## Abstract

Resent experimental and theoretical studies suggested preferential stability of Fe_{3}C over Fe_{7}C_{3} at the condition of the Earth's inner core. Previous studies showed that Fe_{3}C remains in an orthorhombic structure with the space group Pnma to 250 GPa, but it undergoes ferromagnetic (FM) to paramagnetic (PM) and PM to nonmagnetic (NM) phase transitions at 6-8 and 55-60 GPa, respectively. These transitions cause uncertainties in the calculation of the thermoelastic and thermodynamic parameters of Fe_{3}C at core conditions. In this work we determined P-V-T equation of state of Fe_{3}C using the multianvil technique and synchrotron radiation at pressures up to 31 GPa and temperatures up to 1473 K. A fit of our P-V-T data to a Mie-Gruneisen-Debye equation of state produce the following thermoelastic parameters for the PM-phase of Fe_{3}C: V _{0} = 154.6 (1) Å^{3}, K_{T0} = 192 (3) GPa, K_{T}′ = 4.5 (1), γ_{0} = 2.09 (4), θ_{0} = 490 (120) Cyrillic capital letter ka, and q = -0.1 (3). Optimization of the P-V-T data for the PM phase along with existing reference data for thermal expansion and heat capacity using a Kunc-Einstein equation of state yielded the following parameters: V_{0} = 2.327 cm^{3}/mol (154.56 Å^{3}), K_{T0} = 190.8 GPa, K_{T}′ = 4.68, Θ_{E10} = 305 K (which corresponds to θ_{0} = 407 K), γ_{0} = 2.10, e_{0} = 9.2 × 10 ^{-5} K^{-1}, m = 4.3, and g = 0.66 with fixed parameters m _{E1} = 3n = 12, γ_{∞} = 0, β = 0.3, and a _{0} = 0. This formulation allows for calculations of any thermodynamic functions of Fe_{3}C versus T and V or versus T and P. Assuming carbon as the sole light element in the inner core, extrapolation of our equation of state of the NM phase of Fe_{3}C suggests that 3.3 ± 0.9 wt % Cyrillic capital letter es at 5000 Cyrillic capital letter ka and 2.3 ± 0.8 wt % Cyrillic capital letter es at 7000 Cyrillic capital letter ka matches the density at the inner core boundary. Key Points We present a P-V-T EOS for PM-Fe_{3}C with support from thermodynamic analyses We discuss uncertainties in magnetic transitions We applied EOS data for modeling carbon content in the core

Original language | English |
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Pages (from-to) | 5274-5284 |

Number of pages | 11 |

Journal | Journal of Geophysical Research: Solid Earth |

Volume | 118 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2013 Oct |

## Keywords

- X-ray diffraction
- equation of state
- iron carbide
- synchrotron

## ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science