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

Abstract

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 insitu synchrotron X-ray diffraction experiments at 300 K. From each measured phonon DOS, we determined the vibrational free energy (F_(vib)) and mean-square displacement of atoms, 〈u^2〉. The volume dependence of F_(vib) 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 (P_(th)). In addition, we obtained the shape of ε-Fe's melting curve from the volume dependence of our 〈u^2〉, 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 P_(th), we determined the density of ε-Fe under ICB conditions to be 13.50 ± 0.03 g/cm^3, which is 5.5 ± 0.2% higher than the seismically inferred density at the ICB.

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