Synthesis, crystal structure and structure–property relations of strontium orthocarbonate, Sr2CO4

A new orthocarbonate, Sr2CO4, was synthesized under extreme pressure and temperature conditions of 92 GPa and 2500 K, respectively. The crystal structure of the compound s fully characterized in situ by synchrotron single-crystal X-ray diffraction and DFT calculations were employed to provide insight into its equation of state, Raman and IR spectra, and bonding.

A remarkable discovery and a significant extension to our crystal chemical knowledge was, therefore, the synthesis and structural characterization of carbonates, in which sp 3 hybridization leads to the formation of CO 4À 4 tetrahedra instead of the usual triangular sp 2 -hybridized CO 2À 3 groups. The first reports of the synthesis of such novel carbonates were based on synchrotron powder X-ray diffraction and in situ infrared spectroscopy using either magnesite (MgCO 3 ) or ferromagnesite (Mg 0.25 Fe 0.75 CO 3 ) as starting compositions (Boulard et al., 2011(Boulard et al., , 2015. The unequivocal experimental confirmation of carbonates with CO 4 groups came with the utilization of single-crystal X-ray diffraction studies, where the structures of Mg 2 Fe III 2 C 4 O 13 -C2/c , CaMg 0.6 Fe 0.4 C 2 O 6 -Pnma , Mg 2.53 Fe 0.47 C 3 O 9 -C2/m    and MgCO 3 (Binck et al., 2020). In analogy to silicates, the CO 4 tetrahedra may be isolated or connected to other tetrahedra by corner-sharing one or more oxygen atoms, thus forming rings, chains or pyramid-like clusters. Irrespective of the chemical composition, synthesis conditions for carbonates containing CO 4 groups were at extreme conditions with P > 70 GPa and T > 2000 K. More recently, however, DFT calculations predicted that calcium orthocarbonate, Ca 2 CO 4 , may be formed at moderate pressures (Sagatova et al., 2020). Subsequently, this prediction was verified experimentally (Laniel, 2020;Binck et al., 2021) and it was found that Ca 2 CO 4 can be formed at pressures ranging from $20-90 GPa.
It now seems plausible that carbonates containing CO 4 groups can be formed with all elements for which conventional carbonates have been obtained. This would open a whole new field of crystal chemical studies, especially if it could be understood how to influence the polymerization of the tetrahedra. The present investigation supports the hypothesis of the chemical variability of carbonates with sp 3 -hybridized carbon by demonstrating the formation of strontium orthocarbonate, Sr 2 CO 4 .

Experimental
2.1. Synthesis and X-ray diffraction in the laser-heated diamond anvil cell High-pressure single-crystal X-ray diffraction experiments in a laser-heated diamond anvil cell (LH-DAC) were conducted at the P02.2 beamline at PETRA III (DESY, Hamburg, Germany). Strontium azide [Sr(N 3 ) 2 ] and strontium carbonate (SrCO 3 ) were loaded in a BX90 diamond anvil cell (DAC) equipped with diamond anvils with 120 mm culets. The chemical precursors were prepared according to Vogel & Schnick (2018). Molecular nitrogen (N 2 ) was employed as the pressure-transmitting medium. The in situ sample pressure was determined using the known equation of state of gold, also loaded in the sample cavity in the form of micrograins (Dewaele et al., 2008). The sample was compressed to 92 GPa and laser heated to a temperature of 2500 K. Measuring the thermal radiation produced by the sample enabled the accurate determination of its temperature . Under these conditions, strontium carbonate reacted to produce strontium orthocarbonate (Sr 2 CO 4 ). The produced compound was allowed to cool down to 293 K, temperature at which it was probed by X-ray diffraction. The formation of Sr x N y compounds was also observed and will be described in an upcoming publication.
The diamond anvil cell, necessary to generate high pressures, imposes additional constraints in order to obtain highquality single-crystal data. The high energy ( = 0.29521 Å ), small beam size (2 mm Â 2 mm) and high flux of the employed P02.2 beamline of PETRAIII allow the tiny single-crystals (< 1 mm 3 ) to be measured despite the intensity loss due to the scattering of the two 4 mm-thick diamond anvils. Also, the BX90 DAC used here (Kantor et al., 2012) was specifically designed to maximize the angular range at which data could be collected while having sufficient mechanical stability to allow even multi-megabar pressures to be reached. It has an effective X-ray opening of À38 to +38 much larger than most DAC designs. For the vast majority of crystal structures, including that of Sr 2 CO 4 , this opening angle in combination with the high-energy X-ray wavelength allows a sufficient coverage of reciprocal space that permits an unambiguous structural solution. Still, it must be noted that the metallic body of the BX90 blocks more than 60% of all reflections, which explains the lower reflection count and 2 range compared to ambient conditions single-crystal X-ray diffraction datasets.
In the experiments performed here, still images were recorded on a 7 Â 7 grid at the center of the sample after laser heating. With this strategy, the position of the Sr 2 CO 4 single crystal was found. A single-crystal X-ray diffraction data collection was achieved by rotating the DAC in step scans of 0.5 from À38 to +38 around the vertical axis. At each angular step, a diffraction pattern was collected with an acquisition time of 1 s.
For the data analysis, the CrysAlis Pro software (Rigaku, 2014) was utilized. The analysis procedure includes the peak search, the removal of the diamond anvil's parasitic reflections and saturated pixels of the detector, finding reflections belonging to a unique single crystal, the unit-cell determination and the data integration. The crystal structures were then solved with the SHELXT (Sheldrick, 2008)  analysis was previously demonstrated and successfully employed (Bykova, 2015;Laniel et al., 2019;Laniel, Winkler, Bykova et al., 2020;.

Refinement
Crystal data, data collection details and structure refinement details are summarized in Table 1. As these measurements were performed in a DAC, the angular range over which single-crystal data is available is limited. For this reason, the data resolution was insufficient to anisotropically refine the atomic displacement parameters (ADP) of all atoms. Hence, anisotropic displacement parameters were refined only for the strontium atoms, while for the oxygen and carbon atoms the refinement was restricted to isotropic ADP. Due to the synthesis method of Sr 2 CO 4 , nitrogen may have been incorporated into the crystal structure. However, as no significant residual electronic density at chemically relevant distances remains in the crystal, the incorporation of nitrogen is implausible. Moreover, we tested for an unlikely substitution of either carbon or oxygen with nitrogen. An increase in Rfactors was observed when performing the substitution of CÀ!N (ÁR1 = 0.034) or OÀ!N (ÁR1 = 0.013 to 0.033, depending on the substituted O atom). Therefore is no indication of the presence of nitrogen in the crystal structure.

Density functional theory-based calculations
Density functional theory (DFT) calculations have been performed using the CASTEP code (Clark et al., 2005). The code is an implementation of Kohn-Sham DFT based on a plane wave basis set in conjunction with pseudopotentials. The plane wave basis set allows numerically converged results in a straightforward manner to be achieved, as the convergence is controlled by a single adjustable parameter, the plane wave cut-off, which was set to 1020 eV. The norm-conserving pseudopotentials were generated on the fly from the information provided in the CASTEP data base. These pseudopotentials have been tested extensively for accuracy and transferability (Lejaeghere et al., 2016). All calculations employed the GGA-PBE exchange-correlation functional (Perdew et al., 1996). The Brillouin zone integrals were performed using Monkhorst-Pack grids (Monkhorst & Pack, 1976) with spacings between grid points of less than 0.037 Å À1 . Geometry optimizations were defined as being converged when the energy change between iterations was < 0.5 Â 10 À6 eV per atom, the maximal residual force was < 0.01 eV Å À1 , and the maximal residual stress was <0.02 GPa. Phonon frequencies were obtained from density functional perturbation theory (DFPT) calculations. Raman intensities were computed using DFPT in the 2n + 1 theorem approach (Miwa, 2011).

Results and discussion
3.1. Experimental crystal structure of Sr 2 CO 4 at 92 GPa Strontium orthocarbonate, Sr 2 CO 4 crystallizes in the orthorhombic crystal system with space-group symmetry Pnma. At 92 GPa, the unit-cell parameters were determined to be a = 6.214 (12), b = 4.6353 (14) and c = 8.083 (2) Å [V = 232.8 (5) Å 3 ]. The crystal structure is shown in Fig. 1 and Table 1 contains selected crystal data. Eight distinct atoms compose the structure with all, except one oxygen atom (O1), occupying the 4c special Wyckoff position which lies on the ac mirror plane with b = 1 4 and 3 4 . The O1 oxygen atom rests on the 8d general position. The atomic arrangement gives rise to three types of coordination polyhedra: CO 4 , SrO 9 and SrO 11 . At 92 GPa, the CO 4 tetrahedra share corners, edges and faces with the SrO 11 polyhedra, but only share corners and edges   with the SrO 9 polyhedra. The SrO 9 and SrO 11 polyhedra are connected to each other via their faces. While the SrO 9 polyhedra are of irregular shape, the SrO 11 polyhedra form pentacapped trigonal prisms. The CO 4À 4 group has four C-O bonds with lengths of 1.31 (5), 1.37 (2), 1.37 (2) and 1.38 (3) Å , and bond angles that vary between 103.2 (18) and 120 (3) . These values are consistent with those previously reported for carbonates with sp 0 -hybridized carbon Binck et al., 2021). The SrO 9 and SrO 11 polyhedra have an average Sr-O distance of 2.42 (2) and 2.27 (1) Å , respectively, with a minimum and maximum contact length of 2.203 (13) and 2.495 (11) Å , respectively.

DFT calculations
At 92 GPa, the pressure at which Sr 2 CO 4 was synthesized here, the experimentally derived structural model is well reproduced by DFT calculations (Table 1). The satisfactory reproduction of the experimentally determined structural parameters by DFT model calculations allows us to confidently predict properties and to investigate structure-property relations.
3.2.1. Bonding in orthocarbonates. A Mulliken population analysis shows that the three symmetrically independent C-O bonds are very similar: at 1 bar (1 bar = 10 5 Pa) the bond population decreases slightly from 0.7 e Å À3 for the shortest bond to 0.6 e Å À3 for the longest bond. A plot of the electron density difference confirms this. In such a plot (Fig. 2), the difference between the self-consistent electron density and the density obtained by overlapping the electron density of noninteracting atoms is shown.
Clearly, in the CO 4 group there are four very similar covalent C-O bonds. It is instructive to compare the CO 4 groups to those of SiO 4 groups in an isostructural Sr 2 SiO 4 silicate. The C-O bonds are, as expected, shorter ('1.4 Å compared to 1.63 Å for the Si-O bond in the silicate) but the bond populations are very similar ('0.65 e Å À3 ) in both compounds. Another notable difference is the Mulliken charge of Si 4+ to C 4+ , where the former is 1.6 e and the latter is only 0.55 e. The Mulliken charge of Sr 2+ is, in both compounds, '1.5 e, and consequently the Mulliken charge of the O 2À is notably less in Sr 2 CO 4 (À0.9 e) than in isostructural Sr 2 SiO 4 , where it is À1.16 e. So, while there are some crystal chemical similarities, the formation of solid solutions in which SiO 4 groups are substituted by CO 4 groups is unlikely, especially as the volume of the former is about twice that of the latter (Milman et al., 2001).
3.2.2. Compression of orthocarbonates. Fig. 3 shows Isosurface of the electron density difference. The isosurface is plotted for a value of 0.2 e Å À3 and shows those regions in which the electron density, after reaching self-consistency, is larger than the electron density obtained by overlapping electron densities of non-interacting atoms. Clearly, there is charge accumulation halfway along each of the four C-O vectors, which is indicative of the formation of covalent bonds.

Figure 3
(a) Pressure-volume data of Sr 2 CO 4 (this study) and Ca 2 CO 4 (Binck et al., 2021) between 1 bar and 100 GPa. The data is fitted with a third-order Birch-Murnaghan equation of state yielding K 0 = 99.7 (7) GPa, K 0 0 = 4.39 (2) and V 0 = 344.4 (2) Å 3 . (b) Evolution of the unit-cell parameters of Sr 2 CO 4 . The red, green and blue symbols refer to the a, b and c unit-cell parameters, respectively. 1947) to the Sr 2 CO 4 P-V data. From this, a bulk modulus of K 0 = 99.7 (7) GPa was obtained, with a pressure derivative of K 0 0 = 4.39 (2) and an ambient-pressure volume of V 0 = 344.4 (2) Å 3 . In a similar fashion, the change of volume with pressure for the three building blocks of Sr 2 CO 4 , namely CO 4 , SrO 9 and SrO 11 , were calculated and are shown in Fig. 4. As expected from its four rigid C-O single bonds, the CO 4 tetrahedron is found to be very incompressible [K 0 = 355 (5) GPa], while the SrO 9 and SrO 11 display a much lower value of K 0 = 92 (1) GPa and K 0 = 99 (1) GPa, respectively. Strontium orthocarbonate, Sr 2 CO 4 is isostructural to calcium orthocarbonate, Ca 2 CO 4 (Sagatova et al., 2020;Laniel, 2020;Binck et al., 2021). The comparison of the unit-cell parameters of Ca 2 CO 4 and Sr 2 CO 4 shows the expected influence of the cation substitution as the unit-cell volume increases by about 14% when Ca 2+ is substituted by Sr 2+ at ambient pressure. At 100 GPa, the difference between the unit-cell volume is similar (12%).
The isothermal bulk modulus of Ca 2 CO 4 [K 0 = 108 (1) GPa] is 8% larger than that of Sr 2 CO 4 [K 0 = 99.7 (7) GPa] (Fig. 3). Pressure-volume evolution of the three building blocks of Sr 2 CO 4 : CO 4 (a), SrO 9 (b) and SrO 11 (c). As expected from its short and rigid C-O single bonds the CO 4 tetrahedron is found to be very incompressible.
3.2.3. Lattice dynamics of orthocarbonates. It is very well established that DFPT calculations can reliably predict Raman spectra once the underlying structural model is established. For CaCO 3 and MgCO 3 polymorphs this has been demonstrated by Bayarjargal et al. (2018) and Binck et al. (2020), respectively. Raman spectra for SrCO 3 polymorphs have been published by Biedermann et al. (2017). No Raman spectra of Sr 2 CO 4 have been obtained yet, but high-quality data are available for isostructural Ca 2 CO 4 (Binck et al., 2021).
The group theoretical analysis for Sr 2 CO 4 is the same as for Ca 2 CO 4 . Both crystallize in the centrosymmetric space group Pnma, so the Raman active modes cannot be IR active and vice versa. The unit cells of these compounds contain n = 28 atoms each. Of the 3n = 84 modes, 42 are Raman active. Three of the 34 IR-active modes are acoustic phonons and cannot be measured. A group theoretical analysis gives À Raman = 13A g + 8B 1g + 13B 2g + 8B 3g and À IR = 12B 1u + 7B 2u + 12B 3u (acoustic modes not included). In Fig. 5(a), we compare the predicted Raman spectrum of Sr 2 CO 4 to experimental and DFT data for Ca 2 CO 4 at 20 GPa.
As expected, the Raman spectra of Sr 2 CO 4 and Ca 2 CO 4 [Figs. 5(a) and 5(b)] are very similar. We use the DFT data to identify the dominant atomic displacements in the characteristic vibrations. Typical displacement patterns are shown in Fig. 6.
As the phonons with wavenumbers > 500 cm À1 are dominated by modes in which only the CO 4 groups are deformed, the Raman shifts of Sr 2 CO 4 and Ca 2 CO 4 are very similar in that region. Only at lower frequencies are the Raman shifts in Sr 2 CO 4 red-shifted with respect to those in Ca 2 CO 4 due to higher mass of Sr 2+ with respect to Ca 2+ . The predicted pressure dependence of the Raman spectra is shown in Fig. 5, which can now be used to identify Sr 2 CO 4 and carbonates containing CO 4 groups in high-pressure experiments.

Conclusion
The present study has expanded our knowledge of carbonates containing CO 4 groups by adding Sr 2 CO 4 to this family of compounds. The crystal structure of strontium orthocarbonate, Sr 2 CO 4 , was unambiguously determined using singlecrystal X-ray powder diffraction measurements. It was found to be isostructural to another orthocarbonate, Ca 2 CO 4 . The present study has shown yet another way on how to synthesize carbonates with sp 3 -hybridized carbon by a more complex chemical reaction than has been employed in earlier studies. We have used the example of Sr 2 CO 4 to discuss the bonding in this fascinating class of compounds and have identified characteristic features in the lattice dynamics, thus, facilitating the identification of sp 3 -carbon in carbonates by Raman spectroscopy. The pressure stability range of Sr 2 CO 4 and the conditions under which it can be formed have not been explored yet. Such experiments are currently underway.