Search

Knowledge of the abundance and distribution of light elements in the core is fundamental to the understanding of the Earth and other planetary systems. Recent studies (Li et al., 2018; Mashino et al., 2019) suggest the particular importance of carbon for explaining core properties, yet knowledge of carbon partitioning between the outer and inner core is unknown. By using the quasiharmonic approximation, ab initio molecular dynamics, and thermodynamic integration techniques, we have computed the chemical potential of carbon in liquid Fe and solid hcp-Fe at core conditions. We find that substitutional carbon is more stable than interstitial carbon and other carbon defect cluster structures in solid Fe. Lattice strain and overcoordination effects lead to a high chemical potential of C in solid Fe compared to the liquid, and consequently carbon partitions almost completely into the liquid. We find that carbon can account for most of the density jump at the inner-core boundary. This provides an alternative mechanism to the necessity of an oxygen-rich outer core and may have significant implications for the composition and structure of the deep Earth.

The Earth's solid inner core consists mainly of iron (Fe), alloyed with lighter elements. such as silicon (Si). Interpretation of seismic anisotropy and layering requires knowledge of the stable crystal structure in the inner core. We report ab initio density functional theory calculations on the free energy and vibrational stability of pure iron and Fe-Si alloys at conditions representative of the Earth's inner core. For pure Fe the stable phase is already known to be hexagonal close-packed (hcp). However, with the addition of similar to 7 wt.% Si at high temperatures, we observe a transition to the face-centred cubic (fcc) phase. We also produce a phase diagram for the Fe-Si system and show that the inner core may exist in the two-phase region, with coexisting fcc and hcp. This may also explain the low S-velocities observed in the inner core. (C) 2009 Elsevier B.V. All rights reserved.

An investigation of the relative stabilities and equations of state of possible Fe3S polymorphs was conducted using first-principles pseudopotential calculations. These calculations were based on density functional theory and performed using ultrasoft Vanderbilt pseudopotentials within the generalized gradient approximation. In accord with experiment, we found that the tetragonal Fe3P-type polymorph is the only stable phase along the 0 K isotherm as a function of pressure. Fe3S exhibits permanent magnetism at ambient conditions (Fei et al., 2000), but magnetism is suppressed by pressure and temperature, and therefore non-magnetic data are appropriate ones to use for modelling planetary interiors. For this reason, and because the Fe3P-type polymorph of Fe3S contains 32 atoms per unit cell it was impractical to incorporate magnetic properties into the simulations of this phase, we studied the behaviour of the non-magnetic phase. We obtained values of 250 GPa for the bulk modulus, K0, and 4.61 for its first derivative withrespect to pressure, K0′, by fitting a 3rd order Birch-Murnaghan equation of state to the calculated internal energy as a function of volume for the non-magnetic Fe3P-type Fe3S. This suggests that a pressure far greater than that expected in the Martian interior would be needed to achieve a density comparable to that of the Martian core. We therefore conclude that it is unlikely that the core of Mars contains significant amounts of solid Fe3S.

A number of melting curves of various materials have recently been measured experimentally and calculated theoretically, but the agreement between different groups is not always good. We discuss here some of the problems which may arise in both experiments and theory. We also report the melting curves of Fe and Al calculated recently using quantum mechanics techniques, based on density functional theory with generalized gradient approximations. For Al our results are in very good agreement with both low pressure diamond-anvil-cell experiments (Boehler and Ross 1997 Earth Planet. Sci. Lett. 153 223, Hanstrom and Lazor 2000 J. Alloys Compounds 305 209) and high pressure shock wave experiments (Shaner et al 1984 High Pressure in Science and Technology ed Homan et al (Amsterdam: North-Holland) p 137). For Fe our results agree with the shock wave experiments of Brown and McQueen (1986 J. Geophys. Res. 91 7485) and Nguyen and Holmes (2000 AIP Shock Compression of Condensed Matter 505 8 1) and the recent diamond-anvil-cell experiments of Shen et al (1998 Geophys. Res. Lett. 25 373). Our results are at variance with the recent calculations of Laio et al (2000 Science 287 1027) and, to a lesser extent, with the calculations of Belonoshko et al (2000 Phys. Rev. Lett. 84 3638). The reasons for these disagreements are discussed.

Ab initio finite temperature molecular dynamics simulations have been used to calculate the free energy and elasticity of face-centred cubic (fcc) iron at a state point representative of the Earth's inner core. Whilst the free energy of this phase is found to be higher than that of hexagonal-close-packed (hcp) iron, the difference is only 14 meV/atom. It is possible that this difference might be overcome by the presence of light elements, as previous calculations at zero Kelvin have shown that the addition of elements such as silicon stabilise fec-Fe with respect to hcp-Fe by at least 40 meV/atom. The calculated elastic constants at core pressures and temperatures of pure fec-Fe, and of alloys of Fe with sulphur and nickel (Fe(3)S and Fe(3)Ni) derived from the fee structure, lead to average shear wave velocities that are considerably higher than those inferred from seismology; however, these mineralogical and seismological results could be reconciled by the presence of partial melt in the inner core. The calculated P-wave anisotropy of fec-Fe is comparable with the seismological values, but only if there is a high degree of crystal alignment, although the necessity for alignment can be reduced if a layered model for the inner core is invoked. The results presented in this paper therefore suggest that fcc-Fe cannot be ruled out as a candidate for the dominant phase of the Earth's inner core. (c) 2008 Elsevier B.V. All rights reserved.

Atomic-scale materials modelling based on first-principles quantum mechanics is playing an important role in the science of the Earth and the other planets. We outline the basic theory of this kind of modelling and explain how it can be applied in a variety of different ways to probe the thermodynamics, structure and transport properties of both solids and liquids under extreme conditions. After a summary of the density functional formulation of quantum mechanics and its practical implementation through pseudopotentials, we outline the simplestway of applying first-principles modelling, namely static zero-temperature calculations. We show how calculations of this kind can be compared with static compression experiments to demonstrate the accuracy of first-principles modelling at pressures reached in planetary interiors. Noting that virtually all problems concerning planetary interiors require an understanding of materials at high temperatures as well as high pressures, we then describe how first-principles lattice dynamics gives a powerful way of investigating solids at temperatures not too close to the melting line. We show how such calculations have contributed to important progress, including the recent discovery of the post-perovskite phase of MgSiO3 in the D '' layer at the base of the Earth's mantle. A range of applications of first-principles molecular dynamics are then reviewed, including the properties of metallic hydrogen in Jupiter and Saturn, of water, ammonia and methane in Uranus and Neptune, and of oxides and silicates and solid and liquid iron and its alloys in the Earth's deep interior. Recognizing the importance of phase equilibria throughout the planetary sciences, we review recently developed techniques for the first- principles calculation of solid and liquid free energies, melting curves and chemical potentials of alloys. We show how such calculations have contributed to an improved understanding of the temperature distribution and the chemical composition throughout the Earth's interior. The review concludes with a summary of the present state of the field and with some ideas for future developments.

[1] Using first-principles molecular dynamics (MD) simulations, we study the solubility of argon in molten iron at high pressures and temperatures. In particular we explore whether the low pressure immiscibility of liquid Fe and Ar persists to high pressure (130 GPa) and temperature (4500K), or whether they mix. Starting from a variety of Fe/Ar mixtures we find that they always separate rapidly into two liquids. We conclude that there is no evidence for a significant increase in the solubility of Ar in Fe at these conditions. We cannot, therefore, attribute the lower melting temperatures of Fe obtained from DAC experiments compared to those obtained from ab initio calculations and shock experiments, to eutectic melting between Fe and the Ar pressure medium.

Ab initio calculations of the melting properties of copper in the pressure range 0-100 GPa are reported. The ab initio total energies and ionic forces of systems representing solid and liquid copper are calculated using the projector augmented wave implementation of density functional theory with the generalized gradient approximation for exchange-correlation energy. An initial approximation to the melting curve is obtained using an empirical reference system based on the embedded-atom model, points on the curve being determined by simulations in which solid and liquid coexist. The approximate melting curve so obtained is corrected using calculated free energy differences between the reference and ab initio system. It is shown that for system-size errors to be rendered negligible in this scheme, careful tuning of the reference system to reproduce ab initio energies is essential. The final melting curve is in satisfactory agreement with extrapolated experimental data available up to 20 GPa, and supports the validity of previous calculations of the melting curve up to 100 GPa. (C) 2004 American Institute of Physics.

The nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments 1 suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations(2-4) have indicated the possible presence of complex, inner-core layering. Theoretical studies(5,6) currently suggest that the hexagonal close packed (h. c. p.) phase of iron is stable at core pressures and that the body centred cubic (b. c. c.) phase of iron becomes elastically unstable at high pressure. In other h. c. p. metals, however, a high-pressure b. c. c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b. c. c. phase will be stabilized with respect to the h. c. p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core(2-4).

We report phonon densities of states (DOS) of iron measured by nuclear resonant inelastic x-ray scattering to 153 gigapascals and calculated from ab initio theory. Qualitatively, they are in agreement, but the theory predicts density at higher energies. From the DOS, we derive elastic and thermodynamic parameters of iron, including shear modulus, compressional and shear velocities, heat capacity, entropy, kinetic energy, zero-point energy, and Debye temperature. In comparison to the compressional and shear velocities from the preliminary reference Earth model (PREM) seismic model, our results suggest that Earth's inner core has a mean atomic number equal to or higher than pure iron, which is consistent with an iron-nickel alloy.