Session H17: Matter in Extreme Environments: Iron in Planetary Interiors

Chemical equilibrium in the Earth's core

The core of the Earth is a source of thermal energy for the mantle, helping to drive convection, plate tectonics and volcanism. It is mainly formed by iron, but is also contains light impurities. The exact chemical inventory of the core is unknown, but it is believed that oxygen may be present in relatively large quantities, as it is a major element in the mantle. Freezing of the inner core causes oxygen to be released in the liquid, which is thought to be the main form of energy driving core convection at the present day, responsible for the generation of the magnetic field. One of the fundamental questions is therefore how oxygen entered the core in the first place.
Using first principles calculations of chemical potentials we put contraints on the equilibrium concentrations of oxygen between liquid iron and a liquid silicate mixture, representative of long lived magma ocean (MO) at the base of the mantle. We show that the presence of a large fraction of oxygen in the core can be explained by a relatively large thermodynamic advantage of partitioning from the MO into the liquid core.
We also computed chemical potentials in solid ferropericlase, thought to be one of the main constituents of the Earth's mantle, and found that the current oxygen concentration in the core is lower than its equilibrium concentration, suggesting that the mantle may be continually pumping oxygen into the core, even at the present day. This has important consequences for our understanding of convection in the core, supporting the idea of the presence of a stratified, oxygen rich, layer at the top of the core, which may have been observed in the seismological record.   

Transport properties of iron under Earth's core conditions

Transport properties of iron in Earth's core control the dynamo that generates Earth's magnetic field. If the thermal conductivity is high, heat transport is through conduction, and if low by convection. Conventional dynamo theory considered thermal convection primarily to drive the dynamo, but it is also possible to sustain a dynamo through chemical segregation, such as growth of Earth's inner core. We computed the electrical resistivity and thermal conductivity of solid and liquid iron under core conditions, including both electron-ion (electron-phonon) and electron-electron scattering (Xu et al., PRL 121 096601, 2018). We have included saturation effects in different approximations. We find somewhat higher resistivity than recent resistivity measurements and somewhat higher thermal conductivity than recent thermal conductivity measurements. Thermal conductivities are lower than would be obtained using an ideal Wiedemann-Franz Lorenz factor. Electron-electron scattering also decreases the thermal conductivity. Our results are consistent with a convection driven dynamo.   

Ab initio study of iron isotope fractionation during Earth’s core-mantle segregation

Recent studies have revealed that the iron isotope composition of mid-ocean ridge basalts (MORBs) is +0.1‰ richer in heavy Fe isotope (⁵⁶Fe) relative to primitive chondritic meteorites, while basalts from Mars and Vesta have similar Fe isotopic composition as these meteorites. Here we investigate the hypothesis that iron isotope fractionation may have occurred during core formation on Earth. In particular, we compute Fe isotope fractionation factors among the lower mantle phases, bridgmanite (Bdg) and ferropericlase (Fp), and the metal phase at relevant pressure-temperature conditions. We pay particular attention to the effect of the spin crossover in Fe in Bdg and Fp on these fractionation factors. In addition, Fe in Bdg can occupy more than one crystalline site and can be in more than one valence state. In the metal phase, we consider variable amounts of Ni, the other metallic element expected to alloy with Fe in the core. Considering all these possible states of Fe in the silicate, oxide, and metallic phase, we show that the spin crossover in Fe, which does not occur in Mars or Vesta, may have played an important role in the Fe isotope fractionation during core-mantle segregation in the Earth.   

First-principles Anharmonic Free-Energy Calculation of Iron Up to Core Conditions: Implications for Earth Inner Core Crystal Structure

Study of crystalline iron at Earth’s inner-core (IC) conditions finds two main challenges: first, at such high temperatures (> 5000 K, near melting) anharmonic effects are significant; second, due to magnetic phenomena many-body effects (correlation) are important, such that standard ab initio methods (e.g., DFT) fail to reproduce experimental data. To tackle the first difficulty we utilized harmonically-mapped averaging (HMA) to measure anharmonic free energy with orders of magnitude speedup in computation compared to conventional methods. As for the second complication, we apply DMFT (dynamical mean-field theory) to explicitly capture the many-body effects and magnetism on the static lattice energy. Standard DFT is then used to capture quasiharmonic and anharmonic effects.
We apply this hybrid DFT+DMFT approach to the low pressure/temperature region of the phase diagram, where experimental data are available, and find excellent agreement in c/a-ratio, equation-of-state, and fcc-hcp phase coexistence line. Then, we turn to the high pressure/temperature region using the most likely Earth’s IC candidate structures (viz., hcp, bcc, and fcc). We report findings regarding the phase relation between these phases in the vicinity of the IC conditions.
  

Thermodynamic properties of ε-iron with T-dependent phonons

The quasi-harmonic approximation (QHA) is an extremely powerful method for computing thermodynamic properties of materials at high pressures (P) and temperatures (T). However, anharmonicity, electronic excitations in metals, or both, introduce an intrinsic T-dependence on the phonon frequencies. Here, we investigate the effect of electronic excitations on the phonon frequencies and the implication for the thermodynamics properties of ε-Fe at extreme P, T conditions. Phonon-phonon interactions are disregarded here. Because phonon frequencies are T-dependent, we first obtain the entropy using the phonon gas model formula, still valid in the context of phonon-quasiparticles, and then the vibrational free energy by integrating the entropy. We demonstrate that inclusion of the electronic thermal excitation effect on phonon dispersions makes a significant difference in the thermodynamic properties of ε-Fe at Earth’s inner core conditions and beyond.   

A semi-empirical iron EOS for temperature predictions in high pressure shock-ramp experiments

Experiments to determine the multi-Mbar melt temperature of iron through the identification of high pressure solidification are underway. While these measurements are aided by in situ X-ray diffraction, the temperatures in the final ramped states are unconstrained at present. With the regime of P = 2 – 14 Mbar and T= 2000 – 12000 K in mind, we construct a multiphase Fe EOS from a combination of static and dynamic experimental data, together with simple models for single-phase free energies informed by DFT-based molecular dynamics studies. Temperature predictions for the recent shock-ramp experiments using this EOS will be discussed, as well as the sensitivities of these predictions to various choices in the EOS model construction.   

How are light elements present in Earth’s core? An ab initio systematic exploration.

The composition of the light-element phase of the Earth's inner core remains controversial. In the present work we perform a systematic ab initio study of the possible forms that this light-element phase can show at the conditions of the inner core, including Fe_nX (n=1...5; X=S,Mg,H,C,O) compounds. We have performed automated crystalline structure searches for Fe_nX compounds using CALYPSO, and relaxed the candidate structures using VASP. We plotted the convex hulls for the compounds of Fe with each light element, and found the thermodynamically stable compounds at the conditions of the inner core. We calculated their thermal properties and density using phonon analysis and a quasi-harmonic approximation. We finally estimated the maximum abundance of the light elements in the core by comparing their compounds' densities with pure bcc-Fe and the actual density of the inner core. The results are consistent with literature findings for the outer core.(1)

1. Badro J, Cote AS, & Brodholt JP (2014) A seismologically consistent compositional model of Earth's core. Proceedings of the National Academy of Sciences of the United States of America 111(21):7542-7545.   

Viscosity of the Inner Core

The Earth solid inner core (IC), composed mostly by iron, is a highly attenuating medium. This property of the core is at odds with the widely accepted paradigm of the hexagonal close-packed (hcp) phase stability under the inner core conditions, because sound waves propagate through the hcp iron without energy dissipation. We show by first-principles molecular dynamics that the body-centered cubic (bcc) phase of iron, recently demonstrated to be thermodynamically stable under the IC conditions, is considerably less elastic than the hcp phase. Being a crystalline phase, the bcc iron possesses the viscosity close to that of a liquid iron. The attenuation of the inner core is due to the unique diffusion characteristic of the bcc phase. The liquid-like nature of the bcc phase at extreme pressures and temperatures allow to resolve a number of controversies and explain enigmatic features of the Core.   

Exploring Thermal Conductivity of h.c.p. Iron (ε-Fe) at the Earth’s Core Conditions from Direct ab initio Molecular Dynamics Simulations

The exact value of electronic thermal conductivity (κ_el) of ε-Fe under the extreme pressure and temperature conditions still remains poorly known both experimentally and theoretically. Previous experiments reported quite scattered results of κ_el of ε-Fe, which could differ by several folders. By utilizing our newly developed methodology based on direct non-equilibrium ab initio molecular dynamics (NEAIMD) simulation coupled with the concept of electrostatic potential oscillation (EPO), we evaluate the electronic thermal conductivity of iron in h.c.p phase without any artificial manipulation of computational parameters. Unlike the previous theoretical studies, our methodology inherently includes all possible interactions and scattering of electrons under extreme conditions. The results of electronic thermal conductivity of iron in the Earth’s core are consistent with some previous theoretical and experimental results. More importantly, our study provides a totally new physical picture of heat transfer process in iron at Earth's core conditions from the electrostatic potential oscillation point of view. This simulation methodology offers a new approach to study thermal transport property of pure metals in planet's cores with different temperature and pressures.   

Electrical conductivity of silicate liquids at extreme conditions and planetary dynamos

We find that Earth’s earliest magnetic field may have been produced in a deep magma ocean, and that silicate dynamos may exist in super-Earth exoplanets as well. Our conclusions are based on ab initio molecular dynamics simulations and Kubo-Greenwood computations of the electrical conductivity. These show that silicate liquids are semi-metallic at the extreme pressure and temperature conditions characteristic of planetary interiors with conductivity exceeding 10,000 S/m. In silica, the electrical conductivity shows a remarkable non-monotonic dependence on pressure that reveals connections to the underlying atomic structure, and highlights broken charge ordering as a novel compression mechanism. We compare the behavior of silica liquid with that of (Mg,Fe)O liquid and a multi-component composition (MgO-FeO-CaO-Al₂O₃-Na₂O-SiO₂) representative of the bulk silicate Earth.   

Structure Evolutions of Iron Compounds under Pressure Show an Unusual Chemistry in Deep Earth

The terrestrial abundance of many elements, including heavy halogens Cl, Br, and I is approximately one order of magnitude lower than that predicted from their volatilities. One possible explanation is that these heavy elements are sequestered into the Earth’s core. This suggestion is supported by recent computational studies showing that heavy p elements may combine with iron at high pressure. Using first-principles electronic structure calculations and the automatic crystal structure search method based on particle swarm optimization algorithm, we also studied the stability and structures of Fe-halogen compounds under high pressure up to 350 GPa. Our calculations show that the compounds with higher Fe composition become more stable with increasing pressure and the reaction propensity of Fe might become opposite to ambient pressure. Our detailed electronic structure analysis reveals that the charge capture by Fe 3d orbitals and the reduction of the lone pair electrons in halogens are the major factors that govern the structure evolution under increasing pressure. Our results suggest that the distribution of many p-block elements in the Earth core might be much higher than we usually believe.   

Thermal equation of state of ε-Fe at exoplanetary interior conditions

The equation of state (EoS) of hcp-iron (ε-Fe) is essential for investigating physical properties of planetary cores. Despite its importance to geophysics and planetary astronomy, experimental investigations of ε-Fe at relevant conditions are still challenging. Therefore, ab initio calculations can contribute decisively to elucidating the equation of state (EoS) and other properties of this system. In this study, we present ab initio results of the properties of ε-Fe covering a wide range of pressures (0 - 1,400 GPa) and temperatures (300 - 8,000 K). Two new techniques are employed: i) a PAW dataset for iron specially designed for very high-pressure calculations [1], and ii) a free energy calculation approach based on the phonon gas model compatible with temperature dependent phonon frequencies, here produced by thermal electronic excitations. These new features of the calculation produce an isentropic EoS in good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF)[2].
1. K. Sarkar et al., J. Comp. Phys.347,39-55 (2017)
2. R. F. Smith et al., Nature Astronomy. 2, 452–458 (2018)   

Vibrational spectrum throughout the iron spin crossover in ferropericlase (Mg1-xFexO)

Ferropericlase (Fp), (Mg_1-xFe_x)O, is the second most abundant phase in the Earth’s lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), S=2, to low spin (LS), S=0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the large elastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasi-harmonic approximation (QHA), therefore, dynamical and structural stability are essential to the validity of these theories. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio DFT+Usc calculations. We address vibrational modes associated with isolated and (2nd) nearest neighbor Fe atoms undergoing the HS-LS state change. As expected, acoustic modes of this solid solution reproduce the well-known elastic anomalies, but optical modes display unusual features. We show that there are no soft phonon modes across this HS-LS crossover and Fp is dynamically stable at all mantle pressures and relevant iron concentrations.