Equation of State of Liquid Fe₇C₃ and Thermodynamic Modeling of the Liquidus Phase Relations in the Fe‐C System

Abstract

We calculated the pressure‐volume relations of liquids Fe and Fe7C3 up to ∼360 GPa and 3000–8000 K based on the first‐principles molecular dynamics simulations. The results demonstrate that liquid Fe7C3 is similar in compressibility and thermal expansivity to liquid Fe at the Earth's core pressure range. We then obtained a thermodynamic model of the liquidus phase relations in the Fe‐C system at high pressures by using the thermal equation of state (EoS) of liquid Fe7C3 as well as that of liquid Fe3C estimated by interpolation between the volumes of Fe and Fe7C3 calculated in this study. The previously reported eutectic points in the Fe‐Fe3C system are reproduced with interaction parameters that are dependent on temperature but independent on pressure at >∼50 GPa. The melting curve of Fe7C3 should be close to that of Fe, which leads to a change in the eutectic system from Fe‐Fe3C to Fe‐Fe7C3 above 250 GPa as observed by previous experiments. The thermodynamic model also suggests that the solidus and liquidus of Fe3C are relatively low. The Fe‐Fe7C3 liquidus phase relations at the Earth's inner core boundary (ICB) pressure indicate the Fe7C3 inner core is unlikely. While the carbon content in the Earth's outer core may be small, the addition of 1 wt% C to liquid Fe drops the liquidus temperature to crystallize hcp‐Fe by ∼450 K, suggesting that the presence of carbon in the outer core is preferable for a relatively low core‐mantle boundary (CMB) temperature.