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The melting temperature, T m , of hexagonal close-packed (hcp) iron at pressures corresponding to the Earth's core is derived using two thermal physics methods. The first, Gilvarry's rule, follows from the assumption that melting occurs when the root mean square amplitude of atomic vibration is a certain fraction of the interatomic distance. The second, the Stacey–Irvine formula, follows from assuming that the Gibbs free energy of both solid and liquid phases are equal in value. A crucial pressure is 330 GPa, the pressure at which Earth's solid inner core is in thermal equilibrium with its liquid outer core. We find melting temperatures at 330 GPa of 5905 or 6050 K when the Gilvarry and the Stacey–Irvine formulae, respectively, are used. These calculations are made possible by the recent experimental determination of the vibrational Gruneisen parameter, γ vib , and the thermal expansivity, α , up to 360 GPa, at 300 K. These T m (330 GPa) values are in near agreement with the value of 5995 K for hcp iron determined using the dislocation-mediated method. The average result of the three approaches used here indicates that T m (330 GPa )=5980±70 K for hcp iron. This result is consistent with the value of 6000 K for hcp iron sometimes assumed in studies of Earth's core. |
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