# 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

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**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