Equation of state and thermodynamic properties of liquid Fe-O in the Earth’s outer core

Equation of state (EoS) plays a crucial role in the prediction of the composition of the outer core. Here, we calculated pressure (P)-volume (V)-temperature (T) data of liquid iron-oxygen alloys (Fe-X wt.% O, X = 0, 2.8, 6.1, and 9.9) under the outer core conditions (~136-330 GPa, 4000-6000 K) by first-principles molecular dynamics simulations. We established an EoS for liquid Fe-O alloys with parameters including P, T, V, and O concentrations. Consequently, thermodynamic properties of liquid Fe-O alloys such as density (ρ), thermal expansion coefficient, isothermal and adiabatic bulk modulus, and sound velocity (V_P) are calculated. To constrain the O content, we predicted the ρ-P and -P profiles along the geotherm and compared them with data from the Preliminary Reference Earth Model (PREM). We conclude that the adiabatic T profile as a function of depth affects the prediction of O content dramatically. With several anchored T_ICB, the composition of Fe-6.1 wt.% O matches the PREM data with an acceptable range of error. But strictly speaking, the distribution in the outer core is probably uneven. In such case, we state that the O content in the outer core cannot be higher than approximately 6.1 wt.%.