Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ and FeMg_0.5Si_0.5O₃ single crystals were synthesized using the Kawai-type multi-anvil press with the Osugi-type module (Ishii et al., 2019) at Bayerisches Geoinstitut, IRIS-15 (Ishii et al., 2016). A detailed description of the sample synthesis procedure can be found in Liu et al. (2019). The chemical composition of the recovered samples was determined using a JEOL JXA-8200 Electron Probe Microanalyzer (EPMA). The oxidation state of iron was determined by Mössbauer spectroscopy. Within the detection limits of the measurements, all the iron in FeMg_0.5Si_0.5O₃ is represented as Fe³⁺. Approximately 16(4)% of iron in Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ is represented as Fe²⁺ (Supplementary Figure S1).

BX90-type (Kantor et al., 2013) diamond anvil cells with diamond culet sizes ranging from 120 to 250 μm were used for conducting high-pressure experiments. To create a sample chamber between diamonds, rhenium gaskets were pre-indented to a thickness of 30 ± 5 μm. Subsequently, a laser was used to drill a hole in the center of the indented area, creating a sample chamber with a diameter of 50–110 μm depending on diamond culet sizes. Pre-selected single crystals were loaded into the center of the sample chamber together with a ruby sphere for pressure determination (Mao et al., 1986) at low pressures (p <6 GPa). Neon gas was loaded (Kurnosov et al., 2008) around the samples to serve as pressure-transmitting mediums, minimizing the degree of deviatoric stress. Additionally, it was also used for pressure determination at high pressures (p >6 GPa; Fei et al., 2007).

SC-XRD patterns were collected at the ID15B beamline at the European Synchrotron Radiation Facility (ESRF). An X-ray beam with the energy of 30 keV (λ = 0.4133 Å) was used, and diffraction data were collected using a MAR555 flat-panel detector. At each pressure point, SC-XRD data collection was performed in the omega range of ± 38° or ± 32°, depending on the DAC opening angle, with a 0.5° step and exposure time of 1 s for each step. The integration of the reflection intensities and absorption corrections was performed using CrysAlis^Pro (Agilent, 2014). The structure solution and refinement were performed in the isotropic approximation using Jana2006 (Petrícek et al., 2014) with Superflip (Palatinus and Chapuis, 2007) and SHELXT (Sheldrick, 2015).

Energy-domain synchrotron Mössbauer spectroscopy measurements were carried out at the nuclear resonance beamline ID18 at ESRF (Rüffer and Chumakov, 1996), using the synchrotron Mössbauer source (Potapkin et al., 2012). The spot size of the focused beam was approximately 15 μm² × 15 μm². Due to the usage of ⁵⁷Fe in the starting material during sample synthesis, spectral acquisition times were less than 1 h. Therefore, we do not expect an appearance of spectral features associated with the signal obtained from Fe contained in the Be window and lenses, as stated in the previous studies.

At ambient conditions, Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ adopts a LiNbO₃-type structure (space group R3c; Figure 1). The lattice parameters are determined to be a = b = 4.8790(1) Å and c = 12.9112(1) Å. This structure consists of two types of octahedra, oA and oB, forming corundum-like layers stacked along the crystallographic c axis (Ishii et al., 2017). Octahedral oA-sites are occupied by Fe and Mg (with an atomic ratio of 1:1), and oB-sites are occupied by Al and Si (with an atomic ratio of 1:1). On compression, Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ is stable in the LiNbO₃-type structure up to 8 ± 2 GPa (Figure 4), above which it transforms into a distorted perovskite structure (space group Pnma; Figures 1B, 4). As expected from the difference in ionic radii in the octahedral coordination (Shannon, 1976), the volume of oA octahedra is larger than that of oB (Figure 5). The phase transitions occur through the tilt of oB octahedra and a shift of oA-site cations to form eight-fold prismatic sites (pA in Figures 1A, C).

Compared to Fe_0.5Mg_0.5Al_0.5Si_0.5O₃, FeMg_0.5Si_0.5O₃ exhibits a more complex structure, as supported by the systematic absence analysis (Supplementary Figure S2). At ambient conditions, it adopts a corundum derivative structure (space group R3; Figure 1C), with the lattice parameters determined to be a = b = 4.9406(7) Å and c = 13.319(2) Å. Two octahedra, labeled as oA and oA’, are occupied by Fe and Mg, with site occupancies of (Fe_0.6Mg_0.4) and (Fe_0.7Mg_0.3), respectively, and are located in every second layer along the c-direction. Another two octahedra, oB and oB’, are occupied by Si and (Mg_0.7Fe_0.3). The difference in oB- and oB’-site occupancies causes the difference in octahedra volumes at ambient conditions: oB has a volume of 8 Å³, while oB’ has a volume of 10.4 Å³. It is worth noting that oB and oB’ are located in layers along c-directions and do not mix with the layers of oA and oA’ octahedra. It is a new structure, which has not been observed previously for corundum derivatives. Upon compression, FeMg_0.5Si_0.5O₃ is stable in the corundum derivative structure up to 12 ± 2 GPa, above which it transforms into a double-perovskite structure (space group P12/n1; Figures 1D, 4). This structure has some unique features that were not observed in other compositions previously. First, we observed the ordering of cations located on octahedral sites (oB and oB’), which leads to a symmetry decrease from orthorhombic perovskites to monoclinic double perovskites (Figure 1D). As a result, two different oB- and oB’-sites remain distinguishable after phase transition at 12 GPa (Figure 5). Second, we see that a larger pA-site is occupied by Mg and Fe based on single-crystal X-ray diffraction data refinement. The average pA-site Fe³⁺ occupancy is approximately 0.62(3) and is kept for all measured pressure points (Supplementary Figure S3). Another oB-site is occupied only by Si, while the oB’-site contains Fe and sufficient amounts of Mg (∼30%). The derived cation distribution is not an artifact because an attempt to refine structures within the oB-site occupied by both Si and Fe, or oB’ without the Mg-worth refinement quality (R_all increase; see Supplementary Figure S4 for more information). Considering all the available data, we conclude that, in all previously investigated compositions, the pA-site is occupied by Fe_0.6Mg_0.4 and the oB’-site is occupied by Fe_0.7Mg_0.3. More information on structure refinement can be found in Supplementary Tables S1–S3.

Synchrotron Mössbauer spectra were collected up to 95 GPa for FeMg_0.5Si_0.5O₃ (Figure 2) and up to 62 GPa for Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ (Figure 3). The Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ sample contains noticeable amounts of ferrous iron. Due to the broadness of the doublet attributed to pA-site Fe²⁺, the precise determination of Fe³⁺ content at ambient conditions is difficult. However, from the Mössbauer spectra collected at high pressure, we can estimate the Fe²⁺ content to be approximately 16(4)%. This suggests the presence of less than 1% oxygen vacancies, which, however, cannot be detected directly from our microprobe data (uncertainty of the oxygen content is ∼3%). Mössbauer spectroscopy at ambient conditions and at high pressures shows that all iron in FeMg_0.5Si_0.5O₃ is Fe³⁺ (Supplementary Figure S1). Upon compression, Fe³⁺ in Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ does not undergo spin transition (Figure 6).

The near absence of Fe²⁺ in FeMg_0.5Si_0.5O₃ together with the presence of high amounts of Fe³⁺ on oB-sites allowed us to unambiguously distinguish two doublets on Mössbauer spectra, which correspond to Fe³⁺ located on pA- and oB’-crystallographic sites. Even at pressures lower than the expected range for a spin crossover, one could still clearly observe the doublet for Fe³⁺ on oB’-sites (Figure 2). We show that the “New component” that appears in Sinmyo et al. (2017), and which was assigned to low spin Fe³⁺, existed at pressures before the spin crossover but was difficult to observe because of strong overlapping with intense A-site Fe²⁺ and Fe³⁺ doublets. Other evidence for this is the decrease in the Fe³⁺ doublet relative area, as reported by Sinmyo et al. (2017). Furthermore, hyperfine parameters that we associate with Fe³⁺ on oB-sites in FeMg_0.5Si_0.5O₃ double perovskites are similar to those for a non-magnetic doublet, reported by Kupenko et al., 2019, collected on ζ-Fe₂O₃, which has a strongly distorted perovskite-like structure (Bykova et al., 2013; Bykova et al., 2016). Our results are generally consistent with a result on the sample with a composition similar to FeMg_0.5Si_0.5O₃ from Liu et al. (2018), where they reported the central shift (CS) between the high-spin and low-spin states in the order of 0.2 mm/s based on the nuclear forward scattering experiment, which, however, does not allow to unambiguously determine the actual CS values. In agreement with the previous studies, we observe the QS increase with pressure for both studied compositions (Figure 6) (Sinmyo et al., 2017; Xiao et al., 2017; Supplementary Table S4). For example, doublets that correspond to Fe²⁺ on the pA-site in Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ perovskites have QS values of 2.50(5) mm/s at 19 GPa and 3.73(5) mm/s at 62 GPa (Figure 6).

The volume per formula unit, as a function of pressure at an ambient temperature, is shown for the two samples in Figure 4. Discontinuities corresponding to the phase transition from the LiNbO₃-type structure to a perovskite structure in the case of Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ and to phase transition from a new corundum-related structure to the double-perovskite structure in the case of FeMg_0.5Si_0.5O₃ are observed at 8 ± 2 and 12 ± 2 GPa, respectively. The fitting of pressure–volume data for perovskite-structured phases with the second-order Birch–Murnaghan equation of state (BM2–EoS) resulted in a bulk modulus of 212(3) GPa for Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ and a bulk modulus of 199(6) GPa for FeMg_0.5Si_0.5O₃. The bulk moduli of the two perovskites are smaller than that of the MgSiO₃ perovskite (251 GPa, Ballaran et al., 2012).

In the case of FeMg_0.5Si_0.5O₃, we observed an increase in compressibility at pressures above 40 GPa, which is further supported by stress versus the Eulerian strain plot from the inset of Figure 4. The same observation was made by Liu et al. (2018) on a sample with a similar composition. The high-pressure single-crystal X-ray diffraction data allowed us to track individual polyhedral volumes of the studied materials with increasing pressure. Although there is no change in the compressional behavior of pA- and oB-sites in the Al-rich sample, our experimental results clearly demonstrate the softening of Fe³⁺-bearing B’ octahedra in the FeMg_0.5Si_0.54O₃ sample (Figure 5). There is a very weak tendency in the volume increase of SiO₆ (B-site) octahedra with pressure across the spin crossover in oB’. A similar effect was observed in siderite (i.e., decrease in the volume of Fe²⁺O₆ octahedra due to the spin transition and increase in C–O distances in CO₃ groups (Lavina et al., 2010)).

Our data indicate that in the case of Fe_0.5Mg_0.5Al_0.5Si_0.5O₃ perovskites, a pA-site is more compressible than oB, as it was suggested previously (Sinmyo et al., 2017). When our result is considered together with previous data on the bulk compressibility of Fe-rich perovskites (Saikia et al., 2009; Ballaran et al., 2012; Dorfman et al., 2012; Glazyrin et al., 2014; Ismailova et al., 2016; Liu et al., 2018), one could see that it follows the general trend for the bulk modulus decrease with an increase in the Fe³⁺ content (Supplementary Figure S5). Moreover, the calculation of the bulk modulus for the Al-rich sample together with previously reported bulk moduli for Al, the Fe-bearing bridgmanite, allows us to constrain the bulk modulus of the pure FeAlO₃ end-member K₀ = 194 ± 8 GPa (Figure 7). Potentially, one could estimate the composition from polyhedra volumes; however, this result might be affected by the uncertainty of Fe spin and oxidation states.

Although it is generally assumed that the volume collapse of Fe³⁺-rich bridgmanite at pressures above 40 GPa is associated with the spin transition, our new data on the Fe³⁺-bearing octahedra volume remain controversial. Figure 8 shows the oB’ volumes of the FeMg_0.5Si_0.5O₃ sample (Mg and Fe³⁺-bearing octahedra) at all pressures are lower than that reported for pure Fe³⁺ octahedra in andradite, goethite, and hematite, despite the presence of Mg on the oB’-site suggesting a volume increase compared to pure Fe³⁺ octahedra. The low spin state of Fe³⁺ at ambient pressures was previously reported for various metal–organic compounds (Nihei et al., 2007), so one of the possible explanations for the observed effect is the low spin state of octahedral Fe³⁺ at low pressure. Indeed, the estimated ionic radii of Fe³⁺ _0.7Mg_0.3, assuming a low spin state of ferric iron, is lower than that for the high spin state of Fe³⁺.