Phase relations, including the eutectic liquid composition in the Fe-C binary system, remain unclear under the core pressure range, which makes estimating the carbon budget in the Earth's core difficult. To explore this issue, we have conducted melting and subsolidus experiments on Fe-C alloys in a diamond-anvil cell up to 255 GPa. Textural and compositional characterizations of quenched samples show that carbon concentration in the eutectic liquid slightly decreases with increasing pressure and is about 3 wt.% at the inner core boundary (ICB) pressure. The solubility of carbon in solid Fe is found to be almost constant at ~1.0 wt.%. In situ X-ray diffraction data indicate that Fe forms eutectic melting with Fe3C to 203 GPa and with Fe7C3 at 255 GPa. Previous studies on liquid Fe-C alloys suggested that the density of the outer core is explained by liquid Fe containing 1.8 to 4.2 wt.% C. If the liquid core includes <3 wt.% C as a single light element, hexagonal close-packed (hcp) Fe crystallizes at the ICB. However, the carbon content in such solid Fe is ≤1 wt.%, less than that required to account for the inner core density deficit from pure iron. When the outer core includes ≥3 wt.% C, it forms Fe7C3 at the ICB, whose density is too small for the inner core. Carbon is therefore not a primary light element in the core. Nevertheless, the outer core liquid can be Fe-C-Si, Fe-C-S, or Fe-C-H. Such core liquid crystallizes solid Fe with light elements including less than 1 wt.% C, which may explain the density and the sound velocities observed in the inner core.

As the main constituent of planetary cores, pure iron phase diagram under high pressure and temperature is of fundamental importance in geophysics and planetary science. However, previously reported iron-melting curves show large discrepancies (up to 1000 K at the Earth's core-mantle boundary, 136 GPa), resulting in persisting high uncertainties on the solid-liquid phase boundary. Here we unambiguously show that the observed differences commonly attributed to the nature of the used melting diagnostic are due to a carbon contamination of the sample as well as pressure overestimation at high temperature. The high melting temperature of pure iron under core-mantle boundary (4250 ± 250 K), here determined by X-ray absorption experiments at the Fe K-edge, indicates that volatile light elements such as sulfur, carbon, or hydrogen are required to lower the crystallization temperature of the Earth's liquid outer core in order to prevent extended melting of the surrounding silicate mantle.Plain Language Summary Iron is the main constituent of planetary cores; however, there are still large controversies regarding its melting temperature and phase diagram under planetary interior conditions. The present study reconciles different experimental approaches using laser-heated diamond anvil cell with different in situ X-ray diagnostics (absorption, diffraction, and Mossbauer spectroscopy). The main reason of discrepancies (over 1000 K at core-mantle boundary conditions) is attributed to carbon contamination from the diamond anvils and metrology issues related to thermal pressure overestimation. A high-melting temperature for iron at core-mantle boundary pressure would imply the presence of volatile elements in the liquid outer core, such as sulfur, carbon, or hydrogen, in order to lower its crystallization temperature and avoid extended melting of the surrounding silicate mantle.