Oxygen Vacancy Substitution Linked to Ferric Iron in Bridgmanite at 27 GPa

Ferric iron can be incorporated into the crystal structure of bridgmanite by either oxygen vacancy substitution (MgFeO 2.5 component) or charge ‐ coupled substitution (FeFeO 3 component) mechanisms. We investigated the concentrations of MgFeO 2.5 and FeFeO 3 in bridgmanite in the MgO ‐ SiO 2 ‐ Fe 2 O 3 system at 27 GPa and 1700 – 2300 K using a multianvil apparatus. The FeFeO 3 content increases from 1.6 to 7.6 mol.% and from 5.7 to 17.9 mol.% with and without coexistence of (Mg,Fe)O, respectively, with increasing temperature from 1700 to 2300 K. In contrast, the MgFeO 2.5 content does not show clear temperature dependence, that is, ~2 – 3 and < 2 mol.% with and without the coexistence of (Mg,Fe)O, respectively. Therefore, the presence of (Mg,Fe)O enhances the oxygen vacancy substitution for Fe 3+ in bridgmanite. It is predicted that Fe 3+ is predominantly substituted following the oxygen vacancy mechanism in (Mg,Fe)O ‐ saturated Al ‐ free bridgmanite when Fe 3+ is below ~0.025 pfu, whereas the charge ‐ coupled mechanism occurs when Fe 3+ > 0.025 pfu.


Introduction
Bridgmanite, with typical chemical formula (Mg,Fe)SiO 3 , comprises around 80 vol.% of the lower mantle (e.g., Frost, 2008;Ringwood, 1991;Tschauner et al., 2014), and therefore, it dominates the physical and chemical processes of the lower mantle.Due to its variable valence, iron is the most important element that affects the properties of bridgmanite and thus mantle dynamics (e.g., Ismailova et al., 2016).Generally, iron is incorporated into the crystal structure of bridgmanite in the Mg site (A site) with the ferrous valence state.However, it is also known that a large amount of iron in bridgmanite can be in the ferric valence state even under reduced lower mantle conditions (Frost et al., 2004;Frost & McCammon, 2008;Grocholski et al., 2009;Jackson et al., 2005;Lauterbach et al., 2000;McCammon, 1997;McCammon et al., 2004).By analogy with aluminum substitutions in bridgmanite through the formation of MgAlO 2.5 and AlAlO 3 components (Brodholt, 2000;Kojitani et al., 2007;Liu, Ishii, & Katsura, 2017;Liu, Nishi, et al., 2017;Liu, Akaogi, & Katsura, 2019;Liu, Boffa-Ballaran, et al., 2019;Navrotsky, 1999), it is expected that the MgFeO 2.5 (oxygen vacancy mechanism) and FeFeO 3 (charge-coupled mechanism) components, respectively, will be formed by Fe 3+ incorporation through the following reactions (e.g., Hummer & Fei, 2012;Navrotsky, 1999): (1) where the subscripts A and B denote the Mg and Si sites, respectively (we follow the Kröger and Vink, 1956 notation for point defects, i.e., V O a Mg ion on the A site with neutral charge, and Fe′ B represents an Fe 3+ ion on the B site with one effective negative charge).
A question is how much Fe 3+ in bridgmanite can be stored as MgFeO 2.5 and/or FeFeO 3 components under lower mantle conditions.The MgAlO 2.5 component in bridgmanite can reach up to 6.4 mol.% in the MgO-SiO 2 -Al 2 O 3 system depending on pressure, temperature, and Mg/Si atomic ratio, which is expected to significantly affect lower mantle rheology (Liu, Ishii, and Katsura et al., 2017;Liu, Akaogi, & Katsura, 2019;Liu, Boffa-Ballaran, et al., 2019).In the case of the MgO-SiO 2 -Fe 2 O 3 system, although previous studies show that the Fe 3+ occupies the A and B sites nearly equally (Andrault & Bolfan-Casanova, 2001;Catalli et al., 2010), indicating a very small amount of the MgAlO 2.5 component, their experiments were performed within diamond anvil cells where determination of sample chemical compositions are difficult, prohibiting a precise determination of MgFeO 2.5 and FeFeO 3 concentrations.Hummer and Fei (2012) investigated Fe 3+ substitution mechanisms using multianvil experiments; however, their experiments did not reach chemical equilibrium as demonstrated by the coexistence of unreacted MgO and SiO 2 phases.Essentially, previous studies (Andrault & Bolfan-Casanova, 2001;Catalli et al., 2010;Hummer & Fei, 2012;Liu et al., 2018;Sinmyo et al., 2019) used starting materials without saturation of MgO (atomic Mg/Si = 1.0 or lower), which may prohibit the formation of MgFeO 2.5 based on observations that MgAlO 2.5 decreases with decreasing Mg/Si ratio in the MgO-SiO 2 -Al 2 O 3 system because of the reaction 2MgO + Al 2 O 3 = 2MgAlO 2.5 (Liu, Nishi, et al., 2017).In contrast, the Earth's lower mantle contains ferropericlase, and the concentration of MgFeO 2.5 should thus be maximized.
Therefore, the phase relations of bridgmanite with MgFeO 2.5 and FeFeO 3 components, characterized by B site Fe 3+ , may depend on whether periclase (or ferropericlase) coexists or not according to the reaction 2MgO + Fe 2 O 3 = 2MgFeO 2.5 .To clarify this further, we investigated the defect chemistry of bridgmanite in assemblage with a separate MgFe 2 O 4 phase and either presence or absence of a (Mg,Fe) O phase, using a multianvil apparatus.After drying in a vacuum furnace at 420 K, the two mixtures (both MgO-rich and Fe 2 O 3 -rich separated by a piece of Pt foil) were filled into Pt tube capsules (OD = 1.0 mm, ID = 0.8 mm).Each capsule was loaded into an MgO sleeve within a LaCrO 3 heater in a 5 wt.%Cr 2 O 3 -doped MgO octahedron with an edge length of 7.0 mm (the standard 7/3 cell assembly at Bayerisches Geoinstitut), and compressed to 27 GPa at ambient temperature by eight pieces of Fujilloy-TF05 type tungsten carbide anvils with edge length of 26 mm and truncation edge length of 3.0 mm using the multianvil press at Bayerisches Geoinstitut, IRIS-15 (Ishii et al., 2016).

Experimental and Analytical Methods
After reaching the target pressure of 27 GPa, the assembly was heated to a target temperature (1700-2300 K as listed in Table 1) at a ramping rate of 100 K/min measured by a W/Re (D-type) thermocouple.The annealing durations were 9-40 hr  1), which is sufficiently long to achieve chemical equilibrium (Frost & Langenhorst, 2002) as confirmed by the run products.The samples were quenched to room temperature by switching off the heating power and decompressed to ambient conditions over a duration exceeding 15 hr.The recovered run products were mounted in epoxy resin and their cross sections were prepared by polishing with emery papers and diamond pastes.

Sample Characterization
Scanning electron microscope (SEM).SEM analysis was performed on each sample, using a backscattering detector and an acceleration voltage of 20 kV associated with an energy dispersive detector.Run products appeared as coexisting bridgmanite + MgFe 2 O 4 + (Mg,Fe)O and bridgmanite + MgFe 2 O 4 for the MgO-rich and Fe 2 O 3 -rich samples, respectively (Table 1), as observed in backscattering detector images (Figure 1) and SEM-EDS point analysis.No unreacted particles (SiO 2 or Fe 2 O 3 grains) were found in any of the sample capsules.
Microfocus X-ray diffraction (XRD).XRD analysis was performed on the recovered samples using a micro focused X-ray diffractometer (Brucker AXS D8 Discover) equipped with a two-dimensional solid-state  (Greenberg et al., 2017).Pt peaks from sample capsules also appeared in the sample diffraction patterns due to the limited spatial resolution of the diffractometer (Figure 2).
Mössbauer Spectroscopy.Mössbauer spectra were collected over 500 μm diameter spots on samples of 120 μm thickness at room temperature in transmission mode on a constant acceleration Mössbauer spectrometer with a nominal 370 MBq 57 Co high specific activity (point) source in a 12 μm Rh matrix.The velocity scale was calibrated relative to 25 μm thick α-Fe foil using the positions certified for standard reference material no.1541 of the (former) National Bureau of Standards.Line widths of 0.36 mm/s for the outer lines of α-Fe were obtained at room temperature.Measurement times for each spectrum varied from 4 to 8 hr.The effective Mössbauer thickness of samples varied between 5 and 10 mg Fe/cm 2 .Spectra were fit by the program MossA (Prescher et al., 2012) using the full transmission integral to multiple doublets with pseudo-Voigt line shape to account for next nearest neighbor effects.There is no detectable Fe 2+ in bridgmanite from the run products within experimental uncertainty (Figure 3), and we assume that Fe 3+ /ΣFe ≈ 100%.
Electron probe microanalysis (EPMA).Concentrations of major elements (Mg, Si, Fe) in run products were obtained using a JEOL JXA-8200 electron microprobe with a wavelength-dispersive spectrometer operated with an acceleration voltage of 15 kV, a beam current of 5 nA, and a counting time of 20 s.Focused point analysis with an excitation region of ~1 μm was applied.An enstatite single crystal was used as the standard for Mg and Si, metallic Fe was used for Fe, whereas O was calculated by stoichiometry.Since the Pt capsule may absorb Fe from the samples, grains near the capsule wall (within a few microns) with slightly lower Fe% were avoided.The compositions of bridgmanite are listed in where x, y, and z are the atomic numbers per formula (pfu) from EPMA analysis.The Fe 2+ SiO 3 component was excluded since Fe 3+ / ΣFe ≈ 100% based on Mössbauer spectroscopy analysis, which is also confirmed by the low Fe/Mg ratio in ferropericlase.

Total Fe 3+ Concentration in Bridgmanite
The concentration of Fe 3+ in bridgmanite systematically increases from 0.06 to 0.17 pfu and from 0.12 to 0.37 pfu in MgO-rich and Fe 2 O 3 -rich samples, respectively, with increasing temperature from 1700 to 2300 K (Figure 4a).It is noted that only two phases, bridgmanite and MgFe 2 O 4 , coexist in run products of Fe 2 O 3 -rich samples (Table 1).According to the phase rule, there is one more degree of freedom in addition to pressure and temperature in the MgO-SiO 2 -Fe 2 O 3 three-component system, and as a result, the Fe 3+ concentration in bridgmanite should be correlated with the bulk Fe 2 O 3 content in the starting material.
In contrast, three phases, bridgmanite, (Mg, Fe)O, and MgFe 2 O 4 , coexist in the MgO-rich samples (Table 1).With fixed pressure and temperature, the composition of each phase should also be fixed and independent of the bulk composition of the starting material in the three-component system.Therefore, the Fe 3+ contents in the MgO-rich samples should represent the solubility of Fe 3+ in bridgmanite with saturation of (Mg,Fe)O under the given pressure and temperature conditions, that is, from 0.06 to 0.17 pfu with temperatures from 1700 to 2300 K (Figure 4a).

MgFeO 2.5 and FeFeO 3 Concentrations in Bridgmanite by EPMA
The molar fractions of the bridgmanite components, MgSiO 3 , MgFeO 2.5 , and FeFeO 3 were calculated sequentially based on Si, remaining Mg, and remaining Fe, respectively (Table 1).Figure 4b illustrates the proportions of ferric iron components versus temperature and shows that the FeFeO 3 component increases systematically for both MgO-rich and Fe 2 O 3 -rich samples with increasing temperature from 1700 to 2300 K. Bridgmanite in MgO-rich samples has lower proportions of the FeFeO 3 component than in Fe 2 O 3 -rich samples.
The concentration of bridgmanite component MgFeO 2.5 is well below 2 mol.% in Fe 2 O 3 -rich samples although the uncertainty is relatively large.MgO-rich samples have a MgFeO 2.5 concentration of 2 to 3 mol.%at 1700-2300 K (Figure 4(b)).Therefore, the presence of MgO enhances the formation of the MgFeO 2.5 component in bridgmanite, but only slightly in the presence of MgFe 2 O 4 .A similar relationship was also observed in the Fe-free and Al-bearing bridgmanite coexisting with MgO and MgAl 2 O 4 (Liu, Boffa-Ballaran, et al., 2019).In contrast to the temperature-induced increase in the FeFeO 3 component, the concentration of the MgFeO 2.5 component is insensitive to temperature.This could be because either the temperature dependence is hidden by the uncertainty of data points, or because the MgFe O2.5 reaches the maximum solubility even at 1700 K. Thus, the increase of total Fe 3+ with temperature is dominated by increasing FeFeO 3 component, rather than increasing MgFeO 2.5 component.

Fe 3+ Substitution Mechanisms in Bridgmanite
It has been previously proposed that oxygen vacancy substitution by Fe 3+ operates in bridgmanite in addition to the charge-coupled substitution mechanism (e.g., Frost & Langenhorst, 2002;Frost & McCammon, 2008;Walter et al., 2004); however, the concentration and formation condition of the MgFeO 2.5 component have not been well constrained.Andrault and Bolfan-Casanova (2001) and Catalli et al. (2010) found roughly equal distribution of Fe 3+ on Mg and Si sites; nevertheless, sample compositions in these diamond anvil experiments were uncertain due to small sample size.Hummer and Fei (2012) investigated Fe 3+ substitution mechanisms based on well-constrained chemical compositions of bridgmanite samples recovered from large-volume multianvil experiments.They concluded that Fe 3+ substitutes into bridgmanite by a combination of oxygen vacancy (equation 1) and charge-coupled (equation 2) mechanisms when Fe content is low (<0.05 pfu) because Mg content is either higher or In our MgO-rich samples, both Mg and Si contents deviate slightly from theoretical calculations of a pure charge-coupled substitution mechanism (Figure 5).The Mg content is systematically higher than Si within the investigated Fe content range from 0.06 to 0.17 pfu, indicating an oxygen vacancy substitution with formation of a MgFeO 2.5 component.On the other hand, Fe 2 O 3 -rich samples have Mg and Si contents that match a pure charge-coupled mechanism without detectable oxygen vacancy substitution (Figure 5).Therefore, the Fe 3+ substitution mechanism in bridgmanite is dominantly controlled by the saturation condition of MgO, rather than by Fe content.The Mg vacancy substitution mechanism proposed by Hummer and Fei (2012) is not observed in this study, although the exact reason for this discrepancy is unclear.One possible reason is that ferric iron in their iron-rich sample (Fe = 0.074 pfu) might be partially reduced, leading to the formation of a Fe 2+ SiO 3 component.
In Figure 5, the lines of decreasing Mg and Si with increasing Fe 3+ in bridgmanite from MgO-rich samples intersect the corresponding Si-and Mg-vectors for pure MgFeO 2.5 substitution at about 0.025 pfu, suggesting that oxygen vacancy substitution is preferred relative to charge-coupled substitution for low Fe 3+ .When Fe 3+ ≤ 0.025 pfu, the majority of Fe 3+ should follow the oxygen vacancy substitution mechanism.With increasing Fe 3+ , MgFeO 2.5 content increases in this compositional range.When the MgFeO 2.5 content reaches the solubility limit of 0.025 pfu, additional Fe 3+ will follow the charge-coupled mechanism and thus the amount of MgFeO 2.5 remains constant, which appears as nearly parallel curves of Mg or Si contents and pure charge-coupled substitution in Figure 5.

Implications for Bridgmanite Chemistry
The Earth's lower mantle is mainly composed of bridgmanite, ferropericlase, and CaSiO 3 perovskite (Frost, 2008;Ringwood, 1991;Tschauner et al., 2014), meaning that bridgmanite is under MgO-saturated conditions.Since a significant amount of iron in bridgmanite is ferric (Frost et al., 2004;Grocholski et al., 2009;Jackson et al., 2005;Lauterbach et al., 2000;McCammon, 1997;McCammon et al., 2004), the concentration of the MgFeO 2.5 component by oxygen vacancy substitution could be significant.On the other hand, bridgmanite in the lower mantle contains some Al (e.g., Irifune et al., 2010), which could affect the Fe 3+ substitution mechanism via the formation of the FeAlO 3 component with Fe 3+ and Al 3+ occupying A and B sites, respectively (e.g., Richmond & Brodholt, 1998;Zhang & Oganov, 2006as reviewed in Frost & McCammon, 2008).Similarly, Fe 3+ may also affect formation of the MgAlO 2.5 component.The Al/Fe 3+ ratio in Al-bearing bridgmanite under lower mantle conditions is generally larger than 1.0 in both peridotitic and basaltic lithologies (e.g., Mohn & Trønnes, 2016;Nakajima et al., 2012;Prescher et al., 2014), the FeAlO 3 component may thus prohibit oxygen vacancy substitution, although some regions such as harzburgite layers that was brought into the lower mantle by subduction have Al/Fe 3+ ratios smaller than 1.0 (Liu et al., 2018).Studies of iron spin state indicate almost no Fe 3+ (<1%) in the B site because the spin transition for the B site Fe 3+ is observed in Al-free bridgmanite at ~40-60 GPa, but not found in Al-bearing samples (e.g., Liu et al., 2018;Mohn & Trønnes, 2016).Nevertheless, oxygen vacancy substitution is significantly suppressed by pressure (Liu, Nishi, et al., 2017); therefore, it is still unclear how much of the oxygen vacancy component is formed in Al-bearing bridgmanite, especially near the topmost lower mantle.Further studies at ~24-40 GPa in the MgO-SiO 2 -Al 2 O 3 -Fe 2 O 3 system are required.

Figure 3 .
Figure 3. Room temperature Mössbauer spectra of run products (Run I574).The blue and purple doublets correspond to Fe 3+ in bridgmanite and MgFe 2 O 4 phases, respectively, whereas the yellow doublet is assigned to Fe 2+ in (Mg,Fe)O.There is no detectable Fe 2+ in bridgmanite within the data scatter.(top) MgO-rich sample.(bottom) Fe 2 O 3 -rich sample.

Figure 5 .
Figure 5. Mg (open symbols) and Si (filled symbols) per formula unit in bridgmanite (oxygen = 3) as a function of the Fe 3+ content for both MgO-rich and Fe 2 O 3 -rich samples.Error bars represent 1 standard deviation of uncertainty calculated from EPMA measurements in Table 1.Small orange and dark blue symbols are from reference HF12 (Hummer & Fei, 2012).Thin solid and dashed lines indicate theoretical concentrations of Mg, Si per formula unit by pure FeFeO 3 and MgFeO 2.5 substitutions, respectively.Crossovers of Mg, Si pfu in MgO-rich samples (red lines) and theoretical calculations of pure MgFeO 2.5 substitution (thin dashed lines) occur at Fe 3+ ≈ 0.025 pfu.

Table 1
Run Conditions, Phase Assemblage, and Composition of Bridgmanite in Run Products a MgO-rich: mixture of oxides with bulk composition of MgSiO FEI ET AL.(Table