The earth’s core: an approach from first principles

The Earth’s core is largely composed of iron (Fe), alloyed with less dense elements such as sulphur, silicon and/or oxygen. The phase relations and physical properties of both solid and liquid Fe-alloys are therefore of great geophysical importance. As a result, over the past fifty years the properties of Fe and its alloys have been extensively studied experimentally. However, achieving the extreme pressures (up to 360 GPa) and temperatures (~6000K) found in the core provide a major experimental challenge, and it is not surprising that there are still considerable discrepancies in the results obtained by using different experimental techniques. In the past fifteen years quantum mechanical techniques have been applied to predict the properties of Fe. Here we review the progress that has been made in the use of first principles methods to study Fe and its alloys, and as a result of these studies we conclude: (i) that pure Fe adopts an hexagonal close packed structure under core conditions and melts at ~6200 K at 360 GPa, (ii) that thermodynamic equilibrium and observed seismic data are satisfied by a liquid Fe alloy outer core with a composition of ~10 mole% S (or Si) and 8 mole% O crystallising at ~ 5500 K to give an Fe alloy inner core with ~8 mole% S (or Si) and 0.2 mole % O, and (iii) that with such concentrations of S (or Si), an Fe alloy might adopt a body centred cubic structure in all or part of the inner core. In the future the roles of Ni, C, H and K in the core need to be studied, and techniques to predict the transport and rheological properties of Fe alloys need to be developed

Equation of state and elastic properties of face-centered-cubic FeMg alloy at ultrahigh pressures from first-principles

We have calculated the equation of state and elastic properties of face-centered cubic Fe and Fe-rich FeMg alloy at ultrahigh pressures from first principles using the Exact Muffin-Tin Orbitals method. The results show that adding Mg into Fe influences strongly the equation of state, and cause a large degree of softening of the elastic constants, even at concentrations as small as 1-2 at. %. Moreover, the elastic anisotropy increases, and the effect is higher at higher pressures.Comment: 6 figure

Thermodynamic stability of Fe/O solid solution at inner-core conditions

We present a new technique which allows the fully {\em ab initio} calculation of the chemical potential of a substitutional impurity in a high-temperature crystal, including harmonic and anharmonic lattice vibrations. The technique uses the combination of thermodynamic integration and reference models developed recently for the {\em ab initio} calculation of the free energy of liquids and anharmonic solids. We apply the technique to the case of the substitutional oxygen impurity in h.c.p. iron under Earth's core conditions, which earlier static {\em ab initio} calculations indicated to be thermodynamically very unstable. Our results show that entropic effects arising from the large vibrational amplitude of the oxygen impurity give a major reduction of the oxygen chemical potential, so that oxygen dissolved in h.c.p. iron may be stabilised at concentrations up a few mol % under core conditions

Light elements in the Earth’s core

Constraining the core’s composition is essential for understanding Earth accretion, core formation and the sustainment of Earth’s magnetic field. Earth’s outer and inner core exhibit a density deficit relative to pure iron, attributed to the presence of substantial amounts of low atomic number ‘light’ elements, such as sulfur, silicon, oxygen, carbon and hydrogen. However, owing to its inaccessibility, estimates of core composition can only be indirectly obtained by matching results from high-pressure experiments and theoretical calculations with seismic observations. In this Review, we discuss the properties and phase relations of iron alloys under high-pressure and high-temperature conditions relevant to the Earth’s core. We synthesize mineral physics data with cosmochemical and geochemical estimates to give the likely range of compositions for the outer (Fe + 5% Ni + 1.7% S + 0–4.0% Si + 0.8–5.3% O + 0.2% C + 0–0.26% H by weight) and inner (Fe + 5% Ni + 0–1.1% S + 0–2.3% Si + 0–0.1% O + 0–1.3% C + 0–0.23% H by weight) core. While the exact composition of the core remains unknown, tighter constraints on core temperature and better connections between the solid inner core and the liquid outer core compositions will help narrow the range of potential light element compositions

Equation of state for CO and CO₂ fluids and its application on decarbonation reactions at high pressure and temperature

Ab initio molecular dynamics simulations were performed at pressures and temperatures up to 160 GPa and 4000 K, in order to obtain equations of state (EOS) for CO and CO2 fluids. We found that polymerisation of CO and CO2 fluids starts at low pressures, and that including the effect of polymerisation is essential for accurate EOS. EOSs for CO and CO2 determined from methods using experimental data, or classical potentials that ignore the changes in speciation, should be treated with caution when extrapolated beyond the examined pressures and temperatures. The obtained data was fitted into a modified Lee and Kesler EOS for both CO and CO2 fluids. The thermodynamic calculations for the decarbonation reactions of both MgCO3 and CaCO3 using the derived CO2 EOS reproduced the experimental data and theoretical calculations at low pressures. Both MgCO3 and CaCO3 pure phases are found to be stable in the upper mantle compared to CO2. However, they both become destabilised when approaching lower mantle conditions

The thermal expansion of (Fe1-y Ni y )Si

We have measured the thermal expansion of (Fe1-y Ni y )Si for y  =  0, 0.1 and 0.2, between 40 and 1273 K. Above ~700 K the unit-cell volumes of the samples decrease approximately linearly with increasing Ni content. Below ~200 K the unit-cell volume of FeSi falls to a value between that of (Fe0.9Ni0.1)Si and (Fe0.8Ni0.2)Si. We attribute this extra contraction of the FeSi, which is a narrow band-gap semiconductor, to the depopulation of the conduction band at low temperatures; in the two alloys the additional electrons introduced by the substitution of Ni lead to the conduction band always being populated. We have fit the unit-cell volume data with a Debye internal energy model of thermal expansion and an additional volume term, above 800 K, to take account of the volumetric changes associated with changes in the composition of the sample. Using the thermophysical parameters of the fit we have estimated the band gap in FeSi to be 21(1) meV and the unit-cell volume change in FeSi associated with the depopulation of the conduction band to be 0.066(35) Å(3)/unit-cell

Primitive noble gases sampled from ocean island basalts cannot be from the Earth’s core

Noble gas isotopes in plumes require a source of primitive volatiles largely isolated in the Earth for 4.5 Gyrs. Among the proposed reservoirs, the core is gaining interest in the absence of robust geochemical and geophysical evidence for a mantle source. This is supported by partitioning data showing that sufficient He and Ne could have been incorporated into the core to source plumes today. Here we perform ab initio calculations on the partitioning of He, Ne, Ar, Kr and Xe between liquid iron and silicate melt under core forming conditions. For He our results are consistent with previous studies allowing for substantial amounts of He in the core. In contrast, the partition coefficient for Ne is three orders of magnitude lower than He. This very low partition coefficient would result in a 3He/22Ne ratio of ~103 in the core, far higher than observed in ocean island basalts (OIBs). We conclude that the core is not the source of noble gases in OIBs

Thermal Properties of Liquid Iron at Conditions of Planetary Cores

Thermal properties of iron at high pressures (P) and temperatures (T) are essential for determining the internal structure and evolution of planetary cores. Compared to its solid counterpart, the liquid phase of iron is less studied and existing results exhibit large discrepancies, hindering a proper understanding of planetary cores. Here we use the formally exact urn:x-wiley:21699097:media:jgre21861:jgre21861-math-0019 thermodynamic integration approach to calculate thermal properties of liquid iron up to 3.0 TPa and 25000 K. Uncertainties associated with theory are compensated by introducing a T-independent pressure shift based on experimental data. The resulting thermal equation of state agrees well with the diamond anvil cell (DAC) data in the P-T range of measurements. At higher P-T it matches the reduced shock wave data yet deviates considerably from the extrapolations of DAC measurements, indicating the latter may require further examinations. Moreover, the calculated heat capacity and thermal expansivity are substantially lower than some recent reports, which have important ramifications for understanding thermal evolutions of planetary cores. Using Kepler-36b as a prototype, we examine how a completely molten core may affect the P-T profiles of massive exoplanets. By comparing the melting slope and the adiabatic slope along the iron melting line, we propose that crystallization of the cores of massive planets proceeds from the bottom-up rather than the top-down