Introduction

Understanding the physical and chemical characteristics of minerals under high pressure is crucial to understanding the Earth’s composition, structure, and dynamic processes. Exploring the Earth’s mantle velocity structure relies on quantitative knowledge of the elastic properties of mantle minerals1.

Through the carbon cycle, carbon is continuously exchanged from the Earth’s surface to its interior. Studying the physical properties of carbon-bearing materials such as carbonates under high pressure and high temperature is crucial for gaining insight into the Earth’s deep carbon cycle; however, knowledge of the forms, transition mechanisms, and movements of carbon in the deep Earth is still limited2. CaC2O5 is a group of polymorphic carbonate minerals first discovered via first-principles simulation, and the stable structure of CaC2O5 with symmetries of Fdd2, Pc, and C2 was established3. Yao et al. proposed that CaC2O5 undergoes successive structural phase transformations with increasing pressure: Pc to Fdd2 at 38 GPa, Fdd2 to Pc at 72 GPa, and Pc to C2 at 82 GPa. Recently, two new polymorphs of CaC2O5 with Fd\(\bar{3}\)m and I\(\bar{4}\)2d symmetries were discovered by high-pressure DAC experiments and first-principles simulations, and researchers believe that CaC2O5-I\(\bar{4}\)2d can stably exist in the lower mantle from 34 to 45 GPa and may promote the carbon cycle and material transformation in the deep mantle4. Later, Sagatova et al. proposed5 two new polymorphs of CaC2O5 with space groups Fdd2-l and Cc at 0 and 15 GPa by first-principles simulation, respectively, and suggested that CaC2O5-Cc may exist in the upper mantle and mantle transition zone; at pressures of 25 and 50 GPa, they proposed a new polymorph with symmetry of CaC2O5-C2-l and confirmed the structural stability of CaC2O5-I\(\bar{4}\)2d. Although the crystal structure, partial electronic properties, and possible phase transforms of these CaC2O5 polymorphs have been extensively studied, there are no unified results depicting the possible impact of CaC2O5 polymorphs on the mantle or their structural stability and elastic properties.

In this study, to understand the possible model of phase transformation of those CaC2O5 polymorphs and its impact on the mantle structure, composition and deep carbon cycling, the lattice parameters, electronic properties, and elasticity of the 6 polymorphs of CaC2O5 (hereafter referred to as CaC2O5s), including CaC2O5-Cc, CaC2O5-Fdd2, CaC2O5-C2-l, CaC2O5-C2, CaC2O5-I\(\bar{4}\)2d and CaC2O5-Pc, were calculated by first-principles simulation for their respective stable pressure ranges. First-principles calculations have been successfully applied to geosciences to understand mineral properties such as structural, elastic properties, electronic properties, etc., under high pressure and temperature6,7,8,9,10,11. Our results provide insights into the presence of various structural phases of CaC2O5 in the mantle and their effects on the deep mantle.

Results and discussion

Structural stability of CaC2O5-I \(\bar{{{{{{\bf{4}}}}}}}\)2d under high pressure

CaC2O5-I\(\bar{4}\)2d was first synthesized in the laboratory under two pressures of 34 GPa and 45 GPa4. However, Sagatova et al. proposed5 that this mineral can be stable at 25 to 50 GPa from the first-principles simulations, so its stability range is unclear. The thermodynamic properties of minerals are usually evaluated by analyzing their phonon frequencies across the Brillouin Zone12,13,14. Therefore, the phonon dispersion along selected high-symmetry points in the Brillouin zone of CaC2O5-I\(\bar{4}\)2d was calculated at 30 to 100 GPa (see Supplementary Fig. 1). Our calculated results show that lattice vibrations produce negative values in the Brillouin region under pressures between 0 and 34 GPa, which indicates that CaC2O5-I\(\bar{4}\)2d is unstable in this pressure range15. With increasing pressure, the structure shows thermodynamic stability between 34 and 100 GPa.

To further verify the stability of CaC2O5-I\(\bar{4}\)2d, we calculated the Mulliken population to explore whether the electronic properties of CaC2O5-I\(\bar{4}\)2d undergo mutations at high pressure (see Supplementary Table 1). The band spilling parameter for spin component 1 was 0.69%, indicating that our calculated results are reasonable and reliable16.

The Mulliken population analysis of CaC2O5-I\(\bar{4}\)2d at pressures of 34 GPa, 45 GPa, 70 GPa, 85 GPa, and 100 GPa showed that the population of all three C-O bonds was greater than 0.5, with a maximum difference of only 5.17% at different pressures. This result indicates that these bonds are covalent. However, the population values of all three Ca-O bonds are less than 0.1. The population of Ca-Oa and Ca-Ob bonds changes significantly with pressure, while the population of Ca-Oc bonds remains relatively unaffected by pressure. This result indicates that these bonds are ionic. Furthermore, there was no abrupt change in the atomic electronegativity or bond denstiy from 34 to 100 GPa, indicating the stability of CaC2O5-I\(\bar{4}\)2d.

In summary, the phonon dispersion and Mulliken population results show that CaC2O5-I\(\bar{4}\)2d maintains structural stability under 34–100 GPa.

Lattice parameters and density

The lattice parameters (a, b, and c) of CaC2O5s under high pressure were calculated (see Supplementary Fig. 2). To elucidate the differences in the lattice parameters of CaC2O5, 2 × 2 × 1 supercells of CaC2O5-C2 and CaC2O5-Pc and a 2 × 1 × 1 supercell of CaC2O5-Cc were built to ensure consistent atomic numbers in CaC2O5 crystal cells. The lattice constants of CaC2O5s linearly decrease with increasing pressure (R2 > 0.978). Notably, under the same pressure, the lattice parameters, a and b, of CaC2O5-I\(\bar{4}\)2d and CaC2O5-C2-l are very close in value, and the ratio of the lattice parameter, c, of the two polymorphs is constant at 0.8 (±0.05).

The densities of all 6 calculated CaC2O5 polymorphs under high pressure are listed in Fig. 1. Moreover, the densities of the main mineral phases of the lower mantle, such as CaSiO3 perovskite17, MgSiO3 perovskite18, FeOOH19, δ-AlOOH20, and the newly discovered CaO321 under high pressure, and the density of the Preliminary Reference Earth Model (PREM)22 are also listed in Fig. 1.

Fig. 1: Density of CaC2O5s and several lower mantle minerals under high pressure.
figure 1

Comparison of the densitites of CaSiO3 perovskite17 (bule dash line), MgSiO3 perovskite18 (red dash line), FeOOH19 (gold dash line), δ-AlOOH20 (lavender dash line), CaO321 (green dash line) and CaC2O5s (soild line) with that of Earth’s mantle according to the PREM (Black soild line).

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The densities of CaC2O5s increase with increasing pressure, but all the densities are lower than those of the PREM model. Generally, low-density minerals have difficulty entering the deep mantle. However, several low-density minerals, such as δ-AlOOH20 and CaO321, have also been discovered in the lower mantle. Therefore, due to FeOOH18 and silicate minerals with densities higher than those of the PREM are widely present in the mantle, CaC2O5s may play an essential role in regulating and neutralizing the mantle density in the Earth’s lower mantle.

As pressure increases, some clear density transitions occur between different polymorphs of CaC2O5. First, there is a density increase of 8.81%–7.37% from 20 GPa to 30 GPa when CaC2O5-Cc transforms into CaC2O5-C2-l at approximately 660 km, which is very consistent with the increase in density at 660 km in the PREM model, indicating that this structural phase transformation may be one of the reasons for the changes in density here. Second, when CaC2O5-I\(\bar{4}\)2d or CaC2O5-Fdd2 transforms into CaC2O5-Pc and CaC2O5-C2, the density increases by 4.02%–5.88%. The densities of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d show very similar quantities and relationships with pressure.

Elasticity

The elastic parameters of minerals and their dependence on pressure are essential in Earth science for understanding processes ranging from brittle failure to flexure to the propagation of elastic waves. Seismic observations reveal the structure of the Earth, including the radial (one-dimensional) profile, lateral heterogeneity, and anisotropy, which are primarily determined by the elastic parameters of minerals and their dependence on pressure and temperature23. Therefore, to understand the geological properties of CaC2O5, we calculated the elastic constants of CaC2O5s under high pressures, as shown in Fig. 2.

Fig. 2: Elastic constants of CaC2O5s.
figure 2

The elastic constants (C11, C12, C13, C15, C22, C23, C25, C33, C35, C44, C46 and C66) of CaC2O5s at their respective structural phase transition pressures5 were compared (the space group symbol is shown in the figure). Pc, C2, Cc, and C2-l belong to the monoclinic system, with 13 independent elastic constants; Fdd2 belongs to the orthorhombic system, with 9 independent elastic constants; I\(\bar{4}\)2d belongs to the tetragonal system, with 6 independent elastic constants. Elastic constants in the same direction are represented by the same color.

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Based on a theorem for determining the elastic stability of minerals24, the elastic stability of CaC2O5s was investigated, and the results showed that the 6 polymorphs maintain elastic stability within their calculated pressure ranges. Although the space groups of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d are different, their elastic constants show good consistency. Within the same pressure range, C11 of C2-l ≈ C33 of I\(\bar{4}\)2d, C22 and C33 of C2-l ≈ C11 of I\(\bar{4}\)2d, C23 of C2-l ≈ C12 of I\(\bar{4}\)2d, C44 of C2-l ≈ C66 of I\(\bar{4}\)2d, C12 and C13 of C2-l ≈ C13 of I\(\bar{4}\)2d, and C55 and C66 of C2-l ≈ C44 of I\(\bar{4}\)2d; additionally, C15, C25, C35 and C46 of C2-l are very close to 0.

The elastic modulus is an important parameter for describing the physical and chemical properties of minerals. In crystalline systems, assuming that the arrangement direction is random, the bulk modulus (K) and shear modulus (G) can be obtained by the Voigt, Reuss, and Hill formulas25, and the Hill modulus is used here26 based on the average of the Voight and Reuss moduli. The bulk modulus and shear modulus of CaC2O5s were calculated and are shown in Fig. 3a, b. The K and G of CaC2O5s linearly increase with pressure. Among the 6 polymorphs, the K and G of CaC2O5-Fdd2 are the largest, and those of CaC2O5-Cc are the smallest. To further explore the effect of pressure on K and G, the pressure derivatives K’ and G’ were calculated based on linear fitting results of K and G with pressure, respectively. The K’ values of CaC2O5s fall within the range of 3.8 ± 0.3 indicating that the K values of the 6 polymorphs exhibit a similar trend with pressure. The G’ of CaC2O5-C2 has a maximum value of 1.7, and the other 5 polymorphs of CaC2O5 have similar values of 1.2 ± 0.1. K and G of CaC2O5-I\(\bar{4}\)2d and CaC2O5-C2-l show very similar values under high pressure, indicating that they have the same elastic properties.

Fig. 3: Elastic modulus and elastic wave velocity of CaC2O5s.
figure 3

a Bulk modulus (solid line) and b shear modulus (point line) of CaC2O5s (the space group symbol is shown in the figure) within their respective structural phase transformation pressures5. c Shear-wave velocity (VS) and d compressional-wave velocity (VP) of CaC2O5s within their respective structural phase transformation pressures5.

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Generally, understanding the composition, physical state, and structure of the Earth’s interior mainly relies on observing the seismic wave velocity. Quantified seismic velocity data link seismic observations and geological characteristics, such as modal mineral composition and velocity structure. Laboratory measurements and computer simulations of the seismic wave velocity of minerals under appropriate pressure and temperature conditions have long been used to interpret the velocity structure of the Earth, combined with the results of large-scale geophysical imaging techniques27. As a potentially important component of the deep Earth, the seismic wave velocity of CaC2O5 with different symmetries under high pressure is highly important for understanding the structure and composition of the mantle. Therefore, we can calculate the shear-wave (VS) and compressional-wave (VP) velocities of CaC2O5s (see Methods) in Fig. 3c, d.

CaC2O5-Cc has the slowest wave velocity, and CaC2O5-Fdd2 has the largest wave velocity among the 6 polymorphs. As the pressure increases, the wave velocities of CaC2O5s increase. For 6 CaC2O5 polymorphs, the VS values are sorted as Fdd2 > Pc > C2 > I\(\bar{4}\)2d ≈ C2-l > Cc, and the VP values are sorted as Fdd2 > Pc > I\(\bar{4}\)2d ≈ C2-l > C2 > Cc. The wave velocities of CaC2O5-I\(\bar{4}\)2d and CaC2O5-C2-l are very close.

Relationship between CaC2O5-C2-l and CaC2O5-I \(\bar{{{{{{\bf{4}}}}}}}\)2d

As discussed above, some of the characteristics of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d show good consistency. For example, under the same pressure, the lattice parameters a and b, and the density of these two polymorphs are almost the same (the difference is less than 0.02), and the lattice parameter c maintains a constant ratio of 0.8 (Supplementary Fig. 2). The differences in the lattice parameter c of the two polymorphs came from the differences in the bond angle β in their cell structure, namely, 125° in CaC2O5-C2-l and 90° in CaC2O5-I\(\bar{4}\)2d. The VP and VS of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d also exhibit good consistency under the same pressure (the differences in VP and VS are less than 0.08 km s−1 and 0.03 km s−1, respectively) (Fig. 4).

Fig. 4: Electronic properties of CaC2O5s.
figure 4

a The band gap of CaC2O5s (the space group symbol is shown in the figure) within their respective structural transformation pressures. b, c The band structure and density of states of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d at 40 GPa. Blue lines are the band structures, the magenta, orange, and dark blue line represent the contributions of s, p, and d orbitals to the density of states, respectively, and the dark green dot lines represent the total density of states.

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To further verify the relationship between the CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d, we calculated the energy band structure and the density of states under high pressure from CaC2O5s.

The band gap of CaC2O5s varies between 5.108 eV and 7.701 eV under the explored pressure in this work, indicating their insulating properties28 (Fig. 4a). The band gaps of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d are almost the same at the same pressure (the band gap difference is less than 0.02 eV). As the pressure increases, the bandgaps of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d gradually increase; however, the bandgaps of the other 4 polymorphs, CaC2O5-Cc, CaC2O5-Pc, CaC2O5-Fdd2, and CaC2O5-C2, decrease with increasing pressure. Under 10 to 50 GPa, the relative conductivity of CaC2O5s follows the order CaC2O5-Cc > CaC2O5-C2-l ≈ CaC2O5-I\(\bar{4}\)2d; when the pressure is greater than 50 GPa, the relative conductivity of CaC2O5s is as follows the order CaC2O5-C2 > CaC2O5-Fdd2 > CaC2O5-Pc > CaC2O5-I\(\bar{4}\)2d.

The electronic density of states (DOS) and the band structure of CaC2O5-I\(\bar{4}\)2d and CaC2O5-C2-l are nearly identical under the same pressure range (Fig. 4b, c). The difference in the orbitals contributions is less than 0.3%. The characteristics of the DOS of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d are primarily determined by the electrons distributed in the p orbitals. At 40 GPa, the p orbitals contribute approximately 62.94% and 63.12%, respectively, to the total DOS. Moreover, the remaining contributions are attributed to the s orbitals (23.67% and 23.48%) and the d orbitals (13.39% and 13.40%).

The cell parameters, electronic properties, elasticity, and wave velocity of CaC2O5-C2-l and CaC2O5-I\(\bar{4}\)2d under high pressure are almost identical, and the trends with pressure are also almost identical. Hence, these two phases are the same thing.

Effects of CaC2O5s on the structure of the mantle

To explore the effects of CaC2O5 polymorphs on the structure of the mantle, we compared our calculations with the wave velocities of sseveral common mantle minerals (Fig. 5), including wadsleyite29, ringwoodite30, cubic Ca-Pv31, MgSiO3 perovskite18 and CaSiO3 perovskite17 under high pressure. Moreover, the seismic wave velocity of the PREM22 is also presented here.

Fig. 5: Shear-wave velocity (VS) and compressional-wave velocity (VP) of CaC2O5s, the PREM model, and some mantle minerals.
figure 5

Comparison of the seismic wave velocity of wadsleyite, ringwoodite, cubic Ca-Pv31, MgSiO3 perovskite18 and CaSiO3 perovskite17 and CaC2O5s (the space group symbol is shown in the figure) with that of Earth’s mantle according to the PREM22, the black thin dotted line, the gray area, and the black arrows represent the boundaries at which the phase transition begins, the region where the phase transition occurs, and which two types of CaC2O5 undergo the phase transition5, respectively.

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The wave velocities of CaC2O5s under the explored high pressure in this work are lower than those of the PREM model. The wave velocities of CaC2O5s are also lower than those of common minerals in the mantle, including wadsleyite, ringwoodite, MgSiO3 perovskite, and CaSiO3 perovskite; therefore CaC2O5s are a set of low-velocity minerals and may be useful for understanding the origin of the low-velocity layer in the mantle.

From depths of 300 km to 1662 km, the wave velocity increases with pressure. Two significant velocity surges are observed during the phase transformation among the CaC2O5 polymorphs: one is near 660 km depth when the CaC2O5-Cc structure transforms into CaC2O5-I\(\bar{4}\)2d (C2-l), and the other is near 1435 km depth when the CaC2O5-I\(\bar{4}\)2d structure transforms into CaC2O5-Fdd2. Afterwards, from depths of 1662 km to 2500 km, there is a sudden drop in wave velocity when CaC2O5-Fdd2 transforms into CaC2O5-C2 and CaC2O5-Pc near a depth of 1662 km.

CaC2O5-Cc transforms into CaC2O5-I\(\bar{4}\)2d (CaC2O5-C2-l) at 21 GPa (0 K) to 29 GPa (2500 K)5, leading to an increase in VS of 13.84% and an increase in VP of 9.18% (Fig. 5). This phase transformation depth matches the depth of the 660 km discontinuity zone of the mantle32,33. The general view of the seismic wave velocity discontinuity at 660 km in the mantle transition zone is caused by the postspinel phase transformation of ringwoodite (ringwoodite (Mg, Fe)2SiO4 → perovskite (Mg, Fe)SiO3 + ferropericlase (Mg, Fe)O)34. The density of the PREM model increases from 3.99 g cm−3 to 4.38 g cm−3, VS increases from 5.57 km s−1 to 5.95 km s−1, and VP increases from 10.26 km s−1 to 10.75 km s−1 at 660 km, and the increase in density, VS and VP are 0.37 g cm−3, 0.38 km s−1, and 0.49 km s−1, respectively. When CaC2O5-Cc transforms into CaC2O5-I\(\bar{4}\)2d (CaC2O5-C2-l) at a depth of 660 km, its density increases from 3.38 g cm−3 to 3.67 g cm−3 by 0.29 g cm−3, VS increases from 4.25 km s−1 to 4.81 km s−1 by 0.55 km s−1, and VP increases from 9.28 km s−1 to 8.50 km s−1 by 0.78 km s−1. The CaC2O5 and PREM have very similar densities, and the shear-wave velocity increases at 660 km. Therefore, we propose that the transformation of CaC2O5-Cc to CaC2O5-I\(\bar{4}\)2d (CaC2O5-C2-l) may also be one of the origins of wave velocity discontinuity at a depth of 660 km in the mantle transition zone.

Studying the wave velocity structure of the large low-shear-velocity provinces (LLSVPs) in the lower mantle is highly important for understanding the dynamic evolution process of Earth’s interior. LLSVPs play a crucial role in regulating heat flow from the core, facilitating the exchange of matter and energy between the Earth’s deep layers and influencing continental evolution, surface resources, and the environment. LLSVPs are regions with shear wave velocities (VS) several percent lower than those of the surrounding mantle35,36,37,38. There are two large low shear wave velocity bodies that extend thousands of kilometres horizontally and hundreds of kilometres vertically on the Core-Mantle boundary below Africa and the Pacific Ocean38,39,40. There are many controversies about the origin and evolution of these areas41. Thomson et al. proposed a cubic Ca-Pv perovskite that can perfectly match the characteristics of low-shear-velocity minerals in LLSVPs31 (Fig. 5) and is considered an interpretation of the origin of LLSVPs. Here, our calculated VS of CaC2O5-I\(\bar{4}\)2d is almost the same as that of cubic Ca-Pv perovskite, and when CaC2O5-Fdd2 transforms into CaC2O5-C2 as the pressure increases, its VS decreases by 7.4% (Fig. 5). It’s worth noting that CaC2O5-I\(\bar{4}\)2d was synthesized via high-temperature and high-pressure experiments at 34 GPa and 45 GPa by the reaction of CaCO3 + CO24. Moreover, Yao et al. proposed3 that CaC2O5 might react with perovskite (Mg, Ca)SiO3 and ferropericlase MgO in the deep mantle to generate MgCO3, CaCO3, CO2, and perovskite (Mg, Ca)SiO3, etc. LLSVPs not only exhibit low-velocity velocities that are several percent lower than the those of the surrounding mantle but also exhibit higher density than the surrounding components42,43,44. When CaC2O5-Fdd2 transforms into CaC2O5-C2, its density increases by 5.8% (Fig. 1). This trend allows CaC2O5 transformation to more perfectly match the characteristics of LLSVPs. Therefore, we determine that CaC2O5-I\(\bar{4}\)2d and its high-pressure polymorphs are very likely to be in the interior of the LLSVPs region and may serve as a supplement to the Ca-Pv component in LLSVPs or may be one of the main components in LLSVPs.

Based on our calculated density, wave velocity of CaC2O5s, probable phase transformation, and reactions of CaC2O5 in the mantle, a model of the deep carbon cycle is proposed (Fig. 6). Calcium carbonate (CaCO3) and CO2 can reach the deep Earth through subduction plates. The discovery of calcium carbonate inclusions in superdeep diamonds45 and fluid CO2 wrapped in diamonds46 also confirmed the occurrence of calcium carbonate and CO2 in the deep mantle. Therefore, CaC2O5 and its high-pressure polymorphs could be produced by the reaction CaCO3 + CO2 → CaC2O5 at different depths4 in the mantle. CaC2O5-Cc in the shallow mantle transforms into CaC2O5-I\(\bar{4}\)2d at 660 km depth, causing an anomalous increase in wave velocity in the mantle transition zone. Meanwhile, CaC2O5-Fdd2 in the deep mantle may partially transforms into CaC2O5-C2 with increasing pressure, leading to an increase in mantle density but a decrease in shear-wave velocity, which is one of the possible reasons for explaining the origin of LLSVPs42,43,44. During these reactions, CaC2O5 reacts with minerals such as (Mg, Ca)SiO3 perovskite and ferropericlase (MgO) in the lower mantle and produce magnesium carbonate (MgCO3), calcium carbonate (CaCO3), calcium silicate(CaSiO3), and CO23,5. The more stable MgCO3 and CaSiO3 remain in the lower mantle as the main carbonate minerals3 and the main minerals in LLSVPs31, respectively. CaCO3 generated by the reaction may repeat the process of reacting with CO2 to generate CaC2O5 or decompose into CO23,4. CO2 and carbon-bearing minerals can also be transported to the Earth’s shallow through internal dynamic processes. For example, mantle plumes, which are high-temperature environments, facilitate the rise of gaseous carbon dioxide back to the upper mantle and the bottom of the lithosphere. Therefore, CaC2O5 may play a significant role in Earth’s deep carbon cycle as follows: CaC2O5 would transports carbon to the deep Earth while it also undergoes successive structural phase transformations with increasing pressure, after which CO2 and carbon-bearing minerals are produced via reactions of CaC2O5 with minerals that transport carbon to shallow parts of the Earth.

Fig. 6: Schematic diagram of CaC2O5s in the mantle.
figure 6

Crystal structure of CaC2O5s and its possible reactions and reaction environments in the mantle are described. Solid arrows indicate the reaction or phase transition that generates CaC2O5 (the red letter part indicates the phase transition conditions45), while dashed arrows indicate the reaction that generates other substances3.

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The structural, electronic, and elastic properties of CaC2O5s, including those of CaC2O5-Cc, CaC2O5-Fdd2, CaC2O5-C2-l, CaC2O5-C2, CaC2O5-I\(\bar{4}\)2d, and CaC2O5-Pc, were studied under high pressure by first-principles simulation. The calculations show that CaC2O5 is a group of low-density mantle minerals with a low seismic wave velocity. The CaC2O5-I\(\bar{4}\)2d and CaC2O5-C2-l exhibit good agreement in their crystal cell structures, electronic state densities, band structures, and seismic wave velocities, indicating that these two polymorphs can be considered the same.

Changes in seismic wave velocity caused by phase transformation of the CaC2O5-Cc to CaC2O5-I\(\bar{4}\)2d (CaC2O5-C2-l) agree with the wave velocity discontinuity at a depth of 660 km in the mantle transition zone and maybe one of the origins of this discontinuity. Moreover, when CaC2O5-Fdd2 transforms into CaC2O5-C2, its VS decreases by 7.4%, and its density increases by 5.8%, perfectly matching the characteristics of LLSVPs. As the pressure increased, CaC2O5 eventually transformed into CaC2O5-C2. Generally, CaC2O5 and its high-pressure polymorphs may be among the main components of LLSVPs.

Therefore, CaC2O5 exhibits important effects on the structure and composition of the mantle as well as the Earth’s deep carbon cycle. Our work provides different insights for understanding the origin of the wave velocity discontinuity at the depth of 660 km in the mantle transition zone and at the LLSVPs. It also sheds light on the deep carbon cycle model of the Earth.

Methods

The density functional theory (DFT) calculations

First principles calculations are performed using density functional theory47,48 with the plane-wave pseudopotential. The calculations are implemented in the CASTEP code49. The generalized gradient approximation (GGA) with PBE parameterization50 is employed to describe exchange-correlation interactions. OTFG ultrasoft pseudopotentials51,52 are utilized to model electron-ion interactions with a plane-wave energy cutoff set in Table 1. A Monkhorst Pack grid of k-points was employed to sample the Brillouin zone. Table 1 presents the plane-wave energy cutoff and k-points settings for the various CaC2O5 phase states. A convergence criterion of 5 × 10−7 a.u. for total energy is employed for self-consistent-field calculations.

Table 1 The plane-wave energy cutoff and k-points settings of CaC2O5
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CaC2O5s under different pressures are calculated by simultaneously optimizing atomic positions and lattice constants, respectively, using Hellmann-Feynman forces and stresses acting on nuclei and lattice parameters53. The phonon mode is determined by finite displacement calculations54 to ensure molecular stability. Bonding characteristics are determined using Mulliken’s population analysis55,56. Stress-strain relations calculate elastic constants23, where all applied strains have magnitudes of 0.003, and the linear relation was ensured to be sufficient for this strain range. Density of states and partial density of states also caculated by CASTEP code49. Crystal structures were visualized with VESTA57.

Benchmark calculation

The lattice parameters and cell volume of CaC2O5s were calculated and compared with reported values to evaluate the accuracy of the density functional theory approach employed here. Differences between our calculated lattice parameters and volume and previous simulation are less than 1.24%, and the difference with experimental results is 2.98% (Table 2), demonstrating the accuracy of our calculation scheme.

Table 2 Structure and volume of CaC2O5s
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Interestingly, lattice parameters and cell volume of CaC2O5-I\(\bar{4}\)2d from Sagatova5 differ significantly from our simulated results (∆ = 10.68%). The values also differ from the experimental result4. Sagatova5 calculated the lattice parameter at 50 GPa5, which is larger than the experimental value obtained at 34 GPa4.

All crystal structure files of CaC2O5s used in this study can be obtained from the supplementary files (Supplementary Table 2 and Supplementary Fig. 3).

Formula for calculating the velocity of the VS and VP

$${V}_{{{{{{\rm{S}}}}}}}=\sqrt{G/\rho }$$
(1)
$${V}_{{{{{{\rm{P}}}}}}}=\sqrt{(K+4G/3) /\rho }$$
(2)

Where K (GPa) is the bulk modulus, G (GPa) is the shear modulus, and ρ (g cm−3) is the density.