Thermal equation of state of hcp-iron: Constraint on the density deficit of Earth’s solid inner core

We conducted high-pressure experiments on hexagonal close packed iron (hcp-Fe) in MgO, NaCl, and Ne pressure-transmitting media and found general agreement among the experimental data at 300 K that yield the best fitted values of the bulk modulus K₀ = 172.7(±1.4) GPa and its pressure derivative K₀′ = 4.79(±0.05) for hcp-Fe, using the third-order Birch-Murnaghan equation of state. Using the derived thermal pressures for hcp-Fe up to 100 GPa and 1800 K and previous shockwave Hugoniot data, we developed a thermal equation of state of hcp-Fe. The thermal equation of state of hcp-Fe is further used to calculate the densities of iron along adiabatic geotherms to define the density deficit of the inner core, which serves as the basis for developing quantitative composition models of the Earth’s inner core. We determine the density deficit at the inner core boundary to be 3.6%, assuming an inner core boundary temperature of 6000 K.