann (2022) can significantly enhance predicted Fe³⁺/Fe²⁺ ratios in extrapolations above 2000 K.
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Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
                                                                                                            Eq. 5.

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At constant composition and f_O2, we regress 3 weighted-least squares equations: one with a regressed h-coefficient where ΔC_p ≡ 0, (Eq. 7), one with a regressed h-coefficient and fixed ΔC_p (adopted from Hirschmann, 2022) (Eq. 8), and finally fitting both h- and ΔC_p terms (Eq. 9):
                                                                                                            Eq. 7.

                                                                                                            Eq. 8.

                                                                                                            Eq. 9.
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Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
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The Hirschmann (2022) model reproduces VF series well but overestimate ALLF
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The Hirschmann (2022) model overestimates are likely the result of low temperature Fe³⁺/Fe²⁺ data points being fit with a small h-coefficient combined with superimposition of an independently derived, positive ΔC_p term, resulting in positive deviations at elevated temperatures.
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Ultimately, a well defined value of ΔC_p may not be resolvable from the present data; i.e. Hirschman (2022) noted that the effects of ΔC_p should be pronounced at temperatures well above 2000 K.
View in article
Redox conditions in deep magma oceans may be established at extreme temperatures (>3500 K, Hirschmann, 2022; Henningsen et al., 2025) or yet higher on Super-Earths (Young et al., 2024), and so the effect of elevated temperature on silicate melt Fe³⁺/Fe^T at these conditions may be substantial.
View in article
Previous models applied to magma ocean redox (e.g., Deng et al. 2020; Hirschmann, 2022; Zhang et al. 2024, and references therein) reproduce Fe³⁺/Fe^T ratios from experiments at lower temperatures (1250–1500 °C), but when extrapolated to magma ocean temperatures, predict dramatically different Fe³⁺/Fe^T (Hirschmann, 2022).
View in article
However, the Hirschmann (2022) model predicts significantly greater ratios (0.039–0.116), which are likely not realistic.
View in article
A modest effect of extreme temperature on magmatic Fe³⁺/Fe^T indicates that the increase in Fe³⁺/Fe^T ratios found in high temperature-pressure experiments (Armstrong et al., 2019; Kuwahara et al., 2023; Zhang et al., 2024) are owed primarily to the effect of pressure and that models incorporating strong temperature dependent effects on the Fe³⁺/Fe^T of the crystallised mantle (Hirschmann, 2022; Zhang et al. 2024) will require re-examination.
View in article

Henningsen, E.L., Korenaga, J., Marchi, S. (2025) Impact driven redox stratification of Earth’s mantle. Journal of Geophysical Research: Solid Earth 130, e2024JB030817. https://doi.org/10.1029/2024JB030817

Show in context

Two igneous processes in which the temperature dependence of Fe³⁺/Fe²⁺ in magmas is key are redox evolution associated with magmatic cooling and differentiation (Cottrell et al., 2021) and the establishment of oxidised planetary mantles in deep magma oceans (Hirschmann, 2012, 2022; Deng et al., 2020; Henningsen et al., 2025).
View in article
Recent studies pertaining to magma oceans have considered redox conditions in melts equilibrating with core-destined Fe alloy and found, at these extreme conditions (>2500 K), temperature may have a pronounced effect on Fe³⁺/Fe²⁺ ratios (Hirschmann, 2022; Henningsen et al., 2025) and may contribute significantly to the relatively oxidised conditions established during Earth’s mantle solidification.
View in article
Redox conditions in deep magma oceans may be established at extreme temperatures (>3500 K, Hirschmann, 2022; Henningsen et al., 2025) or yet higher on Super-Earths (Young et al., 2024), and so the effect of elevated temperature on silicate melt Fe³⁺/Fe^T at these conditions may be substantial.
View in article
Further, if the temperature dependence of Fe³⁺/Fe^T is strong, then the potential temperature of magma ocean may strongly influence the Fe³⁺/Fe^T of the resulting solidified mantle (Henningsen et al., 2025).
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Recently, Henningsen et al. (2025) argued that melt-alloy equilibration during alloy rain-out (at super-liquidus conditions) produces significantly greater Fe³⁺/Fe^T ratios than equilibration at the base of a MO, at near-liquidus conditions, but this conclusion is based on a strongly temperature dependent model that may not be accurate.
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Jayasuriya, K.D., O’Neill, H.St.C., Berry, A.J., Campbell, S.J. (2004) A Mössbauer study of the oxidation state of Fe in silicate melts. American Mineralogist 89, 1597–1609. https://doi.org/10.2138/am-2004-11-1203

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
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An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
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Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
Eq. 5.

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Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
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Previous models, parameterised from smaller temperature intervals and not optimised for a martian composition, do not reproduce the s as well as Eqs. 7–9, which are calibrated from the present experiments. However, parameterisations from Kress and Carmichael (1991), Jayasuriya et al. (2004; Eq. 12), and Borisov et al. (2018) match experimental values within experimental uncertainties.
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The Jayasuriya et al. (2004; Eq. 10), Righter et al. (2013), and Deng et al. (2020) models yield systematic discrepancies.
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Applied at 100 kPa, 2500–4000 K at 2 logf_O2 units below iron-wüstite (IW-2) (logf_O2-2500 K = −6.34, logf_O2-4000 K = −2.41; Hirschmann, 2021), it predicts Fe³⁺/Fe^T ratios of 0.020–0.046 (Fig. 4), similar to that predicted by Kress and Carmichael (1991) (0.019–0.041) and greater than the models of Jayasuriya et al. (2004) Equation 10 (0.0046–0.0050) and Deng et al. (2020) (0.007–0.032).
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Kilinc, A., Carmichael, I.S.E., Rivers, M.L., Sack, R.O. (1983) The ferric-ferrous ratio of natural silicate liquids equilibrated in air. Contributions to Mineralogy and Petrology 83, 136–140. https://doi.org/10.1007/bf00373086

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Estimates of ΔG_T,P₀ can be derived empirically from experiments on iron-bearing molten silicates by the simplified expression,
Eq. 3.
where a and b are regressed coefficients (Sack et al. 1981; Kilinc et al. 1983; Borisov et al. 2018).
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Kress, V.C., Carmichael, I.S.E. (1988) Stoichiometry of the iron oxidation reaction in silicate melts. American Mineralogist 73, 1267–1274.

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In addition, the few experimental studies designed to isolate the effects of temperature (e.g., Kress and Carmichael, 1988; Moore et al., 1995; Borisov and McCammon, 2010; Aithala et al., 2026) have spanned relatively narrow intervals (≤350 K).
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Kress, V.C., Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe₂O₃ and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology 108, 82–92. https://doi.org/10.1007/Bf00307328

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
View in article
An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
View in article
Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
Eq. 5.

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Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
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Previous models, parameterised from smaller temperature intervals and not optimised for a martian composition, do not reproduce the s as well as Eqs. 7–9, which are calibrated from the present experiments. However, parameterisations from Kress and Carmichael (1991), Jayasuriya et al. (2004; Eq. 12), and Borisov et al. (2018) match experimental values within experimental uncertainties.
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Notably, this model is very similar in both form and values to Kress and Carmichael (1991; h-coefficient = 5235 vs. 4991, ΔC_p = 33.25 vs. 27.9 J/K) suggesting that their model extrapolates well to temperatures beyond its calibration dataset.
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Applied at 100 kPa, 2500–4000 K at 2 logf_O2 units below iron-wüstite (IW-2) (logf_O2-2500 K = −6.34, logf_O2-4000 K = −2.41; Hirschmann, 2021), it predicts Fe³⁺/Fe^T ratios of 0.020–0.046 (Fig. 4), similar to that predicted by Kress and Carmichael (1991) (0.019–0.041) and greater than the models of Jayasuriya et al. (2004) Equation 10 (0.0046–0.0050) and Deng et al. (2020) (0.007–0.032).
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Kuwahara, H., Nakada, R., Kadoya, S., Yoshino, T., Irifune, T. (2023) Hadean mantle oxidation inferred from melting of peridotite under lower-mantle conditions. Nature Geoscience 16, 461–465. https://doi.org/10.1038/s41561-023-01169-4

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
A modest effect of extreme temperature on magmatic Fe³⁺/Fe^T indicates that the increase in Fe³⁺/Fe^T ratios found in high temperature-pressure experiments (Armstrong et al., 2019; Kuwahara et al., 2023; Zhang et al., 2024) are owed primarily to the effect of pressure and that models incorporating strong temperature dependent effects on the Fe³⁺/Fe^T of the crystallised mantle (Hirschmann, 2022; Zhang et al. 2024) will require re-examination.
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Lange, R.A., Navrotsky, A. (1992) Heat capacities of Fe₂O₃-bearing silicate liquids. Contributions to Mineralogy and Petrology 110, 311–320. https://doi.org/10.1007/BF00310746

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An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
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A negative value of ΔC_p conflicts with calorimetric studies of Fe-bearing silicate liquids (Stebbins et al., 1984; Lange and Navrotsky, 1992) and this specific value is not statistically significant, nor does its inclusion improve the fit from the linear Equation 7 model from the perspective of reduced chi square (Table S-4).
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McSween, H.Y., Ruff, S.W., Morris, R.V., Bell, J.F., Herkenhoff, K., Gellert, R., Stockstill, K.R., Tornabene, L.L., Squyres, S.W., Crisp, J.A., Christensen, P.R., McCoy, T.J., Mittlefehldt, D.W., Schmidt, M. (2006) Alkaline volcanic rocks from the Columbia Hills, Gusev crater, Mars. Journal of Geophysical Research: Planets 111, E09S91. https://doi.org/10.1029/2006je002698

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Starting mixes similar to martian basalt Humphrey (McSween et al., 2006; Aithala et al., 2026) were synthesised from high purity reagents for super-liquidus 100 kPa experiments in vertical gas mixing (VF) and aerodynamic-laser-levitation furnace (ALLF) experiments (Table S-1).
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Moore, G., Righter, K., Carmichael, I.S.E. The effect of dissolved water on the oxidation state of iron in natural silicate liquids. Contributions to Mineralogy and Petrology 120, 170–179 (1995) https://doi.org/10.1007/BF00287114

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In addition, the few experimental studies designed to isolate the effects of temperature (e.g., Kress and Carmichael, 1988; Moore et al., 1995; Borisov and McCammon, 2010; Aithala et al., 2026) have spanned relatively narrow intervals (≤350 K).
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Righter, K., Danielson, L.R., Pando, K., Morris, R.V., Graff, T.G., Agresti, D.G., Martin, A.M., Sutton, S.R., Newville, M., Lanzirotti, A. (2013) Redox systematics of martian magmas with implications for magnetite stability. American Mineralogist 98, 616–628. https://doi.org/10.2138/am.2013.4251

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
View in article
Previous models of Fe³⁺/Fe²⁺ in magmas, however, predict significantly different temperature dependencies (e.g., Kress and Carmichael, 1991; Righter et al., 2013; Borisov et al., 2018; Deng et al., 2020; Hirschmann, 2022; Aithala et al., 2026).
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Experimental studies of Fe redox systematics of Fe-rich, martian-relevant magmas from Righter et al. (2013) and Aithala et al. (2026) found that Fe³⁺/Fe²⁺ ratios of these magmas are more sensitive to temperature than Fe-poor silicate liquids. Aithala et al. (2026) concluded that this increased temperature sensitivity could drive significant f_O2 increases relative to standard redox buffers during magmatic cooling and hypothesised that this effect could account for a significant fraction of the f_O2 increases measured within and across martian basalts.
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Following previous work (e.g., Sack et al., 1981; Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013, Borisov et al., 2018; Hirschmann, 2022; Aithala et al., 2026), we combine Equations 2 and 4, replace the logf_O2 stoichiometric coefficient with an empirical parameter, k, the inverse temperature coefficient from Equation 4 with h, and the term with a simple compositional term, ∑d_iX_i, to yield the expression,
Eq. 5.

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Data are compared to thermodynamic models from this study (Eqs. 7–9) and previous parameterisations calculated at logf_O2 = −0.68, P₀ (100 kPa) and average Humphrey composition (Table S-2). KC91 = Kress and Carmichael (1991), J04_10 and J04_12 = Jayasuriya et al., (2004), Eqs. 10 and 12; R13 = Righter et al., (2013), D20 = Deng et al., (2020), H22 = Hirschmann (2022), A26 = Aithala et al., (2026).
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The Jayasuriya et al. (2004; Eq. 10), Righter et al. (2013), and Deng et al. (2020) models yield systematic discrepancies.
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Previous work by Righter et al. (2013) and Aithala et al. (2026) found enhanced temperature sensitivity (i.e. smaller h-coefficient) for martian magmas as compared to models calibrated from terrestrial or simplified-composition silicate liquids.
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The newly regressed h-coefficient of 4894 K from Equation 7 from experiments at 1250–2100 °C is greater than h-coefficient of 3775 K found by Aithala et al.(2026) for the same composition (1250–1500 °C) and significantly exceeds the 1650 K value determined for a shergottitic composition (1300–1500 °C; Righter et al., 2013).
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In addition, the h-coefficient derived from the present study is also consistent with previously investigated compositions despite elevated FeO*, suggesting that compositional influence on the h-coefficient is not supported, despite previous conclusions from Righter et al. (2013) and Aithala et al. (2026).
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Sack, R.O., Carmichael, I.S.E., Rivers, M., Ghiorso, M.S. (1981) Ferric-ferrous equilibria in natural silicate liquids at 1 bar. Contributions to Mineralogy and Petrology 75, 369–376. https://doi.org/10.1007/bf00374720

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Estimates of ΔG_T,P₀ can be derived empirically from experiments on iron-bearing molten silicates by the simplified expression,
Eq. 3.
where a and b are regressed coefficients (Sack et al. 1981; Kilinc et al. 1983; Borisov et al. 2018).
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Stebbins, J.F., Carmichael, I.S.E., Moret, L.K. (1984) Heat capacities and entropies of silicate liquids and glasses. Contributions to Mineralogy and Petrology 86, 131–148. https://doi.org/10.1007/bf00381840

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An expanded version of Equation 3 explicitly accounts for distinct heat capacities (C_p) of FeO and FeO_1.5 in molten silicates (Kress and Carmichael, 1991; Jayasuriya et al., 2004; Deng et al., 2020; Hirschmann, 2022):
Eq. 4.
where ΔC_P = C_P^FeO_1.5−C_P^FeO−0.25C_P^O₂ and T₀ is a reference temperature (generally 1673 K). The value ΔC_P can be derived from calorimetric studies of iron-bearing silicate liquids (27.9 ± 1 0.4 J/K, Stebbins et al., 1984; or 33.25 ± 6.06 J/K, Lange and Navrotsky et al., 1992).
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A negative value of ΔC_p conflicts with calorimetric studies of Fe-bearing silicate liquids (Stebbins et al., 1984; Lange and Navrotsky, 1992) and this specific value is not statistically significant, nor does its inclusion improve the fit from the linear Equation 7 model from the perspective of reduced chi square (Table S-4).
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Young, E.D., Stixrude, L., Rogers, J.G., Schlichting, H.E., Marcum, S.P. (2024) Phase Equilibria of Sub-Neptunes and Super-Earths. The Planetary Science Journal 5, 268. https://doi.org/10.3847/psj/ad8c40

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Redox conditions in deep magma oceans may be established at extreme temperatures (>3500 K, Hirschmann, 2022; Henningsen et al., 2025) or yet higher on Super-Earths (Young et al., 2024), and so the effect of elevated temperature on silicate melt Fe³⁺/Fe^T at these conditions may be substantial.
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Zhang, H.L., Hirschmann, M.M., Cottrell, E., Withers, A.C. (2017) Effect of pressure on Fe3+/ΣFe ratio in a mafic magma and consequences for magma ocean redox gradients. Geochimica et Cosmochimica Acta 204, 83–103. https://doi.org/10.1016/j.gca.2017.01.023

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
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Zhang, H.L., Hirschmann, M.M., Lord, O.T., Rosenthal, A., Yaroslavtsev, S., Cottrell, E., Chumakov, A.I., Walter, M.J. (2024) Ferric iron stabilization at deep magma ocean conditions. Science Advances 10, eadp1752. https://doi.org/10.1126/sciadv.adp1752

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The iron redox speciation, quantified as the Fe³⁺/Fe²⁺ ratio, in magmas is primarily controlled by the chemical potential of oxygen (generally quantified by oxygen fugacity, f_O2), but also influenced by temperature, pressure, and melt composition. The effects of melt composition have been investigated extensively (e.g., Kress and Carmichael, 1991; Jayasuriya et al., 2004; Righter et al., 2013; Borisov et al., 2018; Aithala et al., 2026) and the effect of pressure has garnered considerable recent attention (Zhang et al., 2017, 2024; Armstrong et al., 2019; Deng et al., 2020; Kuwahara et al., 2023).
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Previous models applied to magma ocean redox (e.g., Deng et al. 2020; Hirschmann, 2022; Zhang et al. 2024, and references therein) reproduce Fe³⁺/Fe^T ratios from experiments at lower temperatures (1250–1500 °C), but when extrapolated to magma ocean temperatures, predict dramatically different Fe³⁺/Fe^T (Hirschmann, 2022).
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Without it, models calibrated from very high temperature, high pressure — e.g., experiments from Zhang et al. (2024) at 38–71 GPa and 3600–4400 K — could mis-attribute the effects of temperature and pressure.
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A modest effect of extreme temperature on magmatic Fe³⁺/Fe^T indicates that the increase in Fe³⁺/Fe^T ratios found in high temperature-pressure experiments (Armstrong et al., 2019; Kuwahara et al., 2023; Zhang et al., 2024) are owed primarily to the effect of pressure and that models incorporating strong temperature dependent effects on the Fe³⁺/Fe^T of the crystallised mantle (Hirschmann, 2022; Zhang et al. 2024) will require re-examination.
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Supplementary Information

The Supplementary Information includes:

1. Methods
2. Results
3. Recalculating experiments to common oxygen fugacity and melt composition
4. Applying temperature Equations 7–9 to model silicate liquids of differing compositions and fO2s
Tables S-1 to S-5
Figures S-1 to S-3
Supplementary Information References

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