The unit-cell parameters determined from single-crystal X-ray diffraction (XRD) experiments are reported in Table 1. We observe a phase transition from low-pressure (LP)-P2₁/c to C2/c between 0 and 1.67 (5) GPa and a phase transition from C2/c to high-pressure (HP)-P2₁/c between 29.1 (6) and 34.0 (6) GPa, where values in parentheses are one-sigma uncertainties in the last digit. The structures and phase transition pressures are consistent with those reported in Pakhomova et al. (2017). The ab and cb orientations of the structures are shown in Fig. 1 and the structural information is tabulated in Tables S1 and S2. The zero-pressure volume for the LP-P2₁/c structure is 436.62 (9) ų, in good agreement with the zero-pressure volume of 437.70 (6) ų reported in Hugh-Jones et al. (1994), and slightly lower than the zero-pressure volume of 439.12 (4) ų given in Pakhomova et al. (2017). It is possible that the difference in zero-pressure volumes is due to different sample synthesis conditions and/or difference in Fe:Si ratio. The Fe:Si ratio reported in Pakhomova et al. (2017) is 1.93(3):2.03(3) while the Fe:Si ratio in this study is 1.98(1):2.04(3). Pakhomova et al. (2017) synthesized their ferrosilite crystals at 9.5 GPa and 1100 °C for 30 min, while Hugh-Jones et al. (1994) synthesized their ferrosilite crystals at 8.0 GPa and 1200 °C for 10.5 h. The ferrosilite crystals in this study were synthesized at 3 GPa at a temperature of 1200 °C for 16 h and 1350 °C for 128 h (see Section 2.1 for more details). It is possible that the pressure, temperature and duration of the synthesis has an effect on the Fe:Si ratio and the unit-cell volume. We note that our higher-pressure unit-cell data are also slightly and systematically offset below the values reported by Pakhomova et al. (2017) (Fig. 2).

We fit a third-order Birch–Murnaghan equation of state (Birch, 1947) to our single-crystal XRD data for the C2/c structure with MINUTI 2.0.0 (Sturhahn, 2015); the results of the fit are shown in Fig. 2. We fitted the zero-pressure volume (V₀), the zero-pressure isothermal bulk modulus (K_0T), and the bulk modulus derivative (K′_0T). The fitted zero-pressure isothermal bulk modulus (K_0T) is 106 (2) GPa with a K′_0T of 7.2 (2) and a unit-cell volume of 425.2 (2) ų. Parameter correlations are reported in Tables S3 and S4. Error ellipses for V₀ vs. K_0T, V₀ vs. K′_0T and K_0T vs. K′_0T are shown as insets in Fig. 2. The F–f plot (i.e. normalized pressure (F) against Eulerian strain (f)) for the C2/c structure is also shown in the inset in Fig. 2. The F-f data can be fitted linearly with a nonzero slope, indicating that a third-order Birch–Murnaghan equation of state is appropriate. Consequently, the F-axis intercept corresponds to the fitted K_0T, and a positive slope of the fitted line indicates that K′_0T is larger than 4.

Pakhomova et al. (2017) used the gold and neon equations of state for three pressure measurements and the Mao et al. (1986) ruby scale for the remainder of the pressure measurements. In this study, we used the Dewaele et al. (2008) ruby scale for all our pressure measurements. For a systematic comparison, we converted the Mao et al. (1986) ruby pressures in Pakhomova et al. (2017) to Dewaele et al. (2008) pressures and refitted an equation of state to the pressure–volume data of ferrosilite with the C2/c structure from the single-crystal XRD study of Pakhomova et al. (2017). The resulting equation-of-state parameters are compared in Table 2. The fitted zero-pressure isothermal bulk modulus (K_0T) is 118 (7) GPa with a K′_0T of 6.0 (6) and a unit-cell volume of 425.7 (8) ų. The difference in K_0T may be a result of different synthesis conditions and/or pressure mediums. The larger K_0T relative to our study is consistent with the observations made in a single-crystal study by Finkelstein et al. (2017) that a neon pressure medium may result in a larger K_0T for the sample compared to experiments in a helium pressure medium.

At ambient conditions, naturally-ocurring FeSiO₃ exists as a P2₁/c monoclinic phase (Bowen, 1935; Burnham, 1971; Li et al., 2014) while (Mg,Fe)SiO₃ pyroxenes with less than about 85-90 mol% FeSiO₃ primarily exist in the orthorhombic phase with space group Pbca even though the P2₁/c phase is more thermodynamically stable (Grover, 1972; Angel and Hugh-Jones, 1994). At higher pressures, Mg–Fe pyroxenes undergo phase transitions to denser monoclinic and orthorhombic phases. The nature of these phase transitions and the pressures at which they occur depend on the iron concentration (Dera et al., 2013; Finkelstein et al., 2015). At 300 K, iron-free MgSiO₃ with the orthorhombic (Pbca) symmetry was observed to undergo a phase transition to the C2/c structure at 13.4 GPa with Raman spectroscopy (Zhang et al., 2014) and to the P2₁/c structure at 12–14 GPa with powder X-ray diffraction (Li et al., 2014). Additional experiments on orthorhombic MgSiO₃ are needed to resolve the discrepancy. Single-crystal X-ray diffraction experiments on monoclinic MgSiO₃ with P2₁/c symmetry showed a phase transition to the C2/c structure at about 7–8 GPa upon compression and at about 5 GPa upon decompression (Angel et al., 1992). Room-temperature single-crystal X-ray diffraction experiments have demonstrated that orthorhombic (Mg,Fe)SiO₃ with 8–10 mol% FeSiO₃ undergoes a phase transition from the Pbca space group to a monoclinic structure with space group P2₁/c at about 12 GPa (Finkelstein et al., 2015; Zhang et al., 2012), and that, at about 30 GPa, the P2₁/c structure undergoes a phase transition to an orthorhombic structure with space group Pca2₁, which subsequently transforms to a third orthorhombic phase also with the Pca2₁ space group at about 40 GPa (Finkelstein et al., 2015). Orthorhombic (Mg,Fe)SiO₃ with 82 mol% FeSiO₃ undergoes a phase transition to the P2₁/c structure at 10 GPa, which transitions to a distinct orthorhombic phase with the space group Pbca at 12 GPa, persisting to at least 32 GPa (Dera et al., 2013). Pure FeSiO₃ with both the monoclinic (P2₁/c) symmetry and orthorhombic (Pbca) symmetry undergoes a phase transition to a monoclinic phase with C2/c symmetry at about 1.5 and 4.2 GPa, respectively (Hugh-Jones et al., 1994, 1996; Pakhomova et al., 2017; this study). It should be noted that a phase transition in orthorhombic FeSiO₃ was not observed up to ∼7 GPa with elasticity and Raman scattering measurements conducted by Kung and Li (2014). Monoclinic C2/c ferrosilite then undergoes a phase transition to a high-pressure monoclinic P2₁/c structure at about 32 GPa (Pakhomova et al., 2017; this study). See Fig. 3 for a summary of the room-temperature phase transitions in (Mg,Fe)SiO₃ pyroxenes. Additional experiments are needed to determine how the pressures of the phase transitions are influenced by varying Fe concentrations.

The effect of temperature on the phase transitions in ferrosilite has been explored up to about 8 GPa. At 300–1100 K, FeSiO₃ with P2₁/c symmetry undergoes a phase transition to the C2/c structure between 2 and 5 GPa and at 1200–1600 K, orthorhombic FeSiO₃ with Pbca symmetry undergoes a phase transition to the C2/c structure between 5 and 8 GPa (Woodland and Angel, 1997). Thus, the C2/c structure is favored above 2 GPa at 300 K and above 8 GPa at 1600 K. The subsequent phase transition of the C2/c structure to denser phases has not been investigated at high temperatures.

The LP-P2₁/c ferrosilite has the structure of low clinopyroxene (e.g., ferrohypersthene). It contains two types of FeO₆ octahedra, one that is less distorted (the M1 site) and another that is more distorted (the M2 site) (Fig. 1). The M1 octahedra form edge-sharing chains parallel to corner-sharing chains of SiO₄, while the M2 octahedra are situated within the kinks of the M1 chains. Furthermore, there are two types of symmetrically-distinct SiO₄ chains. One chain shares only corners with the FeO₆ octahedra while the other chain also shares an edge with the M2 FeO₆ octahedra, further distorting the M2 octahedron. The LP-P2₁/c structure transitions to the C2/c structure between 1.5 and 1.7 GPa, where the pressure range has been constrained by our study combined with the studies of Hugh-Jones et al. (1994) and Pakhomova et al. (2017). Upon the phase transition, the two SiO₄ chains become geometrically equivalent, such that none of the SiO₄ tetrahedra share edges with the M2 octahedra, resulting in an increase in symmetry of the structure. At about 32 GPa, half of the SiO₄ chains become octahedrally-coordinated, lowering the symmetry to P2₁/c. In the HP-P2₁/c structure, the M1 octahedra share one of their faces with SiO₆ octahedra; as a result, the M1 octahedra are more distorted than the M2 octahedra. Additional structural information on the LP–P2₁/c and C2/c structures can be found in the studies of Hugh-Jones et al. (1994) and Thompson and Downs (2004), while a thorough description of the structural changes with pressure of the three phases can be found in the study of Pakhomova et al. (2017).

The quadrupole splitting and isomer shift of the iron sites within ferrosilite were determined with time-domain synchrotron Mössbauer spectroscopy as a function of pressure. A quadrupole splitting results from an inhomogeneous electric field at the ⁵⁷Fe nucleus. The electric field gradient is affected by an electron distribution in the valence shell and the long-range lattice environment with non-cubic symmetry. Thus, the quadrupole splitting yields information on local structure, valence, and spin state. An isomer shift arises from a difference in the s electron density at the nucleus in the sample relative to a reference material or a reference iron site within the sample. For single-crystal Mössbauer spectroscopy using synchrotron X-radiation, the orientation of the electric field gradient tensor of each iron site must be specified with respect to the direction and polarization of the X-rays using three Euler angles (α, β, and γ) according to the ZYZ convention of Rose (1957). The Euler angles were calculated using the CONUSS module, “kvzz” using the atomic positions and lattice parameters of each of the three ferrosilite structures, LP-P2₁/c, C2/c, and HP-P2₁/c. The canting angle (the angle between the X-ray polarization direction (σ) and the projection of the base vector [100] onto the surface of the crystal) defines the rotation of the crystal with respect to σ. The two crystallographic sites in ferrosilite are denoted as M1 and M2, corresponding to the smaller and larger octahedral volume, respectively. For LP-P2₁/c and HP-P2₁/c, the M1 and M2 sites produce a total of four nuclear sites distinguishable by their hyperfine fields, M1_A, M1_B, M2_A, and M2_B, due to two distinct orientations of each site. In the LP-P2₁/c and C2/c structures, the larger M2 sites are more distorted than the M1 sites. In the HP-P2₁/c structure, the larger M2 sites are slightly less distorted than the smaller M1 sites. The characteristics of iron's site environment, including size and distortion, are the primary determinants of the pressure at which it will undergo a high-spin-to-low-spin transition.

Synchrotron Mössbauer spectra collected on a single crystal of ferrosilite over a pressure range of 0 to 95 GPa are shown in Fig. 4 (the crystal was oriented with the (100) face perpendicular to the X-ray direction). The spectra were fitted with version 2.1 of the CONUSS software (Sturhahn, 2000), which uses a least-square algorithm to fit iron's hyperfine parameters (e.g., isomer shift, quadrupole splitting, and distribution of the quadrupole splitting expressed as the full width at half maximum) and the sample's material properties (e.g., effective thickness and relative weights of the crystallographic sites). The effective thickness is defined as the product of the volume density of the resonant nuclei, the nuclear resonant cross section, the Lamb–Mössbauer factor, and the sample thickness. The best-fit models are also shown in Fig. 4, and modeled energy-domain spectra for selected pressures are shown in Fig. 5.

At 0 GPa, the spectrum for LP-P2₁/c is fitted with four ferrous iron sites with equal proportions, where the quadrupole splitting values of the two M1 sites and the two M2 sites were set to be equivalent, resulting in two distinct quadrupole splittings, 2.589 (3) (M1_A and M1_B) and 1.977 (5) (M2_A and M2_B) (Table 3). The orientation of the electric field gradients of the two M1 and M2 sites will affect the relative line intensities. The Euler angles of the four sites are reported in Table 4. With increasing pressure, we observe several discontinuities of the features in the synchrotron Mössbauer spectra. The phase transition from LP-P2₁/c to C2/c, identified using single-crystal X-ray diffraction (Section 3.1.1), is observed between the compression points at 0 and 4.5 GPa. Between 4.5 and 31.0 GPa, the spectra of the C2/c phase show gradual changes. The C2/c phase requires three sites, M1_A, M1_B and M2, where M1_A and M1_B have identical quadrupole splittings with different isomer shifts (Table 5). Isomer shifts are reported relative to site M1_A. The relative weight fraction of M1 to M2 sites was fixed to 50:50, while the ratio between M1_A and M1_B was fitted. The Euler angles for the electric field gradient of the two sites are reported in Table 6. All these sites have hyperfine fields characteristic of high-spin ferrous iron in octahedral coordination.

Between 31.0 and 35.1 GPa, ferrosilite undergoes a phase transition from C2/c to HP-P2₁/c. The high-spin HP-P2₁/c phase at 35.1 GPa required four high-spin ferrous iron sites to fit the data. The spectra of the HP-P2₁/c phase could no longer be fitted with the (100) orientation, and required the (110) orientation to produce a low reduced χ². Above 35.1 GPa, a fifth iron site with hyperfine parameters corresponding to a low-spin ferrous iron site (i.e. one with zero quadrupole splitting) is required. The best-fit hyperfine parameters for the HP-P2₁/c structure are reported in Table 7, while the corresponding weight fractions and FWHMs are reported in Table 8. Between 40.3 and 73.5 GPa, the two smaller M1 sites gradually decrease in weight fraction as the low-spin ferrous site increases in weight fraction from 15 to 28%. The two larger M2 sites remain in the high-spin state up to 73.5 GPa. Between 73.5 and 78.7 GPa, the low-spin weight fraction sharply increases from 28 to 53% due to the spin transition in the M2 sites, where the weight fraction of each high-spin M2 site decreases from 25 to 14%. Between 78.7 and 95.1 GPa (the maximum pressure achieved), the total low-spin weight fraction gradually increases up to 67% and may be accompanied by another phase transition. The Euler angles for the electric field gradient of the four high-spin sites are reported in Table 9. The low-spin ferrous iron site is characterized by a symmetric electric field gradient and the Euler angles are not applicable.

The fitted quadrupole splitting values for the LP-P2₁/c, C2/c and HP-P2₁/c structures are shown in Fig. 6 as a function of pressure. The weight fraction of the high-spin and low-spin sites are shown in Fig. 7, demonstrating a discontinuous increase in low-spin population at about 38 and 76 GPa. The correlation matrices for the fitted hyperfine parameters for the LP-P2₁/c, C2/c and HP-P2₁/c structures are reported in Tables S5, S6, and S7, respectively. Due to the smaller number of iron sites, and thus, hyperfine parameters for the C2/c structure, it was possible to fit the effective thickness (Table 5), whereas in the P2₁/c structures, the effective thickness was determined through Monte Carlo searches.

There have been two high-pressure Mössbauer spectroscopy studies examining the behavior of ⁵⁷Fe in (Mg,Fe)SiO₃. McCammon and Tennant (1996) conducted conventional Mössbauer spectroscopy experiments on powdered monoclinic ferrosilite up to about 4 GPa, observing a discontinuity in hyperfine fields around 1.5 GPa, associated with a P2₁/c-to-C2/c phase transition. Zhang et al. (2011) conducted synchrotron Mössbauer spectroscopy experiments on powdered orthorhombic enstatite with the chemical formula (Mg_0.87Fe_0.13)SiO₃ to 14.5 GPa, observing a discontinuity in hyperfine parameters at about 11–12 GPa, likely due to a Pbca to P2₁/c phase transition (Zhang et al., 2012; Zhang et al., 2013).

We conducted single-crystal time-domain synchrotron Mössbauer spectroscopy experiments on monoclinic ferrosilite to higher pressures than in previous studies of (Mg,Fe)SiO₃ pyroxenes. In Fig. 8, we compare the quadrupole splitting values determined in this single-crystal study to the previous powder studies on FeSiO₃ up to about 4 GPa (Dowty and Lindsley, 1973; McCammon and Tennant, 1996) and (Mg_0.98Fe_0.02)^M1(Mg_0.76Fe_0.24)^M2Si₂O₆ up to 28 GPa (Zhang et al., 2011). The magnitude of the quadrupole splitting values determined from this study are generally between the maxima and minima of the quadrupole splitting values in the previous studies. There could be several reasons for this in the case of FeSiO₃. In our study, we used a single crystal that had a relatively long synthesis time (about 5 days) and conducted the experiments in a helium pressure medium. Thus, the difference could be explained by potential differences in iron's environment caused by a difference in heating cycles/duration of the synthesis, inhomogeneity of iron-distribution across or within grains, and/or non-hydrostatic conditions (e.g., Zhang et al., 2011).

At high pressure, iron may undergo a high-spin-to-low-spin transition in mantle minerals (e.g., Badro, 2014). For example, a ∼8% decrease in the octahedral volume of ferrous iron occurs in (Mg_1–xFe_x)O (for x < 0.2) across the high-spin-to-low-spin transition (Tsuchiya et al., 2006). Spin transitions in iron-bearing lower-mantle phases are of particular importance due to their effect on seismically-relevant properties, such as sound velocities and density (Antonangeli et al., 2011; Jackson et al., 2006; Marquardt et al., 2009). The spin transition behavior of ferrosilite is compared to those of ferropericlase, siderite, and silicate glasses in Fig. 9. Siderite (FeCO₃) undergoes a sharp spin transition, observed through a 9% volume drop at about 42 GPa from X-ray diffraction experiments (Lavina et al., 2009; Liu et al., 2015). Ferropericlase with 48 mol% FeO undergoes a gradual high-spin-to-low-spin transition between about 40 and 95 GPa, as determined from powder X-ray diffraction and time-domain synchrotron Mössbauer spectroscopy (Solomatova et al., 2016). Unlike ferropericlase and siderite, basaltic and rhyolitic glasses do not experience a spin transition up to core-mantle boundary pressures at room temperature, determined with time-domain synchrotron Mössbauer spectroscopy (Solomatova et al., 2017). The spin transition behavior in ferrosilite occurs in at least two steps due to the presence of two crystallographically-distinct iron sites: at about 38 and 76 GPa, the M1 and M2 sites begin to undergo a spin transition, respectively. The total high-spin weight fraction in ferrosilite drops from 100% to 85% at ∼37 GPa and from 72% to 47% at ∼76 GPa. At 95 GPa, about a third of the iron sites remain in the high-spin state.