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Published September 2011 | public
Journal Article

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.

Additional Information

© 2011 Elsevier B.V. Received 18 March 2011; revised 2 June 2011; Accepted 4 July 2011. Edited by Kei Hirose. Available online 13 July 2011. We would like to thank D. Zhang, H. Yavas, and J.K. Wicks for assistance during the experiments, and NSF-EAR-0711542, NSF-CAREER-0956166, and Caltech for support of this research. We thank two anonymous reviewers for their comments that helped to improve our manuscript. Use of the Advanced Photon Source was supported by the U.S. D.O.E., O.S., O.B.E.S. (DE-AC02-06CH11357). Sector 3 operations are supported in part by COMPRES (NSF EAR 06-49658).

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023