Melting properties from ab initio free energy calculations: Iron at the Earth's inner-core boundary

Abstract

We present a general scheme to accurately determine melting properties of materials from ab initio free energies. This scheme does not require prior fitting of system-specific interatomic potentials and is straightforward to implement. For the solid phase, ionic entropies are determined from the phonon quasiparticle spectra (PQS), which fully account for lattice anharmonicity in the thermodynamic limit. The resulting free energies are nearly identical (within 10 meV/atom) to those from the computationally more demanding thermodynamic integration (TI) approach. For the liquid phase, PQS are not directly applicable and free energies are determined via TI using the Weeks-Chandler-Andersen (WCA) gas as the reference system. The WCA is a simple, short-range, purely repulsive potential with established equation of states. As such, it is an ideal reference for ab initio TI of liquids. We apply this scheme to determine melting properties of hexagonal close-packed (hcp) iron at the Earth's inner core boundary (P = 330 GPa), a subject of great significance in Earth sciences. The important influences of system size and pseudopotentials are carefully analyzed. The results (melting temperature equals 6170 ± 200 K, latent heat 56 ± 2 kJ/mol, Clapeyron slope 8.1 ± 0.2 K/GPa) are consistent with experiments as well as previous calculations.

Shock Melting Curve of Iron: A Consensus on the Temperature at the Earth's Inner Core Boundary

“…The obtained melting curve of iron overall reaches a consensus between the static and dynamic compressions (Anzellini et al, 2013;Morard et al, 2018), indicating that thermal equilibrium can be quickly established in shocked iron. The current melting curve of iron indicates a melting temperature of~5950(400) K at the ICB, which agrees with most of the recent theories (Alfè, 2009;Dorogokupets et al, 2017;Sun et al, 2018). Our study suggests that the inner core is most likely younger than~0.57 Gyr constrained by the melting curve gradient and the recently determined thermal conductivity of iron at the ICB.…”

“…Previous studies give a range of iron melting temperatures from 5500 to 7000 K at the ICB pressure in the extrapolations of static measurements (e.g., Anzellini et al, 2013; Aquilanti et al, 2015; Morard et al, 2018; Zhang et al, 2016), dynamic measurements (e.g., Bass et al, 1987; Harmand et al, 2015; Ping et al, 2013; Yoo et al, 1993), and theoretical calculations (e.g., Alfè, 2009; Belonoshko et al, 2000; Bouchet et al, 2013; Laio et al, 2000; Sola & Alfè, 2009; Sun et al, 2018). Under the current status of the iron phase diagram with such a considerable uncertainty, the thermal structure and evolution of the core cannot be well constrained.…”

Partitioning of sulfur between solid and liquid iron under Earth’s core conditions: Constraints from atomistic simulations with machine learning potentials

“…To train the GAP models, we carried out a number of density functional theory (DFT) simulations with VASP, with the projector-augmented-wave method (Kresse and Joubert, 1999). We use the PBE form of Generalized Gradient Approximation (GGA) (Perdew et al, 1996) with valence electrons of 16 (valence configuration 3s 2 3p 6 3d 4s ) for iron, which has been demonstrated to closely resemble the all-electron potential and be important for obtaining accurate melting properties (Sun et al, 2018), and 6 (3s 2 3p 4 ) for sulfur.…”

Variationally derived intermediates for correlated free-energy estimates between intermediate states

“…(15) and (16), that we refer to as the correlated variational intermediates (cVI), yield the minimal MSE estimates for cFEP. Figure 2 shows the resulting configuration space densities of the above intermediates for the example of a start state with a harmonic Hamiltonian, H 1 (x) = 1 2 x 2 , and an end state with a quartic one, H N (x) = (x − x 0 ) 4 . Figure 2(a) shows the VI that are optimal for the regular FEP scheme in Fig.…”

“…Free-energy calculations are widely used to investigate physical and chemical processes [1][2][3][4][5][6][7]. Their accuracy is essential to biomedical applications such as computational drug development [8][9][10][11] or material design [12][13][14][15].…”