High-pressure synthesis and crystal structure of iron
sp3-carbonate (Fe2[C4O10]) featuring pyramidal
[C4O10]4- anions

Valentin Kovalev, Dominik Spahr, Bjoern Winkler, Lkhamsuren Bayarjargal,
Lena Wedek, Alena Aslandukova, Anna Pakhomova, Gaston Garbarino, Elena
Bykova

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Valentin Kovalev, Dominik Spahr, Bjoern Winkler, Lkhamsuren Bayarjargal, Lena Wedek, et al. High-pressure synthesis and crystal structure of iron sp3-carbonate (Fe2[C4O10]) featuring pyramidal [C4O10]4- anions. Communications Chemistry, 2025, 8 (1), pp.66. 10.1038/s42004-025-01450-0. hal-05099698

HAL Id: hal-05099698

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# High-pressure synthesis and crystal structure of iron sp³-carbonate (Fe₂[C₄O₁₀]) featuring pyramidal [C₄O₁₀]⁴⁻ anions

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Valentin Kovalev,<fnref n="1" />,✉ Dominik Spahr,<fnref n="1" />,✉ Bjoern Winkler<fnref n="1" />, Lkhamsuren Bayarjargal<fnref n="1" />, Lena Wedek<fnref n="1" />, Alena Aslandukova,²,³, Anna Pakhomova⁴, Gaston Garbarino,⁵⁻⁷ & Elena Bykova<fnref n="1" />

The behavior of iron carbonates at high pressures is relevant for geological processes occurring in Earth interiors. Here, cubic iron sp³-carbonate Fe₂[C₄O₁₀] was synthesized in diamond anvil cell by reacting Fe₂O₃ and CO₂ at 65(4) GPa and 3000(±500) K, simulating the environment of localized thermal anomalies in the mantle. The crystal structure, determined by in situ single-crystal X-ray diffraction, features pyramidal [C₄O₁₀]⁴⁻ anions. The experimental crystal structure corresponds to a structural model from density functional theory calculations. Experimentally determined values for zero-pressure volume V₀ and bulk modulus K₀ are: V₀ = 1059(17) Å³, K₀ = 160(18) GPa, The DFT-calculated Raman spectrum, modeled with zinc substituting iron, matches the experimental one, supporting the structural model's accuracy. Fe₂[C₄O₁₀] remained stable upon decompression down to 25 GPa, below which it amorphized. DFT calculations also reveal a spin crossover of Fe²⁺ cations at 95 GPa, which is significantly higher than in other Fe²⁺-containing carbonates.

Carbonates are widely distributed in the geological environment. They play a significant role as a carbon source in geological processes occurring in the biosphere, hydrosphere and Earth's crust such as diagenesis, weathering and formation of ore deposits<fnref n="1" />⁻⁵. According to recent studies, carbonates could potentially serve as a carbon source during diamond crystallization across different geological environments, for example, as a component of carbonatites⁶⁻¹⁰. Moreover, carbonates are the primary constituents of marine sediments and can be transported together with water and carbonic fluids via subducting slabs into Earth's deep interior where they are involved in redox processes on the core-mantle boundary and in the formation of deep mantle melts³,¹¹.

So-called “conventional” carbonates, such as calcite and aragonite (Ca[CO₃]), dolomite (CaMg[CO₃]₂), siderite (Fe[CO₃]), and many other synthetic and natural species, contain planar trigonal [CO₃]²⁻ anions, where the bonding orbitals of the carbon atoms show sp²-hybridisation¹²,¹³. Recent experiments in diamond anvil cells (DAC) confirm that carbon follows the well-known tendency to increase the coordination number with applied pressure and that it changes its coordination from sp²-trigonal to a sp³-tetrahedral coordination at pressures as low as at ~20 GPa¹⁴⁻¹⁶. It has also

been shown that the tetrahedral coordination of carbon atoms can be recovered even under ambient conditions¹⁵. In addition, both [CO₃]²⁻ and [CO₄]⁴⁻ anions can polymerize at elevated pressures and temperatures. Such novel carbonates were obtained either by a thermal decomposition of single-source precursors¹⁷⁻²⁴ or through a chemical reaction between conventional carbonates and CO₂¹⁵,¹⁶,²⁵⁻²⁸. In case of sp²-carbon, the reactions can lead to the formation of pyrocarbonates [C₂O₅]²⁻²⁹⁻³², while [CO₄]⁴⁻ tetrahedra can be polymerized to four-membered pyramidal units [C₄O₁₀]⁴⁻²⁴⁻²⁶, rings [C₃O₉]⁶⁻¹⁹⁻²¹,³³,³⁴, four-membered linear groups [C₄O₁₃]¹⁰⁻¹⁷,¹⁸,²⁴ and pyroxene-like infinite chains [C₂O₆]⁴⁻²³. A few carbonates with isolated [CO₄]⁴⁻ tetrahedra have been also reported¹⁵,¹⁷,²⁷,²⁸.

The rich crystal chemistry of high-pressure sp³-carbonates brings them closer to the silicates in terms of their structural diversity³⁵. The degree of polymerization of the anions can be estimated using NBO/T (number of non-bridging oxygen per tetrahedron in complex anions) widely adopted for silicates³⁶,³⁷. For isolated [CO₄]⁴⁻ tetrahedra the NBO/T is 4, whereas for [C₄O₁₀]⁴⁻ pyramids the NBO/T is 1. Thus, [C₄O₁₀]⁴⁻ units, having only one non-bridging oxygen atom per tetrahedron, are the most polymerized carbonate anions discovered so far. Only three

<footnote n="1">¹Goethe University Frankfurt, Institute of Geosciences, 60438 Frankfurt am Main, Germany. ²Bayerisches Geoinstitut, University of Bayreuth, 95440 Bayreuth, Germany. ³Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany. ⁴European Synchrotron Radiation Facility, 38000 Grenoble, France. ✉e-mail: kovalev@kristall.uni-frankfurt.de</footnote>
anhydrous carbonates with $[C_4O_{10}]^4-$ pyramids have been reported: isostructural $Mn_2[C_4O_{10}] - Fd\bar{3}m^{24}$ and $Cd_2[C_4O_{10}] - Fd\bar{3}m^{25}$ and $Ca_2[C_4O_{10}] - I\bar{4}2d^{26}$, whose crystal structure is derived from the cubic parent structures through a tetragonal distortion. However, the recent study of barium hydrogencarbonate with similar pyramids has demonstrated that $[C_4O_{10}]^4-$ units can also be hydrated³⁸. The limited amount of experimental data on the formation conditions and properties of $[C_4O_{10}]^4-$ carbonates prompted us to consider the Fe-C-O system, due to the relevance of Fe-carbonates for geochemical processes such as diamond formation³⁹,⁴⁰ and the fact that multiple Fe-carbonates, including polymerized ones, have been already found in high-pressure experiments¹⁷,¹⁸,²⁰,⁴¹.

Here we report a successful synthesis and structural characterization of a cubic iron $sp^3$-carbonate featuring pyramidal $[C_4O_{10}]^4-$ units formed in a reaction between $\eta$-Fe$_2$O$_3$, and CO$_2$ at 65(4) GPa. We describe its high-pressure behavior and its stability on the decompression derived both from the experimental data and from density function theory (DFT) calculations.

## Results and discussion

### Synthesis and structural characterization of Fe₂[C₄O₁₀]

After laser heating of Fe₂O₃ to ~2000 K at 65 GPa (Fig. 1a), we used XRD mapping in order to understand if a chemical reaction had occurred. We observed the appearance of new sharp reflections on the diffraction images across the heated sample. After analyzing SCXRD data collected in several points nearby the heated area, we could determine that, the peaks belong to either $\eta$-Fe₂O₃ with a post-perovskite structure (space group Cmcm, $a$ = 2.6752(3) Å, $b$ = 8.616(3) Å, $c$ = 6.4374(14) Å) or to CO₂-V (space group I42d, $a$ = 3.4862(4) Å, $c$ = 5.7085(5) Å) (Fig. 1b). Careful analysis of the heated area using powder XRD map data have shown that no other phases are present (Fig. 1c). The presence of CO₂-V corresponds to its stability field⁴² and unit cell parameters are in an agreement with the previously determined values at similar pressures⁴³,⁴⁴.

According to previous studies, $\eta$-Fe₂O₃ is stable in a wide pressure range from 50 to 110 GPa at temperatures above 1500 K, while at sufficiently high temperatures (>2700-3000 K), it can partially reduce forming Fe²⁺-bearing oxides, such as Fe₅O₇⁴⁵. The absence of Fe₅O₇ in the heated sample provides sufficient evidence that the temperature during heating did not exceed 2700 K.

After we found that an initial heating up to ~2000 K was insufficient to induce a reaction, we performed a second laser heating experiment at higher temperatures (~3000 K) (Fig. 2a). As a result, XRD patterns measured on a 2D grid across the sample chamber changed dramatically, suggesting a reaction between the iron oxide and CO₂ or carbon from diamond anvils. From the newly appeared reflections we could identify iron carbonate $Fe^{3+}_4[C_3O_{12}]$ (S.G.: R3c, $a$ = 12.9816(16) Å, $c$ = 5.3019(12) Å)¹⁷ in the central

part of the sample (Fig. 2c, d). This phase was previously observed among the products of thermal decomposition of siderite, FeCO₃, at 74(1) GPa above 1750(100) K. In contrast, on the rims of the sides of the heated sample, we have found partially reduced Fe²⁺-bearing Fe₅O₇ (space group C2/m, $a$ = 8.8096(7) Å, $b$ = 2.6369(10) Å, $c$ = 8.0464(5) Å, $\beta$ = 105.63(8)°)⁴⁵, suggesting that $\eta$-Fe₂O₃ experienced heating at temperatures above 2700 K⁴⁵ (Fig. 2c, e).

Nevertheless, several reflections could not be assigned to $Fe^{3+}_4[C_3O_{12}]$ or Fe₅O₇ (Fig. 3a). The unknown phase can be found in the whole sample volume (Fig. 2b, c). According to the analysis of our subsequently collected SCXRD data, these peaks belong to a novel iron carbonate with a chemical composition $Fe_2[C_4O_{10}] - Fd\bar{3}m$ ($a$ = 9.3992(13) Å). Based on charge balance considerations, this compound contains only Fe²⁺. We suggest that iron from the starting $\eta$-Fe³⁺₂O₃ was completely reduced after higher-temperature heating to ~3000 K at 65 GPa. The co-occurrence of Fe₂[C₄O₁₀] with non-reduced Fe³⁺₄C₃O₁₂ and partially reduced Fe₅O₇ points to the significant temperature gradients due to the non-uniform heating and insufficient thermal insulation from the diamond anvils.

The crystal structure of $Fe_2[C_4O_{10}] - Fd\bar{3}m$ at 65 GPa was refined to $R_1$ = 3.31%, $wR_2$ = 9.02% with a data/parameter ratio of 126/13 (~9.6), pointing to the high quality of the refinement. For this dataset, as well as for those collected at 57, 52 and 44 GPa, the number of reflections was sufficient to refine anisotropic displacement parameters for all atoms. The resulting $R_1$ values do not exceed 5%, with data/parameter ratio from 7.2 to 8.0, indicating the good quality of the refinements.

During decompression starting at 31 GPa, a significant reduction and broadening of the reflection intensities belonging to Fe₂[C₄O₁₀] (Fig. 3c), can be observed, suggesting the onset of amorphization. The number of reflections also decreases drastically. To maintain a sufficient data-to-parameter ratio (6-7 reflections per refined parameter), only the iron atoms were refined using an anisotropic approximation. The last XRD dataset for Fe₂[C₄O₁₀] with reliable structure refinement ($R_1$ = 7.22%) was collected at 25 GPa. Below this pressure, the quality of the sample deteriorated significantly, and it was no longer possible to identify the compound from the XRD pattern (Fig. 3c). The final results of the refinements of the crystal structure of Fe₂[C₄O₁₀] with the atomic coordinates and bond distances at different pressure points are given in Table 1.

In the crystal structure of Fe₂[C₄O₁₀] (Fig. 4a), carbon atoms are in a $sp^3$-hybridization state and coordinated by four oxygen atoms forming $[CO_4]^4-$ tetrahedra. Each $[CO_4]^4-$ polyhedron, in turn, shares their corners with three neighboring tetrahedra forming $[C_4O_{10}]^4-$ "super-tetrahedral" pyramidal anions (Fig. 4b). The oxygen atoms are arranged in a close cubic packing. In the super-tetrahedra bridging C-O2 bonds are longer than the terminal C-O1 bonds. At 65 GPa, C-O1 and C-O2 bonds are 1.269(6) Å and 1.3750(18) Å, respectively (Table 1). Similar differences can be observed not

<figure><img src="image_4.png" /><figcaption>**Fig. 1 |** Results of the CO₂-laser treatment of the sample. a Sample chamber with $\eta$-Fe₂O₃ and a transparent ruby sphere in CO₂-pressure medium after laser heating to ~2000 K at 65 GPa; (b) distribution of the phases based on X-ray diffraction; (c) XRD pattern showing the presence of $\eta$-Fe₂O₃ and CO₂-V in the spot #988 of the XRD map.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2** | Results of YAG-laser treatment of the sample. a Sample chamber after heating to ~3000 K at 65 GPa localized in the central part of η-Fe₂O₃; (b) and (c)—distribution of the novel Fe₂[C₄O₁₀] phase across the chamber based on Raman map (band wavelength 876 cm⁻¹) and X-ray diffraction, respectively, together with other</figcaption></figure>

identified phases; XRD patterns showing identified phases in (d) the central part and in (e) the outer part of the heated sample. In the central part, the iron carbonate phase Fe³⁺[C₃O₁₂] was detected, while in the outer part we observed partially reduced Fe²⁺-bearing Fe₅O₇, indicating different temperature conditions across the sample.

<figure><img src="image_6.png" /><figcaption>**Fig. 3** | Identification of the novel phase Fe₂[C₄O₁₀]. a Fragment of XRD frame at ω = 0° at 65(4) GPa with peaks belonging to Fe₂[C₄O₁₀] (shown by black circles). White bars are gaps in DECTRIS EIGER detector; (b) reciprocal space reconstruction for Fe₂[C₄O₁₀] corresponding to the (h1l) plane. Reflections belonging to Fe₂[C₄O₁₀] are marked with black circles and located at the nodes of the unwarp grid;</figcaption></figure>

(c) XRD patterns collected for Fe₂[C₄O₁₀] on decompression from 57 to 15 GPa demonstrating a shift of characteristic reflections to lower-2θ region and a gradual deterioration of the sample with decreasing pressure highlighted by drops in intensities of reflections and their broadening. Characteristic reflections for Fe₂[C₄O₁₀] are shown by red.
<table><caption>Table 1 | Details of crystal structure refinements for Fe₂[C₄O₁₀] (S.G.: Fd̄3m; Z = 8; Fe1 16 d (0, 0, 0.5), C1 32e (x, x, z), O1 32e (x, x, z), O2 48 f (x, 3/8, 3/8)) at high pressures</caption><thead><tr><th></th><th>Pressure, GPa</th><th>65(4)</th><th>57(4)</th><th>52(4)</th><th>44(4)</th><th>31(4)<sup>a</sup></th><th>25(4)<sup>a</sup></th></tr></thead><tbody><tr><td>a, Å</td><td></td><td>9.3392(13)</td><td>9.4330(10)</td><td>9.4862(9)</td><td>9.5696(7)</td><td>9.7291(16)</td><td>9.778(3)</td></tr><tr><td>V, Å<sup>3</sup></td><td></td><td>830.4(3)</td><td>839.4(3)</td><td>853.6(2)</td><td>876.36(19)</td><td>920.9(5)</td><td>934.9(7)</td></tr><tr><td>ρ<sub>calc</sub>, g/cm<sup>3</sup></td><td></td><td>5.115</td><td>5.060</td><td>4.976</td><td>4.847</td><td>4.612</td><td>4.543</td></tr><tr><td>μ, mm<sup>-1</sup></td><td></td><td>1.194</td><td>1.517</td><td>1.492</td><td>1.453</td><td>1.383</td><td>1.362</td></tr><tr><td>2θ<sub>min</sub> for data<br>collection (°)</td><td></td><td>3.948</td><td>4.314</td><td>4.290</td><td>4.252</td><td>6.832</td><td>4.162</td></tr><tr><td>2θ<sub>max</sub> for data<br>collection (°)</td><td></td><td>39.086</td><td>42.318</td><td>41.990</td><td>40.404</td><td>36.756</td><td>31.140</td></tr><tr><td>Reflections<br>collected</td><td></td><td>485</td><td>373</td><td>346</td><td>357</td><td>152</td><td>177</td></tr><tr><td>Independent<br>reflections</td><td></td><td>126</td><td>103</td><td>94</td><td>105</td><td>68</td><td>63</td></tr><tr><td>Independent<br>reflections [I > 2σ(I)]</td><td></td><td>111</td><td>98</td><td>86</td><td>97</td><td>53</td><td>45</td></tr><tr><td>Refined<br>parameters</td><td></td><td>13</td><td>13</td><td>13</td><td>13</td><td>9</td><td>9</td></tr><tr><td>R<sub>int</sub></td><td></td><td>0.0261</td><td>0.0274</td><td>0.0357</td><td>0.0227</td><td>0.0472</td><td>0.0693</td></tr><tr><td>R(o)</td><td></td><td>0.0260</td><td>0.0157</td><td>0.0194</td><td>0.0127</td><td>0.0500</td><td>0.0675</td></tr><tr><td>R<sub>1</sub> [I > 2σ(I)]</td><td></td><td>0.0333</td><td>0.0331</td><td>0.0304</td><td>0.0406</td><td>0.0724</td><td>0.0722</td></tr><tr><td>wR<sub>2</sub> [I > 2σ(I)]</td><td></td><td>0.0908</td><td>0.0794</td><td>0.0789</td><td>0.1203</td><td>0.1815</td><td>0.1695</td></tr><tr><td>R<sub>1</sub></td><td></td><td>0.0379</td><td>0.0349</td><td>0.0323</td><td>0.0422</td><td>0.0883</td><td>0.0996</td></tr><tr><td>wR<sub>2</sub></td><td></td><td>0.0917</td><td>0.0797</td><td>0.0795</td><td>0.1211</td><td>0.1899</td><td>0.1819</td></tr><tr><td>S (F<sup>2</sup>)</td><td></td><td>1.161</td><td>1.141</td><td>1.124</td><td>1.239</td><td>1.192</td><td>1.186</td></tr><tr><td>Δρ<sub>max</sub> (e/Å<sup>3</sup>)</td><td></td><td>0.65</td><td>0.75</td><td>0.60</td><td>0.95</td><td>0.72</td><td>1.11</td></tr><tr><td>Δρ<sub>min</sub> (e/Å<sup>3</sup>)</td><td></td><td>-0.68</td><td>-0.74</td><td>-0.67</td><td>-0.67</td><td>-0.68</td><td>-0.87</td></tr><tr><td>x, z (C1)</td><td></td><td>0.0401(3), 0.2099(3)</td><td>0.0404(2), 0.2096(2)</td><td>0.0407(2), 0.2093(2)</td><td>0.0410(4), 0.2090(4)</td><td>0.0421(12), 0.2079(12)</td><td>0.0417(14), 0.2083(14)</td></tr><tr><td>x, z (O1)</td><td></td><td>0.0378(2), 0.7122(2)</td><td>0.0376(2), 0.7124(2)</td><td>0.0372(2), 0.7128(2)</td><td>0.0367(3), 0.7133(3)</td><td>0.0344(9), 0.7156(9)</td><td>0.0349(9), 0.7151(9)</td></tr><tr><td>x (O2)</td><td></td><td>0.0435(3)</td><td>0.0433(2)</td><td>0.0428(2)</td><td>0.0416(3)</td><td>0.0385(9)</td><td>0.0376(11)</td></tr><tr><td>U<sub>eq</sub> (Fe1)</td><td></td><td>0.0098(3)</td><td>0.0148(3)</td><td>0.0105(3)</td><td>0.0177(5)</td><td>0.0262(15)</td><td>0.0299(17)</td></tr><tr><td>U<sub>eq/iso</sub> (C1)</td><td></td><td>0.0079(5)</td><td>0.0146(7)</td><td>0.0092(7)</td><td>0.0175(11)</td><td>0.027(4)</td><td>0.034(6)</td></tr><tr><td>U<sub>eq/iso</sub> (O1)</td><td></td><td>0.0086(6)</td><td>0.0139(6)</td><td>0.0106(6)</td><td>0.0176(9)</td><td>0.028(3)</td><td>0.024(4)</td></tr><tr><td>U<sub>eq/iso</sub> (O2)</td><td></td><td>0.0081(5)</td><td>0.0127(5)</td><td>0.0090(5)</td><td>0.0161(8)</td><td>0.025(2)</td><td>0.021(3)</td></tr><tr><td>d (Fe1...O1), Å</td><td></td><td>2.0567(12)</td><td>2.0656(11)</td><td>2.0790(11)</td><td>2.1005(17)</td><td>2.150(6)</td><td>2.158(6)</td></tr><tr><td>d (Fe1...O2), Å</td><td></td><td>2.555(3)</td><td>2.566(3)</td><td>2.5862(15)</td><td>2.615(3)</td><td>2.666(8)</td><td>2.710(8)</td></tr><tr><td>d (C1...O1), Å</td><td></td><td>1.269(6)</td><td>1.273(5)</td><td>1.281(5)</td><td>1.288(7)</td><td>1.29(3)</td><td>1.30(3)</td></tr><tr><td>d (C1...O2), Å</td><td></td><td>1.3750(18)</td><td>1.3778(17)</td><td>1.3810(16)</td><td>1.385(3)</td><td>1.384(8)</td><td>1.389(9)</td></tr><tr><td>Data collection</td><td></td><td>ESRF, ID27, EIGER2 X CdTe<br>9 M detector, λ ~ 0.37 Å</td><td>ESRF, ID15b, EIGER2 X CdTe 9 M detector, λ ~ 0.41 Å</td><td></td><td></td><td></td><td></td></tr><tr><td>CCDC number</td><td></td><td>2393312</td><td>2393315</td><td>2393316</td><td>2393313</td><td>2393314</td><td>2393311</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>Fig. 4 | The crystal structure of Fe₂[C₄O₁₀]. a View along c; (b) arrangement of [CO₄]⁺ tetrahedra in a polymerized pyramidal unit [C₄O₁₀]⁺ (C-O bond lengths correspond to 65 GPa); (c) assemblage of [FeO₁₂] icosahedra (green) and six surrounding [C₄O₁₀]⁺ pyramids (brown) through common edges.</figcaption></figure>

<footnote>aThermal displacements for C1, O1 and O2 are in isotropic approximation.</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 5** | Evolution of interatomic distances with increasing pressure. a C-O bond lengths in high-pressure carbonates featuring [C₄O₁₀]⁺ pyramidal units as a function of pressure; (b) Fe-O bond lengths in Fe₂C₄O₁₀ and Fe²⁺-bearing compounds as a function of pressure. The error bars for some data points are smaller than symbols used.</figcaption></figure>

only in the pyramidal units of isostructural carbonates Cd₂[C₄O₁₀]²⁵, Ca₂[C₄O₁₀]²⁶ and Mn₂[C₄O₁₀]²⁴ (Fig. 5a), but also in other polymerized groups, such as [C₄O₁₃]¹⁰⁻ truncated chains in Fe₄[C₄O₁₃], [C₃O₃]⁶⁻ three-membered rings in Mg₃[C₃O₉] and [C₂O₆]⁴⁻ pyroxene-like chains in high-pressure Ca[CO₃]-P₂₁/c. At ~75 GPa, the values for terminal and bridging C-O bonds in the [C₄O₁₃]¹⁰⁻ units are reported to lie within the ranges 1.275(6)-1.340(7) Å and 1.357(9)-1.394(9) Å, respectively¹⁷. In the case of [C₃O₉]⁶⁻ rings in Mg₃[C₃O₉] at 98 GPa, the reported bond lengths for the bridging C-O bonds are within the range 1.38(3)-1.409(19) Å, while the terminal bonds are shorter, of 1.287(18)-1.294(3) Å⁴⁶. Similarly, for theoretically predicted Ca[CO₃]-P₂₁/c with [C₂O₆]⁴⁻ pyroxene-like chains, terminal and bridging C-O bond lengths are reported as 1.316(0) Å and 1.415(0) Å at 60 GPa, respectively⁴⁷.

[C₄O₁₀]⁺ units form large cavities occupied by Fe²⁺ cations. Each Fe²⁺ cation is coordinated by twelve oxygen atoms (six Fe-O1 at a distance of 2.0567(12) Å, and six Fe-O2 at 2.555(3) Å at 65 GPa), forming a distorted icosahedron (Fig. 4c). In contrast, Fe²⁺ occupies smaller sites in structures of other Fe²⁺-bearing carbonates, such as FeCO₃ and Fe₄C₄O₁₃. In Fe₄C₄O₁₃, Fe²⁺ atoms occupy bicapped prisms with a Fe-O average bond length of 2.0314 Å at 97 GPa¹⁷, while FeCO₃ follows a calcite structural type, with Fe-O bond length of 1.845(3) Å at 66 GPa⁴⁸. Based on the Fe-O bond lengths, Fe²⁺ in Fe₂[C₄O₁₀] remains in the high-spin state up to the highest pressure studied (65 GPa). In the calculations carried out at 50, 70, and 90 GPa, both high spin and low spin configurations were obtained. In all these calculations, the enthalpies for different high spin arrangements were quite similar, where the difference between the ferromagnetic state and a high spin antiferromagnetic state was ~0.3 eV per unit cell. The low spin configurations were substantially less stable at low pressures. However, the enthalpy difference between the low-spin and high-spin states decreased from 2.65 eV per unit cell at 50 GPa linearly to 0.36 eV per unit cell at 90 GPa. An extrapolation implies that the spin crossover would be induced at 95 GPa, which is the highest known value among known Fe²⁺-bearing compounds. For example, in siderite Fe[CO₃], having Fe²⁺ in a smaller octahedral coordination, the spin crossover occurs between 44 and 45 GPa⁴⁸⁻⁵⁰. This transition pressure is well reproduced by DFT-PBE-GGA calculations such as those carried out here⁵¹. In wüstite, B1-FeO, with an octahedral

coordination of Fe²⁺ atoms, similar to that in siderite, the spin crossover occurs at 74 GPa⁵²,⁵³, but Fe-O bonds in wüstite are longer than those in siderite (Fig. 5b). Therefore, the presence of larger-volume coordination polyhedra around iron atoms can contribute to a higher pressure for spin crossover of Fe²⁺ atoms in Fe₂[C₄O₁₀].

Density functional theory (DFT) calculations for iron compounds can be demanding due to partially filled 3d-orbitals and variable spin states⁵⁴,⁵⁵. We investigated the influence of an on-site Coulomb correction with the +U-approach but found the effect to be very small. To avoid high-demand computations with complex spin systems, we performed the calculations by substituting iron with zinc atoms in the crystal structure. Zinc is slightly heavier than iron, hence we expect a minor red-shift of Raman bands; however, its ionic radius ($r_i(Zn^{2+}) = 0.74Å$) is comparable to that of high-spin Fe²⁺ ($r_i(Fe^{2+}) = 0.78Å$)⁵⁶. Additionally, Zn²⁺ exhibits no spin alignment or spin transitions, as all 3d-orbitals are occupied. Therefore, Zn²⁺ can be considered as a geometric analog for Fe²⁺, making it a suitable substitute that could facilitate the performed calculations. As a result, the experimental Raman spectrum for Fe₂[C₄O₁₀] – Fd$\overline{3}$m at 65 GPa is in a good agreement with the calculated one for hypothetical Zn₂[C₄O₁₀] – Fd$\overline{3}$m at the same pressure (Fig. 6), which is consistent with the assumption that there is essentially no coupling of the spin arrangement with the lattice dynamics and confirming the structural model. We have also measured and calculated Raman spectra for the coexisting CO₂-V phase at 65 GPa and used it as a benchmark.

Three new modes at 692, 876 and 1068 cm⁻¹ were observed in the Raman spectrum (Fig. 6). According to group theory analysis, the crystal structure of Fe₂[C₄O₁₀] has following Raman-active modes: 3A₁g + 3Eg + 7T₂g. We could assign the observed modes as T₂g (692 cm⁻¹) and A₁g (876, 1068 cm⁻¹) corresponding to complex vibrations of C-O bonds in [C₄O₁₀]⁺ pyramidal anions, according to the DFT calculations.

A comparison of the experimental and DFT-calculated spectra for Fe₂[C₄O₁₀] and Zn₂[C₄O₁₀], respectively, demonstrates the expected consistency, even considering the complete substitution of iron with zinc in the crystal structure. Moreover, the calculated Raman spectrum for Cd₂C₄O₁₀²⁵ is also similar to that described above in terms of relative mode intensities and positions (Fig. 6).
<figure><img src="image_9.png" /><figcaption>**Fig. 6 |** Results of spectroscopic measurements for Fe₂[C₄O₁₀] and coexisting CO₂-V. There is an agreement between experimental (black) Raman spectrum of Fe₂[C₄O₁₀] at 65 GPa and calculated one based on Zn substitution for isostructural hypothetical Zn₂[C₄O₁₀] (blue). Characteristic modes for CO₂-V are marked with red asterisks (*). Calculated Raman spectrum for Zn₂[C₄O₁₀] also shows a striking resemblance to that of Cd₂[C₄O₁₀]²⁵ confirming that these compounds are structurally similar.</figcaption></figure>

## Compressional behavior of Fe₂[C₄O₁₀]

The compressibility of Fe₂[C₄O₁₀] was assessed by analyzing the unit cell volume data obtained from the solution and refinement of the crystal structure as a function of pressure⁶⁶, in our case - in a pressure range from 65 to 25 GPa. Additionally, we performed DFT-based geometrical optimizations (= relaxation) of Fe₂[C₄O₁₀] structures over a wider pressure range (0–90 GPa) to compare with the available experimental data. For the equation of state, the results of those calculations in which all Fe²⁺ ions were in the high spin state were employed, as these were more stable than low-spin configurations up to pressures of 95 GPa.

Due to a limited number of collected pressure points and absence of an experimental V₀ value (Fig. 3c), we found it reasonable to fit our P-V data using the second-order Birch-Murnaghan equation of state⁵⁷ (Fig. 7a), with V₀ treated as a fitted parameter. For the comparison with the computed data, they were fitted using the same approach. The resulting values for bulk modulus and unit cell volume extrapolated to zero pressure were similar (Table 2). Additional verification for the choice of the equation of state (EOS) comes from the plot of normalized stress F versus Eulerian strain f⁸ (Fig. 7b). This plot shows that the strain-stress data points, within the experimental uncertainties, follow the straight horizontal line, supporting the validity of the second-order Birch-Murnaghan EOS in describing the compressibility data.

Nevertheless, the experimental data within the 25–65 GPa pressure range show a reasonable agreement with theoretical data obtained from DFT calculations (Table 2). Structural relaxation for the phase at different pressures revealed only minor differences between C-O and Fe-O bonds (Fig. 5) from experimental and calculated data. Such changes can directly influence the unit cell parameters and volume, which is obviously anticipated. Here, the discrepancy between experimental and theoretical unit cell volumes of Fe₂[C₄O₁₀] does not exceed 3%, pointing to an accuracy of the

structural model. Slightly higher values for the calculated unit cell volumes can be explained by the underbonding effect, where the values of bond lengths are slightly overestimated due to intrinsic short-comings of the DFT-PBE-GGA calculation approach employed here⁵⁹.

The theoretical high-pressure data for similar Ca₂[C₄O₁₀] and Cd₂[C₄O₁₀] were also analyzed here in order to reveal the effect of cation radius on the bulk modulus within this group of carbonates. The calculated datasets for these compounds were fitted using both second-order and third-order Birch-Murnaghan equations. In our considerations we used ionic radii for six-fold coordinated atoms, and in the case of iron—in a high-spin state⁶⁰. The summarized data for different carbonates containing [C₄O₁₀]⁺ units is shown on Table 2. The bulk moduli for carbonates containing [C₄O₁₀]⁺ units follow the trend of increasing bulk modulus with decreasing cation radius. While this behavior was previously demonstrated for calcite-type carbonates⁶¹, it is shown here for the first time in high-pressure carbonates with polymerized units. It is reasonable to expect that future synthesized carbonates with similar anions would follow the trend, highlighting the need for further investigations.

Among the iron carbonates, the compressibility and equations of state have been only analyzed for siderite Fe[CO₃] and Fe₂[CO₃]₃. It was shown that siderite exhibits an anisotropic compression behavior due to its trigonal crystal structure. The spin crossover in siderite at 44–45 GPa is accompanied by a sharp decrease of the unit cell volume from ~230 Å³ (high-spin Fe[CO₃]) to ~208 Å³ (low-spin Fe[CO₃]). There is also a significant increase of the bulk modulus from 110(2) GPa (K'₀ = 4.6(2)) to 148(12) GPa (K'₀ fixed at 5) and, consequently, in the acoustic velocity after the spin pairing is complete¹⁸⁻⁵⁰. No phase and electronic transitions were identified in Fe₂[CO₃]₃ on compression up to 40 GPa. The bulk modulus K₀ derived from high-pressure XRD data is 138(34) GPa (K'₀ fixed at 4)⁶². In contrast to FeCO₃ and Fe₂[CO₃]₃, Fe₂[C₄O₁₀] contains different anionic unit, making a direct comparison of its bulk modulus and associated structural changes with those for other iron carbonates unreasonable.

## Implications to studies of high-pressure carbonates

Iron-bearing carbonates are well studied due to their significant role in deep Earth's processes, for example, formation of carbonatitic fluids and their transportation to the surface via upcoming mantle flows (plumes)³⁹,⁴⁰. It was previously shown that the phase with a Fe₄[C₃O₁₂] composition can be synthesized over a wide range of PT-conditions from different iron-bearing precursors such as FeO, Fe₂O₃ and FeOOH⁴¹; however, reliable structural data for this compound were initially unavailable. Later studies determined the trigonal crystal structure of Fe₄[C₃O₁₂] and confirmed its stability above 74(1) GPa and 1750(100) K. In addition, the crystal structure of co-existing iron carbonate Fe₄[C₄O₁₃] was also determined¹⁷,⁶³. Our findings, based on the PT-conditions used for the synthesis of Fe₂[C₄O₁₀], also suggest that Fe₂[C₄O₁₀] could be stable under the conditions corresponding to the middle part of the lower mantle. However, the temperature used in the experiment (~3000 K) exceeds the one expected at the Earth's depth corresponding to 65 GPa (~2400–2500 K)⁶⁴. Given the significant temperature gradients inside the sample chamber after the second heating together with experimental temperature uncertainties, we propose that localized thermal anomalies, such as those around mantle plumes, could create short-lived higher-temperature conditions (at least 200–400 K above the surrounding mantle)⁶⁵⁻⁶⁸, where [C₄O₁₀]⁺ units could be stabilized. Such plumes could also be enriched in carbon-bearing phases⁶⁹ and hence provide a potential source of carbon for the synthesis. Consequently, the co-presence of high-pressure conditions, elevated localized temperatures, and carbon-rich environment within these thermal anomalies could create favorable conditions for the formation and stabilization of Fe₂[C₄O₁₀].

## Conclusions

We report the successful discovery of Fe₂[C₄O₁₀], a novel iron sp³-carbonate with [C₄O₁₀]⁺ pyramidal groups, synthesized in diamond anvil cells under the high PT-conditions (65(4) GPa, 3000 (500) K), simulating carbon-rich environments probably existing in localized thermal anomalies in the lower
<figure><img src="image_10.png" /><figcaption>Fig. 7 | Evolution of the unit cell volume for Fe₂[C₄O₁₀] on decompression.</figcaption></figure>

a Experimental and calculated unit cell volumes of Fe₂[C₄O₁₀] as a function of pressure (filled and empty squares, respectively). The error bars for the volumes are smaller than symbols. The second-order Birch-Murnaghan equations of state for the

calculated and experimental datasets are shown by blue and black lines, respectively; (b) normalized pressure (F) as a function of Eulerian strain (f) calculated for the P-V data collected on decompression; the horizontal dash line is the second-order fit of Birch Murnaghan equation of state.

<table><caption>Table 2 | Comparison of bulk moduli for M₂[C₄O₁₀] (M = Ca, Cd, Fe) as a function of ionic radius</caption><thead><tr><th>Composition</th><th>Space group</th><th>Data</th><th>V<sub>0</sub>, Å<sup>3</sup></th><th>K<sub>0</sub>, GPa</th><th>K'<sub>0</sub>, GPa<sup>-1</sup></th><th>Ionic radius, Å<sup>a</sup></th><th>Ref.</th></tr></thead><tbody><tr><td rowspan="3">Fe₂[C₄O₁₀]</td><td rowspan="3">Fd3m</td><td>DFT</td><td>2<sup>nd</sup></td><td>1084(4)</td><td>152(3)</td><td>4.0</td><td rowspan="3">0.78</td><td rowspan="3">This work</td></tr><tr><td></td><td>3<sup>rd</sup></td><td>1092(2)</td><td>127(3)</td><td>4.93(12)</td></tr><tr><td>EXP</td><td>2<sup>nd</sup></td><td>1059(17)</td><td>160(18)</td><td>4.0</td></tr><tr><td rowspan="2">Cd₂[C₄O₁₀]</td><td rowspan="2">Fd3m</td><td>DFT</td><td>2<sup>nd</sup></td><td>1186.4(6)</td><td>132(3)</td><td>4.0</td><td rowspan="2">0.95</td><td rowspan="2">25</td></tr><tr><td></td><td>3<sup>rd</sup></td><td>1196.8(8)</td><td>112.2(5)</td><td>5.21(3)</td></tr><tr><td rowspan="2">Ca₂[C₄O₁₀]</td><td rowspan="2">I42d</td><td>DFT</td><td>2<sup>nd</sup></td><td>611(3)</td><td>110(3)</td><td>4.0</td><td rowspan="2">1</td><td rowspan="2">26</td></tr><tr><td></td><td>3<sup>rd</sup></td><td>616.7(2)</td><td>93.4(4)</td><td>4.83(2)</td></tr></tbody></table>

mantle. The crystal structure of the compound has been determined by single-crystal X-ray diffraction, and it is similar to those of Mn₂[C₄O₁₀], Cd₂[C₄O₁₀] and Ca₂[C₄O₁₀]. These compounds, together with hydrated barium carbonate, collectively constitute a group of highly polymerized carbonates. Fe₂[C₄O₁₀] shows no phase transitions within a relatively broad pressure range between 65 to 25 GPa on cold decompression. The structural and spectroscopic characteristics of Fe₂[C₄O₁₀] were examined in conjunction with DFT calculations, confirming the accuracy of the structural model for Fe₂[C₄O₁₀] at 65 GPa and during decompression. Additionally, DFT calculations suggest a high-spin/low-spin transformation of Fe²⁺ atoms at 95 GPa.

## Methods

### Preparation of diamond anvil cell

We used DAC with the mini-BX90 design⁷⁰ to generate high pressure in the experiment. Diamond anvils with culet size of 200 µm and an opening angle of ±30° were fixed in WC seats and aligned to ensure the uniaxial compression behavior. A rhenium gasket with ~200 µm thickness was placed between diamond anvils and was pre-indented to a thickness of approximately 30 µm. A circular hole with a diameter of approximately 100 µm was drilled by a Nd:YAG pulsed laser in the center of the indentation to prepare a sample chamber.

The single crystals of ⁵⁷Fe-enriched hematite (α-⁵⁷Fe₂O₃) were grown at 7 GPa and 1073 K in a 1200-tonne Sumitomo press installed at the Bavarian Geoinstitute⁴⁵. As a precursor, a 1:1 mixture of a powder of non-enriched hematite (α-Fe₂O₃) of 99.998% purity and a pure powder of ⁵⁷Fe₂O₃ (96.64%-enriched) was used. A particle of dark-brown α-⁵⁷Fe₂O₃ with

dimensions of 40 × 30 × 5 µm was placed inside the sample chamber (Fig. 1a). Then, the DAC was cooled down to approximately 100 K, and cryogenically loaded with CO₂-I (dry ice)³². The loading process was carried out under an inert argon atmosphere to minimize contamination from atmospheric moisture. In the experiment, CO₂ served as both a pressure-transmitting medium and a chemical reactant⁷¹. Carbon dioxide is a non-hydrostatic pressure-transmitting medium, and based on previous similar studies²⁶,²⁸⁻³⁰, we estimate the uncertainty in the pressure determination to be around 4 GPa. Experimental pressures in the sample chamber were determined from the positions of XRD lines of CO₂-V⁴³,⁴⁴. Due to non-hydrostatic effects, the pressure was unevenly distributed across the sample chamber, therefore we determined the pressures at the specific positions where the grains of Fe₂[C₄O₁₀] were located.

### Laser heating

The DAC compressed to 65 GPa was laser-heated twice. The first heating was performed using an in-house double-sided laser heating system, equipped with a pulsed CO₂ laser (Coherent Diamond K-250, λ = 10.6 µm)⁷². The sample was heated for 5 min with a maximum temperature of ~2000 (±100) K. The temperature was controlled by adjusting the radiation power from both sides of the sample. The laser was focused on a ~30 × 30 µm area, thereby providing uniform heating of the whole sample (Fig. 1a).

The second heating procedure was conducted using a one-sided laser-heating system at the ID27 high-pressure beamline (Nd:YAG IR laser, IPG Photonics, λ = 1064 nm, ESRF, Grenoble, France). The laser beam was focused on the central part of the sample's surface, forming a spot of

<footnote>aThe values for ionic radii are based on¹⁰.</footnote>
approximately 10 × 10 µm. The sample was heated up to a maximum temperature of ~3000 (±500) K for a few seconds (Fig. 2a). Due to the localized nature of the heating, we expect that the temperature gradients across the sample could reach ±500 K.

## X-Ray diffraction experiments and data processing

Each laser heating treatment described above was followed by a detailed X-ray diffraction mapping in order to determine the best spots for collecting of single-crystal X-ray diffraction data. Two-dimensional X-ray diffraction maps were collected from the entire sample chamber covering the sample, pressure-transmitting medium and partially rhenium gasket. The precision of the collected maps is defined by the scan ranges along the y and z axes and the number of steps (frames) per line. XRD maps were analyzed with the XDI software<sup>73</sup>; the DIOPTAS<sup>74</sup> software package was used for phase analysis. The calibration parameters for XDI and DIOPTAS (sample-to-detector distance, coordinates of the beam center, tilt angle, and tilt plane rotation angle of the detector images) were refined using powder XRD pattern collected from NIST CeO<sub>2</sub> standard.

X-ray diffraction data collection at 65(4) GPa was performed at ID27 high-pressure beamline at ESRF, Grenoble, France (λ ~ 0.37 Å, EIGER2 X CdTe 9 M photon-counting detector, X-ray beam size ~ 1.5(H) x 1.5 (V) µm²). The single-crystal XRD images were collected while rotating the DAC about a single ω-axis from -30° to +30° with steps of 0.5° and 1 s acquisition per frame.

The DAC then was decompressed in five steps down to ~25(4) GPa and the XRD data were collected at ID15b high-pressure beamline, ESRF (λ ~ 0.41 Å, EIGER2 X CdTe 9 M photon-counting detector, X-ray beam size ~ 1.5(H) x 1.5 (V) µm²). Similar to the experiment at ID27, the XRD maps were used to identify the best spots for SCXRD data collection. The pressure on decompression was estimated using a diamond anvil Raman gauge<sup>75</sup>. Below 25 GPa, the sample became amorphous and no reasonable XRD data could be collected.

After both laser heating treatments, the reaction products were composed of multiple crystalline samples. These samples consist of randomly-oriented crystalline grains with varying sizes, resulting in a typical 2D XRD picture, where smaller grains produce powder rings, and larger grains appear as distinct spots. The DAFi<sup>76</sup> software, dedicated for handling multi-grain XRD data, was used to identify the most-intense crystals suitable for further processing in Crysalis<sup>Pro</sup> (unit cell determination, integration of the reflection intensities and empirical absorption correction). The calibration of the instrument model of CrysAlis<sup>Pro</sup> was performed using a single-crystalline vanadinite Pb<sub>5</sub>(VO<sub>4</sub>)<sub>3</sub>Cl (a = 10.3174 Å, c = 7.3378 Å, Z = 2, space group P6<sub>3</sub>/m). The calibration parameters included the sample-to-detector distance, the detector's origin, offsets of the goniometer angles, rotation of the X-ray beam and the detector around the instrumental axis.

The obtained data on unit cell volumes as a function of pressure were processed using EOSFIT7-GUI software<sup>57</sup>. The P-V dataset was fitted using the third-order Birch-Murnaghan equation of state<sup>56</sup> to derive the values for bulk modulus $K_0$, the unit cell volume extrapolated to zero pressure $V_0$ and bulk modulus derivative $K'_0$. Birch-Murnaghan equations of state are widely employed for studies of carbonates at high pressures, as well as carbonates with similar anionic groups<sup>25,26</sup>, therefore this approach was also adopted in the current work.

## Structure solution and refinement

The crystal structures of iron oxides and carbonates obtained in this study were solved using SHELXT<sup>77</sup>, a structure solution program that uses the algorithm of intrinsic phasing. After structure solution positions of iron atoms were determined, while the remaining atoms (carbon and oxygens) were located from the difference Fourier maps. The crystal structures were refined against $F^2$ on all data by full-matrix least-squares with the SHELXL<sup>78</sup> software. SHELXT and SHELXL programs were implemented in the Olex<sup>2</sup> software package<sup>79</sup>. The detailed summary of the crystal structure refinements at different pressures together with unit cell parameters, atomic

coordinates, and atomic thermal displacement parameters is given in Table 1.

## Raman spectroscopy

The Raman map with dimensions 60 × 70 µm² was recorded from the DAC at 65 GPa heated to ~3000 (±500) K. The data were collected using a dedicated setup comprised of WITec UHTS300 spectrometer (spectral resolution 0.1 cm⁻¹) with a motorized stage alpha300R confocal microscope and a DR316B low dark-current deep depletion CCD camera. Raman spectra were collected using a 532-nm excitation UHTS300S庁 GREEN_NIR laser source and 100 mW of its power with a 50x/0.35 Olympus SLMPL objective. The map obtained is based on 16800 Raman spectra (120 points for each of 140 map lines with 1 s integration time) collected from studied rectangular area.

## Density function theory calculations

First-principles calculations were carried out within the framework of density functional theory (DFT), employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and the plane wave/pseudopotential approach implemented in the CASTEP simulation package<sup>29,80,81</sup>. "On the fly" norm-conserving or ultrasoft pseudopotentials generated using the descriptors in the CASTEP data base were employed in conjunction with plane waves up to a kinetic energy cutoff of 1440 eV or 630 eV, for norm-conserving and ultrasoft pseudopotentials, respectively. The accuracy of the pseudopotentials is well established<sup>82</sup>. Spin polarised calculations were carried out both with and without a local Coulomb correction (+U). The CASTEP implementation of DFT + U adopts a simplified, rotationally invariant approach, where only external parameter required is the effective value of the on-site Coulomb parameter, U, for each affected orbital. In the present case, a value of 2.5 eV was chosen for the Fe-d-orbitals. A Monkhorst-Pack grid was used for Brillouin zone integrations<sup>83</sup>. We used a distance between grid points of <0.023 Å⁻¹. Convergence criteria for geometry optimization included an energy change of <5 × 10⁻⁶ eV atom⁻¹ between steps, a maximal force of <0.008 eV Å⁻¹ and a maximal component of the stress tensor <0.02 GPa. Phonon frequencies were obtained from density functional perturbation theory (DFPT) calculations<sup>84,85</sup>. Raman intensities were computed using DFPT with the "2n + 1" theorem approach<sup>86</sup>.

## Data availability

The crystallography information files (CIFs) for the compound Fe₂[C₄O₁₀] at different pressures reported in this study have been deposited at Cambridge Crystallography Data Center under deposition numbers 2393311-2393316. The data can be downloaded free of charge from https://www.ccdc.cam.ac.uk/data_request/cif.

Received: 13 November 2024; Accepted: 5 February 2025;
Published online: 05 March 2025

## References

1. Hirschmann, M. M. Comparative deep Earth volatile cycles: The case for C recycling from exosphere/mantle fractionation of major (H₂O, C, N) volatiles and from H₂O/Ce, CO₂/Ba, and CO₂/Nb exosphere ratios. *Earth Planet. Sci. Lett.* **502**, 262–273 (2018).

2. McKenzie, N. R. et al. Continental arc volcanism as the principal driver of icehouse-greenhouse variability. *Science* **352**, 444–447 (2016).

3. Dasgupta, R., Jackson, M. G. & Lee, C.-T. A. Major element chemistry of ocean island basalts — Conditions of mantle melting and heterogeneity of mantle source. *Earth Planet. Sci. Lett.* **289**, 377–392 (2010).

4. Kelemen, P. B. & Manning, C. E. Reevaluating carbon fluxes in subduction zones, what goes down, mostly comes up. *Proc. Natl Acad. Sci. USA* **112**, E3997–E4006 (2015).

5. Hazen, R. M. & Schiffries, C. M. Why deep carbon? *Rev. Mineral. Geochem.* **75**, 1–6 (2013).
6. Kopylova, M., Navon, O., Dubrovinsky, L. & Khachatryan, G. Carbonatitic mineralogy of natural diamond-forming fluids. *Earth Planet. Sci. Lett.* **291**, 126–137 (2010).

7. Bataleva, Y. V., Palyanov, Y. N., Borzdov, Y. M., Kupriyanov, I. N. & Sokol, A. G. Synthesis of diamonds with mineral, fluid and melt inclusions. *Lithos* **265**, 292–303 (2016).

8. Bataleva, Y. V., Palyanov, Y. N., Sokol, A. G., Borzdov, Y. M. & Palyanova, G. A. Conditions for the origin of oxidized carbonate-silicate melts: Implications for mantle metasomatism and diamond formation. *Lithos* **128–131**, 113–125 (2012).

9. Bureau, H. et al. Diamond growth in mantle fluids. *Lithos* **265**, 4–15 (2016).

10. Timmerman, S., Spivak, A. V. & Jones, A. P. Carbonatitic melts and their role in diamond formation in the deep earth. *Elements* **17**, 321–326 (2021).

11. Dasgupta, R., Hirschmann, M. M. & Dellas, N. The effect of bulk composition on the solidus of carbonated eclogite from partial melting experiments at 3 GPa. *Contrib. Miner. Pet.* **149**, 288–305 (2005).

12. Reeder, R. J. Crystal chemistry of the rhombohedral carbonates. *Rev. Mineral. Geochem.* **11**, 1–47 (1983).

13. Speer, J. A. Crystal chemistry and phase relations of orthorhombic carbonates. *Rev. Mineral. Geochem.* **11**, 145–190 (1983).

14. Lobanov, S. S. & Goncharov, A. F. Pressure-Induced sp²-sp³ transitions in carbon-bearing phases. in *Carbon in Earth's Interior* 1–9 (2020).

15. Spahr, D. et al. Tetrahedrally coordinated sp³-hybridized Carbon in Sr₂CO₄ orthocarbonate at ambient conditions. *Inorg. Chem.* **60**, 5419–5422 (2021).

16. Binck, J. et al. Synthesis of calcium orthocarbonate, Ca₂CO₄·Pnma at P-T conditions of Earth's transition zone and lower mantle. *Am. Mineralogist* **107**, 336–342 (2022).

17. Cerantola, V. et al. Stability of iron-bearing carbonates in the deep Earth's interior. *Nat. Commun.* **8**, 15960 (2017).

18. Merlini, M., Hanfland, M., Salamat, A., Petitgirard, S. & Müller, H. The crystal structures of Mg₂Fe₂C₄O₁₃, with tetrahedrally coordinated carbon, and Fe₁₃O₁₉, synthesized at deep mantle conditions. *Am. Mineralogist* **100**, 2001–2004 (2015).

19. Merlini, M. et al. Dolomite-IV: Candidate structure for a carbonate in the Earth's lower mantle. *Am. Mineralogist* **102**, 1763–1766 (2017).

20. Boulard, E., Pan, D., Galli, G., Liu, Z. & Mao, W. L. Tetrahedrally coordinated carbonates in Earth's lower mantle. *Nat. Commun.* **6**, 6311 (2015).

21. Boulard, E. et al. New host for carbon in the deep Earth. *Proc. Natl Acad. Sci. USA* **108**, 5184–5187 (2011).

22. Oganov, A. R., Glass, C. W. & Ono, S. High-pressure phases of CaCO₃: Crystal structure prediction and experiment. *Earth Planet. Sci. Lett.* **241**, 95–103 (2006).

23. Lobanov, S. S. et al. Raman spectroscopy and X-ray diffraction of sp³ CaCO₃ at lower mantle pressures. *Phys. Rev. B* **96**, 104101 (2017).

24. Chariton, S. The elastic properties and the crystal chemistry of carbonates in the deep Earth. (Universität Bayreuth, Bayreuth, 2020).

25. Wang, Y. et al. Synthesis and Structure of Two New Cadmium Carbonates at Extreme Conditions. *Cryst. Growth Des.* **24**, 4143–4150 (2024).

26. König, J. et al. Novel Calcium sp³ Carbonate Ca₂CO₅·I₄2d May Be a Carbon Host in Earth's Lower Mantle. *ACS Earth Space Chem.* **6**, 73–80 (2022).

27. Laniel, D. et al. Synthesis, crystal structure and structure–property relations of strontium orthocarbonate, Sr₂CO₄. *Acta Crystallogr B Struct. Sci. Cryst. Eng. Mater.* **77**, 131–137 (2021).

28. Spahr, D. et al. Sr₃[CO₄]O antiperovskite with tetrahedrally coordinated sp³-hybridized carbon and OSr₆ octahedra. *Inorg. Chem.* **60**, 14504–14508 (2021).

29. Spahr, D. et al. High-pressure synthesis of acentric sodium pyrocarbonate, Na₂[C₂O₅]. *Dalton Trans.* **53**, 40–44 (2024).

30. Spahr, D. et al. Sr[C₂O₅] is an inorganic pyrocarbonate salt with [C₂O₅]²⁻- complex anions. *J. Am. Chem. Soc.* **144**, 2899–2904 (2022).

31. Spahr, D. et al. Twisted [C₂O₅]²⁻-groups in Ba[C₂O₅] pyrocarbonate. *Chem. Commun.* **59**, 11951–11954 (2023).

32. Spahr, D. et al. Synthesis and structure of Pb[C₂O₅]: An inorganic pyrocarbonate salt. *Inorg. Chem.* **61**, 9855–9859 (2022).

33. Maeda, F. et al. Diamond formation in the deep lower mantle: A high-pressure reaction of MgCO₃ and SiO₂. *Sci. Rep.* **7**, 40602 (2017).

34. Binck, J. et al. Phase stabilities of MgCO₃ and MgCO₃-Il studied by Raman spectroscopy, X-ray diffraction, and density functional theory calculations. *Phys. Rev. Mater.* **4**, 055001 (2020).

35. Merlini, M., Milani, S. & Maurice, J. Structures and Crystal Chemistry of Carbonate at Earth's Mantle Conditions. in *Geophysical Monograph Series* (eds. Manning, C. E., Lin, J. & Mao, W. L.) 87–95 (Wiley, 2020). https://doi.org/10.1002/9781119508229.ch9.

36. Mysen, B. & Richet, P. Silicate Glasses and Melts. (Elsevier, 2018).

37. Klein, C., Dutrow, B. & Dana, J. D. The 23rd edition of the manual of mineral science:(after James D. Dana). (No Title) (2008).

38. Spahr, D. et al. Single crystal diffraction study of Ba[H₄C₄O₁₀] [H₃C₄O₁₀][H₂CO₃][HCO₃], a hydrous mixed sp²/sp³ -carbonate. *Chem. Commun.* **61**, 161–164 (2025).

39. Stachel, T., Harris, J. W., Brey, G. P. & Joswig, W. Kankan diamonds (Guinea) II: lower mantle inclusion parageneses. *Contrib. Miner. Pet.* **140**, 16–27 (2000).

40. Dobretsov, N. L. & Shatskiy, A. F. Deep carbon cycle and geodynamics: the role of the core and carbonatite melts in the lower mantle. *Russian Geol. Geophysics* **53**, 1117–1132 (2012).

41. Boulard, E. et al. Experimental investigation of the stability of Fe-rich carbonates in the lower mantle. *J. Geophys. Res.* **117**, 2011JB008733 (2012).

42. Iota, V. & Yoo, C.-S. Phase diagram of carbon dioxide: Evidence for a new associated phase. *Phys. Rev. Lett.* **86**, 5922–5925 (2001).

43. Datchi, Dr. F. & Weck, Dr. G. X-ray crystallography of simple molecular solids up to megabar pressures: application to solid oxygen and carbon dioxide. *Zeitschrift für Kristallographie – Crystalline Materials* **229**, 135–157 (2014).

44. Goncharov, A. F. et al. Assessing the stability fields of molecular and polymeric CO₂. *Phys. Rev. Mater.* **7**, 053604 (2023).

45. Bykova, E. et al. Structural complexity of simple Fe₂O₃ at high pressures and temperatures. *Nat. Commun.* **7**, 10661 (2016).

46. Chariton, S. et al. The crystal structures of Fe-bearing MgCO₃ sp²- and sp³-carbonates at 98 GPa from single-crystal X-ray diffraction using synchrotron radiation. *Acta Crystallogr E Cryst. Commun.* **76**, 715–719 (2020).

47. Pickard, C. J. & Needs, R. J. Structures and stability of calcium and magnesium carbonates at mantle pressures. *Phys. Rev. B* **91**, 104101 (2015).

48. Chariton, S. et al. Seismic detectability of carbonates in the deep Earth: A nuclear inelastic scattering study. *Am. Mineralogist* **105**, 325–332 (2020).

49. Lavina, B. et al. Structure of siderite FeCO₃ to 56 GPa and hysteresis of its spin-pairing transition. *Phys. Rev. B* **82**, 064110 (2010).

50. Lavina, B. et al. Siderite at lower mantle conditions and the effects of the pressure-induced spin-pairing transition. *Geophys. Res. Lett.* **36**, 2009GL039652 (2009).

51. Ming, X. et al. First-principles study of pressure-induced magnetic transition in siderite FeCO₃. *J. Alloy. Compd.* **510**, L1–L4 (2012).

52. Greenberg, E. et al. Phase transitions and spin state of iron in FeO under the conditions of Earth's deep interior. *Phys. Rev. B* **107**, L241103 (2023).

53. Fischer, R. A. et al. Equation of state and phase diagram of FeO. *Earth Planet. Sci. Lett.* **304**, 496–502 (2011).

54. Dubrovinsky, L., Narygina, O. & Kantor, I. Effect of Spin Transitions in Iron on Structure and Properties of Mantle Minerals. in *High-Pressure Crystallography* (eds. Boldyreva, E. & Dera, P.) 231–240 (Springer
Netherlands, Dordrecht, 2010). https://doi.org/10.1007/978-90-481-9258-8_20.

55. Shahnas, M. H., Peltier, W. R., Wu, Z. & Wentzcovitch, R. The high-pressure electronic spin transition in iron: Potential impacts upon mantle mixing. *J. Geophys. Res.* **116**, B08205 (2011).

56. Katsura, T. & Tange, Y. A simple derivation of the Birch–Murnaghan Equations of State (EOSs) and comparison with EOSs derived from other definitions of finite strain. *Minerals* **9**, 745 (2019).

57. Gonzalez-Platas, J., Alvaro, M., Nestola, F. & Angel, R. EosFit7-GUI: a new graphical user interface for equation of state calculations, analyses and teaching. *J. Appl Crystallogr* **49**, 1377–1382 (2016).

58. Angel, R. J. Equations of State. *Rev. Mineral. Geochem.* **41**, 35–59 (2000).

59. Perdew, J. P., Burke, K. & Emzerhof, M. Generalized gradient approximation made simple. *Phys. Rev. Lett.* **77**, 3865–3868 (1996).

60. Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. *Acta Cryst.* **A** **32**, 751–767 (1976).

61. Zhang, J. & Reeder, R. J. Comparative compressibilities of calcite-structure carbonates; deviations from empirical relations. *Am. Mineralogist* **84**, 861–870 (1999).

62. Bayarjargal, L. et al. High-Pressure Synthesis of an Iron Carbonate, $Fe_2[CO_3]_3$. *Inorg. Chem.* https://doi.org/10.1021/acs.inorgchem.4c03177 (2024).

63. Albers, C. et al. $Fe^{3+}$-hosting carbon phases in the deep Earth. *Phys. Rev. B* **105**, 085155 (2022).

64. Winter, J. D. *Principles of Igneous and Metamorphic Petrology*. (Prentice Hall, New York Munich, 2010).

65. Schilling, J.-G. Fluxes and excess temperatures of mantle plumes inferred from their interaction with migrating mid-ocean ridges. *Nature* **352**, 397–403 (1991).

66. Herzberg, C. et al. Temperatures in ambient mantle and plumes: Constraints from basalts, picrites, and komatiites. *Geochem Geophys Geosyst* **8**, 2006GC001390 (2007).

67. Dannberg, J. & Gassmöller, R. Chemical trends in ocean islands explained by plume–slab interaction. *Proc. Natl Acad. Sci. USA* **115**, 4351–4356 (2018).

68. Koppers, A. A. P. et al. Mantle plumes and their role in Earth processes. *Nat. Rev. Earth Environ.* **2**, 382–401 (2021).

69. Wang, X.-J. et al. Recycled ancient ghost carbonate in the Pitcairn mantle plume. *Proc. Natl. Acad. Sci. USA* **115**, 8682–8687 (2018).

70. Kantor, I. et al. BX90: A new diamond anvil cell design for X-ray diffraction and optical measurements. *Rev. Sci. Instrum.* **83**, 125102 (2012).

71. Scelta, D. et al. Spray-loading: A cryogenic deposition method for diamond anvil cell. *Rev. Sci. Instrum.* **89**, 053903 (2018).

72. Bayarjargal, L., Fruhner, C.-J., Schrodt, N. & Winkler, B. $CaCO_3$ phase diagram studied with Raman spectroscopy at pressures up to 50 GPa and high temperatures and DFT modeling. *Phys. Earth Planet. Inter.* **281**, 31–45 (2018).

73. Hrubiak, R., Smith, J. S. & Shen, G. Multimode scanning X-ray diffraction microscopy for diamond anvil cell experiments. *Rev. Sci. Instrum.* **90**, 025109 (2019).

74. Prescher, C. & Prakapenka, V. B. *DIOPTAS*: a program for reduction of two-dimensional X-ray diffraction data and data exploration. *High. Press. Res.* **35**, 223–230 (2015).

75. Akahama, Y. & Kawamura, H. Pressure calibration of diamond anvil Raman gauge to 310 GPa. *J. Appl. Phys.* **100**, 043516 (2006).

76. Aslandukov, A., Aslandukov, M., Dubrovinskaia, N. & Dubrovinsky, L. *Domain Auto Finder (DAFI) program: the analysis of single-crystal X-ray diffraction data from polycrystalline samples*. *J. Appl Crystallogr* **55**, 1383–1391 (2022).

77. Sheldrick, G. M. *SHELXT* – Integrated space-group and crystal-structure determination. *Acta Crystallogr A Found. Adv.* **71**, 3–8 (2015).

78. Sheldrick, G. M. Crystal structure refinement with *SHELXL*. *Acta Crystallogr C. Struct. Chem.* **71**, 3–8 (2015).

79. Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. *OLEX2*: a complete structure solution, refinement and analysis program. *J. Appl Crystallogr* **42**, 339–341 (2009).

80. Hohenberg, P. & Kohn, W. Inhomogeneous Electron Gas. *Phys. Rev.* **136**, B864–B871 (1964).

81. Clark, S. J. et al. First principles methods using CASTEP. *Z. f. ür. Kristallographie - Crystalline Mater.* **220**, 567–570 (2005).

82. Lejaeghere, K. et al. Reproducibility in density functional theory calculations of solids. *Science* **351**, aad3000 (2016).

83. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. *Phys. Rev. B* **13**, 5188–5192 (1976).

84. Baroni, S., De Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. *Rev. Mod. Phys.* **73**, 515–562 (2001).

85. Refson, K., Tulip, P. R. & Clark, S. J. Variational density-functional perturbation theory for dielectrics and lattice dynamics. *Phys. Rev. B* **73**, 155114 (2006).

86. Miwa, K. Prediction of Raman spectra with ultrasoft pseudopotentials. *Phys. Rev. B* **84**, 094304 (2011).

## Acknowledgements

E.B. acknowledges the support of Deutsche Forschungsgemeinschaft (DFG Emmy-Noether Project No. BY101/2-1) and Johanna-Quandt-Universitäts-Stiftung. B.W. is grateful for support by the Dassault Systems Science Ambassador program and the Deutsche Forschungsgemeinschaft (DFG WI1232). We gratefully thank the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron beam time under proposal numbers HC-5471 (https://doi.org/10.15151/ESRF-ES-1445120038) and CH-7016 (https://doi.org/10.15151/ESRF-ES-1719222845). We would like to thank A.P. and G.G. for assistance and support in using beamline ID27 and ID15b.

## Author contributions

V.K., D.S., L.W., A.A. and L.B. prepared and performed experiments. B.W. performed DFT calculations. A.P. and G.G. managed the synchrotron beam lines ID27 and ID15b at the ESRF. E.B. supervised the project.

## Funding

Open Access funding enabled and organized by Projekt DEAL.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s42004-025-01450-0.

**Correspondence** and requests for materials should be addressed to Valentin Kovalev.

**Peer review information** *Communications Chemistry* thanks Hongbo Wang and the other, anonymous, reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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