Ab initio melting temperatures of bcc and hcp iron under the Earth's inner core condition

There has been a long debate on the thermodynamic stability of iron phases under the Earth's inner core conditions, mainly due to the considerable uncertainty in determining the melting temperatures of iron phases. In the present study, we utilized a semi-empirical potential fitted to high-temperature \textit{ab initio} data to perform a thermodynamic integration from classical systems described by this potential to \textit{ab initio} systems. This method provides a smooth path for the thermodynamic integration and significantly reduces the uncertainty caused by the finite size effect within 15 K. Our results suggest the hcp phase is the ground state of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10s meV/atom.