Computational searches for iron carbide in the Earth's inner core

We have used density-functional-theory methods together with a structure searching algorithm to determine stable structures and stoichiometries of mixtures of iron and carbon at high pressures and zero temperature. The most favorable stoichiometries at Earth's inner-core pressures ($\sim$350 GPa) are those with between about 20$\%$ and 35$\%$ carbon atoms. The most stable stoichiometries were found to be (Fe and C), Fe${}_3$C, Fe${}_7$C${}_3$, and Fe${}_2$C. The latter has not to our knowledge been discussed previously in relation to the Earth's core. The stoichiometries Fe${}_4$C and Fe${}_5$C${}_2$ were found to be close to stability at Earth's inner-core pressures. We find that Fe${}_7$C${}_3$ is unstable to decomposition into Fe${}_3$C $+$ 2Fe${}_2$C at pressures greater than $\sim$330 GPa. At 150 GPa only Fe, C, Fe${}_3$C, and Fe${}_7$C${}_3$ are stable. Formation of Fe/C compounds is energetically more favorable at 350 GPa than at 150 GPa. We also report a new phase for Fe${}_3$C with $Cmcm$ symmetry to be more stable than the well-known cementite phase at 350 GPa. A number of pressure-induced phase transitions are identified in Fe${}_3$C, Fe${}_3$C${}_2$, FeC, Fe${}_8$C, and FeC${}_2$. The lowest enthalpy Fe/C phases were found to be metallic at the pressures studied.

Figure 1

Convex hull plot for various stoichiometries of Fe and C at (a) 350 GPa and (b) 150 GPa. The red-circled points are structures known prior to this work.

Figure 2

Variation of the enthalpies of Fe${}_7$C${}_3$ and of Fe${}_3$C $+$ 2Fe${}_2$C with pressure, showing that Fe${}_3$C $+$ 2Fe${}_2$C is more stable above $\sim$330 GPa.

Figure 3

Structures for various stoichiometries of Fe and C found from searching at 350 GPa. The structures are those listed in Table .

Figure 4

Plots of relative enthalpy against pressure for (a) Fe${}_8$C, (b) Fe${}_3$C, (c) Fe${}_3$C${}_2$, (d) FeC, and (e) FeC${}_2$. The reference structures appear as horizontal lines at 0 eV.

Figure 5

Volume-pressure plot for the Fe${}_3$C cementite and $Cmcm$ structures. Experimental data for the cementite structure are also shown.[28]

Figure 6

Electronic densities of states for (a) the cementite and (b) $Cmcm$ phases of Fe${}_3$C, and for the lowest enthalpy structures lying close to or on the convex hull at 350 GPa for (c) Fe${}_5$C${}_2$ and (d) Fe${}_7$C${}_3$ and Fe${}_2$C. Each plot shows the total density of states and its decomposition into contributions from Fe and C. The Fermi energies are at 0 eV.