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.

Abstract

Carbonates containing CO₄ groups as building blocks have recently been discovered. A new orthocarbonate, Sr₂CO₄ is synthesized at 92 GPa and at a temperature of 2500 K. Its crystal structure was determined by in situ synchrotron single-crystal X-ray diffraction, selecting a grain from a polycrystalline sample. Strontium orthocarbonate crystallizes in the orthorhombic crystal system (space group Pnma) with CO₄, SrO₉ and SrO₁₁ polyhedra as the main building blocks. It is isostructural to Ca₂CO₄. DFT calculations reproduce the experimental findings very well and have, therefore, been used to predict the equation of state, Raman and IR spectra, and to assist in the discussion of bonding in this compound.

1. Introduction  

Carbonates have been studied extensively, from the viewpoints of both geoscience and material science [see e.g. Orcutt et al. (2019 ▸) and references therein]. In nature, the most prominent representatives at ambient conditions are two polymorphs of CaCO₃, namely calcite and aragonite. At ambient conditions, calcite, aragonite and dolomite account for more than 90% of the natural carbonates (Reeder, 1983 ▸). Additional geologically relevant phases are dolomite [CaMg(CO₃)₂], magnesite (MgCO₃) and siderite (FeCO₃). Numerous other carbonates have been found in nature, or have been synthesized for scientific or industrial purposes. Most carbonates are either isostructual to calcite (), to the related structure of dolomite () or to orthorhombic aragonite (Pmcn). Carbonates with large cations (cation radius > 1 Å) tend to crystallize in the orthorhombic aragonite structure type [e.g. cerussite (PbCO₃), witherite (BaCO₃) and strontianite (SrCO₃)], while most carbonates with smaller cations tend to crystallize in the calcite or dolomite structure type {e.g. magnesite (MgCO₃), dolomite [CaMg(CO₃)₂], siderite (FeCO₃), rhodochrosite (MnCO₃), otavite (CdCO₃) and smithsonite (ZnCO₃) [Liu & Lin (1997 ▸)]}. However there are exceptions as, for example, alkali metals form monoclinic structures [e.g. Li₂CO₃ (C2/c), K₂CO₃ (C2/c) and Na₂CO₃ (C2/m)]. In the last few years, a plethora of new carbonate phases have been discovered in high-pressure studies and complex phase diagrams have been established [e.g. CaCO₃ has at least 13 polymorphs from ambient conditions to 140 GPa and 2500 K (Ono et al., 2007 ▸; Ishizawa et al., 2013 ▸; Lobanov et al., 2017 ▸; Gavryushkin et al., 2017 ▸; Bayarjargal et al., 2018 ▸)]. However, until recently, it was thought that nearly planar CO₃ groups [see Winkler et al. (2000 ▸) and references cited therein for a discussion on the planarity] were the defining feature of carbonates.

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 tetrahedra instead of the usual triangular sp ²-hybridized 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 (MgCO₃) or ferromagnesite (Mg_0.25Fe_0.75CO₃) as starting compositions (Boulard et al., 2011 ▸, 2015 ▸). The unequivocal experimental confirmation of carbonates with CO₄ groups came with the utilization of single-crystal X-ray diffraction studies, where the structures of Mg₂FeC₄O₁₃-C2/c (Merlini et al., 2015 ▸), CaMg_0.6Fe_0.4C₂O₆-Pnma (Merlini et al., 2017 ▸), Mg_2.53Fe_0.47C₃O₉-C2/m (Chariton et al., 2020 ▸), FeC₃O₁₂-R3c and FeFeC₄O₁₃-C2/c (Cerantola et al., 2017 ▸) were solved. More recently, Chariton (2020 ▸) has solved the crystal structures of MnC₂O₅- and Mn₄C₄O₁₃-C2/c. A combination of theoretical structure predictions and Raman spectroscopy data was used to demonstrate the formation of sp ³-hybridized CaCO₃ (Lobanov et al., 2017 ▸) and MgCO₃ (Binck et al., 2020 ▸). In analogy to silicates, the CO₄ 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 CO₄ groups were at extreme conditions with P > 70 GPa and T > 2000 K. More recently, however, DFT calculations predicted that calcium orthocarbonate, Ca₂CO₄, 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 Ca₂CO₄ can be formed at pressures ranging from ∼20–90 GPa.

It now seems plausible that carbonates containing CO₄ 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, Sr₂CO₄.

2. 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(N₃)₂] and strontium carbonate (SrCO₃) were loaded in a BX90 diamond anvil cell (DAC) equipped with diamond anvils with 120 µm culets. The chemical precursors were prepared according to Vogel & Schnick (2018 ▸). Molecular nitrogen (N₂) 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 (Fedotenko et al., 2019 ▸). Under these conditions, strontium carbonate reacted to produce strontium orthocarbonate (Sr₂CO₄). 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_xN_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 high-quality single-crystal data. The high energy (λ = 0.29521 Å), small beam size (2 µm × 2 µm) and high flux of the employed P02.2 beamline of PETRAIII allow the tiny single-crystals (< 1 µm³) 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 −38° to +38° much larger than most DAC designs. For the vast majority of crystal structures, including that of Sr₂CO₄, 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 2θ range compared to ambient conditions single-crystal X-ray diffraction datasets.

In the experiments performed here, still images were recorded on a 7 × 7 grid at the center of the sample after laser heating. With this strategy, the position of the Sr₂CO₄ 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 −38° 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 ▸) structure solution program using intrinsic phasing and refined within the JANA2006 software (Petříček et al., 2014 ▸). The procedure for DAC single-crystal X-ray diffraction data acquisition and analysis was previously demonstrated and successfully employed (Bykova, 2015 ▸; Laniel et al., 2019 ▸; Laniel, Winkler, Bykova et al., 2020 ▸; Laniel, Winkler, Fedotenko et al., 2020 ▸).

2.2. 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 Sr₂CO₄, 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 R-factors was observed when performing the substitution of CN (ΔR1 = 0.034) or ON (ΔR1 = 0.013 to 0.033, depending on the substituted O atom). Therefore is no indication of the presence of nitrogen in the crystal structure.

Table 1. Crystal data on the Sr₂CO₄ compound for single-crystal X-ray diffraction measurements performed at 92 GPa.

Crystal data
Chemical formula	Sr2CO4
M r	251.2
Crystal system, space group	Orthorhombic, Pnma
Temperature (K)	293
a exp, b exp, c exp (Å)	6.214 (12), 4.6353 (14), 8.083 (2)
a DFT, b DFT, c DFT (Å)	6.2223, 4.6497, 8.687
V exp (Å3)	232.8 (5)
V DFT (Å3)	233.4
Z	4
Radiation type, wavelength (Å)	Synchrotron, 0.29521
μ (mm−1)	4.31
Crystal size (mm)	0.001 × 0.001 × 0.001
Data collection
Diffractometer	Esperanto-CrysAlis PRO-abstract goniometer imported esperanto images on P02.2 at PETRA III
Absorption correction	Multi-scan (CrysAlis PRO). Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.
T min, T max	0.339, 1
No. of measured, independent and observed [I > 3σ(I)] reflections	676, 230, 170
R int	0.054
(sin θ/λ)max (Å−1)	0.887
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.045, 0.051, 2.48
No. of reflections	230
No. of parameters	26
Δρmax, Δρmin (e Å−3)	2.23, −1.55

Computer programs: CrysAlis PRO 1.171.40.55a (Rigaku Oxford Diffraction, 2019 ▸).

2.3. 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⁻¹. Geometry optimizations were defined as being converged when the energy change between iterations was < 0.5 × 10⁻⁶ eV per atom, the maximal residual force was < 0.01 eV Å⁻¹, 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 ▸).

3. Results and discussion  

3.1. Experimental crystal structure of Sr₂CO₄ at 92 GPa  

Strontium orthocarbonate, Sr₂CO₄ 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) ų]. 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 a c mirror plane with b = and . The O1 oxygen atom rests on the 8d general position. The atomic arrangement gives rise to three types of coordination polyhedra: CO₄, SrO₉ and SrO₁₁. At 92 GPa, the CO₄ tetrahedra share corners, edges and faces with the SrO₁₁ polyhedra, but only share corners and edges with the SrO₉ polyhedra. The SrO₉ and SrO₁₁ polyhedra are connected to each other via their faces. While the SrO₉ polyhedra are of irregular shape, the SrO₁₁ polyhedra form pentacapped trigonal prisms. The CO 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 (Chariton et al., 2020 ▸; Binck et al., 2021 ▸). The SrO₉ and SrO₁₁ 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.

Figure 1.

(a) Crystal structure of the Sr₂CO₄ orthocarbonate at 92 GPa. (b) Viewed along the a axis, when the atoms lying on the a c mirror plane (b = and ) are clearly visible. (c) Polyhedral representation of Sr₂CO₄. (d) The three building blocks of Sr₂CO₄, namely: CO₄, SrO₁₁ and SrO₉ (top to bottom).

3.2. DFT calculations  

At 92 GPa, the pressure at which Sr₂CO₄ 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 = 10⁵ Pa) the bond population decreases slightly from 0.7 e Å⁻³ for the shortest bond to 0.6 e Å⁻³ 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 non-interacting atoms is shown.

Figure 2.

Isosurface of the electron density difference. The isosurface is plotted for a value of 0.2 e Å⁻³ 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.

Clearly, in the CO₄ group there are four very similar covalent C—O bonds. It is instructive to compare the CO₄ groups to those of SiO₄ groups in an isostructural Sr₂SiO₄ 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⁻³) in both compounds. Another notable difference is the Mulliken charge of Si⁴⁺ to C⁴⁺, where the former is 1.6 e and the latter is only 0.55 e. The Mulliken charge of Sr²⁺ is, in both compounds, ≃1.5 e, and consequently the Mulliken charge of the O²⁻ is notably less in Sr₂CO₄ (−0.9 e) than in isostructural Sr₂SiO₄, where it is −1.16 e. So, while there are some crystal chemical similarities, the formation of solid solutions in which SiO₄ groups are substituted by CO₄ 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 the fit of a third-order Birch–Murnaghan equation of state (Birch, 1947 ▸) to the Sr₂CO₄ P–V data. From this, a bulk modulus of K ₀ = 99.7 (7) GPa was obtained, with a pressure derivative of K ₀′ = 4.39 (2) and an ambient-pressure volume of V ₀ = 344.4 (2) ų. In a similar fashion, the change of volume with pressure for the three building blocks of Sr₂CO₄, namely CO₄, SrO₉ and SrO₁₁, were calculated and are shown in Fig. 4 ▸. As expected from its four rigid C—O single bonds, the CO₄ tetrahedron is found to be very incompressible [K ₀ = 355 (5) GPa], while the SrO₉ and SrO₁₁ display a much lower value of K ₀ = 92 (1) GPa and K ₀ = 99 (1) GPa, respectively.

Figure 3.

(a) Pressure–volume data of Sr₂CO₄ (this study) and Ca₂CO₄ (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′ = 4.39 (2) and V ₀ = 344.4 (2) ų. (b) Evolution of the unit-cell parameters of Sr₂CO₄. The red, green and blue symbols refer to the a, b and c unit-cell parameters, respectively.

Figure 4.

Pressure–volume evolution of the three building blocks of Sr₂CO₄: CO₄ (a), SrO₉ (b) and SrO₁₁ (c). As expected from its short and rigid C—O single bonds the CO₄ tetrahedron is found to be very incompressible.

Strontium orthocarbonate, Sr₂CO₄ is isostructural to calcium orthocarbonate, Ca₂CO₄ (Sagatova et al., 2020 ▸; Laniel, 2020 ▸; Binck et al., 2021 ▸). The comparison of the unit-cell parameters of Ca₂CO₄ and Sr₂CO₄ shows the expected influence of the cation substitution as the unit-cell volume increases by about 14% when Ca²⁺ is substituted by Sr²⁺ at ambient pressure. At 100 GPa, the difference between the unit-cell volume is similar (12%).

The isothermal bulk modulus of Ca₂CO₄ [K ₀ = 108 (1) GPa] is 8% larger than that of Sr₂CO₄ [K ₀ = 99.7 (7) GPa] (Fig. 3 ▸). This is similar to the relation of the compressibility of aragonite [K ₀ = 69 (1) GPa] and strontianite [K ₀ = 62 (1) GPa]. The CO₄ tetrahedra in both Sr₂CO₄ and Ca₂CO₄ are very incompressible [for Sr₂CO₄: K ₀ (CO₄) = 355 (5) GPa, for Ca₂CO₄: K ₀ (CO₄) = 360 (38) GPa], even compared to SiO₄ tetrahedra [K ₀ (SiO₄) = ∼300 GPa] (Binck et al., 2020 ▸).

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 CaCO₃ and MgCO₃ polymorphs this has been demonstrated by Bayarjargal et al. (2018 ▸) and Binck et al. (2020 ▸), respectively. Raman spectra for SrCO₃ polymorphs have been published by Biedermann et al. (2017 ▸). No Raman spectra of Sr₂CO₄ have been obtained yet, but high-quality data are available for isostructural Ca₂CO₄ (Binck et al., 2021 ▸).

The group theoretical analysis for Sr₂CO₄ is the same as for Ca₂CO₄. 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 Γ_Raman = 13A_g + 8B_1g + 13B_2g + 8B_3g and Γ_IR = 12B_1u + 7B_2u + 12B_3u (acoustic modes not included). In Fig. 5 ▸(a), we compare the predicted Raman spectrum of Sr₂CO₄ to experimental and DFT data for Ca₂CO₄ at 20 GPa.

Figure 5.

(a) Comparison of a DFT-calculated Raman spectrum of Sr₂CO₄ (purple, this study), to DFT-calculated (green) and experimental (red) Raman spectra of Ca₂CO₄ at ∼20 GPa as obtained by Binck et al. (2021 ▸). (b) DFT-calculated Raman spectra of Sr₂CO₄ at different pressures. The shift of Raman modes towards higher frequencies implies positive Grüneisen parameters for all modes. All DFT-calculated Raman spectra have their x axis (Raman shift) multiplied by a scaling factor of 4%.

As expected, the Raman spectra of Sr₂CO₄ and Ca₂CO₄ [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 ▸.

Figure 6.

Displacement patterns in typical Raman modes of Sr₂CO₄ at 20 GPa. Arrows indicate the displacement of the atoms during the specific vibration. Low-frequency modes [e.g. (a)] are dominated by relative motions of the CO₄ groups against the Sr ions. Intermediate frequencies [e.g. (b)] are mainly due to displacements/rotations of the CO₄ groups, while the Sr ions are at rest. Raman shifts > 500 cm⁻¹ [(c), (d) and (e)] are due to various bending and stretching vibrations in the CO₄ groups, while the Sr ions are at rest.

As the phonons with wavenumbers > 500 cm⁻¹ are dominated by modes in which only the CO₄ groups are deformed, the Raman shifts of Sr₂CO₄ and Ca₂CO₄ are very similar in that region. Only at lower frequencies are the Raman shifts in Sr₂CO₄ red-shifted with respect to those in Ca₂CO₄ due to higher mass of Sr²⁺ with respect to Ca²⁺. The predicted pressure dependence of the Raman spectra is shown in Fig. 5 ▸, which can now be used to identify Sr₂CO₄ and carbonates containing CO₄ groups in high-pressure experiments.

4. Conclusion  

The present study has expanded our knowledge of carbonates containing CO₄ groups by adding Sr₂CO₄ to this family of compounds. The crystal structure of strontium orthocarbonate, Sr₂CO₄, was unambiguously determined using single-crystal X-ray powder diffraction measurements. It was found to be isostructural to another orthocarbonate, Ca₂CO₄. 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 Sr₂CO₄ 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 Sr₂CO₄ and the conditions under which it can be formed have not been explored yet. Such experiments are currently underway.

Supplementary Material

CCDC reference: 2052128

Funding Statement

This work was funded by Bundesministerium für Bildung und Forschung grant 05K19WC1 to Natalia Dubrovinskaia and Leonid Dubrovinsky. Deutsche Forschungsgemeinschaft grants DU 954-11/1, DU 393-9/2, DU 393-13/1, FOR2125, and WI1232. Swedish Government Strategic Research Area in Materials Science on Functional Materials at Link oping University grant 2009 00971 to Natalia Dubrovinskaia.