Session B24: Matter at Extreme Conditions: Planetary Materials I

Sound Speed in Shock-Compressed Iron up to 3 TPa

The formation of terrestrial planets involves high-velocity impacts of iron-rich planetesimals in the later stages of accretion. The distribution of iron and other highly siderophile elements within the resulting planets depends on the thermodynamic evolution of the heated material after pressure release from the shock states produced by the impact. Sound speed is a critical thermodynamic property that provides information about how a material evolves after isentropic release from the shock state, and is directly connected to other thermodynamic derivatives such as the bulk modulus, Gruneisen parameter, and specific heat. We report sound speed measurements in iron shocked from 500 GPa up to 3000 GPa. Steady shocks were produced simultaneously in the iron sample and a sound speed-reference (alpha-quartz) using a pedestal laser pulse shape. Pressure perturbations were then launched simultaneously through the sample and reference by specially-tailored laser power modulations. Sound speed was deduced using the arrival time of the perturbation sequence at the shock front after emerging into a transparent window using high-precision velocimetry. Our results show the sound speed in shocked iron is less than 10% higher than recent isentrope measurements of the sound speed at 20 g/cc. The proximity of the Hugoniot to the isentrope sound speed, consistency with iron release measurements, and implications for impact vaporization of iron will be discussed.   

Phase diagram of iron under the Earth Core pressures

The Earth core consists mainly of iron subjected to pressures from 1.3 to 3.6 Mbar and temperatures from about 3000 K to 7000 K.

While pressures are known rather precisely, the temperature range is less known. The phase diagram of iron allows to set 

tight constraints on the temperature within the Earth and provide interpretaion of seismic data. We used a combination of 

quasi ab initio embedded-atom model and density functional theory to perform molecular dynamic calculations of free energies of

liquid, hexagonal close packed (hcp) and body-centered cubic (bcc) iron phases. These calculations tell us that in the pressure range between 1.2 and 3.6

Mbar the sequence of iron phases on increasing temperature is hcp-bcc-liquid. This is in agreement with some experimental data, yet

there are experiments that do not observe the bcc phase. However, our phase diagram is a perfect match to the latest seismic data that rules

out the hcp phase as irrelevant for the Earth Inner Core mineralogy. Namely, that seismic study tells us that the directions of fast and slow

propagation of sound in the Earth Inner Core cross at the angle of 54 degrees. The same angle in the bcc phase (directions 100 and 111) is equal

to 54.73 degrees. There is no such angle in the hcp phase. This is an ultimate evidence for the bcc stability in the Inner Core.

We also demonstrate that all previous calculations of free energies of the bcc phase are inconclusive since they have been performed for too small computational cells.

We demonstarted that cells with at least 1000 atoms are needed to get converged results, Since the iron in the Inner Core can contribute to the

Earth-protecting magnetic field, our result has long reaching consequences for magnetic field generation both on Earth and exoplanets.    

Ab Initio Investigation of the Cooperative Diffusion in Body-Centered Cubic Iron Under Inner Core Conditions of Earth and Super-Earth Exoplanets

In the decades old scientific controversy of the most stable phase of iron at the Earth’s inner core (IC) conditions, the thermodynamic stability of the body-centered cubic (bcc) phase is recently suggested due to cooperative diffusion of atoms in the (110) plane.^1,2 In this presentation, we provide new, in-depth understandings of the mechanism of cooperative diffusion by using ab initio molecular-dynamics simulations. Our studies find the cooperative diffusion operates along the 〈111〉 direction, which offers the least energy barrier. Even with relatively small cells, we have been able to capture cooperative diffusion in bcc iron in Earth’s IC conditions. We also find bcc iron can be stabilized by phonon interactions and facilitated by electron thermal effects. Our calculations at higher pressures (super-Earth core conditions) have yielded similar results. These results provide important insights and useful knowledge for future experimental and theoretical studies of iron under extreme pressures and temperatures that are greatly relevant to high-energy-density and planetary sciences.

1. A. B. Belonoshko et al., Nature Geosci. 10, 312 (2017).

2. A. B. Belonoshko et al., Phys. Rev. B 104, 104103 (2021).   

Transport Properties of Fe-X (X = C, S, O, H) at extreme conditions

The transport properties of iron alloys with light elements such as carbon, sulfur, oxygen, and hydrogen are important factors for the heat transport of Earth’s and other planetary cores. In this study, we computed the electrical resistivity and thermal conductivity for hcp iron and iron alloys with Density Functional Theory (DFT) up to and beyond Earth core pressures and temperatures. We have used Korringa-Kohn-Rostoker (SPR-KKR) with a coherent potential approximation (CPA) for both compositional scattering and phonon scattering within a Debye model. We have compared with experiments and with scattering from disordered supercells and first-principles molecular dynamics and find good agreement for Fe-Si. We find that electrical resistivity has a strong negative slope with temperature from impurity scattering, whereas phonon scattering gives a positive slope.   

Electrical Conductivity of Iron under Earth-Core Conditions from Time-Dependent Density Functional Theory

Time-dependent density functional theory (TDDFT) enables calculating electronic transport properties in the warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In the real-time formalism of TDDFT (RT-TDDFT), the electrical conductivity is directly computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm's law in WDM. Without relying on the methods of diagonalization, the method is computationally fast compared to linear-response TDDFT (LR-TDDFT). We present TDDFT calculations of the electrical conductivity in iron within the pressure and temperature ranges found in Earth's core and discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood (KG) formalism and dielectric models.    

Thermal-Induced Evolution of Magnetic Properties of FeO2 Under High Pressures

Pyrite-type FeO₂ is a crystalline compound that is the stable form of iron oxide in the pressure range of ~80 GPa to over 200 GPa. Here, we have performed density functional theory (DFT) calculations on this system using the GGA+U exchange-correlation functional, principally along the ρ = 7.1 g/cm³ isochore up to temperatures above 3500 K (corresponding to the Earth’s lowermost-mantle conditions), to explore the evolution of the magnetic properties under thermal effects. The DFT results suggest a magnetic state transition induced by temperature at ~1000 K. The behavior of the electronic properties such as thermal and electric conductivity, and thermodynamic properties such as specific heat have been explored with regard to the change of magnetic states in FeO₂.   

Two-step nucleation of the Earth's inner core

It has long been assumed the Earth’s solid inner core started to grow when molten iron cooled to its melting point. However, the nucleation mechanism, a necessary step of crystallization, has not been well understood. Recent studies found it requires an unrealistic degree of undercooling to nucleate the stable hexagonal close-packed (hcp) phase of iron, which can never be reached under actual Earth’s core conditions. This contradiction has been referred to as the inner core nucleation paradox. Using a persistent-embryo method and molecular dynamics simulations, we demonstrate that the metastable body-centered cubic (bcc) phase of iron has a much higher nucleation rate than the hexagonal close-packed (hcp) phase under inner-core conditions. Thus, the bcc nucleation is likely to be the first step of inner core formation instead of direct nucleation of the hcp phase. This mechanism reduces the required undercooling of iron nucleation, which provides a key factor to solving the inner-core nucleation paradox. The two-step nucleation scenario of the inner core also opens a new avenue for understanding the structure and anisotropy of the present inner core.   

Iron-rich Fe-O compounds at Earth's core pressures

Oxygen is the most abundant element on Earth. While pervasive in the mantle, its presence in the core is still a subject of debate but critical to our understanding of the core-mantle co-evolution and geomagnetic field generation. Thus far, iron monoxide (FeO) is the only known stoichiometric compound in the Fe-FeO system, and the existence of iron-rich Fe-O compounds (Fe_nO with n > 1) has long been questioned. Here we report that iron reacts with FeO and Fe₂O₃ at 220-260 GPa and 3,000-3,500 K in laser-heated diamond-anvil cells. Using the adaptive genetic algorithm, we find the reaction products consist of a series of Fe_nO stoichiometric compounds and solid solutions (e.g., Fe₂₅O₁₃ and Fe₂₈O₁₄) whose X-ray diffraction patterns agree well with Le Bail refinements of the experimental reaction products. Like ε-Fe, Fe_nO compounds have a typical hexagonal close-packed layered structure, featuring oxygen-only layers between iron layers. Our results suggest that Fe-rich Fe_nO compounds with unique physical properties become stable under Earth's solid inner core conditions.   

The post-perovskite transition in Fe- and Al-bearing bridgmanite

The major phase of the Earth's mantle, (Al,Fe)-bearing bridgmanite, transitions to the post-perovskite (PPv) phase at Earth's deep lower mantle conditions. Despite extensive experimental and ab initio investigations, there are still important aspects of this transformation that need clarification. Here, we address this transition in (Al³⁺, Fe³⁺)-, (Al³⁺)-, (Fe²⁺)- and (Fe³⁺)-bearing bridgmanite using ab initio calculations. We find that the seismic features produced by the PPv transition depend distinctly on the chemical composition. For instance, Fe³⁺-, Al³⁺-, or (Al³⁺, Fe³⁺)-alloying increase the transition pressure, while Fe²⁺-alloying has the opposite effect. Consequently, the absence of a D" seismic discontinuity or signature of a double-crossing of the PPv phase boundary point to a Fe²⁺-poor and Fe³⁺-rich bridgmanite composition with profound implications for the redox state of the deep lower mantle. These chemistry-specific seismic features together, along with thermochemical equilibrium calculations will be fundamental for resolving the chemical composition of the D" region by direct inspection of tomographic images.   

Predicting the phase behaviors of high-pressure materials

Experimental synthesis and characterization of high-pressure materials are extremely difficult, so first-principles methods based on quantum mechanics can play a crucial role. However, the high computational costs of these methods typically prevent rigorous predictions of macroscopic quantities at finite temperatures including the phase behaviors. In this talk, I will discuss how to enable such predictions by combining advanced statistical mechanics with data-driven machine learning interatomic potentials. As an example, we computed the  low-pressure phase diagram of water from density functional theory at the hybrid level, accounting for thermal fluctuations, proton disordering and nuclear quantum effects. We then mapped the phase diagram of superionic water, which helps resolve the composition of ice giants. As a final example, we simulated the high-pressure hydrogen system with converged system size and simulation length, and found, contrary to established beliefs, supercritical behaviour of liquid hydrogen above the melting line.