The Effect of Fe‐Al Substitution on the Crystal Structure of MgSiO3 Bridgmanite

The crystal chemistry of ten well‐characterized bridgmanite single‐crystals with Fe and Al contents ranging from 0 to 0.40 atoms per two‐cation formula units were investigated by single‐crystal X‐ray diffraction. Structural refinements indicate that Fe3+ and Al mainly occupy the Mg and Si sites, respectively, when present in similar proportions. Molar volumes of bridgmanite endmember components were refined using data from this and previous studies and found to decrease in the order Fe3+Fe3+O3 > MgFe3+O2.5 > Fe3+AlO3 > MgAlO2.5 > AlAlO3 > Fe2+SiO3 > MgSiO3. Fe3+AlO3 charge‐coupled substitution leads to an anisotropic increase of B‐O bond distances, resulting in more distorted octahedral B sites and in a more significant increase of the c‐axis with respect to the a‐ and b‐axes. Valence bond calculations indicate that the A site is more compressible than the B site for all bridgmanite samples studied, implying that octahedral tilting and distortion will dominate the bridgmanite compression mechanism. Guided by these crystal chemical observations, bulk moduli of bridgmanite endmember components were estimated using results of previous studies. The volume changes of equilibria controlling the speciation of bridgmanite components were then calculated at conditions relevant to the top of Earth's lower mantle. The proportion of oxygen vacancy components is predicted to decrease with pressure. While the stability of the bridgmanite Fe3+AlO3 component will drive charge disproportionation to produce iron metal at the top of the lower mantle, this appears to be much less favorable by 50 GPa. An increase in the proportion of the Fe3+Fe3+O3 bridgmanite component, however, may favor the formation of iron metal at higher pressures.

M O 3 join (Frost & Langenhorst, 2002;Kojitani et al., 2007;Lauterbach et al., 2000;Vanpeteghem et al., 2006;Walter et al., 2004) and (b) an oxygen vacancy (OV) substitution where trivalent cations substitute for Si 4+ at the B site and charge balance is achieved by the creation of oxygen vacancies, that is,   (Frost & Langenhorst, 2002;Kojitani et al., 2007;Lauterbach et al., 2000;Walter et al., 2006). The former CC mechanism results in the affinity of Al-bearing Brg for Fe 3+ , which may have a strong influence on the redox state of the lower mantle (Frost et al., 2004;Lauterbach et al., 2000;McCammon, 1997). The latter OV mechanism is responsible for the formation of defect perovskites such as those found along the CaTiO 3 pervoskite-CaFeO 2.5 brownmillerite join (Becerro et al., 1999) where the oxygen vacancies formed likely have a strong influence on transport properties .
Despite the potentially important effects of Fe 3+ and Al substitution in Brg on lower mantle phase equilibria and redox state (Frost & Langenhorst, 2002;Irifune et al., 2010;Nakajima et al., 2012;Wood & Rubie, 1996) in addition to elasticity (Boffa Ballaran et al., 2012;Glazyrin et al., 2014;Kurnosov et al., 2017;Mao et al., 2017), rheological, and transport properties (Holzapfel et al., 2005;Ohta et al., 2008;Xu et al., 1998), the mechanisms by which Fe 3+ and Al are accommodated into the Brg structure under differing conditions and compositions and how the different mechanisms affect the crystal chemistry of Brg are still not well constrained. This makes it difficult to evaluate the results of high-pressure studies particularly in terms of their applicability to the lower mantle. A determination of the partial molar volumes of Brg components, for example, is essential not only for constraining their effect on Brg density but also for a thermodynamic analysis of how the proportions of different Brg trivalent components will change with bulk composition or pressure in the lower mantle as a result of changes in partitioning or oxygen fugacity (fo 2 ). Due to the existence of several substitution mechanisms and the necessity to accurately determine both volumes and compositions (including Fe 3+ /∑Fe ratio), very few data can currently be used for this purpose. The influence of trivalent cations on the crystal structure of Brg is also important for providing a mechanistic understanding of their effects on elastic and transport properties.
The MgSiO 3 Brg structure, space group Pbnm (Horiuchi et al., 1987;Ito & Matsui, 1978;Yagi et al., 1978) consists of a three-dimensional framework of corner-linked SiO 6 octahedra (B site) forming cavities occupied by Mg in bi-capped prism coordination (A site) described by eight oxygens with Mg-O distances smaller than 2.5 Å and 4 Mg-O distances larger than 2.7 Å (Figure 1a). This structure derives from an ideal cubic structure, with space group Pm m 3 , through the tilting and distortion of the octahedral framework (e.g., Glazer, 1972;Howard & Stokes, 1998Thomas, 1989). Several studies have experimentally examined the effect of Al and/or Fe 3+ substitution on the unit-cell volume and equation of state (EoS) of Brg (Andrault et al., 2007;Boffa Ballaran et al., 2012;Catalli et al., 2010Catalli et al., , 2011Lundin et al., 2008;Nishio-Hamane et al., 2008;Ono et al., 2004;Saikia et al., 2009;Tange et al., 2009;Walter et al., 2004Walter et al., , 2006; however, very few studies have examined the structural variations in Brg associated with different cation substitutions, and the characterization of samples in the existing studies rarely extends to measurements of Fe 3+ /∑Fe ratios. Several studies have suggested that Fe 2+ substitutes mainly for Mg on the A site (Jephcoat et al., 1999;Kudoh et al., 1990;Parise et al., 1990;Sinmyo et al., 2011) while it has also been proposed that Fe 3+ can substitute onto the Brg B site (Catalli et al., 2010;Hummer & Fei, 2012) and in Fe free Brg Al clearly also substitutes onto the A site (Grüninger et al., 2019;Liu, Akaogi, & Katsura, 2019;Liu, Ballaran, et al., 2019;Liu et al., 2017;Stebbins et al., 2003). However, no structural parameters have been reported that might allow the consequences of these substitutions to be examined. Vanpeteghem et al. (2006) studied the crystal chemistry of Fe 3+ and Al-bearing Brg by means of single-crystal X-ray diffraction (XRD) and proposed that all Fe occupies the A site and that with increasing Fe 3+ and Al content, the molar volume, the average A-O and B-O bond distances, and the BO 6 octahedra tilting all increase. This is in good agreement with the subsequent study of Glazyrin et al. (2014) on an Fe 3+ and Al-rich Brg. However, the presence of impurities as well as the lack of knowledge on the Fe 3+ /∑Fe ratio for the samples covered in these studies do not allow the contrasting effects of the different cation substitutions to be constrained.
In this study, single-crystal X-ray diffraction measurements were performed on ten well-characterized single-crystals of Brg with varying Fe 3+ and Al contents from 0 to 0.40 atoms pfu, principally to determine the partial molar volumes of the Brg components. Some Brg samples were synthesized in assemblages with coexisting ferropericlase (Fp) to obtain the same silica activity as expected in a peridotitic lower mantle and to ensure a suitable environment to assess the importance of the OV substitution mechanism (Litasov et al., 2003;Navrotsky, 1999). The different substitution mechanisms were then carefully characterized in the recovered samples using a combination of electron microprobe, Mössbauer spectroscopy, and electron energy-loss spectroscopy measurements. The results of the single-crystal X-ray structural refinements provide insights into how the different cation substitution mechanisms affect the distortion of the Brg structure and as a consequence its elastic behavior. Moreover, based on the determined molar volumes of different Brg endmember components and previously reported elastic data, the stabilities of different Brg components with increasing pressure are estimated. at 1650°C for 15 min in a 1 atm furnace followed by rapid quenching of the platinum crucible in water. The crushed glass powders were then ground under ethanol, cold pressed into pellets and then fired in a CO 2 -CO gas-mixing furnace at 1250°C and at an fo 2 1 log unit above the iron-wüstite buffer (IW) for 48 h. To ensure that all Fe 3+ was reduced in the rapidly quenched pellets, the samples were re-ground and re-fired at identical conditions for another 48 h. The recovered samples consisted of pyroxene containing only Fe 2+ , as confirmed by means of Mössbauer spectroscopy. Glass En83 was not reduced and thus contained both Fe 2+ and Fe 3+ as a result of the glass making process in air. In order to study the influence of Fe and Al substitution on the crystal chemistry of Brg, large high-quality single-crystals with various compositions are needed. To achieve this, several strategies were followed (see Table S1 for details). In most experiments, pyroxene (En95, En93, and En88) or glass (En83) starting powders were mixed together with 5-10 HUANG ET AL.  The orthorhombic distortion from the cubic aristotype perovskite structure is due to the in-phase (ϕ) and out-of-phase (θ) tilting of the octahedral framework. The atomic displacements associated with the orthorhombic distortion are also shown.

Sample Syntheses
wt.% (Mg 0.9 Fe 0.1 )O, which was similarly synthesized and reduced so as to contain minimal Fe 3+ (Table S1). In some Brg synthesis experiments, Fe metal (6-9 μm size powder) or hematite was also added to achieve relatively low or high fo 2 (Table S1). Water was added to all samples either using a syringe or as hydroxides (Mg[OH] 2 or Al [OH] 3 ) in order to promote the growth of large single-crystals. For one synthesis experiment (S6631), the starting material consisted of a ground mixture of MgO, Mg(OH) 2 , Al(OH) 3 , SiO 2, and Fe 2 O 3 designed to produce a (Mg 0.8 Fe 0.2 ) (Si 0.8 Al 0.2 )O 3 + 10 wt.% H 2 O bulk composition.
The final starting compositions (Table S1) were loaded into gold foil capsules of 1.8 mm length and 0.8 mm diameter that were then placed inside platinum tubes 2 mm long and 1.0 mm in diameter, which were welded close at each end. The synthesis experiments were performed using 7 mm edge length Cr 2 O 3 -doped MgO octahedra and tungsten carbide cubes with truncations of 3 mm edge length that were compressed using a multi-anvil apparatus with a maximum compressive force equivalent to 1,200 tonnes. A LaCrO 3 tube heater was employed and temperature was estimated from the electrical power. The samples were first pressurized up to ∼25 GPa, and then heated at 1300°C-1700°C for 2-12 h (Table S1). Textures indicate that this method results in smaller thermal gradient than when thermocouples are placed into each experiment. The runs were then quenched by turning off the electric power, and the pressure was released slowly over 20 h.

Sample Characterization
The recovered samples were mounted in epoxy resin and polished for microstructural observation and chemical analysis. Preliminary phase identification was performed using a micro-focused X-ray powder diffractometer (XRD; Bruker, D8 DISCOVER) equipped with a two-dimensional solid-state detector (VÅN-TEC500) and micro-focus Co-Kα radiation source (IμS) operated at 40 kV and 500 μA. A scanning electron microscope (SEM) (Zeiss Gemini 1530) equipped with a field emission gun and an energy-dispersive X-ray spectrometer (EDXS) was used to observe the sample textures and to characterize potential minor phases, which may be below the detection limit of XRD. Chemical compositions (Table 1) were analyzed with a JEOL JXA-8200 electron microprobe (EPMA), operating at 15 kV and 5 nA. The crystals of Brg were analyzed with a 3-μm defocused beam, to reduce beam damage, and all other solid phases were measured with a point beam. Counting times per element were 10 s on the peak and 5 s on the background. The following calibration standards were used: enstatite for Mg and Si, Fe metal for Fe, and corundum for Al. MgSiO 3 akimotoite single crystals, synthesized at 22 GPa and 1873 K, were used as a secondary standard for Mg and Si as akimotoite has a density close to that of Brg but is not beam sensitive. The analyses only proceeded once a Mg/Si ratio of one was obtained using the akimotoite standard. More than 20 points for each sample were measured in order to check the homogeneity of the Brg crystals.
The Fe 3+ /∑Fe ratios in the Brg samples (Table 1) were determined using either Mössbauer spectroscopy or electron energy-loss spectroscopy (EELS). For two experiments, S6631, which contained Brg with ∼0.26 Fe atoms pfu and H4615, whose starting material was enriched with 95% 57 Fe, we used single-crystals of Brg for the Mössbauer measurements. In particular, for S6631 only one very large (∼250 × 250 × 50 μm 3 ) crystal was used; whereas for H4615 three single-crystals (∼70 × 70 × 20 μm 3 ) were packed together to obtain a sufficient volume. Thick sections of multi-phase assemblages were used for other experiments with the thickness determined to produce an absorber thickness of ∼5 mg Fe/cm 2 to avoid saturation effects. Mössbauer spectra were recorded in transmission mode for 20 to 48 h over sample regions of ∼100-500 μm in diameter at room temperature using a constant acceleration Mössbauer spectrometer with a nominal 370 MBq 57 Co point source in a 12 μm Rh matrix. The velocity scale was calibrated relative to α-Fe. Spectra were fitted to pseudo-Voigt line shapes using the MossA program (Prescher et al., 2012), and the full transmission integral was used. The peaks of Fe in Brg were fitted by quadrupole doublets; the width and area of each quadrupole doublet component were constrained to be equal in the Mössbauer spectra collected for the polycrystalline samples, whereas the area ratio of doublet components was free to vary for samples S6631, H4615, and S6689, since quadrupole doublets of single crystals and samples with preferred crystal orientation may show area asymmetry (see Text S1, Figure S1 and Table S2 for details).
For two samples, S6732 and S6805, the Fe 3+ /∑Fe ratio of Brg was determined using Fe-L 2,3 electron energy-loss near-edge structure (ELNES) spectroscopy because the synthesis runs contained larger proportions of Fp than in the other samples, which made separation of the individual contributions to Mössbauer spectra impossible. ELNES spectra were collected using an analytical transmission electron microscope (ATEM, Philips CM20FEG) equipped with a parallel electron energy-loss spectrometer (PEELS Gatan 666), operating at 200 kV. TEM thin foils were prepared using either conventional Ar-milling or a focused ion beam (FIB) instrument. The TEM experiments were performed at −170°C using a liquid nitrogen-cooling holder. Fe-L 2,3 edge ELNES spectra were collected in diffraction modes at the thinnest part of the ionthinned sample and a typical ELNES spectrum for Brg is shown in Figure S2. Quantification of the Fe-L 2,3 edge ELNES was performed following the procedure described by van Aken et al. (1998) and van Aken and Liebscher (2002), using an empirically calibrated universal curve. The EELSA program (https://github. com/CPrescher/EELSA) was used to evaluate the Fe 3+ /∑Fe ratios reported in Table 1. The time-series analyses of the spectra showed that the measured ratios did not change significantly with increasing electron irradiation time up to 80 s of acquisition, which would otherwise indicate iron oxidation during the EELS measurement (Lauterbach et al., 2000).

Single-Crystal X-Ray Diffraction and Structural Refinements
Two further samples, H3004 and S4253, synthetized in a previous study (Boffa Ballaran et al., 2012) and having respectively a MgSiO 3 endmember composition and a very Fe and Al-rich composition HUANG ET AL. , have been used in this study together with those recovered from the syntheses performed in this study. Ten single-crystals of Brg with Fe and Al contents varying from 0 to 0.40 atoms pfu were selected based on their optical appearance, lack of twinning, and their narrow diffraction profiles. Unit-cell lattice parameters were determined using the eight-position centering method (Angel et al., 2000;King & Finger, 1979) on a HUBER four-circle diffractometer equipped with Mo Kα radiation operating at 50 kV and 40 mA and a point detector operated using the SINGLE software (Angel & Finger, 2011). Intensity data were collected at ambient conditions using an Xcalibur diffractometer with Mo Kα radiation (λ = 0.71073 Å) operated at 50 kV and 40 mA, equipped with a CCD detector and a graphite monochromator. Omega scans were chosen to obtain full coverage of the reciprocal sphere up to 2θ max = 80°, with an exposure time of 20 s/frame and a step size of 0.5° at a crystal-detector distance of 45.1 mm.
Lorentz and polarization factors together with an analytical absorption correction based on the crystal shape were performed for the correction of the reflection intensities using the CrysAlis package (Oxford Diffraction, 2006). Symmetrically equivalent reflections were merged and structure refinements were performed based on F 2 using the SHELX97 program package (Sheldrick, 2008) in the WinGx System (Farrugia, 1999). The structure refinements were carried out in space group Pbnm starting with the atomic coordinates reported by Horiuchi et al. (1987). Neutral scattering factors for Mg, Si, Al, Fe, and oxygen were used (Allen et al., 1992), and all atoms were refined anisotropically. In order to model the cation distribution of Al and Fe between the A-and B-sites, we have taken the following steps: (a) the occupancies of Fe and Mg were refined at the A site with their sum constrained to be equal to 1; (b) since refinements using the scattering factors of Si and Fe at the B site always resulted in a negative occupancy of Fe, the B site has been refined using only the Si scattering factor with the occupancy of Si free to vary; (c) oxygen occupancies have been fixed to the value of 1, given that the amount of vacancies indicated by the EPMA analyses is well below the sensitivity of the structural refinements. Details of data collection and refinement parameters, fractional occupancies, atomic coordinates and anisotropic displacement parameters are provided in a Crystallographic Information File (CIF) in the supplementary information.

Al and Fe Substitution Mechanisms in Bridgmanite
The assemblages recovered from the high-pressure syntheses are summarized in Table S1, and the average compositions of the Brg crystals are reported in Table 1. The Fe and Al contents of these well-characterized Brg samples extend up to 0.40 Fe and 0.36 Al atoms pfu, respectively. Based on cation radii, it would seem logical that Fe 3+ partitions more favorably into the Brg A site and Al 3+ into the B site (Shannon, 1976) as proposed previously (McCammon et al., 2013;Vanpeteghem et al., 2006). As the Mössbauer spectra (see Text S1, Figure S1 and Table S2) are inconclusive in determining the Fe 3+ site assignment (Lin et al., 2013;McCammon, 1998), we follow the assumption that cations partition between the two sites in accordance with their radii. Several lines of evidence in the single-crystal diffraction results support this, as will be shown later. A simple procedure is followed, therefore, to estimate the site occupancies based on the EPMA analyses, whereby the B site is first filled with the Al cations and the A site with Fe 3+ . If Si + Al are larger than 1, extra Al is placed on the A site and conversely, if Mg + Fe 2+ + Fe 3+ are larger than 1, extra Fe 3+ is placed on the B site. The resulting cation distribution between the A and B sites and the proportions of Brg components are reported in Table 1. For most of the samples, this procedure indicates insignificant amounts of Fe 3+ entering the B site, but sample S6838 is determined to have ∼0.04(1) atoms pfu of Fe 3+ at the B site (Table 1). This occurs because the amount of Fe 3+ cations exceeds those of Al.
The mean atomic numbers (m.a.n.) of cations at the A-and B-sites determined by means of the single-crystal structural refinements are in good agreement with the cation assignments resulting from EPMA analyses (Table S3), providing some confirmation for the preference of Fe 3+ and Al for the A and B sites, respectively, when both are present. The small differences between the two estimates are likely due to the combined uncertainties of the structural refinement and chemical analyses. The existence of at least some amount of trivalent cation disorder between the two sites cannot be excluded, although as discussed later, if this were significant it would show up in the molar volumes and octahedral bond distances.
The Brg compositions along with well-characterized samples from previous studies (Frost & Langenhorst, 2002;Lauterbach et al., 2000;Liu et al., 2020;Saikia et al., 2009) can be plotted in a ternary diagram with respect to the (Mg, Fe 2+ )O-SiO 2 -(Al, Fe 3+ ) 2 O 3 components ( Figure S3). Substitution trends expected along the CC MgSiO 3 -(M 3+ ) 2 O 3 join (where M 3+ = Fe 3+ or Al 3+ ) and the OV MgSiO 3 -MgM 3+ O 2.5 joins are also indicated. Note that the OV component MgM 3+ O 2.5 is essentially MgAlO 2.5 as samples displaying this component contain negligible B site Fe 3+ . Similarly, the CC component, M 3+ M 3+ O 3 , is mainly Fe 3+ AlO 3 . As expected, the samples are mainly dominated by the CC substitution (mainly Fe 3+ AlO 3 ) in spite of the fact that some of them were synthesized in the presence of Fp, which has been shown to promote the OV mechanism in iron-free samples (Liu, Akaogi, & Katsura, 2019;Liu, Ballaran, et al., 2019;Navrotsky et al., 2003). Some samples deviate slightly from the trend but the OV component does not exceed 0.04 pfu for the investigated single-crystals. Three samples (S6732, S6848, and S6805) also contain a considerable amount of Fe 2+ SiO 3 (7-12 mol.%) component, which enables us to examine the effect of Fe 2+ on the Brg structure and S6838 contains 4 mol.% of the Fe 3+ Fe 3+ O 3 component, which provides some information on the effects of Fe 3+ on the Brg B-site.

Molar Volumes of (Fe, Al)-Bearing MgSiO 3 Bridgmanite
The unit-cell lattice parameters and molar volumes of the Brg single-crystals investigated in this study are reported in Table 2. The molar volumes (V m ) of the investigated samples are plotted against the sum of their endmember components and compared with published data in Figure 2. The trend defining the Fe 2+ SiO 3 substitution is well constrained by studies that used iron or graphite capsules to ensure minimal Fe 3+ contents (Jephcoat et al., 1999;McCammon et al., 1992;Tange et al., 2009). The V m of the Fe 2+ SiO 3 endmember, assuming a linear relation between the endmember volumes, is 25.35(2) cm 3 /mol, calculated using a linear fit through these data. The trend defining the variation of the Brg V m along the MgSiO 3 -Fe 3+ AlO 3 join has been constrained using only volumes reported for samples for which Fe 3+ /∑Fe ratios were measured and for which the Fe 2+ SiO 3 and OV components were minimal. The volumes were linearly corrected for the contribution of the Fe 2+ SiO 3 component (i.e., The resulting molar volume for the Fe 3+ AlO 3 endmember is 27.09(6) cm 3 /mol. Most samples investigated in this study lie between the two linear trends of the Fe 3+ AlO 3 and Fe 2+ SiO 3 substitution mechanisms (Figure 2a). The V m of the remaining Brg samples (Table 2) were then expressed in terms of the summation of molar volumes of the four endmember components in order to constrain . This resulted in the value 26.70(18) cm 3 /mol, which is statistically identical to the value of MgAlO 2.5 V of 26.64(10) cm 3 /mol reported by Liu, Akaogi, and Katsura (2019) from an examination of iron-free samples. This implies that the creation of OV has a similar effect on the structure of Brg independent of whether this substitution occurs in an Feand Al-bearing or just an Al-bearing system, which further supports the notion that in the Fe-and Al-bearing system very little Fe 3+ enters the B site. Sample S6838 plots above the Fe 3+ AlO 3 trend, which is consistent with it being the only sample where the Fe 3+ content is significantly larger than Al, which then forces Fe 3+ onto the B-site to provide charge balance through an Fe 3+ Fe 3+ O 3 component. Even a small component of B-site Fe 3+ therefore leads to an obvious effect on V m , which again supports the concept that very little Fe 3+ enters the B-site unless Fe 3+ > Al. From previous analyses reported for Al-free samples (Catalli et al., 2010;Hummer & Fei, 2012), it is possible to estimate the V m of the Fe 3+ Fe 3+ O 3 endmember to be 29.55(3) cm 3 /mol, which is the largest in the systems examined, explaining why the V m of the investigated Brg is so sensitive to this endmember. For completeness, it is also possible to estimate a V m of 27.65(1) cm 3 /mol for the MgFe 3+ O 2.5 endmember using analyses reported by Hummer and Fei (2012). The molar volumes for the different Brg endmembers, therefore, decrease in the order Fe 3+ Fe 3+ O 3 > MgFe 3+ O 2.5 > Fe 3+ AlO 3 > MgAlO 2.5 > AlAlO 3 > Fe 2+ SiO 3 > MgSiO 3 (Table 3). It should be noted that this analysis assumes a linear dependence of V m on composition as there are no detectable deviations from ideal mixing over the accessible compositional range.   Results from previous studies, which have not been included in the fitting procedure to obtain the endmember molar volumes due to uncertainties in the compositions or the presence of other elements, are also plotted for comparison in Figure 2b. Studies on (Mg,Fe 2+ )SiO 3 Brg, which either reported nominal compositions (Andrault et al., 2001;Lundin et al., 2008;Mao et al., 1991;Parise et al., 1990) or reported small amounts of Fe 3+ in the investigated samples (Mao et al., 2017 Bm6) give Brg molar volumes that lie very close to the Fe 2+ SiO 3 trend (Figure 2b). Some of the diamond anvil cell (DAC) experiments reporting only Fe 3+ AlO 3 substitution based on the starting compositions fall exactly on our Fe 3+ AlO 3 trend (Andrault et al., 2001;Nishio-Hamane et al., 2008), while others deviate (Catalli et al., 2011;Nishio-Hamane et al., 2005). Where these volumes are larger than the MgSiO 3 -Fe 3+ AlO 3 join some Fe 3+ may have entered the B site, most likely due to the proportion of Fe 3+ being greater than Al. Where volumes are smaller than the trend this may be due to iron reduction to form some Fe 2+ SiO 3 component or iron loss during laser heating. The large deviation of the Fe 3+ AlO 3 -rich samples reported by Vanpeteghem et al. (2006) is most likely due to the presence of additional Na and Ti in some of these samples (Figure 2b). The three data points from Liu et al. (2020) have larger molar volumes than our Fe 3+ AlO 3 substitution trend, which may result from inaccuracy in the determination of the Brg volumes due to the use of a micro-focused XRD. The V 0 reported for a very Fe-rich Brg with the composition (Mg 0.46 Fe 3+ 0.53 ) (Si 0.49 Fe 3+ 0.51 ) O 3 (Liu et al., 2018) was 2% larger than predicted from our Fe 3+ Fe 3+ O 3 trend line, most likely because the room pressure volume in Liu et al. (2018) was determined by extrapolating back to room pressure using a second order Birch-Murnaghan EoS. Nonetheless, this result is consistent with the Fe 3+ Fe 3+ O 3 endmember having the largest V m of the components considered.
We can try to rationalize the endmember V m for the different substitutions in terms of the A and B site polyhedral volumes. For the samples from this study, the single-crystal diffraction refinements can be used to precisely determine these polyhedral volumes. However, as such structural data do not exist for other components, we have to estimate these volumes from the unit-cell lattice parameters. These calculations assume that the orthorhombic structure arises from the tilting of regular and undistorted octahedra, and as already reported (Mitchell, 2002;Sinmyo et al., 2014;Zhao et al., 1993aZhao et al., , 1993b, the values obtained underestimate the actual tilting and octahedral bond lengths due to distortions. However, if we compare the octahedral volumes, V B , obtained from the structural refinements with that calculated from an average B-O bond distance obtained from the lattice parameters as <B-O> = b * c/(4 * a) (Mitchell, 2002), we observe near parallel trends with increasing Fe 3+ AlO 3 substitution ( Figure 3). Therefore, we can use the unit-cell lattice parameters reported in previous studies (Hummer & Fei, 2012;Liu, Akaogi, & Katsura, 2019;Liu, Ballaran, et al., 2019;Liu et al., 2017;Tange et al., 2009) in order to describe, at least as a first approximation, the variation of V B as a function of different cation substitutions (Figure 3). V B increases with AlAlO 3 substitution (green triangles) with almost the same slope as that observed for the Fe 3+ AlO 3 substitution, as expected, given the substitution of the larger Al cation ( VI r Al = 0.675 Å, Shannon, 1976) for the smaller Si cation ( VI r Si = 0.540 Å) at the B site. The difference in molar volumes between the Fe 3+ AlO 3 and AlAlO 3 components is therefore likely due to differences in the extent of octahedral tilting, given the different radii of Fe 3+   increases V B to a much larger extent (yellow square) and is the primary reason for the very large molar volume of the Fe 3+ Fe 3+ O 3 component. As expected, the Fe 2+ SiO 3 substitution (blue circles) has practically no effect on the octahedral volume, since Fe 2+ substitutes only at the A site. The marginal decrease of V B observed for the data reported by Tange et al. (2009) is very likely a secondary effect due to a decrease of the octahedral tilting in these Brgs. The slightly larger molar volume of the Fe 2+ SiO 3 component with respect to the Brg endmember is therefore due simply to the larger A site.

Distortion of the Perovskite-Type Structure of Bridgmanite
The orthorhombic distortion of the Brg structure with respect to the ideal cubic 3 Pm m aristotype is due to the tilting of the octahedral units and can be described using tilt components around "pseudo-cubic" axes, that is, around the axes of the cubic aristotype structure (Glazer, 1972). The simplest method for calculating the tilt angles is to derive them from the unit-cell lattice parameters but as already mentioned this assumes that the octahedral framework is rigid and regular and tilting angles calculated in this way are usually underestimated (e.g., Mitchell, 2002;Sinmyo et al., 2014). More realistic tilt angles can be calculated using the atomic coordinates of the oxygen atoms (Kennedy et al., 1999;Zhao et al., 1993aZhao et al., , 1993b whose displacements from the cubic atomic positions result not only from tilting but also from the distortion of the octahedral sites. A clear and unambiguous way to separate the effects of distortion and tilting of perovskite structures is provided by analysis of the irreducible representations (Irreps) describing the displacive modes of the A cation and oxygens from the atomic positions of the cubic aristotype structure (Howard & Stokes, 1998, 2002Perez-Mato et al., 2010). The five mode displacements for the Pbnm space group associated with the points X (0, 0, 1/2), M (1/2, 1/2, 0), and R (1/2, 1/2, 1/2) of the Brillouin zone are the in-phase and out-of-phase tilt patterns, represented by the two Irreps M 3 + and R 4 + , respectively; an octahedral basal distortion represented by the Irrep M 2 + , and the Irreps R 5 + and X 5 + each of which describe displacements of both the oxygen atoms and the A cations away from their positions in the cubic aristotype, which for the A cations is the center of an undistorted polyhedron ( Figure 1; the notation is taken from Miller & Love, 1967). The program ISODISTORT (Campbell et al., 2006) has been used to decompose the Brg structures refined in this study into these five symmetry-adapted modes with respect to ideal parent cubic structures that have identical volumes to that of our samples (Table S4). plitudes; however, amplitudes of the X 5 + and R 5 + modes related to the displacement of the A cations (X 5 + A and R 5 + A) and the amplitude of the X 5 + mode related to the displacement of the oxygen atoms (X 5 + O) are not negligible and indicate that Fe 3+ AlO 3 substitution causes an even greater degree of distortion of both B and A sites than found in MgSiO 3 Brg (Figure 4) The oxygens and A-site cation displacements caused by the substitution of different cations determine the variations of bond distances, polyhedral distortions, and unit-cell parameters, which all ultimately control the compressibility behavior of these Brgs. By analyzing the structural changes occurring in the samples, the effects of several different substitution mechanisms can be resolved to some extent. Substitution of Al into the B-site causes an increase in the octahedral volume due to the larger size of this cation with respect to Si. As the oxygen displacements have to follow the symmetry rules, as described by the Irreps, the increase in the three different B-O bond distances, as Al is added, cannot be uniform and as shown in Figure 5a is quite anisotropic. The B-O1 bond distances involve the apical oxygens (O1) whose displacements (R 4 + and X 5 + O; Figure 1b) occur on the a-b plane away from the A cations and are, therefore, less restricted in their motion than the O2. As a result, the B-O1 bond distances increase more steeply, giving rise to an elongation of the   octahedron as the Fe 3+ AlO 3 component is added (Figure 5a). Since the B-O1 bond distance lies mainly along the c-axis (Figure 1a), this unit-cell lattice parameter shows the greatest increase with Fe 3+ AlO 3 substitution (Figure 5b). The variation of the other B-O2 bond distances (Figure 5a) results from displacements of the O2 atoms (R 4 + and M 3 + , Figure 1b) that cause an increase in octahedral tilting, which is favored by the replacement of Mg by the smaller Fe 3+ cation at the A-site, as described in the next paragraph. However, since each O2 atom forms a shorter B-O2 bond on one octahedron but is part of a longer B-O2 bond in the adjacent octahedron, a uniform elongation of both lengths is not possible; and as a consequence, the shortest distance increases more steeply than the longer in order to accommodate the larger Al cation. In this way, the two nonequivalent B-O2 bonds become more similar in length with increasing Fe 3+ AlO 3 , implying that the basal plane of the octahedron becomes more regular. The variation of the two nonequivalent B-O2 distances also determines in part the variation of the a and b unit-cell parameters (Figure 5b). The b-axis increases more than the a-axis upon Fe 3+ AlO 3 substitution because the shorter B-O2 distance lies mainly in this direction. Sample S6838, which has Fe 3+ > Al and is calculated to contain 0.04(1) atoms pfu of Fe 3+ in the octahedral site (labeled in Figure 5a as Fe 3+ Fe 3+ O 3 bearing) clearly displays B-O bond distances that deviate from the general Fe 3+ AlO 3 trend. B-O bond distances appear, therefore, to be very sensitive to Fe 3+ substitution into the B site. Such a low concentration of Fe 3+ at the B site would not be resolved in the refinement of the B-O bond distances, if there were significant disordering of Fe 3+ and Al between the A and B sites in the investigated Brgs, further supporting the cation assignment strategy followed in this study.
Samples S6732, S6848, and S6805, which contain up to 0.12 atoms pfu of Fe 2+ , have B-O distances that do not deviate significantly from the Fe 3+ AlO 3 trend, implying that Fe 2+ SiO 3 substitution has no apparent influence on the octahedral volume, V B , in agreement with the results shown in Figure 3. The Fe 2+ SiO 3 substitution affects only slightly the c-and b-axes, as shown by the samples analyzed by Tange et al. (2009) (Figure 5b) and as expected due to the substitution of Mg for just slightly larger Fe 2+ at the A site. However, it does have a small effect on the a-axis, with samples analyzed by Tange et al. (2009) following a similar trend as that defined by the samples investigated in this study (Figure 5b). This may be explained by the displacement of the slightly larger Fe 2+ more toward the center of the A site (Figures 4b and 4c). Note, however, that these changes are small compared to the changes occurring along the other two axes due to the incorporation of Al into the octahedron; and therefore, result in a much smaller increase in molar volume (Figure 2a) along the MgSiO 3 -Fe 2+ SiO 3 join. The samples analyzed by Vanpeteghem et al. (2006) broad agreement with our results, except the sample with the highest Fe 3+ AlO 3 content which also contains 0.03 atoms pfu of Ti in the octahedral site and, therefore, has much longer B-O bond distances (Figure 5a). (Figure 6a) to decrease and the other longer distances (Figures 6b and 6c) to increase. These changes are due both to the displacement of the Fe 3+ at the A-site toward one side of the A polyhedron, as clearly seen in the increase of the X 5+ A and R 5+ A modes (Figures 1b, 4b and 4c) and due to the tilting of the octahedra (R 4 + and M 3 + ) in order to better coordinate the smaller A cations. As a consequence, the distortion of the A site increases. We can expect that Al substitution into the A site, through an AlAlO 3 component for example, will result in an even larger off-center displacement than Fe 3+ given its smaller radius, which will further lead to a distortion of the A site and a larger increase in the octahedral tilting. This is supported by the deviation of sample S7241, which is the only sample with some Al on the A site and also plots below the R 5 + A curve in Figure 4c and above the curve for X 5 + A in Figure 4b (indicated by black arrows). This can explain the smaller unit-cell parameters of the AlAlO 3 samples (Figure 5b) in spite of them having octahedral volumes similar to the Fe 3+ AlO 3 samples (Figure 3).

Substitution of Fe 3+ into the A site causes the four shorter individual A-O bond distances
On the other hand, substitution of Fe 2+ at the A site decreases the A-site distortion as well as the octahedral tilting. In fact, for the three Brg samples (S6732, S6848, and S6805) containing a larger amount of Fe 2+ , the X 5 + A and R 5 + A modes are even smaller than those of the endmember MgSiO 3 (Figures 4b and 4c) that is, the cations are closer to the ideal cubic position. As a consequence, these three samples plot off some of the A-O distances trends ( Figure 6). Moreover, the slightly larger Fe 2+ cations require a smaller octahedral tilting (R 4 + in Figures 1b and 4a) for their coordination. The individual A-O bond lengths of Brg from Vanpeteghem et al. (2006) also agree with our experiments, with the small deviations ascribable to the presence of other elements, as mentioned previously ( Figure 6).

Compressibility and Distortion of Bridgmanite With Pressure
Using the structural information obtained in this study, it is possible to rationalize how changes in tilting and distortion that occur upon certain substitutions are likely to influence the Brg bulk modulus (K). This can be used to evaluate previous experimental and ab initio determinations of these effects for different Brg substitutions, which are often in poor agreement. While the room pressure and temperature isothermal bulk modulus of endmember MgSiO 3 Brg is quite accurately determined to be 251 ± 2 GPa through compression experiments on MgSiO 3 Brg single-crystal (Boffa Ballaran et al., 2012), the effects on the Brg EoS of the substitution of other components are still quite poorly constrained. There are discrepancies, for example, as to whether the incorporation of Al into Brg would make it more or less compressible (Andrault et al., 2001;Daniel et al., 2001Daniel et al., , 2004Kubo et al., 2000;Walter et al., 2004Walter et al., , 2006Yagi et al., 2004;Zhang & Weidner, 1999).
The compressibility of Brg will depend on the strength of the individual cation-oxygen bonds and, therefore, on the octahedral (β B ) and A-site (β A ) compressibilities. The bulk moduli of different Brg endmembers relative to the MgSiO 3 endmember can be rationalized in terms of changes in tilting and distortion occurring in the Brg structure whilst accommodating cation substitution. It has been shown that the relative compressibility β B /β A can be directly deduced from the basic bond-valence parameters (Brown & Altermatt, 1985) and bond lengths measured at room pressure (Angel et al., 2005;Zhao et al., 2004), according to the equation:   <1 implying that the A site is more compressible than the octahedral site (Angel et al., 2005) and that, therefore, the compression of the octahedral framework will be mainly responsible for the bulk compressibility of Brg. The M A /M B ratio also increases with increasing Fe 3+ AlO 3 substitution, implying an increase in octahedral compressibility and/or a decrease in the A-site compressibility with respect to MgSiO 3 Brg. The increase in octahedral compressibility is due to Al substituting for Si at the B site and it is likely the major cause of the previously reported decrease in the bulk modulus of Brg by Fe 3+ AlO 3 substitution (Boffa Ballaran et al., 2012;Nishio-Hamane et al., 2008). Since the same type of octahedral substitution also occurs in AlAlO 3 , this component should also have a smaller bulk modulus than MgSiO 3 . Substitution of Fe 3+ at the octahedral site should further increase its compressibility resulting in an even more compressible Fe 3+ Fe 3+ O 3 component. Due to the presence of both Al at the octahedral site and oxygen vacancies, we would expect MgAlO 2.5 Brg to be softer than AlAlO 3 . Following the same argument, we would expect MgFe 3+ O 2.5 Brg to be the softest of all components.
Based on this information, we attempt to make estimates for the room pressure and temperature bulk modulus of different Brg endmembers by selecting studies from the literature and using the relation, where K and V are the bulk modulus and volume, respectively, of a Brg with mixed composition, x i is the mole fraction of the component i in the Brg of mixed composition and K i and V i are the bulk modulus and molar volume of the pure i component. The bulk modulus of pure MgSiO 3 Brg as well as the experimental data used to constrain the bulk modulus of Fe 3+ AlO 3 are taken from the single-crystal compression study of Boffa Ballaran et al. (2012). Sample S4253 in this previous study contains a high proportion of the Fe 3+ AlO 3 component (0.37 pfu) and thus should provide good constraints on the endmember value of K i , which is determined to be 224 GPa. There are significant discrepancies in the literature as to the extent to which Al on its own influences Brg compressibility. Some studies show a substantial decrease of K i (8%-12%) even with a small amount of Al (5-7.7 mol.%) (Daniel et al., 2001;Kubo et al., 2000;Zhang & Weidner, 1999) while others predict a smaller effect, that is, a ∼2.5% decrease with 10 mol.% Al (Daniel et al., 2004;Walter et al., 2004). This discrepancy may well result from differing proportions of AlAlO 3 CC and MgAlO 2.5 OV components in the investigated samples, with higher compressibilities related to the latter (Daniel et al., 2004;Walter et al., 2004). One of the only studies to specifically address this is the ab initio study of Brodholt (2000). By normalizing the values in this previous study to account for the fact that the generalized gradient approximation (GGA) tends to underestimate K i by about 7%-8% (Brodholt, 2000), a value for the AlAlO 3 endmember of 200 GPa is obtained, which is in good agreement with the trend reported by Walter et al. (2004). The different cation substitutions at the A site should obviously account for the different compressibilities of the Fe 3+ AlO 3 and AlAlO 3 components. Although Fe 3+ is larger than Al and would, therefore, be expected to be more compressible, the calculations described above imply that Fe 3+ AlO 3 is slightly stiffer than AlAlO 3 . This is likely due to the slightly greater off-center displacement of Al with respect to Fe 3+ (Figures 4b and 4c), which leads to an increase in the longer A-O bonds. Interestingly, as described in Section 3.3, Fe 2+ SiO 3 substitution causes the opposite effect, making the A cation more centered in the polyhedron, which might be coupled to a small increase in the bulk modulus upon Fe 2+ substitution, as proposed in some studies (e.g., Boffa Ballaran et al., 2012;Dorfman et al., 2013;Kiefer et al., 2002;Lundin et al., 2008;Mao et al., 2011).
Making the same GGA correction to the data of Brodholt (2000) gives a K i for the MgAlO 2.5 endmember of 163 GPa. This increase in the compressibility (35%) is slightly larger than that (25%) proposed by Ross et al. (2002) based on a comparison between the CaFeO 2.5 brownmillerite structure and OV-free perovskites. These could both be overestimates, however, as they consider OVs to be fully ordered, which is most likely HUANG ET AL.

10.1029/2021JB021936
15 of 21   Catalli et al. (2010). The resulting value of 155 GPa is in excellent agreement with the value of 157 GPa obtained from the theoretical study of Shukla et al. (2016). As Fe 3+ Fe 3+ O 3 substitution will cause a large decrease in the bulk modulus of Brg, studies on the effect of Fe 2+ SiO 3 substitution need to be very clear on the iron oxidation state of the samples. Values of K i for different Brg endmembers are summarized in Table S5. Due to the lack of experimental and theoretical constraints, the bulk modulus of MgFe 3+ O 2.5 is assumed to be identical to that of the MgAlO 2.5 component in the following discussion.

Variation of Different Bridgmanite Components With Pressure
The molar volumes and isothermal bulk moduli of different Brg endmembers determined in this study, together with other thermodynamic data tabulated in Table S5, can be used to calculate the volume changes (ΔV) associated with different equilibria involving the Brg components, Fp and iron metal at different pressures (Table 4). This allows the likely effect of pressure on the proportions of Brg components to be assessed. The values of ΔV are calculated at high-pressure and temperature using the modified Tait equation of state (TEOS) (Holland & Powell, 2011) and either using the EoS parameters for each Brg component given in Table S5 or assuming that all Brg component bulk moduli are identical to the bulk modulus of MgSiO 3 Brg. A comparison between the two ΔV estimates is used to provide some considerations of the likely uncertainties on ΔV.
Equilibria (1) and (2) (Table 4), which monitor respectively the preference for the formation of the OV components versus the CC equivalents, have relatively large negative values of ΔV at all conditions examined, regardless of the EoS parameters used. This implies that pressure will drive these equilibria to the right, favoring the CC substitution mechanism over the OV substitution at the top of the lower mantle, in good agreement with recent experimental studies (Liu et al., 2017;Walter et al., 2006). Equilibrium (3) (Table 4) examines the preference for Fe 3+ and Al ordering with increasing pressure. The sign of the ΔV can be seen to vary depending on the EoS parameters used. The study of Catalli et al. (2010) implies a relatively high compressibility for Fe 3+ Fe 3+ O 3 Brg, leading to positive estimates for equilibrium (3), which would favor disordering of Fe 3+ and Al onto both sites with increasing pressure. This agrees with several experimental and computational studies that suggest that Fe 3+ enters the B-site of Fe and Al-bearing Brg at pressures above 50 GPa, likely due to the high-spin to low-spin transition of octahedrally coordinated Fe 3+ with consequent reduction of its cation size (Catalli et al., 2011;Fujino et al., 2012;Hsu et al., 2012). Although other studies have, however, questioned these results (Glazyrin et al., 2014;Kupenko et al., 2015), some degree of Al/Fe 3+ disorder seems plausible within the current uncertainties. Equilibrium (4) describes the disproportionation of Fe 2+ to produce the Fe 3+ AlO 3 Brg component and iron metal. While the equilibrium ΔV is predicted to be negative at 25 GPa, at 50 GPa it becomes positive, irrespective of the EoS parameters used, suggesting that the proportion of iron metal formed in the mantle decreases with increasing pressure. However, the HUANG ET AL.  Table S5. Details are described in the text and notes of Table S5.  Table 4). In this case, the disproportionation of Fe 2+ to form Fe 3+ Fe 3+ O 3 and iron metal is still favored at 50 GPa. Above 50 GPa, the high-spin to low-spin transition of Fe 2+ in Fp may eventually drive equilibrium (5) to the left. This tendency for the amount of disproportionated metal to first increase and then decrease with pressure would mean that the fo 2 would also first decrease and then increase with pressure. As a result, the deep lower mantle maybe less reduced than the shallower region, although there is no reason to believe that the effect is sufficient for the fo 2 to be raised significantly above the IW buffer (Huang et al., 2021). Higher temperatures during magma ocean crystallization may have further suppressed the amount of metal formed through disproportionation due to the requirement for lower Fe 3+ contents in Brg in equilibrium with iron metal at these conditions (Boujibar et al., 2016;Frost et al., 2004;Huang et al., 2021). As indicated above, metal production may have then been further suppressed at pressures above 50 GPa, although removal of metal by core forming liquids as they pass through the shallow lower mantle remains a viable mechanism for mantle oxidation.
A relatively sharp decrease in the Fe 3+ /∑Fe ratio of Brg in the presence of iron metal was reported between 35 and 51 GPa in the laser heated DAC study of Shim et al. (2017). In this study, Brg coexisted with metallic iron but in some experiments a small amount of silica was detected. As the experiments did not contain Fp, the experiments of Shim et al. (2017) may be explained at these pressures by considering the volume changes of equilibria (6) and (7) (Table 4). Both equilibria show positive volume changes at 25 and 50 GPa, regardless of the bulk modulus assumptions made (Table 4), implying that the Fe 3+ /∑Fe ratio in Brg should decrease with pressure as observed by Shim et al. (2017). However, such a decrease might not be expected for a pyrolitic mantle containing Fp, for which equilibria (4) and (5) (Table 4) are likely more applicable. Fe and Al-rich Brg in subducted oceanic crust would coexist with free silica in the lower mantle (Akaogi, 2007;Hirose et al., 2005). Since our calculation shows that pressure may not favor FeO charge disproportionation in silica saturated systems, when considering also the more oxidized nature and smaller proportion of Brg in oceanic crust compared with pyrolitic mantle, disproportionation to form iron metal might not be expected to occur in subducted oceanic crust.

Conclusions
The crystal chemistry of ten well-characterized Al and Fe-bearing Brg single-crystals with Fe and Al contents ranging from 0 to 0.40 atoms pfu were investigated by single-crystal X-ray diffraction. Structural refinements confirm the preference of Fe 3+ and Al for the A and B sites, respectively. Charge-coupled substitution is dominant for trivalent cations (Fe 3+ and Al 3+ ) and the oxygen vacancy component does not exceed 0.04 pfu for the investigated Brg crystals. Through the site assignment, a small amount of Fe 3+ (0.04 atoms pfu) was found to enter the B site in one of the samples due to the concentration of Fe 3+ exceeding Al. In one Al-rich sample (Al > Fe 3+ ) a small amount of Al is assigned to the A site. Based on the compositions and molar volumes of Brg, the molar volumes of important Brg endmember components were refined by linear regression, using also data from previous studies, and found to decease in the order Fe 3+ Fe 3+ O 3 > MgFe 3+ O 2.5 > Fe 3+ AlO 3 > MgAlO 2.5 > AlAlO 3 > Fe 2+ SiO 3 > MgSiO 3 .
Fe 3+ AlO 3 substitution leads to increasing octahedral tilting to accommodate the smaller A cations. Moreover, the B-O bond distances increase anisotropically with the longest B-O1 bonds increasing the most and the longer B-O2 bond increasing the least, resulting in a more distorted octahedron but with a more regular basal plane. As the B-O1 bond lies along the c-axis, it increases more than the b-and a-axis upon Fe 3+ AlO 3 substitution. The larger displacement of the A cation from the center position of the A polyhedron also causes the four shorter individual A-O bond distances to decrease and the other longer distances to increase. The Al-rich sample, which hosts some Al on the A site, shows a greater off-center A cation displacement, which probably contributes to the smaller molar volume increase for AlAlO 3 substitution and may explain higher compressibilities proposed for this endmember compared to Fe 3+ AlO 3 . In contrast, Fe 2+ SiO 3 substitution decreases the R 4 + octahedral tilting and A site displacement, giving rise to the least distorted