Melting and thermal pressure of hcp-Fe from the phonon density of states

We directly probed the phonon density of states (DOS) of hexagonal close-packed iron (ε-Fe) with high statistical quality between pressures of 30 GPa and 151 GPa using nuclear resonant inelastic X-ray scattering and in situ synchrotron X-ray diffraction experiments at 300 K. From each measured phonon DOS, we determined the vibrational free energy (Fvib) and mean-square displacement of atoms, 〈u2〉. The volume dependence of Fvib is directly related to the vibrational thermal pressure, which we combine with previously reported theoretical values for the electronic and anharmonic thermal pressures to find the total thermal pressure (Pth). In addition, we obtained the shape of ε-Fe’s melting curve from the volume dependence of our 〈u2〉, and anchored it with an experimentally determined melting point to obtain the high-pressure melting behavior of ε-Fe. Considering thermal pressure and anharmonic effects, we found ε-Fe’s melting temperature at the pressure of Earth’s core–mantle boundary (P = 135 GPa) to be 3500 ± 100 K. Extrapolating our melting curve to the pressure of the inner-core boundary (ICB, P = 330 GPa), where Earth’s solid inner-core and liquid outer-core are in contact, we determined a melting temperature for ε-Fe of 5600 ± 200 K. Finally, combining this temperature constraint with our Pth, we determined the density of ε-Fe under ICB conditions to be 13.50 ± 0.03 g/cm3, which is 5.5 ± 0.2% higher than the seismically inferred density at the ICB.