# First Principles Calculation of the Stability of Iron Bearing Carbonates at High Pressure Conditions

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Calculation of MgCO${}_{3}$ Polymorphs under Pressure

#### 2.2. Structure Modeling of (Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$

#### 2.3. High Pressure Transitions of MgCO${}_{3}$ and (Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$

## 3. Discussion

## 4. Conclusions

## 5. Methods

#### 5.1. First Principles Calculation

#### 5.2. LDA+U${}_{ic}$ Calculation

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Merlini, M.; Crichton, W.A.; Hanfland, M.; Gemmi, M.; Muller, H.; Kupenko, I.; Dubrovinsky, L. Structures of dolomite at ultrahigh pressure and their influence on the deep carbon cycle. Proc. Natl. Acad. Sci. USA
**2012**, 109, 13509–13514. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Boulard, E.; Gloter, A.; Corgne, A.; Antonangeli, D.; Auzende, A.; Perrillat, J.; Guyot, F.; Fiquet, G. New host for carbon in the deep Earth. Proc. Natl. Acad. Sci. USA
**2011**, 108, 5184–5187. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Biellmann, C.; Gillet, P.; Guyot, F.; Peyronneau, J.; Reynard, B. Experimental evidence for carbonate stability in Earth’s lower mantle. Earth Planet. Sci. Lett.
**1993**, 118, 31–41. [Google Scholar] [CrossRef] - Gillet, P. Stability of magnesite (MgCO
_{3}) at mantle pressure and temperature conditions: A raman spectroscopic study. Am. Miner.**1993**, 78, 1328–1331. [Google Scholar] - Fiquet, G.; Guyot, F.; Kunz, M.; Matas, J. Andrault, D.; Hanfland, M. Structural refinements of magnesite at very high pressure. Am. Miner.
**2002**, 87, 1261–1265. [Google Scholar] [CrossRef] - Shatskiy, A.; Litasov, K.D.; Palyanov, Y.N.; Ohtani, E. Phase relations on the K
_{2}CO_{3}-CaCO_{3}-MgCO_{3}join at 6 GPa and 900–1400 °C: Implications for incipient melting in carbonated mantle domains. Am. Miner.**2016**, 101, 437–447. [Google Scholar] [CrossRef] - Isshiki, M.; Irifune, T.; Hirose, K.; Ono, S.; Ohishi, Y.; Watanuki, T.; Nishibori, E.; Tanaka, M.; Sakata, M. Stability of magnesite and its high-pressure form in the lowermost mantle. Nature
**2004**, 427, 60–63. [Google Scholar] [CrossRef] - Maeda, F.; Ohtani, E.; Kamada, S.; Sakamaki, T.; Hirao, N.; Ohishi, Y. Diamond formation in the deep lower mantle: A high-pressure reaction of MgCO
_{3}and SiO_{2}. Sci. Rep.**2017**, 7, 40602. [Google Scholar] [CrossRef] [Green Version] - Palyanov, Y.N. Mantle-slab interaction and redox mechanism of diamond formation. Proc. Natl. Acad. Sci. USA
**2013**, 110, 20408–20413. [Google Scholar] [CrossRef] [Green Version] - Kelemen, P.B.; Manning, C.E. Reevaluating carbon fluxes in subduction zones, what goes down, mostly comes up. Proc. Natl. Acad. Sci. USA
**2015**, 112, E3997–E4006. [Google Scholar] [CrossRef] [Green Version] - Oganov, A.R.; Ono, S.; Ma, Y.; Glass, C.W.; Garcia, A. Novel high-pressure structures of MgCO
_{3}, CaCO_{3}and CO_{2}and their role in Earth’s lower mantle. Earth Planet. Sci. Lett.**2008**, 273, 38–47. [Google Scholar] [CrossRef] - Pickard, C.; Needs, R.J. Structures and stability of calcium and magnesium carbonates at mantle pressures. Phys. Rev. B
**2015**, 91, 104101. [Google Scholar] [CrossRef] [Green Version] - Franzolin, E.; Schmidt, M.W.; Poli, S. Ternary Ca-Fe-Mg carbonates: subsolidus phase relations at 3.5 GPa and a thermodynamics solid solution model including order/disorder. Contrib. Miner. Petrol.
**2011**, 161, 213–227. [Google Scholar] [CrossRef] [Green Version] - Liu, J.; Lin, J.-F.; Prakapenka, V.B. Ferromagnesite as a potential deep-mantle carbon carrier. Sci. Rep.
**2015**, 5, 7940. [Google Scholar] [CrossRef] [Green Version] - Solomatova, N.V.; Asimow, P.D. First-principles calculations of high-pressure iron-bearing monoclinic dolomite and single-cation carbonates with internally consistent Hubbard U. Phys. Chem. Miner.
**2018**, 45, 293–302. [Google Scholar] [CrossRef] - Boulard, E.; Menguy, N.; Auzende, A.L.; Bureau, H.; Antonangeli, D.; Corgne, A.; Morard, G.; Siebert, J.; Perrillat, J.P.; Guyot, F.; et al. Experimental investigation of the stability of Fe-rich carbonates in the lower mantle. J. Geophys. Res.
**2012**, 117, B02208. [Google Scholar] [CrossRef] [Green Version] - Lavina, B.; Dera, P.; Downs, R.T.; Prakapenka, V.; Rivers, M.; Sutton, S.; Nicol, M. Siderite at lower mantle conditions and the effects of the pressure-induced spin-apiring transition. Geophys. Res. Lett.
**2009**, 36, L23306. [Google Scholar] [CrossRef] [Green Version] - Lavina, B.; Dera, P.; Downs, R.T.; Yang, W.; Sinogeikin, S. Meng, Y.; Shen, G.; Schiferl, D. Structure of siderite FeCO
_{3}to 56 GPa and hysteresis of its spin-pairing transition. Phys. Rev. B**2010**, 82, 064110. [Google Scholar] [CrossRef] [Green Version] - Mattila, A.; Pylkkanen, T.; Rueff, J.-P.; Huotari, S.; Vanko, G.; Hafland, M.; Lehtinen, M.; Hamalainen, K. Pressure induced magnetic transition in siderite FeCO
_{3}studied by x-ray emission spectroscopy. J. Phys. Condens. Matter**2007**, 19, 386206. [Google Scholar] [CrossRef] - Farfan, G.; Wang, S.; Ma, H.; Caracas, R.; Mao, W.L. Bonding and structural changes in siderite at high pressure. Am. Miner.
**2012**, 97, 1421. [Google Scholar] [CrossRef] - Lin, J.-F.; Liu, J.; Jacobs, C.; Prakapenka, V.B. Vibrational and elastic properties of ferromagnesite across the electronic spin-pairing transition of iron. Am. Miner.
**2012**, 97, 583. [Google Scholar] [CrossRef] - Hsu, H.; Huang, S.C. Spin crossover and hyperfine interactions of iron in (Mg,Fe)CO
_{3}ferromagnesite. Phys. Rev. B**2016**, 94, 060404. [Google Scholar] [CrossRef] - Cococcioni, M.; de Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B
**2005**, 71, 035105. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Tsuchiya, T.; Hase, A. Computational support for a pyrolitic lower mantle containing ferric iron. Nat. Geosci.
**2015**, 8, 556–560. [Google Scholar] [CrossRef] - McCammon, C. Perovskiate as a possible sink for ferric iron in the lower mantle. Nature
**1997**, 387, 694–696. [Google Scholar] [CrossRef] - Zhang, F.; Oganov, A.R. Valence state and spin transitions of iron in Earth’s mantle silicates. Earth Planet. Sci. Lett.
**2006**, 249, 436–443. [Google Scholar] [CrossRef] - Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev.
**1964**, 136, B864–B871. [Google Scholar] [CrossRef] [Green Version] - Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev.
**1965**, 140, A1133–A1138. [Google Scholar] [CrossRef] [Green Version] - Troullier, N.; Martins, J.L. Efficient pseudopotential for plane wave calculations. Phys. Rev. B
**1991**, 43, 1993–2006. [Google Scholar] [CrossRef] - Tsuchiya, T.; Tsuchiya, J.; Umemoto, K.; Wentzcovitch, R.M. Phase transition in MgSiO
_{3}perovskite in the earth’s lower mantle. Earth Planet. Sci. Lett.**2004**, 224, 241–248. [Google Scholar] [CrossRef] - Ichikawa, H.; Tsuchiya, T.; Tange, Y. The P-V-T equation of state and thermodynamic properties of liquid iron. J. Geophys. Res. Solid Earth
**2013**, 119, 240–252. [Google Scholar] [CrossRef] - Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B
**1990**, 41, 7892–7895. [Google Scholar] [CrossRef] [PubMed] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188–5192. [Google Scholar] [CrossRef] - Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G.L.; Cococcioni, M.; Dabo, I.; et al. Quantum ESPRESSO: A modular and open-sourcesoftware project for quantum simulations of materials. J. Phys. Condens. Matter
**2009**, 21, 395502. [Google Scholar] [CrossRef] - Tsuchiya, T.; Wentzcovitch, R.M.; da Silva, C.R.S.; de Gironcoli, S. Spin transition in magnesiowustite in earth’s lower mantle. Phys. Rev. Lett.
**2006**, 96, 198501. [Google Scholar] [CrossRef] [Green Version] - Fukui, H.; Tsuchiya, T.; Baron, A.Q.R. Lattice dynamics calculations for ferropericlase with internally consistent LDA+U method. J. Geophys. Res.
**2012**, 117, B12202. [Google Scholar] [CrossRef]

**Figure 1.**Optimized structures and polyhedral volumes (M1, M2, and M3 sites) of P$\overline{1}$ and C2/m MgCO${}_{3}$ polymorphs at 120 GPa.

**Figure 3.**Enthalpies of P$\overline{1}$-(Mg${}_{0.833}$,Fe${}_{0.167}$)CO${}_{3}$ structures with respect to the lowest enthalpy configuration.

**Figure 4.**Enthalpies of C2/m-(Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$ structures with respect to the lowest enthalpy configurations. Calculations reveal that the structure with LS-Fe atoms at M3 sites was highly unstable.

**Figure 5.**(

**a**) Relative enthalpies of MgCO${}_{3}$ polymorphs with respect to that of the C2/m phase. These calculations are based on the LDA method. (

**b**) Relative enthalpies of (Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$ under pressure with respect to that of the HS-C2/m phase. These calculations are based on the LDA+${U}_{ic}$ method.

**Figure 6.**(

**a**) The thin lines correspond to the relative enthalpy of MgCO${}_{3}$+ SiO${}_{2}$ with respect to MgSiO${}_{3}$-bridgmanite + CO${}_{2}$. The full/dashed lines indicate the relative enthalpy of the HS/LS- (Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$+ SiO${}_{2}$ with respect to the HS-(Mg${}_{0.833}$Fe${}_{0.167}$)SiO${}_{3}$-bridgmanite + CO${}_{2}$. (

**b**) The relative stability of (Mg${}_{0.833}$Fe${}_{0.167}$)CO${}_{3}$+ MgSiO${}_{3}$-bridgmanite and HS-(Mg${}_{0.833}$Fe${}_{0.167}$)SiO${}_{3}$-bridgmanite + MgCO${}_{3}$ as a function of pressure. The thick lines indicate the enthalpies of the reactions containing the lowest enthalpy phase of (Mg,Fe)CO${}_{3}$ as shown in Figure 5b.

**Table 1.**Optimized structural parameters of P$\overline{1}$ and C2/m phases of MgCO${}_{3}$ polymorphs.

P$\overline{1}$ structureat 100 GPa | ||||

a = 5.178 Å, b = 5.206 Å, c = 7.242 Å, $\alpha =69.85\xb0,\beta =81.64\xb0,\gamma =78.04\xb0$ | ||||

(Pickard and Needs [12]: a = 5.211 Å, b = 5.238 Å, c = 7.268 Å, $\alpha =70.030\xb0,\beta =81.904\xb0,\gamma =78.272\xb0$ at 100 GPa) | ||||

Atom | Wyckoff position | Atomic coordinates | ||

x | y | z | ||

Mg1(M1) | 2i | 0.7414 | 0.2541 | 0.0022 |

Mg2(M2) | 2i | 0.5669 | 0.4731 | 0.3143 |

Mg3(M3) | 2i | 0.0636 | 0.1784 | 0.6501 |

C1 | 2i | 0.2237 | 0.2078 | 0.0295 |

C2 | 2i | 0.0812 | 0.3351 | 0.3092 |

C3 | 2i | 0.4398 | 0.9790 | 0.3231 |

O1 | 2i | 0.1277 | 0.1522 | 0.8965 |

O2 | 2i | 0.0086 | 0.2930 | 0.1470 |

O3 | 2i | 0.8794 | 0.3896 | 0.4232 |

O4 | 2i | 0.3461 | 0.9572 | 0.1548 |

O5 | 2i | 0.3752 | 0.3872 | 0.9623 |

O6 | 2i | 0.2030 | 0.0682 | 0.4149 |

O7 | 2i | 0.2249 | 0.5252 | 0.2622 |

O8 | 2i | 0.5465 | 0.7397 | 0.4278 |

O9 | 2i | 0.6110 | 0.1433 | 0.2692 |

C2/m structure at 120 GPa | ||||

a = 8.0417 Å, b = 6.4468 Å, c = 6.8273 Å, $\beta $ = 103.84° | ||||

(Oganov et al. [11]: a = 8.0945 Å, b = 6.4881 Å, c = 6.8795 Å, $\beta $ = 103.98° at 120 GPa) | ||||

Atom | Wyckoff position | Atomic coordinates | ||

x | y | z | ||

Mg1(M1) | 4g | 0.0000 | 0.7536 | 0.0000 |

Mg2(M2) | 4i | 0.3229 | 0.5000 | 0.6975 |

Mg3(M3) | 4i | 0.9353 | 0.5000 | 0.6555 |

C1 | 8j | 0.3701 | 0.3214 | 0.3273 |

C2 | 4i | 0.2315 | 0.5000 | 0.0363 |

O1 | 4i | 0.0926 | 0.5000 | 0.8961 |

O2 | 8j | 0.3490 | 0.1665 | 0.4299 |

O3 | 8j | 0.5081 | 0.3095 | 0.2675 |

O4 | 4i | 0.3661 | 0.5000 | 0.9729 |

O5 | 4i | 0.3522 | 0.5000 | 0.4276 |

O6 | 8j | 0.2253 | 0.3320 | 0.1595 |

**Table 2.**Comparison between previously reported calculation results for high-pressure transition of MgCO${}_{3}$ and those obtained in this study.

GGA [12] | GGA (This Study) | LDA (This Study) | |
---|---|---|---|

R$\overline{3}$c → P$\overline{1}$ | 85 | 85 | 62 |

P$\overline{1}$ → C2/m | 101 | 95 | 80 |

C2/m → P2${}_{1}$2${}_{1}$2${}_{1}$ | 144 | 145 | 130 |

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**MDPI and ACS Style**

Tsuchiya, J.; Nishida, R.; Tsuchiya, T.
First Principles Calculation of the Stability of Iron Bearing Carbonates at High Pressure Conditions. *Minerals* **2020**, *10*, 54.
https://doi.org/10.3390/min10010054

**AMA Style**

Tsuchiya J, Nishida R, Tsuchiya T.
First Principles Calculation of the Stability of Iron Bearing Carbonates at High Pressure Conditions. *Minerals*. 2020; 10(1):54.
https://doi.org/10.3390/min10010054

**Chicago/Turabian Style**

Tsuchiya, Jun, Risa Nishida, and Taku Tsuchiya.
2020. "First Principles Calculation of the Stability of Iron Bearing Carbonates at High Pressure Conditions" *Minerals* 10, no. 1: 54.
https://doi.org/10.3390/min10010054