Carbonate is a dominant carbon-bearing material in the Earth’s crust, mainly in pelagic marine sediment which can be delivered into the deep mantle by the subduction of oceanic crust and sediments.^[1] Owing to the low solubility of carbon in mantle silicate, carbon is mainly stored in a separate phase which might be carbonate.^[2] Thermodynamic models indicated that carbonates are stable during cold subduction.^[3] An inclusion in ultra-deep diamonds, with CaCO , ferropericlase, perovskites, stishovite and others lower mantle minerals component, suggested that these carbonates stably exist in the lower mantle.^[4,5] To understand the global carbon cycle on a geologic scale, it is necessary to study the stability, structure and elastic property of carbonate under high pressure.^[6]

Calcite is the most stable CaCO phase under ambient conditions and there have been a lot of reports about structures and thermodynamic properties.^[7–10] Calcite transforms into aragonite in the upper mantle conditions.^[11–13] Aragonite, considered to be stable in the mantle for a long time, was regarded as the main carbon-bearing phase in the Earth’s interior. Recently, reports asserted the phase transformation from aragonite to a new structure of calcium carbonate at about 40 GPa.^[14,15] The new phase has orthorhombic symmetry (Pmmn) and remains stable at least up to 86 GPa, named post-aragonite.^[14] Besides, at about 130 GPa–140 GPa, experimental and theoretical studies found that a pyroxene-type structure CaCO (C222 with a chain of CO tetrahedron becomes more stable than post-aragonite, which could persist up to 192 GPa.^[15,16] Furthermore, Pickard and Needs^[17] thought that a new CaCO structure with space group -h and chain of CO tetrahedron, are more stable than C222 above 67 GPa. The discovery of these new CaCO high pressure structures has attracted considerable attention to rethink the role of CaCO in the carbon cycle. However, after the post-aragonite, C222 and -h structures are found, elastic properties of CaCO at high pressures are rarely studied, and the CaCO high-pressure structures have been controversial.

First-principle calculations are widely used to study the structural, electronic, elastic and thermodynamic properties, and phase transition of minerals.^[18–21] In this study, we investigate the stability and elastic properties of aragonite, post-aragonite and the -h-CaCO structure at high pressure up to 150 GPa with first-principle calculations. We show results and discussion of a full set of elastic constants, wave velocity and velocity anisotropies, which are important for understanding a carbon reservoir and the role of carbon in the deep mantle.

First-principle calculations are based on the density functional theory (DFT) incorporated with ultrasoft pseudopotential technique,^[22] as implemented in the CASTEP code.^[23] General gradient approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) functional was employed to describe the exchange-correlation interaction.^[24] A convergence of the plane-wave expansion was obtained with a cut-off of 450 eV for all calculations. Brillouin zone sampling was performed by the Monkhorst–Pack scheme. The k mesh was for all calculations.

The structures of aragonite, post-aragonite and -h-CaCO adopted for this study possessed orthorhombic, orthorhombic and monoclinic symmetries with space groups Pnma, Pmmn, and -h, respectively. Simulations were performed at external pressures of 0 GPa–40 GPa for aragonite, 40 GPa–65 GPa for post-aragonite, and 65 GPa–150 GPa for -h-CaCO , respectively. The lattice constants and the atomic coordinates were simultaneously optimized under given pressures.

The stress tensor on the unit cell of a crystal structure can be directly calculated from the stress theorem^[25] within the ultrasoft pseudopotential framework. At each pressure, a full set of elastic constants was computed by the homogeneous deformation method.^[26] The full elastic constant tensors of orthorhombic and monoclinic structures have nine and thirteen independent components, respectively. Taking the Voight–Reuss–Hill average of simulated elastic constants and density, we determined the values of their bulk modulus , shear modulus ( , compressional ( , and shear ( wave velocity according to the following equations,^[27] 1

The lattice constants and the atomic coordinates are simultaneously optimized under given pressures. For aragonite, full optimization of the unit-cell yields lattice parameters of a = 5.002 Å, b = 8.014 Å, c = 5.792 Å at 0 GPa, which are in excellent agreement with previous experimental and theoretical results.^[28,29] The average deviation is smaller than 1%. For post-aragonite, the calculated unit-cell parameters are a = 4.062 Å, b = 4.592 Å, c = 3.988 Å at 66.4 GPa and a = 3.873 Å, b = 4.451 Å, c = 3.879 Å at 110 GPa, respectively, which are in good accord with the results by Oganov, et al. ^[15] and Ono, et al. ^[14] The deviation is only about 1%–2%. Overall, our simulation schemes are efficient and in general agreement with the existing experimental data and theoretical data.

To investigate the phase stabilities and phase transition pressures of three polymorphs of CaCO , the relative enthalpy (to post-aragonite) and pressure curves are plotted in Fig. 1. According to the principle of thermodynamics, the structure with the lower energy is more stable. From Fig. 1, we find that the post-aragonite phase becomes more stable than aragonite above 40 GPa, which is consistent with previous DFT simulation and experiment results (Oganov, et al. ^[15] and Ono, et al. ^[14]). The -h-CaCO becomes more stable than post-aragonite and -CaCO above 65 GPa, in accord with the 67 GPa.^[17] Consequently, our calculations were conducted at 0 GPa–40 GPa for aragonite, 40 GPa–65 GPa for post-aragonite, and 65 GPa–150 GPa for -h-CaCO , respectively.

Fig. 1.

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	Fig. 1. (color online) Variations of calculated enthalpy difference relative to the post-aragonite phase with pressure.

According to calculated pressures and volume data of the three phases, we obtain their equations-of state (EOS) parameters (equilibrium volume , bulk modulus , and its pressure derivative ) by fitting the third-order Birch–Murnaghan equation. The fitted parameters are shown in Table 1. For aragonite, the three fitted parameters are Å , GPa, and , respectively, which are in agreement with those presented by Li et al. ^[29] and Ono et al. ^[14] If is fixed at 4, the fitting yields results of Å and GPa, which are in excellent agreement with data obtained by Fisler et al.,^[30] and are slightly larger than the value of 65.4 reported by Martens et al. ^[31] A linear fit to the axial ratios , , versus pressure yields the linear axial compressibility of aragonite: GPa , GPa , and GPa , giving axial compressibility values in the order of , indicating anisotropy in the compression behavior. These results are in consistence with previous studies.^[29,30,32] For post-aragonite, with all parameters unrestrained, we obtain Å , GPa, and if is fixed at 4, the fitted results are Å , GPa, close to the data of Å , GPa reported by Ono et al. ^[14] Similarly, for -h-CaCO , Å , GPa, are obtained.

Table 1.

Table 1.

Table 1. Calculated equations of state for aragonite, post-aragonite, and the -h-CaCO at 0 K, and their comparisons with previous experimental and theoretical data. .   /Å /GPa References Aragonite 232.50 66.09 4.64 this study 226.71(±0.01) 65.24(±0.24) 4.95(±0.12) Li et al. (2015)[29] 227.2(±1.0) 67.1(±6.3) 4.7(±0.8) Ono et al. (2005)[14] 233.84 66.9 4.48 Oganov et al. (2006)[15] 64.8 4 (fixed) Martinez et al. (1996)[32] Post-aragonite 106.44 81.93 4.49 this study 101.76 112.84 4 (fixed) this study 98.3(±1.9) 127(±14) 4 (fixed) Ono et al. (2005)[14] 109.74 90(±13) 4.94 Oganov et al. (2006)[15] -h-CaCO 218.02 56.55 5.40 this study

Table 1. Calculated equations of state for aragonite, post-aragonite, and the -h-CaCO at 0 K, and their comparisons with previous experimental and theoretical data. .

The complete elastic constants at given pressure for the three CaCO structures are presented in Table 2 and Fig. 2. Under ambient conditions, the calculated longitudinal elastic constants of aragonite at 0 GPa are , , and GPa. In comparison with the results presented by Liu et al.,^[33] the average deviation is smaller than 3%. The order of shows the compression behaviors in different directions (c > b > a), which is consistent with the trend shown in the EOS parameters. At 40 GPa, the off-diagonal elastic constant starts to fall. These changes might be a precursor of the phase transition (see Figs. 2(a)–2(c)).

Fig. 2.

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	Fig. 2. (color online) Calculated elastic constants under given pressure for [(a)–(c)] aragonite, [(d)–(f)] post-aragonite, and [(g)–(i)] -h-CaCO .

Table 2.

Table 2.

Table 2. Calculated values of elastic constants (in unit GPa), bulk modulus, shear modulus (in unit GPa), and compressional and shear wave velocity (in units km/s) under pressure P (in unit GPa) at 0 K. . P B G Aragonite 0 162.57 107.81 96.48 41.91 36.44 19.59 53.65 26.42 42.77 66.42 33.77 6.27 3.45 5 201.32 128.79 119.91 47.39 44.13 25.54 78.50 40.93 63.14 88.35 38.97 6.80 3.59 10 239.97 152.44 143.48 52.29 51.46 32.21 102.90 55.56 84.25 110.69 44.09 7.29 3.72 14 263.94 185.14 157.22 62.48 56.19 32.44 111.35 70.17 105.38 128.05 48.33 7.63 3.83 20 312.25 215.08 180.56 74.52 61.36 36.90 139.30 83.55 130.73 152.76 53.70 8.06 3.94 24 334.47 229.52 198.63 80.15 65.26 37.01 160.23 94.92 147.88 169.48 54.98 8.28 3.94 30 371.14 262.24 219.05 89.40 70.43 41.77 184.33 108.94 170.65 191.44 59.98 8.61 4.05 34 400.90 296.74 227.58 100.22 74.76 46.87 200.32 116.12 187.24 205.35 65.55 8.84 4.18 40 457.65 329.79 247.20 112.95 78.79 55.04 212.95 122.61 210.63 224.86 73.31 9.15 4.36 Post-aragonite 40 323.23 499.22 530.69 129.46 12.97 29.61 150.26 147.11 135.63 241.49 66.70 9.02 4.05 45 350.70 529.25 566.12 140.19 22.26 30.87 161.74 162.63 144.75 260.06 77.46 9.36 4.32 50 385.24 566.94 597.04 150.61 35.65 34.70 170.92 175.89 159.27 280.01 89.84 9.73 4.61 55 412.70 603.27 628.35 163.47 45.99 37.39 181.20 191.51 170.39 298.82 99.14 10.01 4.80 60 443.60 634.70 656.90 172.55 56.27 38.92 190.37 205.42 181.51 316.84 106.87 10.25 4.95 65 472.02 664.97 689.62 184.00 65.31 41.45 199.22 218.17 194.76 334.72 114.78 10.48 5.09 -h CaCO 65 528.33 565.99 498.62 176.11 128.79 241.78 330.70 230.85 284.15 5.52 87.17 20.24 88.97 357.98 143.17 11.02 5.63 70 556.73 592.27 525.20 187.19 132.75 253.18 348.42 242.07 298.36 3.48 90.68 21.17 92.78 376.46 149.89 11.21 5.72 80 614.38 641.33 584.75 206.25 137.60 274.61 380.43 258.51 326.64 –1.40 98.10 22.97 99.38 411.89 162.29 11.56 5.87 90 673.46 692.77 643.53 226.45 139.38 295.44 412.16 275.92 355.43 –6.57 103.37 26.60 105.54 447.72 174.33 11.89 6.02 100 722.95 743.72 698.74 246.39 147.26 315.62 442.93 293.73 384.27 –11.61 110.90 26.65 111.45 482.33 186.46 12.19 6.15 110 782.50 791.06 755.15 263.61 152.51 334.59 472.16 310.53 411.07 –17.06 118.57 27.70 117.19 516.63 197.81 12.46 6.28 120 837.02 843.38 816.30 283.77 157.18 355.40 503.21 326.24 438.14 –23.12 123.97 31.06 122.48 551.64 210.27 12.75 6.41 130 893.83 891.81 873.65 302.20 161.59 373.25 532.08 340.83 464.49 –29.11 130.96 32.40 127.28 585.19 221.26 13.00 6.52 140 947.71 937.33 932.83 320.94 164.31 389.70 557.89 356.32 491.30 –32.61 137.77 33.11 132.68 617.88 231.59 13.22 6.61 150 1004.04 981.80 993.82 338.71 170.45 407.72 586.19 370.76 516.13 –39.06 144.22 36.28 137.75 650.88 242.96 13.46 6.72

Table 2. Calculated values of elastic constants (in unit GPa), bulk modulus, shear modulus (in unit GPa), and compressional and shear wave velocity (in units km/s) under pressure P (in unit GPa) at 0 K. .

In the post-aragonite phase, the elastic constants exhibit a different behavior from that of aragonite. The and of post-aragonite are almost the same and both of them are larger than in the entire pressure range (40 GPa–65 GPa). It indicates that the a axis of post-aragonite is more compressible than b and c axes. The compression results reflect the characteristic of layered mineral that this structure is more compressive in the direction perpendicular ([100] directions here in this work) to the layers (layers parallel to the [001] and [010] directions) (see Figs. 2(d)–2(f)).

For -h-CaCO , the values of , , and are close at 65 GPa–150 GPa, implying that a, b, and c axes have similar compression behaviors. The shear elastic constants and off-diagonal elastic constants of -h-CaCO increase smoothly with pressure and show different sizes with and , respectively. Compared with post-aragonite at 65 GPa, -h-CaCO exhibits smaller longitudinal elastic constants except and larger off-diagonal and shear elastic constants except (see Figs. 2(g)–2(i)). The differences in density, and discontinuities between aragonite and post-aragonite at 40 GPa are 5.39%, 1.43%, and 7.08%, respectively.

The density discontinuity is in good accord with the result given by Oganov et al.,^[15] and those density, and discontinuities at 65 GPa between post-aragonite and -h-CaCO are 1.86%, 5.11%, and 10.66%, respectively. The huge density increase, with relatively small bulk and shear modulus differences, leads to smaller acoustic velocities of post-aragonite. Besides, larger acoustic velocities appear in -h-CaCO and C222 -CaCO so that the two phases have a chained structure and almost similar acoustic velocities. It indicates that the polymerization of CO tetrahedron, leading a more compact structure, can increase the acoustic velocity of CaCO (see Fig. 3).

Fig. 3.

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	Fig. 3. (color online) Variations of calculated (a) densities and (b) wave velocities for aragonite, post-aragonite, -h-CaCO , C222 -CaCO with pressure.

Single crystal wave velocities in various crystallographic directions are determined by Christoffel’s equation^[34] 2 where , , n, V, and are elastic constants, density, propagation, wave velocity, and Kronecker delta, respectively.

Figure 4 shows the acoustic wave velocities of three structures along different crystalline directions. For aragonite, P-wave propagates fastest in the [100] direction and slowest in the [001] direction. Whereas, the P-wave velocity of post-aragonite is the fastest in the [001] and [010] direction, and slowest in the [110] direction. -h-CaCO propagates fastest in the [111] direction, and slowest in the direction [ ]. These results are in agreement with the orders of elastic constants for aragonite, for post-aragonite, and for -h-CaCO . Moreover, the largest shear wave splitting ( ) directions switch from [010] to [111] for aragonite at about 10 GPa, from [001] to [011] for post-aragonite at about 50 GPa, and from [010] to [111] at about 120 GPa for -h-CaCO , respectively. It means that when the transition occurs, the fastest propagation direction of the P-wave and the splitting direction of the largest shear wave are changed. Meanwhile, these changes also reflect structural changes from a block structure of aragonite to a layered structure of post-aragonite and to a chained structure of -h-CaCO .

Fig. 4.

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	Fig. 4. (color online) Calculated profiles of anisotropy and shear wave splitting of (a) aragonite, (b) post-aragonite, (c) -h-CaCO with pressures by using the calculated elastic constants.

Azimuthal anisotropy values ( , for P and S waves at different pressures are defined as 3 4 where , , , and are the maxima and minima of and velocities, respectively. The and are two orthogonally polarized velocities, and is the maximum difference between and along the same direction of propagation. Figure 5(a) shows azimuthal anisotropies for P and S waves of three CaCO phases at given pressure. There are strong shear anisotropies in carbonates especially for post-aragonite and -h-CaCO . Aragonite exhibits 25.60%–30.60% anisotropy and 29.60%–44.92% anisotropy. With pressure increasing, the of aragonite first decreases under pressure lower than 10 GPa and then increases under pressure of 10 GPa–40 GPa. The minimum of 29.6% is present in aragonite at 10 GPa. The post-aragonite phase has abnormally high anisotropy. At pressure in a range of 40 GPa–65 GPa, post-aragonite exhibits 25.90%–32.10% anisotropy and 74.34%–104.30% splitting anisotropy. The triangular CO units lead to anisotropy of elastic properties of aragonite and post-aragonite. Especially for post-aragonite, the CO units show a layered distribution, which further increases the anisotropy up to 104.30%. The As of post-aragonite presents a sharp decrease at 40 GPa and subsequently keeps falling up to 65 GPa. It may be caused by the decreasing of layer distance with pressure increasing (Fig. 5(b)). The -h-CaCO shows a 22.30%–25.40% anisotropy and a 42.81%–48.00% anisotropy. This means that the phase transition leads to small changes in elastic velocity but abnormally large changes in the elastic anisotropies, especially for shear wave anisotropies.

Fig. 5.

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	Fig. 5. (color online) (a) Variations of calculated azimuthal anisotropy for P and S waves of aragonite (green), post-aragonite (blue), and -h-CaCO (purple) with pressure. (b) Variation of calculated layer distance of post-aragonite with pressure.

Figures 6 and 7 show the comparisons of shear anisotropy and isotropic wave velocities among the three carbonate phases, and other mantle minerals: MgSiO perovskite (Mg–Pv), post-perovskite (Mg–PPv), CaSiO perovskite (Ca–Pv), (Mg, Fe)O ferropericlase (Fp), calcium ferrite-type MgAl O (CF) and new hexagonal aluminous (NAL) phase.^[35–38] Clearly, CaCO high pressure polymorphs have higher wave velocity anisotropies and lower wave velocity than silicate mineral and other carbonate in the whole pressure range. At high pressures, the velocity of CaCO are less than PREM till the outer core pressure, which means that the existence of CaCO could shed light on the low velocity region in the deep mantle, especially the bottom of the lower mantle.

Fig. 6.

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	Fig. 6. (color online) (a) Variations of azimuthal anisotropy for shear wave of aragonite, post-aragonite, and -h-CaCO (this study) with pressure, compared with those of magnesite,[39] siderite,[40] periclase (MgO), and Mg-Pv,[41] Fp and Mg-PPv,[42] Ca-Pv,[43] and Fe-bearing and Fe-free NAL.[44]

Fig. 7.

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Fig. 7. (color online) Comparisons of (a) and (b) between carbonates and other major candidate minerals of subducted basalt at high pressure. The values from the PREM model were also plotted for comparison. Circle: CaCO (this study); blue square: magnesite;[39] red pentacle: Siderite;[40] olivine: Mg–Pv;[45] red: Ca–Pv;[46] purple: Fe-NAL phase;[44] royal: Mg–PPv;[47] orange: CF phase;[48] black: PREM.[49]

In summary, stabilities and elastic properties of three high pressure polymorphs of CaCO are investigated based on first principles calculations. Calculations are conducted at 0 K and 0 GPa–40 GPa for aragonite, 40 GPa–65 GPa for post-aragonite, and 65 GPa–150 GPa for -h-CaCO , respectively. By fitting the third-order Birch–Murnaghan equation of state, the values of bulk modulus and pressure derivative are 66.09 GPa and 4.64 for aragonite, 81.93 GPa and 4.49 for post-aragonite, 56.55 GPa and 5.40 for -h-CaCO , respectively, which are in excellent agreement with previous experimental and theoretical data. A full set of elastic constants, acoustic velocities and anisotropy of the three high-pressure CaCO phases is investigated. High shear anisotropy and low acoustic velocities are presented in three CaCO high pressure phases. These results could have very important geophysical significance for ascertaining the chemical composition and velocity structure of the Earth’s lower mantle.