Thermal equation of state and thermodynamic properties of iron carbide Fe3C to 31 GPa and 1473 K

Abstract

AbstractResent experimental and theoretical studies suggested preferential stability of Fe3C over Fe7C3 at the condition of the Earth's inner core. Previous studies showed that Fe3C 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 Fe3C at core conditions. In this work we determined P‐V‐T equation of state of Fe3C 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 Fe3C: V0 = 154.6 (1) Å3, KT0 = 192 (3) GPa, KT′ = 4.5 (1), γ0 = 2.09 (4), θ0 = 490 (120) К, 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: V0 = 2.327 cm3/mol (154.56 Å3), KT0 = 190.8 GPa, KT′ = 4.68, ΘE10 = 305 K (which corresponds to θ0 = 407 K), γ0 = 2.10, e0 = 9.2 × 10−5 K−1, m = 4.3, and g = 0.66 with fixed parameters mE1 = 3n = 12, γ∞ = 0, β = 0.3, and a0 = 0. This formulation allows for calculations of any thermodynamic functions of Fe3C 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 Fe3C suggests that 3.3 ± 0.9 wt % С at 5000 К and 2.3 ± 0.8 wt % С at 7000 К matches the density at the inner core boundary.