Main

The concept of deep magma oceans covering parts of the Earth during its earliest history is well established. Evidence that supports the development of such oceans includes energy balance calculations of large impacts1,2,3, a wide range of geochemical data including the observed siderophile element depletions of the silicate mantle and the tungsten isotopic signature of mantle rocks4,5,6,7,8,9. Canonical geochemical models for core formation argue that the mantle depletion of siderophile elements reflects chemical equilibration between molten metal and molten mantle silicate at pressures and temperatures that are assumed to coincide with conditions near the floors of magma oceans8,9,10,11,12,13,14,15,16.

One major problem with magma ocean formation models is that experimental data on the solidus of deep primitive mantle materials have not converged to accepted values to date (Fig. 1)17,18,19,20. In core formation models attempting to explain siderophile element depletions14,15,16,21, the mantle solidus parametrization based on experiments of Andrault et al.20 is commonly used, but more recent results differ by up to 200–250 °C (ref. 18) and ~400 °C (ref. 22). In addition, some recent studies have indicated that fO2 may strongly affect the solidus and liquidus of natural rock compositions containing redox-sensitive compounds such as iron and carbonate23,24. At ambient pressure, oxygen fugacity may even affect melting behaviour in systems without any redox-sensitive compounds25.

Fig. 1: The solidus temperature profile of primitive materials in Earth’s mid-mantle pressure range at different oxygen fugacities.
figure 1

Closed diamonds: this study (pyrolite composition at fO2 = IW + 2.0), including ±50 °C uncertainties (described in the note of Table 1); open diamonds: Ishii et al.19 (minimum solidus temperatures, indicated by the red arrows, for a pyrolite composition at estimated IW − 1.2); open circles: Herzberg et al.17 (KLB-1 peridotite composition, estimated IW − 1.2); open squares: Andrault et al.20 (chondritic mantle composition, oxygen fugacity not determined but more oxidized than IW − 1.2); crosses: Pierru et al.22 (pyrolitic mantle composition, oxygen fugacity estimated to be about IW + 2). All data are presented as mean values with ± standard errors (the latter when provided by the authors; Source Data Fig. 1). Dashed lines show predicted solidi at fO2 conditions invoked in siderophile element-based core formation models (IW − 1, IW − 2 and IW − 4), predicted based on equation (1).

Source data

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It is now generally accepted that the oxygen fugacity in Earth’s mantle varied significantly during accretion and core formation as Earth was forming and subsequently during mantle evolution. Core formation studies indicate that the mantle depletions of siderophile elements can be explained in scenarios where either oxygen fugacity in deep magma oceans increases during accretion from highly reducing levels of ~IW − 4 to IW − 2 (refs. 8,16,21,26; IW, iron-wüstite) or oxygen fugacity decreases from IW − 1 to IW − 2 (ref. 12). Subsequently further oxidation of the upper mantle occurs27,28,29, leading to the present-day mantle oxygen fugacity of ~IW + 4 (ref. 30). Here we quantify the effect of fO2 on the solidus of a primitive mantle composition at mantle transition zone pressures to constrain the conditions at the floor of a deep terrestrial magma ocean. We conducted melting experiments at pressures equivalent to mantle depths between ~470 km and ~720 km using a typical mantle pyrolite composition31 at oxidizing conditions (IW + 2).

High-pressure experiments

A series of experiments were performed by using a multi-anvil press double capsule technique at pressures of 16–26 GPa, with a mixture of magnetite and haematite (MH) crystals in the outer capsules. In two additional experiments (one with a rhenium capsule, one with the double capsule set-up used for the MH-bearing experiments), we added small iridium (Ir) grains to serve as a sliding oxygen fugacity sensor24,32,33, to quantify the oxygen fugacity both in our experiments and those in literature data melting experiments using more reducing Re capsules19,34,35,36. All experiments were run at nominally anhydrous conditions. Details of starting material synthesis, experimental design and conditions of our experiments and oxygen fugacity calculations are given in Methods.

Results are summarized in Table 1 and Supplementary Table 1. The chemical compositions of minerals and silicate melts of all experiments, representative backscatter electron microscope images of samples and phase assemblages of each sample are shown in Methods, Supplementary Table 1 and Extended Data Figs. 1 and 2, respectively.

Table 1 Summary of experimental results
Full size table

At 16 GPa and 1,600 °C, below the pyrolite solidus, the mineral assemblage is composed of wadsleyite and garnet. At 1,700 °C at this pressure, melt is present and the phase assemblage is wadsleyite + garnet + melt (2 wt%). At 1,800 °C, the phase assemblage is garnet + wadsleyite + melt (14 wt%). At 21 GPa and 1,800 °C, the mineral assemblage is ringwoodite + garnet. At 1,900 °C, just above the solidus, the phase assemblage is ringwoodite + garnet + ferropericlase + melt (1 wt%). At 2,000 °C, only garnet survives and the melt percentage increases to 82 wt%. Finally, at 26 GPa, the mineral assemblages at the subsolidus temperatures of 1,700, 1,900 and 2,000 °C are the same and composed of bridgmanite + ferropericlase + CaSiO3-rich perovskite (davemaoite)37. At 2,100 °C, the solidus has been crossed. The solid phase assemblage stays the same and the melt percentage is about 3 wt%. The mineral assemblages below the solidus are consistent with previous subsolidus work on pyrolite in this pressure range19.

One of the Ir-bearing experiments (26 GPa, 1,900 °C) shows that the fO2 of the double capsule experiments is IW + 2.0 ( ± 0.1). This is lower than expected from a simple extrapolation of the low-pressure, low-temperature calibration of the fO2 at the MH buffer. This could in part be due to the fact that both magnetite and haematite experience phase transitions at high pressure. In addition, because of the deliberately low water contents in our nominally anhydrous experiments, we cannot prove that the fH2 in the inner and outer capsule are equal (a prerequisite for the buffering of oxygen fugacity to occur). The second Ir-bearing experiment in a Re capsule (26 GPa, 2,200 °C) yields an fO2 of IW − 1.2 ( ± 0.2). The fO2 value below IW indicates that iron should be partially metallic in such experiments. As discussed in the Supplementary Information, some metallic iron, dissolved in the Re capsule (Extended Data Fig. 3), is indeed present in our Ir-bearing experiment and has also been reported in previous high-pressure studies using Re capsules36,38.

Effect of oxygen fugacity on deep mantle solidus

Figure 1 shows that changing the oxygen fugacity by three log units significantly affects the pyrolite solidus at mid-mantle pressures. At IW + 2.0, the solidus of the pyrolite composition is bracketed to TIW+2.0sol = 1,680 ± 25 °C at 16 GPa, 1,900 ± 25 °C at 21 GPa and 2,050 ± 50 °C at 26 GPa. Ishii et al.19 performed experiments on the same pyrolite composition in rhenium capsules (IW − 1.2) yielding minimum solidi TIW−1.2sol = 2,135 °C at 16 GPa, 2,230 °C at 21 GPa and 2,280 °C at 26 GPa (Fig. 2). In our study, the solidus is thus significantly lower, by >450 °C at 16 GPa, >330 °C at 21 GPa and >230 °C at 26 GPa, all due to an increase by 3.2 log units in fO2.

Fig. 2: Comparison between temporal evolutions of Earth’s mantle temperature and the mantle solidus at different pressures.
figure 2

a, 16 GPa (470 km depth). b, 21 GPa (580 km depth). c, 26 GPa (710 km depth). Closed symbols are calculated using equation (1), based on core formation at 4.5 Ga proceeding from IW − 4 (ref. 26) or IW − 1 (ref. 12) to IW − 2 (ref. 52), followed by mantle self-oxidation according to Stagno and Fei30. The fO2 used for the open symbols in a–c is the highest fO2 value of natural samples at the corresponding ages53,54. The other fO2 buffers relative to IW (Fe-FeO) are expressed as FMQ = IW + 4 log units (FMQ: Fe2SiO4-Fe3O4-SiO2)56. The dashed lines in panels a–c show mantle temperature evolution curves derived from surface potential temperatures Tp of 1,750, 1,725, 1,700, 1,650 and 1,610 °C at 4, 3.5, 3, 2.5 and 2 Ga (refs. 46,47). Adiabatic temperature gradients of 0.45 °C km−1 (<410 km depth), 0.4 °C km−1 (410–660 km depth) and 0.35 °C km−1 (>660 km depth), and changes of adiabatic temperature by 60 °C at 410 km, by 43 °C at 520 km and by −34 °C at 660 km from Katsura et al.57 were adopted to calculate mantle temperatures. All data are presented as mean values. The error bars of modelled temperatures are ±110 °C from equation (1) (Source Data Fig. 2).

Source data

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Our experiments and those of Ishii et al.19 were performed using the same high-pressure assembly design both in terms of materials and dimensions and using the same pressure calibration methods. Interlaboratory differences in assembly characteristics and pressure–temperature calibration (which do exist39) cannot cause the observed difference. Our results indicate that the oxygen fugacity-induced shift of the pyrolite solidus is significant from the mantle transition zone to the top of the lower mantle and that the increase of the solidus over a decrease of 3.2 log fO2 units fO2 is at least 340 ± 110 °C, on average, over this depth range. This is equivalent to moving the floor of a magma ocean at a given temperature down by ~200 km over this fO2 range.

This strong sensitivity is probably due to a combination of pressure and compositional effects. The enhanced stability of melt over minerals at a given pressure and temperature as fO2 is increased must be related to higher abundances of incompatible elements at oxidized conditions. The increased abundances of trivalent iron (and perhaps oxygen itself)25,40,41 in our IW + 2.0 experiments lower the activities of the other (cation-bearing) components in silicate melt compared with lower-fO2 experiments, increasing melt stability. Qualitatively, similar shifts towards lower melting temperatures at higher fO2 were identified in experiments on an iron-rich simplified mantle composition at pressures and temperatures comparable to ours23, but the fO2 conditions were not quantified in this case. At lower pressures, Shahar et al.24 found a 200 °C drop in solidus temperature when fO2 changes from IW + 2.5 to IW + 4.5 in a carbonated mantle composition at 2 GPa. This is comparable in magnitude to our result and suggests the fO2 effects are not restricted to the IW − 1.2 to IW + 2.0 range.

Our finding may help explain why the high-pressure solidi of pyrolite22 and of chondrite18 are 200–400 °C lower than earlier works17,34,42,43. Although Pierru et al.22 and Andrault et al.18 did not determine the fO2 in their run products, their synthetic starting material contained significant amounts of Fe3+, and their experiments were surrounded by MgO capsules. This probably imposed higher fO2 (potentially similar to the fO2 of IW + 2 observed in our double capsule experiments) than in earlier experimental solidus studies that used more reducing rhenium or graphite capsules17,18,42,43.

Implications for core formation models

Core formation models that try and explain the observed siderophile element depletions in Earth’s mantle all invoke significant mantle oxygen fugacity increases and/or decreases during Earth accretion and core formation, due to temporal variations in the redox state of impactors and lower mantle self-oxidation. Some studies find that observed mantle depletions can be reproduced if initial Earth formation at 4.5 billion years ago (Ga) was characterized by highly reduced conditions, due to early accretion of reduced rocky bodies (IW − 4) (refs. 21,26), with Earth’s mantle fO2 progressively increasing during core formation to ~IW − 2. Other lines of evidence point to the likelihood of a more oxidized start (IW − 1) with the mantle reducing during the core formation process12,13,14. After core formation was complete, further evolution of mantle oxidation state occurred through mantle self-oxidation, until the present-day value (around the fayalite–magnetite–quartz buffer, corresponding to IW + 4) was reached at about 3 Ga (refs. 29,30,44).

Siderophile element-based core formation models all use a single literature solidus parametrization irrespective of mantle fO2 evolution. But extrapolation of our results indicates that Earth’s mantle should have very high solidus temperatures if early accretion and core formation were characterized by very reduced conditions, whereas lower solidi would be more appropriate in models starting with more oxidized building blocks. To estimate the mantle solidus at a given fO2, we performed a simple linear extrapolation of our data and those of Ishii et al.19. Given the small numbers of experiments assessing the effect of fO2 on melting (this study and refs. 23,24), covering very different bulk compositions and pressure ranges, coupled with the limited extent of the extrapolation, we consider this appropriate at this time. The predicted increase in solidus temperature at low fO2 would be smaller if the increase in solidus as a function of fO2 is less than linear. On the other hand, the decrease in silicate FeO content at such low fO2 values would increase solidus temperatures beyond any increases due to low values of fO2 (ref. 45). Linear extrapolation yields:

$${T}_{{\rm{solidus}}}^{\,{f_{\rm{O}}}_{2}}\left(\pm {110\,}^{\circ} {\rm{C}}\right)={{{T}}}_{{\rm{solidus}}}^{\,{\rm{IW}}+2.0}+\frac{340}{3.2}{\Delta \log f_{\rm{O}}}_{2},$$
(1)

with ∆log fO2 the difference in log units between IW + 2.0 and the target fO2. Equation (1) predicts that the solidus of Earth’s mantle at IW − 2 is ~2,105–2,470 °C at 16–26 GPa. At IW − 4, solidus temperatures increase to ~2,320–2,680 °C over this pressure range, whereas at IW − 1 the solidus would be ~2,000–2,370 °C. These values differ substantially compared to existing data (Fig. 1).

Combining equation (1) with the mantle self-oxidation curve summarized in Stagno and Fei30, the evolution of mantle solidus temperatures at pressures between 16 and 26 GPa as a function of time can be calculated for any mantle fO2 evolution trajectory (Fig. 2). Figure 2 also shows estimates of the average mantle temperature at these pressures as a function of time based on geodynamic evolution models46,47. Solidus temperatures at pressures between 16 and 26 GPa exceed mantle temperature estimates by ~300–500 °C over the first 100 Ma of Earth’s history (the time during which core formation occurred11,48) if core formation started reduced, with most extreme differences at the earliest times. Our results indicate that if Earth was as reduced during core formation as proposed in some siderophile element-depletion core formation models5,6,7,8,9,11,15,16, initial temperatures in a deep magma ocean must have been substantially higher than suggested from current geodynamic models.

At an fO2 of IW − 4 (ref. 26), our model suggests the following pressure dependence of the solidus:

$$\,{T}_{{\rm{solidus}}}^{\,{\rm{IW}}-4}\left(\pm 110^\circ {\rm{C}}\right)=36.7\times P\left({\rm{GPa}}\right)+1,740,{{{R}}}^{2}=0.99.$$
(2)

The solidus of the early Earth’s mantle at a pressure of 40 GPa is calculated to be ~3,210 °C, >500 °C higher than the average temperature at the bottom of a magma ocean at this depth of ~2,700 °C used by Wade and Wood16 in their reduced-start core formation model. If the early Earth was as reduced as suggested by these core formation models, very high temperatures would thus be required to form the deep magma oceans in those models. Such temperatures may be feasible due to giant impacts, for example, the Moon-forming impact49,50,51 that has been suggested to have caused the final stage of core–mantle equilibration in Earth48. If core formation started at more oxidizing conditions (~IW − 1), the solidus at 40 GPa would be ~2,900 °C, still higher than assumed in siderophile element-based core formation models. Given the very strong effect of oxygen fugacity on high-pressure mantle melting, models of core formation and the thermal evolution of the early Earth need to be re-evaluated. At a minimum, geochemical models in which oxygen fugacity variations during core formation are assessed should take into account the large variations in mantle melting temperatures that accompany such variations.

Oxidized Archaean magmas

Our results could also provide an explanation for the apparent discrepancy between the modelled low oxygen fugacities predicted for the Earth’s deep mantle after completion of core formation (IW − 2; refs. 33,52) and the high oxygen fugacities observed in Archaean (>3.0 Ga) magmatic rocks formed by deep mantle melting53. Mantle oxygen fugacity estimates from samples >3.0 Ga old, based on V partitioning between olivine and melt in picritic and komatiitic rocks53 and on the Ce content in Hadean zircons, yield high values of up to FMQ + 3.4 (refs. 53,54,55), equivalent to ~ IW + 7.4. These values are ~2–8 log units higher than expected from a linear mantle self-oxidation trend between 4.5 and 3.0 Ga ago, starting at IW − 2 (refs. 26,30). In contrast, in mantle-derived rocks younger than 3.0 Ga, the range of mantle fO2 values derived from a mantle self-oxidation trend and is comparable with the fO2 derived from V/Sc ratios in the samples, around IW + 2 to IW + 6 (ref. 55).

Open symbols in Fig. 2 show the calculated 16, 21 and 26 GPa mantle solidi at the fO2 values observed in Archaean deep mantle-derived samples as a function of time. Before 3 Ga, these solidi are several hundred to >1,000 °C lower than the solidi of the ambient mantles at the corresponding time. After 3 Ga, this difference in solidi is much smaller. We do not claim that all Archaean magmatic samples were formed through mantle melting at mantle pressures in the 16–26 GPa range. However, it is clear from our analysis that oxidized mantle sources are far more likely to melt than more reduced mantle sources. As a result, oxidized magmatic samples are far more likely to be formed than reduced magmatic samples. A heterogeneous distribution of oxygen in Earth’s mantle during the Archaean (after completion of the magma ocean stage) would thus provide a plausible explanation for the discrepancy between the identification of oxidized magmatic samples in a mantle that on average is still reduced.

Finally, we note that if the solidus shifts identified here persist to lower pressures, even minor variations in oxygen fugacity could lead to significant variations in magma production in the Earth and in the mantles of other rocky planets. Magma generation could occur by raising oxygen fugacity without increasing the water and/or CO2 content of mantle sources, and without raising the mantle temperature, and magma production in oxidized mantles (for example, in Mars) could be higher than in more reduced mantles of similar composition.

Methods

Starting materials

The pyrolite starting material is identical to that used in Ishii et al.19. It was prepared by mixing Mg2SiO4 (40.2), MgSiO3 (37.5), Fe2SiO4 (7.1), CaSiO3 (8.0), NaAlSiO4 (1.5), TiO2 (0.3), Al2O3 (4.8), Cr2O3 (0.3) and NiO (0.4), where numbers in parentheses are contents in mol%, which follows the pyrolite composition of McDonough and Sun31, excluding MnO, K2O and P2O5. Mg2SiO4 forsterite, MgSiO3 enstatite, Fe2SiO4 fayalite, CaSiO3 pseudo-wollastonite and NaAlSiO4 carnegieite were first synthesized and prepared for use, with the detailed synthesis methods described in Ishii et al.58. The starting composition powder was stored at 110 °C for at least 24 h before use.

Experiments

Ten high-pressure experiments (Supplementary Table 1) were conducted using a double capsule technique with a fine-grained mixture of magnetite and haematite (MH) in the outer capsule and the starting material in the inner capsule. To quantify oxygen fugacities in these experiments and in experiments from the literature, one additional double capsule experiment contained a mixture of the starting material and fine grains of iridium metal, and a final experiment contained a mixture of the starting material and fine grains of Ir in a Re single capsule. Sample pressures and temperatures ranged between 16 and 26 GPa and 1,600 and 2200 °C, respectively. Experiments were performed with Kawai-type 6–8 multi-anvil presses at Bayerisches Geoinstitut, Universität Bayreuth, Germany. Experiments at 16–21 GPa and 26 GPa were performed using 10- and 12-MN split-sphere-type multi-anvil presses, respectively. Details of the pressure calibrations are shown in Keppler and Frost59. The 15-MN multi-anvil press with the Osugi-type guide block system (IRIS-15)60,61 was used to conduct 26 GPa experiments. Pressure was calibrated in separate runs using the transition of pyrope to bridgmanite plus corundum and alumina content in bridgmanite (ref. 62 provides additional details).

The MH powder was prepared by mixing magnetite and haematite oxide powders (at a mass ratio of ~1:1) in an agate mortar for 60 min to promote mechanical homogeneity. We adopted a double-Pt capsule technique for the experiments. An inner Pt capsule (0.4 mm inner diameter (ID), 0.5 mm outer diameter (OD), 0.6–1.0 mm length), made of a Pt foil with two ends flattened, was loaded with starting material. The inner capsule was inserted into a larger diameter Pt capsule (0.8 mm ID, 1 mm OD, 2 mm length). The MH powder was filled between the inner and outer capsules. Then the outer capsule was closed with two Pt discs (0.8 mm diameter and 0.15 mm thickness) and stored at 150 °C overnight to purge moisture before welding.

Tungsten carbide anvils with 3 mm-truncated edge length (Fujilloy, TF05) and 4 mm-truncated edge length (ha-7%, hawedia) were used in combination with a pressure medium of Cr2O3-doped semi-sintered MgO octahedra with 7 and 10 mm-edge lengths to generate 26 GPa and 16–21 GPa (7/3 and 10/4 assemblies, respectively). A LaCrO3 furnace was put in the central part of the octahedron. Two LaCrO3 and Mo lids were placed at both ends of the heater for 7/3 and 10/4 assemblies, respectively. A ZrO2 thermal insulator sleeve surrounded the heater in the 10/4 assembly. The double-capsuled sample in an MgO sleeve was placed in the central part of the furnace. To monitor the sample temperature, a thermocouple of W5%Re–W26%Re was inserted from the middle of the edges of the octahedron, and its hot junction was set at the centre of the capsule surface. No pressure effect on thermoelectromotive force of the thermocouple was considered.

All experiments were first pressurized to the target pressure at a constant rate taking 4–5 h, and then the temperature supplied by electrical power was raised at a ramp of 100 °C min−1 to aim temperatures of 1,600–2,100 °C. After arrival at the aim temperature, the experiments were kept at constant temperature, and the samples were kept at the targeted pressure and temperature for 0.5–12 h and then quenched by turning off the power. After temperature quench, the press load was slowly decreased for 12–15 h, and the cell assembly was recovered to room pressure–temperature conditions.

Analytical techniques

Experimental run products were mounted in epoxy, polished and carbon-coated for back-scattered electron (BSE) imagery used to assess the texture and mineralogy and for quantitative compositional measurements using electron microprobe analysis (EMPA). Texture of the recovered samples was observed using a field-emission-type scanning electron microscope (SEM) (Zeiss LEO 1530 Gemini) with a detector for BSE imaging and an energy dispersive X-ray spectrometer (Oxford X-MaxN). The chemical composition of the run product phases (minerals, melts and metals) was determined using a JEOL JXA-8800M Electron Microprobe at the Testing Center of Shandong Bureau of China Metallurgical Geology Bureau and checked for contamination. For minerals and melts, the analysis process used an accelerating voltage of 15 kV and a beam current of 20 nA for Si, Ti, Al, Cr, Fe, Mg, Ca, Na and Ni. The mineral and melt proportions were determined by mass balance calculations using EMPA data for run product phases. We used focused beams of 1 μm diameter for small crystals and 10 μm diameter for larger melt pools with quench texture, respectively. Composition of each phase was determined with average values of 3–10 analysis points. Analyses were calibrated against primary standards of natural samples of forsterite for Mg and Si, jadeite for Na, wollastonite for Ca, and fayalite for Fe and synthetic oxides of corundum for Al, rutile for Ti, eskolaite (Cr2O3) for Cr and nickel oxide for Ni. For glasses, Si, Al and Ca were calibrated on Smithsonian basaltic glass standard VG-2. The compositions of iron-bearing iridium-rich and rhenium-rich metals were determined using an accelerating voltage of 15 kV and a beam current of 20 nA and calibrated with Structure Probe, Inc. metal standards. The peak counting time was set to 10 seconds, and the electron beam size was adjusted to spot (less than 1μm). The Ir phase in our experiments varies in size from < 1 micron to >5 micron in diameter. Clean analyses of the smallest grains are impossible. The excitation volume in this case always contains fractions of surrounding phases, shown by the detection of Si and O. Analyses of bigger grains show no such contamination and totals of the microprobe measurements of Ir and Fe together are very close to 100% in this case.

Peak heights were converted to concentrations using standard values. Peak count times were 20 seconds and background count time 10 s. Submicron-sized melt pockets, found in experiments at temperatures just above the solidus, could not be analysed successfully by EPMA. Their compositions were estimated semi-quantitatively using uncalibrated SEM-EDS measurements. Although the SEM-EDS analyses of very small melt pools are not very accurate, the percentages of melt in these experiments is so low (<3 wt%) that these inaccuracies do not lead to major errors in the mass balance calculations. In all cases, total iron is reported as FeO, although in reality melts and garnet can contain Fe3+ due to the oxidizing environment provided by the MH mixture.

The average compositions of minerals and silicate melts of all experiments are shown in Supplementary Table 1, with standard deviations supplied in Supplementary Table 2. BSE images of representative run products are shown in Extended Data Fig. 1, as are the results of mass balance calculations to obtain phase proportions.

Oxygen fugacity calculations

Oxygen fugacities were measured using iridium metal as a sensor24,32,33 in experiments L-1 and L-2 (Supplementary Table 1). Oxygen fugacities were calculated relative to the fO2 of the Fe-FeO (IW) redox buffer using the following equilibrium reaction:

$$2{\rm{Fe}}+{{\rm{O}}}_{2}=2{\rm{FeO}}$$
(R1)

with activity–composition relations for metallic metal in Fe-Ir alloy and iron oxide in ferropericlase (fp). fO2 is calculated using equation (3):

$$\Delta \log f_{{\rm{O2}}}\left({\rm{IW}}\right)=2\log {a}_{{\rm{FeO}}}^{{\rm{fp}}}-2\log {a}_{{\rm{Fe}}}^{{\rm{Fe}}\mbox-{\rm{Ir}}}$$
(3)

where activity a is defined as molar fraction X times activity coefficient γ.

\({a}_{{\rm{FeO}}}^{{\rm{fp}}}\) was determined using a binary regular solution model63 using:

$${RT}\,{\mathrm{ln}}{\gamma }_{{\rm{FeO}}}^{{\rm{fp}}}=\left(11,000+0.011P\right){\left(1-{X}_{{\rm{FeO}}}^{\,{\rm{fp}}}\right)}^{2}$$
(4)

with P in bar, T in K and R the gas constant. As in ref. 32, Fe3+ contents of fp were not determined and total iron contents were used in the calculation of \({X}_{{\rm{FeO}}}^{\,{\rm{fp}}}\). Given the Fe-poor, Mg-rich nature of the fp in our experiments \({X}_{{\rm{FeO}}}^{\,{\rm{fp}}}\, <\, 0.05\), their Fe3+ content is probably very small, with a minimal effect on calculated fO2 values.

\({a}_{{\rm{Fe}}}^{{\rm{Fe}}\mbox-{\rm{Ir}}}\) was calculated using a binary asymmetric regular solution model64, fitted to X-ray diffraction data for face-centred cubic Fe-Ir alloy, yielding a set of Margules parameters, WG (ref. 32). Activity coefficients γ for Fe in Fe-Ir alloy are given by:

$${RT}\,{\mathrm{ln}}{\gamma }_{{\rm{Fe}}}^{{\rm{Fe}}-{\rm{Ir}}}=2{X}_{{\rm{Fe}}}{X}_{{\rm{Ir}}}{W}_{\mathrm{G,Ir-Fe}}+{\left({X}_{{\rm{Ir}}}\right)}^{2}{W}_{\mathrm{G,Fe-Ir}}-2{G}^{\,X}$$
(5)

In equation (5), GX is the excess Gibbs free energy of mixing, calculated as follows:

$${G}^{\,X}={X}_{{\rm{Fe}}}{X}_{{\rm{Ir}}}\left({{X}_{{\rm{Ir}}}W}_{\mathrm{G,Fe-Ir}}+{X}_{{\rm{Fe}}}{W}_{\mathrm{G,Ir-Fe}}\right)$$
(6)

In equations (5) and (6), \({W}_{\mathrm{G,Ir-Fe}}\) and \({W}_{\mathrm{G,Fe-Ir}}\) are Margules parameters, which are dependent on P, T and composition according to equation (7):

$${W}_{{\mathrm{G}},{\rm{i}}-{\rm{j}}}={W}_{{\mathrm{H}},1{\rm{bar}},{\rm{i}}-{\rm{j}}}-T{W}_{\mathrm{S}}+\left(P-1\right){W}_{{\mathrm{V}},{\rm{i}}-{\rm{j}}},$$
(7)

with P in bar and T in K. WH, WS and WV are enthalpy, entropy and volume Margules parameters, respectively. \({W}_{\mathrm{H,1bar,Ir-Fe}}=-70,161\,{\rm{J}}\,{{\rm{mol}}}^{-1}\), \({W}_{\mathrm{H,1bar, Fe-Ir}}=-59,179\,{\rm{J}}\,{{\rm{mol}}}^{-1}\), \({W}_{\mathrm{S}}=-5\,{\rm{J}}\,{{\rm{mol}}}^{-1}\,{{\rm{K}}}^{-1}\), \({W}_{\mathrm{V,Ir-Fe}}=0.00904\,{\rm{J}}\,{{\rm{bar}}}^{-1}\) and \({W}_{\mathrm{V,Fe-Ir}}=0.06103\,{\rm{J}}\,{{\rm{bar}}}^{-1}\) (all values from ref. 32). Uncertainties in the calculated fO2 values are 0.1–0.2 log units (1σ), estimated from propagating the standard deviations in the EMPA measurements of the iron content of iridium and ferropericlase reported in Supplementary Table 2.

Oxygen fugacity in Re capsules

The oxygen fugacity in Re capsules at high pressures and high temperatures is generally thought to be above the fO2 of the IW buffer system35,65 and below that of the Re-ReO2 buffer because oxidized Re is not detected after such experiments. In this work, the iridium sliding sensor experiment in a Re capsule (26 GPa, 2,200 °C) yields an fO2 of IW − 1.2 ( ± 0.2). No separate Fe-rich metal grains were identified in the experimental charge, but EMPA analyses of the Re capsule reveal the presence of some Fe metal in the capsule wall adjacent to the sample–capsule interface (Extended Data Fig. 3). Concentrations above 1 wt% Fe are found within 5 μm of the interface. Fe concentrations drop with increasing distance from the interface and are still measurable at a distance of almost 30 μm from the sample. These values are qualitatively consistent with an earlier study38 at lower pressure (5 GPa) and lower temperature (1,800 °C) that reported a similar maximum Fe concentration and shorter Fe penetration distance into the Re capsule (Extended Data Fig. 3).

Phase relations at high pressure–temperature at f O 2 = IW + 2.0 ( ± 0.1)

Phase relations in the double capsule experiments of this study (MH powder) are plotted in Extended Data Fig. 2 and are compared to the phase relation diagram at IW − 1.2 (in Re capsules) after Ishii et al.19. Compared with the previous study that started with the same pyrolite composition at 12–28 GPa and 1,600–2,200 °C at fO2 = IW − 1.2 (ref. 19), our experiments at fO2 = IW + 2.0 with MH powder yield the same mineral assemblages at subsolidus conditions, 16 and 26 GPa and 1,600–2,000 °C, such as Wd + Gt at 16 GPa and Bg + Fp + Cpv at 26 GPa. At 21 GPa and 1,900 °C, the mineral assemblage at IW + 2.0 is Rw + Gt + Fp, consistent with the one of Rw + Fp + Gt (+ Cpv) below the solidus at IW − 1.2.