The goal of this proposal is to establish density profiles of the Earth’s inner core by determining equations of state (EOS) of iron alloys at inner core conditions. The inner core has 3-4% density deficit compared with density of pure Fe. Interpretation of the density deficit requires accurate density measurements of the candidate Fe alloys at pressure and temperature conditions of the inner core. Following our successful compression experiments at ESRF (ES-1441) at inner-core pressures, we will focus on determination of thermal EOS of Fe and Fe-alloys up to 365 GPa and 3500 K. The proposed experiments include thermal EOS of pure Fe, Fe-1.37wt%C, Fe-4wt%Si, and a ternary Fe alloy, Fe-1wt%C-3wt%Si. The results will be direct compared with the observed core density that will allow a determination of the composition of the inner core. It is expected that we will need at least 12 shifts to complete the proposed project.