High-pressure behavior of iron carbide (Fe_7C_3) at inner core conditions

摘要

Carbon is a plausible light element candidate in the Earth's core owing to its cosmic abundance and its chemical affinity for iron. Recent experimental studies on Fe-C phase relations at high pressures have demonstrated that Fe_7C_3 iron carbide is a likely candidate for the Earth's inner core. Using electronic structure calculations, we determine the equation of state, the full elastic constant tensor, and the sound wave velocities for Fe_7C_3, up to inner core pressures. We find that Fe_7C_3 is ferromagnetic (fm) at low pressure, and that its compression behavior is well represented by a third-order Birch Murnaghan finite strain expression with V_0~(fm) = 9.1 A~3/atom, K_0~(fm) = 231 GPa, and K_0~(fm) = 4.4. Under compression the magnetic moments of the Fe atoms gradually decrease, and at ～67 GPa the magnetic moment is lost. The high-pressure nonmagnetic phase (nm) has distinct finite strain parameters with V_0~(nm) = 8.8 A~3/atom, K_0~(nm) = 291 GPa, and K'_0~(nm) = 4.5. Calculated elastic constants show softening associated with the loss of magnetization. In addition, we have conducted nuclear resonant inelastic X-ray scattering experiments on 57Fe enriched Fe_7C_3 at 1 bar and 300 K. On the basis of our nuclear resonant inelastic X-ray scattering spectra we have derived a Debye sound velocity of 3.18 km/s. The experimentally determined value is in good agreement with the computational predictions, based on athermal single elastic constants. The static P wave velocity at inner core pressures agrees well with seismological constraints, whereas the S wave velocity is greater by 30%. On the basis of the density of Fe_7C_3 at inner core conditions, we predict that the maximum possible carbon content of the inner core is around 1.5 wt %.