High-pressure syntheses were performed with the multianvil apparatus available at the Department of Earth Sciences, University of Milan (DES-UM), starting from stoichiometric CaSiO₃ gel prepared following the procedure proposed by Hamilton and Henderson (1968). Two syntheses were conducted. The first synthesis (S1) was performed at 4 GPa and 700 °C, overlapping the conditions reported in the literature (Chatterjee et al., 1984). The gel used was calcinated at 1000 °C for 10 min. A standard MgO-octahedron with a 25 mm edge length (25 M assembly) with graphite furnace, an S-type thermocouple and a 3 mm diameter gold capsule were used. The second synthesis was performed with a similar experimental setup, at 4.5 GPa and 800 °C. For this synthesis, the gel used was not further calcinated. Excess of pure H₂O was added in all the experiments as a fluxing agent. Experimental details are listed in Table 1. Temperature is accurate to ± 20 °C, with no pressure correction for the e.m.f. of the thermocouple, and pressure uncertainties were assumed to be ± 3 % according to the accuracy of calibrant reactions (Fumagalli and Poli, 2005).

To obtain single crystals of pseudowollastonite, the procedure proposed by Yang and Prewitt (1999) was followed. A stoichiometric composition of CaSiO₃ (starting from CaCO₃ and SiO2) was firstly decarbonated and successively melted at 1600 °C in a platinum crucible. The obtained glass was further heated at 1200 °C for 72 h, and single crystals of pseudowollastonite were synthesized (synthesis SX).

All the multianvil syntheses were analyzed by electron microprobe analysis (EMPA). Half of the capsules have been embedded in epoxy resin to obtain mounts suitable for the analysis. The mounts were then polished with ethanol to avoid chemical reaction with pure water. The chemical composition was determined by chemical microanalyses in wavelength-dispersive spectroscopy (EMPA-WDS) mode at DES-UM, using a Jeol 8200 instrument operating at 15 nA and 15 kV. The results of the analysis of different samples are reported in Table 2. Backscattered electron images are shown in Fig. 1a, b.

High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images and 3D electron diffraction (3D ED) data were collected using a Zeiss Libra 120 Plus TEM, operating at 120 kV and equipped with a LaB₆ source, at the Center for Materials Interfaces of the Istituto Italiano di Tecnologia (IIT; Pontedera, Italy) and a Jeol JEM-F200 field emission gun, operating at 200 kV, at the Center for Instrument Sharing of the University of Pisa (CISUP; Pisa, Italy). The former is equipped with an omega filter, a single-electron Amsterdam Scientific Instruments (ASI) Timepix hybrid pixel detector (512×512 pixels) and a Bruker XFlash 6T-60 SDD detector for energy-dispersive X-ray spectroscopy (EDX). The latter is equipped with an ASI CheeTah hybrid single-electron detector (512×512 pixels). By inserting the smallest condenser aperture (5 µm for the Zeiss TEM, and 10 µm for the Jeol TEM) and defocusing the electron beam, a parallel beam (approx. 150 and 30 nm for Zeiss and Jeol, respectively) was used for ED data collection. We first located the candidate crystals for 3D ED in STEM mode (Fig. S1). Then, we performed the 3D ED experiments either in precession-assisted (PEDT) stepwise mode using the Zeiss TEM or in continuous (cRED) mode using the Jeol TEM (Gemmi and Lanza, 2019; Gemmi et al., 2019). Regardless of the chosen acquisition method, diffraction patterns were collected by the detector while tilting the selected crystals up to 120° under the electron beam. The data collected in cRED mode had an integration angle of 0.13°, while the PEDT data were collected with a precession semi-angle of 1°. The data used for structure solution were collected in PEDT.

Finally, PETS2 software was used for data reduction and unit cell determination, integration and merging (Palatinus et al., 2019). The reconstructed reciprocal volume from 3D ED data is displayed using VESTA software (Momma and Izumi, 2011). The structure was solved using SHELXT and refined with SHELXL (Sheldrick, 2015a, b) through the program Olex2 (Dolomanov et al., 2009).

Single crystals from S2 and SX were characterized with X-ray diffraction using the four-circle κ-geometry Rigaku XtaLAB Synergy diffractometer, available at DES-UM. The diffractometer is equipped with a PhotonJet (Mo) X-ray source, operating at 50 kV and 1 mA, with monochromatized Mo K_α radiation and with a hybrid pixel array detector located 62 mm from the sample position. X-ray diffraction data were indexed and integrated with CrysAlis RED software (Rigaku Oxford Diffraction, 2018). Structural refinement was handled with Jana2006 software (Petříček et al., 2014), and structural solution was performed with a charge-flipping algorithm, using Superflip software (Palatinus et al., 2007).

High-pressure in situ single-crystal diffraction experiments were then performed on the new HP CaSiO₃ polymorph and pseudowollastonite. A single crystal from S2 (10×20×30 µm³) was loaded in a 600 µm culet membrane diamond anvil cell (DAC), with a stainless steel gasket and methanol–ethanol (4:1) as the pressure medium. X-ray data were collected up to 9.9 GPa and in decompression to assess whether hydrostatic conditions have been maintained during the experiment. A pseudowollastonite single crystal (10×20×20 µm³) was loaded in a 300 µm culet BX90-type DAC (Kantor et al., 2012) with a rhenium gasket and neon as the pressure medium. A second pseudowollastonite single crystal (20×25×30 µm3) was selected and loaded in a 600 µm culet DAC with methanol–ethanol (4:1) as the pressure medium. All the X-ray diffraction data were collected at the Xpress beamline at the Elettra synchrotron, Trieste, Italy (Lotti et al., 2020). During experiments, pressure was calibrated using ruby fluorescence (Mao et al., 1986).

Low- to high-temperature experiments were performed using a pre-tested single crystal of the HP CaSiO₃ phase placed in a quartz capillary with a diameter of 0.1 mm (Fig. S2) at the XRD1 beamline (Elettra synchrotron, Trieste, Italy). The low-temperature range 100–300 K was obtained with a liquid-nitrogen cryostat, while the high temperature, up to 766 K, was reached with a gas blower.

Diffraction data were handled as mentioned previously, and the obtained pressure–volume and temperature–volume data were then fitted with the Birch–Murnaghan equation of state (EoS; Birch, 1947) and the modified EoS from Holland and Powell (1998), respectively, using EosFit7-GUI software (Gonzales-Platas et al., 2016).

Micro-Raman spectra were collected with a Horiba LabRAM HR Evolution confocal micro-Raman spectrometer at the DES-UM equipped with ultra-low-frequency (ULF) filters. Laser light, excited with the 532 nm and 100 mW emission of a Nd:YAG laser source, was focused through a 100× objective (NA aperture of 0.9), giving a spot size of approximately 1 µm. The system was calibrated using a 520.7 cm⁻¹ line of a silicon wafer. Scattered light was collected in backscattering geometry, using a diffraction grating of 600 lines mm⁻¹ and a Peltier-cooled charge-coupled detector. To balance the signal-to-noise ratio, five accumulations of 60 s each with a 25 % reduced laser power were collected for parabreyite, and two perpendicularly polarized spectra were collected. All spectra were collected on the same samples analyzed with an electron microprobe. For comparison, we also measured the Raman spectrum of breyite, synthesized at 6 GPa and 1500 °C in a previous study (Milani et al., 2021). The breyite signal was collected with four accumulations of 20 s each with a 50 % laser power. In all the cases, the sample spot was visually examined under the microscope to ensure the absence of sample damage due to the laser irradiation.

Average EMPA results for the different syntheses are reported in Table 2, while backscattered electron images are reported in Fig. 1a, b. In S1 (Fig. 1a), the run products consist of small crystals ranging from sub-micrometric to a size of 10–15 µm. The dark gray area, which covers the largest area of the image, has a CaSiO₃ composition. The lighter gray crystals present a Ca : Si ratio of 2:1, corresponding to the larnite composition. In this case, the total measured oxides sum to approximately 94 %, suggesting possible hydration for this phase. The chemical composition and textural features of this experimental product are quite similar to the ones reported by Németh et al. (2017) for synthesis performed at higher pressure. The synthesis S2 (Fig. 1b) consists of crystals with a 100 µm average size of CaSiO₃. Minor amounts of SiO₂ and CaCO₃ (darker crystals), likely resulting from the slight carbonation of the dried gel, are also present.

The obtained crystals were studied by combining both electron and X-ray diffraction. Unit cell parameters and the volume of the measured crystals are reported in Table 3.

3D ED analysis of the lower-temperature synthesis (S1) revealed the presence of a heavily disordered phase with two well-defined unit cell parameters, a= 8.2 Å, c= 10.5 Å and β= 90°, and a strong streaking along the b* reciprocal direction, which hampers a straightforward unit cell determination (Fig. 2). The crystals usually display an irregular crystal habit formed by thin sheets stacked along b* (Fig. 2). If a semi-automatic indexing is carried out, PETS2.0 delivers an orthorhombic unit cell with b= 17.4 Å, which coincides with the cell proposed by Chatterjee et al. (1984) for their wollastonite-IIm phase. However, any attempt to solve the structure with the electron diffraction data extracted with this orthorhombic cell failed, suggesting that the cell is a result of the disorder, but the real underlying structure has a different geometry. To solve this mystery, we performed the peak search with a very high I/σ ratio (> 15) with the aim to collect only the maxima along the streaking direction. Projected along special directions perpendicular to c*, the peak table shows features characteristic of twinning (see Fig. 2 bottom right). In fact, the peaks could be indexed by two triclinic unit cells with a= 8.2 Å, b= 9.3 Å, c= 10.5 Å, α= 74°, β= 90° and γ= 77 Å, related by a 180° rotation along the b axis. The twinning occurs through reticular merohedry (Nespolo and Ferraris, 2004), with a fourfold orthorhombic super cell (a= 8.2 Å, b= 34.8 Å, c= 10.5 Å) being the twin lattice. Interestingly, a similar twinning, with different unit cell parameters, arises in the iodine salt of agomelatine (Skořepová et al., 2016), and it is widely described in Petříček et al. (2016). Therefore, in the case of the absence of disorder and the presence of two twinned individuals, the diffraction could be wrongly indexed with the fourfold orthorhombic cell. Structure solution attempts on single datasets failed since they were also affected by a low completeness (always below 60 %), in addition to the disorder and the twinning. We tried to improve the completeness by merging two datasets coming from two different crystals (still twinned), obtaining a final completeness of 62 % up to a resolution of 0.7 Å. With this dataset we could solve ab initio the crystal structure in space group P1‾. Due to the low quality of the data, the kinematical refinement converges with a quite-high R value of 38 % (Table S1).

The second synthesis (S2), planned with a slightly larger water content and higher temperature to promote possible crystal growth, resulted in larger crystal domains. A few crystal grains suitable for single-crystal X-ray diffraction were successfully isolated. Some of them appeared twinned, but the diffraction spots were successfully indexed using the unit cell determined by 3D ED. After careful selection, single-crystal domains were also measured. X-ray diffraction analysis identified the unit cell parameters a= 8.1713(2) Å, b= 9.3318(2) Å, c= 10.4382(2) Å, α= 73.902(2)°, β= 89.8888(19)° and γ = 77.489(2)°, as well as vol = 745.14(3) ų, compatible with the S1 sample. The X-ray diffraction intensities allowed for the ab initio structure solution of this HP CaSiO₃ polymorph. The charge-flipping algorithm converged to a triclinic structure with space group P1‾, corresponding to an Robs value of 3.42 % and GOF(all)= 1.53. Atomic coordinates and refinement details are reported in Table 4. Remarkably, the structural model coincides with the one derived by 3D ED. The two models compared using the COMPSTRU tools of the Bilbao crystallographic server (De La Flor et al., 2016) differ on average with 0.11 Å in their atomic positions.

The crystal structure is characterized by a threefold tetrahedra ring configuration surrounded by distorted calcium polyhedra (Fig. 3), and it is similar to the structure of pseudowollastonite and breyite, which are stable at higher temperatures at low and high pressures, respectively (Fig. 4). According to its similar topology and pressure of occurrence, we propose naming the new polymorph parabreyite, following the nomenclature rules reported by Nickel and Grice (1998).

However, from a structural perspective, the relative orientation of the silicon tetrahedra in breyite, parabreyite and pseudowollastonite is significantly different. As shown in Fig. 4, in the pseudowollastonite structure the tetrahedra rings have the outer edges pointing in almost the same direction, while in the breyite structure, one face of the three tetrahedra is nearly coplanar. In the parabreyite structure, two of the three tetrahedra point in almost the same direction, while the third one has the opposite orientation. In the a--b plane, the orientation of adjacent rings alternates. The variation in the tetrahedra orientation has a clear effect on the density of these structures as well. Considering the measured unit cell parameters (Table 3), the calculated density of pseudowollastonite is ρpseudo= 2.92 g cm⁻³, and it is significantly lower than the density of the two high-pressure polymorphs, which is ρparabreyite= 3.11 and ρbreyite= 3.08 g cm⁻³. For breyite, the density was obtained from the synthetic sample measured by Milani et al. (2021), which is consistent with the value ρbreyite= 3.07 g cm⁻³ reported by Brenker et al. (2021) for the natural sample. Breyite and parabreyite share almost the same density also because of the presence of two different calcium sites in both structures. Specifically, they show a 1:2 ratio of larger eightfold coordinated sites and smaller sixfold distorted octahedral sites.

Micro-Raman spectra collected on synthetic breyite (synthesized in Milani et al., 2021) and parabreyite (this study) were interpreted according to literature studies on threefold ring CaSiO₃ structures (Richet et al., 1998; Brenker et al., 2021). As reported, the Raman shift region between 130 and 430 cm⁻¹ corresponds to the silicate network along with the Ca–O stretching vibration. The intermediate region between about 430 and 745 cm⁻¹ is probably related to the Si–O–Si stretching and bending bridging bonds. The higher frequencies, between 900 and 1000 cm⁻¹, represent Si–O stretching vibrations with non-bridging O atoms, while the peak at around 1040 cm⁻¹ corresponds to the Si–O stretching vibration with bridging O atoms. The Raman spectra of breyite and parabreyite are reported in Fig. 5. The spectra of breyite exhibit similar characteristics to those reported by Brenker et al. (2021), with slight variations that could be attributed to minor chemical differences. When comparing the spectra of breyite and parabreyite, the first noticeable distinction appears in the Ca–O region, where the peak of breyite at 127 cm⁻¹ is absent in the parabreyite structure. To verify that this feature is not related to a particular orientation of the parabreyite crystal, we collected the spectrum with a perpendicular polarization on the same crystal. Other spectra collected on crystals with different orientations did not show the occurrence of a peak in this region. In parabreyite, the dominant peak at around 660 cm⁻¹ is shifted to a higher Raman shift value, while the Si–O stretching region is characterized by different peak positions.

A single crystal of parabreyite was loaded in a diamond anvil cell to perform in situ high-pressure X-ray diffraction in the 0–10 GPa range. No discontinuity has been observed in the pressure interval investigated. The volume–pressure data were fitted using EoSFit-GUI software (Gonzales-Platas et al., 2016) with a second-order Birch–Murnaghan equation of state (BM2) due to horizontal Eulerian strain (fe) vs. a normalized stress (Fe) plot (Angel et al., 2000) and a χw2 value of 0.56 (max ΔP = -0.15). The bulk modulus resulted in K0= 90.6(5) GPa with Kp = 4 (implied value). The V0 value was inferred from EoS extrapolation and is V0= 746.6(2) ų. Data and the relative equation of state are plotted in Fig. 6 and detailed in Table S2.

The high-pressure behavior of pseudowollastonite has also been studied in the interval between 0 and 10.10(5) GPa, with DAC having 600 µm culet diamonds (psew_HP 600). Using the EoSFit7-GUI program (Gonzales-Platas et al., 2016), the Eulerian finite strain (fe) vs. normalized stress (Fe) plot strongly suggests a third-order Birch–Murnaghan equation of state to fit the data, since it shows a positive slope. The bulk modulus resulted in K0= 81(2) GPa, with Kp = 5.9(5) and Kpp = -0.12 (implied value). Least square fitting parameters are χw2= 0.52 and maximum ΔP = 0.18. No phase transition has been observed in the interval analyzed. The second experiment was performed in the 0–13.64(5) GPa interval, with DAC having 300 µm culet diamonds (psew_HP 300). In this case, the Fe-fe plot suggested a third-order Birch–Murnaghan equation of state that resulted in K0= 76(3) GPa, with Kp = 6.6(7) and Kpp = -0.17 (implied value). Least square fitting parameters are χw2= 4.31 and maximum delta pressure = 0.24. The obtained values are compatible with the experiment in the 600 µm culet DAC within 1σ. The bulk modulus obtained in this study is consistent with the value obtained by re-fitting the data published by Yang et al. (1999) with a second-order Birch–Murnaghan equation of state, which is K0= 85(2) GPa (χw2= 4.53, maximum delta pressure = -0.14). Data are reported in Fig. 7, while the unit cell parameters for each pressure increment are reported in Table S3. The Eulerian finite strain (fe) vs. normalized stress (Fe) plots for the different high-pressure runs are reported in Fig. S3.

One single crystal of parabreyite was measured in the temperature interval 100–766 K. No discontinuity or phase transition was observed in the studied interval. Unit cell parameters and volume obtained by X-ray diffraction are reported in Table S4. The volume–temperature data were fitted with the modified thermal equation of state by Holland and Powell (1998) to have a good fit for the low-temperature data as well. The obtained parameters are V0= 752.570(13) ų, α0= 5.21(5) and α1= -0.83(4), with χw2= 0.84. Data and the equation of state are reported in Fig. 8. For comparison, the same equation of state was used to fit the thermal expansion data available for breyite in the literature (Anzolini et al., 2016). The obtained values for breyite resulted in V0= 376.41(3) ų, α0= 4.55(13) and α1= -0.95(19), with χw2= 5.11. Within 1σ, the thermal expansion parameter α0 of parabreyite is larger than the one of breyite.