D. Alfè $^{a,b}$, L. Vočadlo$^{a}$, G. D. Price$^{a}$,and M. J. Gillan $^{b}$
$^{a}$ Research School of Geological and Geophysical Sciences, Birkbeck and University College London, Gower Street, London WC1E 6BT, United Kingdom. $^{b}$ Physics and Astronomy Department, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Ab initio techniques based on density functional theory in the projector-augmented-wave implementation have been used to calculate the free energy and a range of other thermodynamic properties of liquid and solid iron at high pressures and temperatures relevant to the Earth’s core. The ab initio free energy for the liquid phase is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the ab initio system, with thermal averages computed by ab initio molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated using identical ab initio techniques to obtain the melting curve and volume and entropy of melting. Several research groups have recently reported ab initio calculations of the melting properties of iron based on density functional theory, but there have been unexpectedly large disagreements between results obtained by different approaches. As a test of the accuracy of our methods, we have also simulated the melting behaviour of aluminium, and find excellent agreement with experiment. Furthermore, we have analyzed the relations between the two main approaches, based either on calculation of the free energies of solid and liquid, or on direct simulation of the two coexisting phases. Although both approaches rely on the use of classical reference systems consisting of parametrized empirical interaction models, we point out that in the free energy approach the final results are independent of the reference system, whereas in the current form of the coexistence approach they depend on it. We have established a scheme for correcting the predictions of the coexistence approach for differences between the reference and ab initio systems. To illustrate the practical operation of the scheme, we present calculations of the high-pressure melting properties of iron using the corrected coexistence approach, which agree closely with earlier results from the free energy approach. A quantitative assessment is also given of finite-size errors, which we show can be reduced to a negligible size.