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Constraining the melting temperature of iron under Earth's inner core conditions is crucial for understanding core dynamics and planetary evolution. Here, we develop a deep potential (DP) model for iron that explicitly incorporates electronic entropy contributions governing thermodynamics under Earth's core conditions. Extensive benchmarking demonstrates the DP's high fidelity across relevant iron phases and extreme pressure and temperature conditions. Through thermodynamic integration and direct solid-liquid coexistence simulations, the DP predicts melting temperatures for iron at the inner core boundary, consistent with previous \textit{ab initio} results. This resolves the previous discrepancy of iron's melting temperature at ICB between the DP model and \textit{ab initio} calculation and suggests the crucial contribution of electronic entropy. Our work provides insights into machine learning melting behavior of iron under core conditions and provides the basis for future development of binary or ternary DP models for iron and other elements in the core.

Davemaoite, i.e., $CaSiO_3$ perovskite (CaPv), is the third most abundant phase in the lower mantle and exhibits a tetragonal-cubic phase transition at high pressures and temperatures. The phase boundary in CaPv has recently been proposed to be close to the cold slab adiabatic and cause mid-mantle seismic wave speed anomalies (Thomson et al., Nature 572, 643, 2019). In this study, we utilized accurate deep-learning-based simulations and thermodynamic integration techniques to compute free energies at temperatures ranging from 300 to 3,000 K and pressures up to 130 GPa. Our results indicate that CaPv exhibits a single cubic phase throughout lower-mantle conditions. This suggests that the phase diagram proposed by Thomson et al. requires revision, and mid-mantle seismic anomalies are likely attributable to other mechanisms.

Hydrous and nominally anhydrous minerals (NAMs) are a fundamental class of solids of enormous significance to geophysics. They are the water carriers in the deep geological water cycle and impact structural, elastic, plastic, and thermodynamic properties and phase relations in Earth's forming aggregates (rocks). They play a critical role in the geochemical and geophysical processes that shape the planet. Their complexity has prevented predictive calculations of their properties, but progress in materials simulations ushered by machine learning potentials is transforming this state of affairs. Here, we adopt a hybrid approach that combines deep learning potentials (DP) with the SCAN meta-GGA functional to simulate a prototypical hydrous system. We illustrate the success of this approach to simulate $\delta$-AlOOH ($\delta$), a phase capable of transporting water down to near the core-mantle boundary of the Earth (~2,900 km depth and ~135 GPa) in subducting slabs. A high-throughput sampling of phase space using molecular dynamics simulations with DP-potentials sheds light on the hydrogen-bond behavior and proton diffusion at geophysical conditions. These simulations provide a pathway for a deeper understanding of these crucial components that shape Earth's internal state.

Ni is the second most abundant element in the Earth's core. Yet, its effects on the inner core's structure and formation process are usually disregarded because of its electronic and size similarity with Fe. Using ab initio molecular dynamics simulations, we find that the bcc phase can spontaneously crystallize in liquid Ni at temperatures above Fe's melting point at inner core pressures. The melting temperature of Ni is shown to be 700-800 K higher than that of Fe at 323-360 GPa. hcp, bcc, and liquid phase relation differ for Fe and Ni. Ni can be a bcc stabilizer for Fe at high temperatures and inner core pressures. A small amount of Ni can accelerate Fe's crystallization at core pressures. These results suggest Ni may substantially impact the structure and formation process of the solid inner core.

MgSiO_3-perovskite (MgPv) plays a crucial role in the Earth's lower mantle. This study combines deep-learning potential (DP) with density functional theory (DFT) to investigate the structural and elastic properties of MgPv under lower mantle conditions. To simulate complex systems, we developed a series of potentials capable of faithfully reproducing DFT calculations using different functionals, such as LDA, PBE, PBEsol, and SCAN meta-GGA functionals. The obtained predictions exhibit remarkable reliability and consistency, closely resembling experimental measurements. Our results highlight the superior performance of the DP-SCAN and DP-LDA in accurately predicting high-temperature equations of states and elastic properties. This hybrid computational approach offers a solution to the accuracy-efficiency dilemma in obtaining precise elastic properties at high pressure and temperature conditions for minerals like MgPv, which opens a new way to study the Earth's interior state and related processes.

Terrestrial exoplanets are of great interest for being simultaneously similar to and different from Earth. Their compositions are likely comparable to those of solar-terrestrial objects, but their internal pressures and temperatures can vary significantly with their masses/sizes. The most abundant non-volatile elements are O, Mg, Si, Fe, Al, and Ca, and there has been much recent progress in understanding the nature of magnesium silicates up to and beyond ~3 TPa. However, a critical element, Fe, has yet to be systematically included in materials discovery studies of potential terrestrial planet-forming phases at ultra-high pressures. Here, using the adaptive genetic algorithm (AGA) crystal structure prediction method, we predict several unreported stable crystalline phases in the binary Fe-Mg and ternary Fe-Mg-O systems up to pressures of 3 TPa. The analysis of the local packing motifs of the low-enthalpy Fe-Mg-O phases reveals that the Fe-Mg-O system favors a BCC motif under ultra-high pressures regardless of chemical composition. Besides, oxygen enrichment is conducive to lowering the enthalpies of the Fe-Mg-O phases. Our results extend the current knowledge of structural information of the Fe-Mg-O system to exoplanet pressures.

The quasi-harmonic approximation (QHA) is a powerful method that uses the volume dependence of non-interacting phonons to compute the free energy of materials at high pressures (P) and temperatures (T). However, anharmonicity, electronic excitations in metals, or both, introduce an intrinsic T-dependence on phonon frequencies, rendering the QHA inadequate. Here we present a Python code, pgm, to compute the free energy and thermodynamic property within the phonon gas model (PGM) that uses T-dependent phonon quasiparticle frequencies. In this case, the vibrational contribution to the Helmholtz free energy is obtained by integrating the vibrational entropy, which can be readily calculated for a system of phonon quasiparticles. Other thermodynamic properties are then obtained from standard thermodynamic relations. We demonstrate the successful applications of pgm to two cases of geophysical significance: cubic CaSiO3-perovskite (cCaPv), a strongly anharmonic insulator and the third most abundant phase of the Earth's lower mantle, and NiAs-type (B8) FeO, a partially covalent-metallic system. This is the oxide endmember of a recently discovered iron-rich Fe$_n$O alloy phase likely to exit in the Earth's inner core., Comment: 26 pages, 9 figures, 5 tables

Using an artificial neural-network machine learning interatomic potential, we have performed molecular dynamics simulations to study the structure and dynamics of Fe90Si3O7 liquid close to the Earth's liquid core conditions. The simulation results reveal that the short-range structural order (SRO) in the Fe90Si3O7 liquid is very strong. About 80% of the atoms are arranged in crystalline-like SRO motifs. In particular, ~70% of Fe-centered clusters can be classified as either hexagonal-close-pack (HCP/HCP-like) or icosahedral (ICO/ICO-like) SRO motifs. The SRO clusters centered on Fe, Si, or O atoms are strongly intermixed and homogenously distributed throughout the liquid. The atomic structure of the liquid and the fractions of dominant SRO clusters are not sensitive to pressure/temperature used in the simulations except that the SRO of the O-centered clusters is enhanced close to inner core pressures. The O diffusion coefficient is about 2-3 times larger than the Fe and Si ions and increases more rapidly in the deeper core regions.

FeO is a crucial phase of the Earth's core, and its thermodynamic properties are essential to developing more accurate core models. It is also a notorious correlated insulator in the NaCl-type (B1) phase at ambient conditions. It undergoes two polymorphic transitions at 300 K before it becomes metallic in the NiAs-type (B8) structure at $\sim$100 GPa. Although its phase diagram is not fully mapped, it is well established that the B8 phase transforms to the CsCl-type (B2) phase at core pressures and temperatures. Here we report a successful \textit{ab initio} calculation of the B8$\leftrightarrow$B2 phase boundary in FeO at Earth's core pressures. We show that fully anharmonic free energies computed with the PBE-GGA + Mermin functional reproduce the experimental phase boundary within uncertainties at $P > 240$ GPa, including the largely negative Clapeyron slope of $-52 \pm 5$ MPa/K. This study validates the applicability of a standard DFT functional to FeO under Earth's core conditions and demonstrates the theoretical framework that enables complex predictive studies of this region.

At ambient pressure, bulk SrCoO$_{3}$ is a ferromagnetic (FM) metal in cubic perovskite structure. By contrast, magnetic properties of epitaxial SrCoO$_{3}$ thin films, especially at high tensile strain ($\varepsilon \gtrsim 3$\%), remain unclear: Previous calculations had predicted antiferromagnetic (AFM) states more energetically favorable in this regime, but recent experiments indicated a FM insulating state. In this work, using first-principles calculations, we perform an extensive search for the structural, spin, magnetic, and orbital states of SrCoO$_{3}$ thin films. Our calculations indicate that at $0 < \varepsilon \lesssim 2.5$\%, SrCoO$_{3}$ favors a FM half-metallic state with intermediate-spin ($t_{2g}^{5}e_{g}^{1}$-like) Co exhibiting $d^{6}\underline L$ character. At $\varepsilon \gtrsim 2.5$\%, a FM insulating state with high-spin ($t_{2g}^{4}e_{g}^{2}$-like) Co dominates. This FM insulating state is achieved via complicated orbital ordering, cooperative Jahn--Teller distortion, and octahedral tilting about all three crystal axes., Comment: 15 pages, 4 figures

Subduction zones transport water into Earth's deep interior through slab subduction. Serpentine minerals, the primary hydration product of ultramafic peridotite, are abundant in most subduction zones. Characterization of their high-temperature elasticity, particularly their anisotropy, will help us better estimate the extent of mantle serpentinization and the Earth's deep water cycle. Lizardite, the low-temperature polymorph of serpentine, is stable under the P-T conditions of cold subduction slabs (< 260{\deg}C at 2 GPa), and its high-temperature elasticity remains unknown. Here we report ab initio elasticity and acoustic wave velocities of lizardite at P-T conditions of subduction zones. Our static results agree with previous studies. Its high-temperature velocities are much higher than previous experimental-based lizardite estimates with chrysotile but closer to antigorite velocities. The elastic anisotropy of lizardite is much larger than that of antigorite and could better account for the observed large shear-wave splitting in some cold slabs such as Tonga.

The primary phase of the Earth's lower mantle, (Al, Fe)-bearing bridgmanite, transitions to the postperovskite (PPv) phase at Earth's deep 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 and validate our results against experiments on similar compositions. Consistent with experiments, our results show that the onset transition pressure and the width of the two-phase region depend distinctly on the chemical composition: a) Fe3+-, Al3+-, or (Al3+, Fe3+)-alloying increases the transition pressure, while Fe2+-alloying has the opposite effect; b) in the absence of coexisting phases, the pressure-depth range of the Pv-PPv transition seems quite broad to cause a sharp D" discontinuity (< 30 km); c) the average Clapeyron slope of the two-phase regions are consistent with previous measurements, calculations in MgSiO3, and inferences from seismic data. In addition, d) we observe a softening of the bulk modulus in the two-phase region. The consistency between our results and experiments gives us the confidence to proceed and examine this transition in aggregates with different compositions computationally, which will be fundamental for resolving the most likely chemical composition of the D" region by analyses of tomographic images., Comment: 20 pages, 5 figures, 1 table

There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Because of the solid-liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi-empirical potential fitted to high-temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly reduces the uncertainty caused by the finite-size effect. Our results suggest the hcp phase is the stable phase of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10s meV/atom near the melting temperature., Comment: 4 figures

To address the effects of lattice anharmonicity across the perovskite to post-perovskite transition in MgSiO$_3$, we conduct calculations using the phonon quasiparticle (PHQ) approach. The PHQ is based on \textit{ab initio} molecular dynamics and, in principle, captures full anharmonicity. Free energies in the thermodynamic limit ($N \rightarrow \infty$) are computed using temperature-dependent quasiparticle dispersions within the phonon gas model. Systematic results on anharmonic thermodynamic properties and phase boundary are reported. Both the local density approximation (LDA) and the generalized gradient approximation (GGA) calculations are performed to provide confident constraints on these properties. Anharmonic effects are demonstrated by comparing results with those obtained using the quasiharmonic approximation (QHA). The inadequacy of the QHA is indicated by its overestimation of thermal expansivity and thermodynamic Gr\"{u}neisen parameter and its converged isochoric heat capacity in the high-temperature limit. The PHQ phase boundary has a Clapeyron slope ($dP/dT$) that increases with temperature. This result contrasts with the nearly zero curvature of the QHA phase boundary. Anharmonicity bends the phase boundary to lower temperatures at high pressures. Implications for the double-crossing of the phase boundary by the mantle geotherm are discussed.

Third-order elasticity (TOE) theory is predictive of strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an "effective" third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. We extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.

Using artificial neural-network machine learning (ANN-ML) to generate interatomic potentials has been demonstrated to be a promising approach to address the long-standing challenge of accuracy versus efficiency in molecular dynamics (MD) simulations. Here, taking the Fe-Si-O system as a prototype, we show that accurate and transferable ANN-ML potentials can be developed for reliable MD simulations of materials at high-pressure and high-temperature conditions of the Earth's outer core. The ANN-ML potential for Fe-Si-O system is trained by fitting to the energies and forces of related binaries and ternary liquid structures at high pressures and temperatures obtained by first-principles calculations based on density functional theory (DFT). We show that the generated ANN-ML potential describes well the structure and dynamics of liquid phases of this complex system. The efficient ANN-ML potential with DFT accuracy provides a promising scheme for accurate atomistic simulations of structures and dynamics of complex Fe-Si-O system in the Earth's outer core.

Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate \textit{ab initio} investigations of lattice anharmonicity encounter difficulties owing to the cumbersome computations. Here we introduce the phonon quasiparticle approach and review its application to various materials. This method efficiently and reliably addresses lattice anharmonicity by combining \textit{ab initio} molecular dynamics and lattice dynamics calculations. Thus, in principle, it accounts for full anharmonic effects and overcomes finite-size effects typical of \textit{ab initio} molecular dynamics. The validity and effectiveness of the current approach are demonstrated in the computation of thermodynamic and heat transport properties of weakly and strongly anharmonic systems.

$\delta$-AlOOH ($\delta$) is a high-pressure hydrous phase that participates in the deep geological water cycle. At 0 GPa, $\delta$ has asymmetric hydrogen bonds (H-bonds). Under pressure, it exhibits H-bond disordering, tunneling, and finally, H-bond symmetrization at ~18 GPa. This study investigates these 300 K pressure-induced state changes in $\delta$ with ab initio calculations. H-bond disordering in $\delta$ was modeled using supercell multi-configuration quasiharmonic calculations. We examine: (a) energy barriers for proton jumps, (b) the pressure dependence of phonon frequencies, (c) 300 K compressibility, (d) neutron diffraction pattern anomalies, and (e) compare ab initio bond lengths with measured ones. Such thorough and systematic comparisons indicate that: (a) proton "disorder" has a restricted meaning when applied to $\delta$. Nevertheless, H-bonds are disordered between 0 and 8 GPa, and a gradual change in H-bond configuration results in enhanced compressibility. (b) several structural and vibrational anomalies at ~8 GPa are consistent with the disappearance of a particular (HOC-12) H-bond configuration and its change into another one (HOC-11*). (c) between 8-11 GPa, H-bond configuration (HOC-11*) is generally ordered, at least in short- to mid-range scale. (d) between 11.5-18 GPa, H-bond lengths approach a critical value that impedes compression, resulting in decreased compressibility. In this pressure range, especially approaching H-bond symmetrization at ~18 GPa, anharmonicity and tunneling should play an essential role in the proton dynamics. Further simulations accounting for these effects are desirable to clarify the protons' state in this pressure range.

Iron oxides are fundamental components of planet-forming materials. Understanding the Fe-O system's behavior and properties under high pressure can help us identify many new phases and states possible in exoplanetary interiors, especially terrestrial ones. Using the adaptive genetic algorithm (AGA), we investigate the structure of iron oxides for a wide range of stoichiometries ($0.25\leq x_O \leq 0.8$) at 1, 2, and 3 TPa. Five unreported ground-state structures with Fe$_2$O, FeO, Fe$_3$O$_5$, FeO$_2$, and FeO$_4$ compositions are identified. The calculated density of states (DOS) suggests that, except for FeO$_4$, all phases are metallic, but their carrier densities decrease with increasing pressure and oxygen content. The cluster alignment analysis of stable and metastable phases shows that several motifs may co-exist in a structure of iron oxides with low O content. In contrast, most iron oxides with high O content adopt a simple BCC motif at TPa pressures. Our results provide a crystal structure database of iron oxides for modeling and understanding the interiors of exoplanets., Comment: 7 pages, 9 figures

We present LDA+$U_{sc}$ calculations of high-spin (HS) and low-spin (LS) states in ferropericlase (fp) with an iron concentration of 18.75$\%$. The Hubbard parameter $U$ is determined self-consistently with structures optimized at arbitrary pressures. We confirm a strong dependence of $U$ on the pressure and spin state. Static calculations confirm that the antiferromagnetic configuration is more stable than the ferromagnetic one in the HS state, consistent with low-temperature measurements. Phonon calculations guarantee the dynamical stability of HS and LS states throughout the pressure range of the Earth mantle. Compression curves for HS and LS states agree well with experiments. Using a non-ideal mixing model for the HS to LS states solid solution, we obtain a crossover starting at $\sim$45 GPa at room temperature and considerably broader than previous results. The spin-crossover phase diagram is calculated, including vibrational, magnetic, electronic, and non-ideal HS-LS entropic contributions. Our results suggest the mixed-spin state predominates in fp in most of the lower mantle., Comment: 8 pages, 8 figures

Oxygen solubility in solid iron is extremely low, even at high pressures and temperatures. Thus far, no Fe-O compounds between Fe and FeO endmembers have been reported experimentally. We observed chemical reactions of Fe with FeO or Fe$_2$O$_3$ $in\ situ$ x-ray diffraction experiments at 220-260 GPa and 3,000-3,500 K. The refined diffraction patterns are consistent with a series of Fe$_n$O (n $>$ 1) compounds (e.g., Fe$_{25}$O$_{13}$ and Fe$_{28}$O$_{14}$) identified using the adaptive genetic algorithm. Like $\epsilon$-Fe in the hexagonal close-packed (hcp) structure, the structures of Fe$_n$O compounds consist of oxygen-only close-packed monolayers distributed between iron-only layers. $Ab\ initio$ calculations show systematic electronic properties of these compounds that have ramifications for the physical properties of Earth's inner core., Comment: 6 pages, 4 figures

In this work, we introduce an open-source $\texttt{Julia}$ project, $\texttt{express}$, an extensible, high-throughput, high-level workflow framework that aims to automate $\textit{ab initio}$ calculations for the materials science community. $\texttt{Express}$ is shipped with well-tested workflow templates, including structure optimization, equation of state (EOS) fitting, phonon spectrum (lattice dynamics) calculation, and thermodynamic property calculation in the framework of the quasi-harmonic approximation (QHA). It is designed to be highly modularized so that its components can be reused across various occasions, and customized workflows can be built on top of that. Users can also track the status of workflows in real-time, and rerun failed jobs thanks to the data lineage feature $\texttt{express}$ provides. Two working examples, i.e., all workflows applied to lime and akimotoite, are also presented in the code and this paper.

Ferropericlase (fp), (Mg$_{1-x}$Fe$_x$)O, the second most abundant mineral in the Earth's lower mantle, is expected to be an essential component of super-Earths' mantles. Here we present an ab initio investigation of the structure and magnetic ground state of fp up to $\sim$ 3 TPa with iron concentrations (x$_{Fe}$) varying from 0.03 to 0.12. Calculations were performed using LDA+U$_{sc}$ and PBE exchange-correlation functionals to elucidate the pressure range for which the Hubbard U (U$_{sc}$) is required. Similar to the end-members FeO and MgO, fp also undergoes a B1 to B2 phase transition that should be essential for modeling the structure and dynamics of super-Earths' mantles. This structural transition involves a simultaneous change in magnetic state from a low spin (LS) B1 phase with iron total spin S=0 to an intermediate spin (IS) B2 phase with S=1. This is a rare form of pressure/strain-induced magnetism produced by local cation coordination changes. Phonon calculations confirm the dynamical stability of the iron B2-IS state. Free energy calculations are then carried out including vibrational effects and electronic and magnetic entropy contributions. The phase diagram is then obtained for low concentration fp using a quasi-ideal solid solution model. For x$_{Fe}$ > 0.12 this approach is no longer valid. At ultra-high pressures, there is an IS to LS spin state change in Fe in the B2 phase, but the transition pressure depends sensitively on thermal electronic excitations and on x$_{Fe}$.

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, which is 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 the actual Earth's core conditions. This contradiction leads to the inner core nucleation paradox [1]. Here, 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 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 solve 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., Comment: 8 pages, 4 figures. Supplementary information uploaded with the source files

Being a lithophile element at ambient pressure, magnesium is long believed to be immiscible with iron. A recent study by Gao et al. [1] showed that pressure turns magnesium into a siderophile element and can produce unconventional Fe-Mg compounds. Here, we extend the investigation to exoplanetary pressure conditions using an adaptive genetic algorithm-based variable-composition structural prediction approach. We identify several Fe-Mg phases up to 3 TPa. Our cluster alignment analysis reveals that most of the predicted Fe-Mg compounds prefer a BCC packing motif at terapascal pressures. This study provides a more comprehensive structure database to support future investigations of the high-pressure structural behavior of Fe-Mg and ternary, quaternary, etc. compounds involving these elements., Comment: 6 pages, 7 figures

Fe, Mg, and O are among the most abundant elements in terrestrial planets. While the behavior of the Fe-O, Mg-O, and Fe-Mg binary systems under pressure have been investigated, there are still very few studies of the Fe-Mg-O ternary system at relevant Earth's core and super-Earth's mantle pressures. Here, we use the adaptive genetic algorithm (AGA) to study ternary Fe$_x$Mg$_y$O$_z$ phases in a wide range of stoichiometries at 200 GPa and 350 GPa. We discovered three dynamically stable phases with stoichiometries FeMg$_2$O$_4$, Fe$_2$MgO$_4$, and FeMg$_3$O$_4$ with lower enthalpy than any known combination of Fe-Mg-O high-pressure compounds at 350 GPa. With the discovery of these phases, we construct the Fe-Mg-O ternary convex hull. We further clarify the composition- and pressure-dependence of structural motifs with the analysis of the AGA-found stable and metastable structures. Analysis of binary and ternary stable phases suggest that O, Mg, or both could stabilize a BCC iron alloy at inner core pressures., Comment: 9 pages, 8 figures

The thermodynamic properties of hcp-iron ({\epsilon}-Fe) are essential for investigating planetary cores' internal structure and dynamic properties. Despite their importance to planetary sciences, experimental investigations of {\epsilon}-Fe at relevant conditions are still challenging. Therefore, ab initio calculations are crucial to elucidating the thermodynamic properties of this system. Here we use a free energy calculation scheme based on the phonon gas model compatible with temperature-dependent phonon frequencies. We investigate the effects of electronic thermal excitations, which introduces a temperature dependence on phonon frequencies, and the implication for the thermodynamic properties of {\epsilon}-Fe at extreme pressure (P) and temperature (T) conditions. We disregard phonon-phonon interactions, i.e., anharmonicity and their effect on phonon frequencies. Nevertheless, the current scheme is also applicable to T-dependent anharmonic frequencies. We conclude that the impact of thermal electronic excitations on vibrational properties is not significant up to ~ 4,000 K at 200 GPa but should not be ignored at higher temperatures or pressures. However, the static free energy, Fst, must always include the effect of thermal excitation fully in a continuum of Ts. Our results for isentropic equations of state show good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF)., Comment: 29 pages, 9 figures

Lattice thermal conductivity ($\kappa_{lat}$) of MgSiO$_3$ postperovskite (MgPPv) under the Earth's lower mantle high pressure-temperature conditions is studied using the phonon quasiparticle approach by combing \textit{ab initio} molecular dynamics and lattice dynamics simulations. Phonon lifetimes are extracted from the phonon quasiparticle calculations, and the phonon group velocities are computed from the anharmonic phonon dispersions, which in principle capture full anharmonicity. It is found that throughout the lowermost mantle, including the D" region, $\kappa_{lat}$ of MgPPv is ~25% larger than that of MgSiO$_3$ perovskite (MgPv), mainly due to MgPPv's higher phonon velocities. Such a difference in phonon velocities between the two phases originates in the MgPPv's relatively smaller primitive cell. Systematic results of temperature and pressure dependences of both MgPPv's and MgPv's $\kappa_{lat}$ are demonstrated.

The Wu-Wentzcovitch semi-analytical method (SAM) is a concise and predictive formalism to calculate the high-pressure and high-temperature (high-PT) thermoelastic tensor (Cij) of crystalline materials. This method has been successfully applied to materials across different crystal systems in conjunction with ab initio calculations of static elastic coefficients and phonon frequencies. Such results have offered first-hand insights into the composition and structure of the Earth's mantle. Here we introduce the cij package, a Python implementation of the SAM-Cij formalism. It enables a thermoelasticity calculation to be initiated from a single command and fully configurable from a calculation settings file to work with solids within any crystalline system. These features allow SAM-Cij calculations to work on a personal computer and to be easily integrated as a part of high-throughput workflows. Here we show the performance of this code for three minerals from different crystal systems at their relevant PTs: diopside (monoclinic), akimotoite (trigonal), and bridgmanite (orthorhombic).

Here we present an ab initio prediction of an order-disorder transition (ODT) from $I\bar{4}2d$-type to a Th$_3$P$_4$-type phase in the cation sublattices of Mg$_2$GeO$_4$, a post-post-perovskite (post-PPv) phase. This uncommon type of prediction is achieved by carrying out a high-throughput sampling of atomic configurations in a 56-atom supercell followed by a Boltzmann ensemble statistics calculation. Mg$_2$GeO$_4$ is a low-pressure analog of $I\bar{4}2d$-type Mg$_2$SiO$_4$, a predicted major planet-forming phase of super-Earths' mantles. Therefore, a similar ODT is anticipated in $I\bar{4}2d$-type Mg$_2$SiO$_4$ as well, which should impact the internal structure and dynamics of these planets. The prediction of this Th$_3$P$_4$-type phase in Mg$_2$GeO$_4$ enhances further the relationship between the crystal structures of Earth/planet-forming silicates and oxides at extreme pressures and those of rare-earth sesquisulfides at low pressures.

We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framework of the phonon gas model. Accurate free energy calculations enable us to investigate cubic CaPv's thermodynamic properties and thermal equation of state, where anharmonic effects are demonstrated. The present methodology provides an important theoretical approach for exploring phase boundaries, thermodynamic, and thermoelastic properties of strongly anharmonic materials at high pressures and temperatures.

Thermal conductivity ($\kappa$) of mantle minerals is a fundamental property in geodynamic modeling. It controls the style of mantle convection and the time scale of the mantle and core cooling. Cubic CaSiO$_3$ perovskite (CaPv) is the third most abundant mineral in the lower mantle (LM) (7 vol%). However, despite its importance, no theoretical or experimental estimate of CaPv's $\kappa$ exists. Theoretical investigations of its properties are challenging because of its strong anharmonicity. Experimental measurements at relevant high pressures and temperatures are equally challenging. Here we present $ab$ $initio$ results for CaPv's $\kappa$ obtained using an established phonon quasiparticle approach that can address its strong anharmonicity. We also offer experimental measurements of $\kappa$. Predictions and measurements are in good agreement and reveal a surprisingly large $\kappa$ for cubic CaPv. Despite its relatively low abundance, CaPv's $\kappa$ might increase the lower mantle $\kappa$ by approximately 10%, if accounted for. $\kappa$ of mantle regions enriched in crust material will be more strongly impacted.

Using the LDA+$\textit{U}_\text{sc}$ method, we present calculations phase relations of iron monoxides involving five polytypes in multiple spin-state configurations. The Hubbard parameter $U$ is determined self-consistently simultaneously with the occupation matrix and structures at arbitrary pressures. The Hubbard parameter strongly depends on pressure, structure, and spin state. Comparison with experimental structural data indicates the LDA+$\textit{U}_\text{sc}$ can predict structure, compression curves, phase relations, and transition pressures very well for the insulating B1 and iB8 states. However, it requires additional calculations using the Mermin functional that includes the electronic entropic contribution to the free energy to obtain an nB8 metallic state and a consistent iB8 to nB8 insulator-to-metal transition pressure.

Ferropericlase (Fp), (Mg$_\mathrm{1-x}$Fe$_\mathrm{x}$)O, is the second most abundant phase in the Earths 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 significant thermo-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 is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin-crossover using $\textit{ab initio}$ DFT+Usc calculations. We address vibrational modes associated with isolated and (2nd) nearest neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient while optical modes are the most affected. We show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

Several of NASA missions (TESS, JWST, WFIRST, etc.) and mission concepts (LUVOIR, HabEx, and OST) emphasize the exploration and characterization of exoplanets, and the study of the interstellar medium. We anticipate that a much broader set of chemical environments exists on exoplanets, necessitating data from a correspondingly broader set of chemical reactions. Similarly, the conditions that exist in astrophysical environments are very different from those traditionally probed in laboratory chemical kinetics studies. These are areas where quantum mechanical theory, applied to important reactions via well-validated chemical kinetics models, can fill a critical knowledge gap. Quantum chemical calculations are also introduced to study interior of planets, photochemical escape, and many critical chemical pathways (e.g. prebiotic environments, contaminations, etc.) After years of development of the relevant quantum chemical theories and significant advances in computational power, quantum chemical simulations have currently matured enough to describe real systems with an accuracy that competes with experiments. These approaches, therefore, have become the best possible alternative in many circumstances where performing experiments is too difficult, too expensive, or too dangerous, or simply not possible. In this white paper, several existing quantum chemical studies supporting exoplanetary science, planetary astronomy, and astrophysics are described, and the potential positive impacts of improved models associated with scientific goals of missions are addressed. In the end, a few recommendations from the scientific community to strengthen related research efforts at NASA are provided.

The composition of the lower mantle $-$ comprising 56% of Earth's volume $-$ remains poorly constrained. Among the major elements, Mg/Si ratios ranging from $\sim$0.9$-$1.1, such as in rocky solar-system building blocks (or chondrites), to $\sim$1.2$-$1.3, such as in upper-mantle rocks (or pyrolite), have been proposed. Geophysical evidence for subducted lithosphere deep in the mantle has been interpreted in terms of efficient mixing and thus homogeneous Mg/Si across most of the mantle. However, previous models did not consider the effects of variable Mg/Si on the viscosity and mixing efficiency of lower-mantle rocks. Here, we use geodynamic models to show that large-scale heterogeneity with viscosity variations of $\sim$20$\times$, such as due to the dominance of intrinsically strong (Mg,Fe)SiO$_3-$bridgmanite in low-Mg/Si domains, are sufficient to prevent efficient mantle mixing, even on large scales. Models predict that intrinsically strong domains stabilize degree-two mantle-convection patterns, and coherently persist at depths of $\sim$1,000$-$2,200 km up to the present-day, separated by relatively narrow up-/downwelling conduits of pyrolitic material. The stable manifestation of such "bridgmanite-enriched ancient mantle structures" (BEAMS) may reconcile the geographical fixity of deep-rooted mantle-upwelling centers, and fundamental geophysical changes near 1,000 km depth (e.g. in terms of seismic-tomography patterns, radial viscosity increase, lateral deflections of rising plumes and sinking slabs). Moreover, these ancient structures may provide a reservoir to host primordial geochemical signatures.

Thermal equations of state (EoS) are essential in several scientific domains. However, experimental determination of EoS parameters may be limited at extreme conditions, therefore, {\it ab~initio} calculations have become an important method to obtain them. Density Functional Theory (DFT) and its extensions with various degrees of approximations for the exchange and correlation (XC) energy is the method of choice, but large errors in the EoS parameters are still common. The alkali halides have been problematic from the onset of this field and the quest for appropriate DFT functionals for such ionic and relatively weakly bonded systems has remained an active topic of research. Here we use DFT + van der Waals functionals to calculate vibrational properties, thermal EoS, thermodynamic properties, and the B1 to B2 phase boundary of NaCl. Our results reveal i) a remarkable improvement over the performance of standard Local Density Approximation and Generalized Gradient Approximation functionals for all these properties and phase transition boundary, as well as ii) great sensitivity of anharmonic effects on the choice of XC functional.

The highest pressure form of the major Earth-forming mantle silicate is MgSiO3 post-perovskite (PPv). Understanding the fate of PPv at TPa pressures is the first step for understanding the mineralogy of super-Earths-type exoplanets, arguably the most interesting for their similarities with Earth. Modeling their internal structure requires knowledge of stable mineral phases, their properties under compression, and major element abundances. Several studies of PPv under extreme pressures support the notion that a sequence of pressure induced dissociation transitions produce the elementary oxides SiO2 and MgO as the ultimate aggregation form at ~3 TPa. However, none of these studies have addressed the problem of mantle composition, particularly major element abundances usually expressed in terms of three main variables, the Mg/Si and Fe/Si ratios and the Mg#, as in the Earth. Here we show that the critical compositional parameter, the Mg/Si ratio, whose value in the Earth's mantle is still debated, is a vital ingredient for modeling phase transitions and internal structure of super-Earth mantles. Specifically, we have identified new sequences of phase transformations, including new recombination reactions that depend decisively on this ratio. This is a new level of complexity that has not been previously addressed, but proves essential for modeling the nature and number of internal layers in these rocky mantles., Comment: Submitted to Earth Planet. Sci. Lett., 28 pages, 6 figures

Elastic anomalies produced by the spin crossover in ferropericlase have been documented by both first principles calculations and high pressure-temperature experiments. The predicted signature of this spin crossover in the lower mantle is, however, subtle and difficult to geophysically observe within the mantle. Indeed, global seismic anomalies associated with spin transitions have not yet been recognized in seismologic studies of the deep mantle. A sensitive seismic parameter is needed to determine the presence and amplitude of such a spin crossover signature. The effects of spin crossovers on Bullen's parameter, $\eta$, are assessed here for a range of compositions, thermal profiles, and lateral variations in temperature within the lower mantle. Velocity anomalies associated with the spin crossover in ferropericlase span a depth range near 1,000 km for typical mantle temperatures. Positive excursions of Bullen's parameter with a maximum amplitude of $\sim$ 0.03 are calculated to be present over a broad depth range within the mid-to-deep lower mantle: these are largest for peridotitic and harzburgitic compositions. These excursions are highest in amplitude for model lower mantles with large lateral thermal variations, and with cold downwellings having longer lateral length-scales relative to hot upwellings. We conclude that predicted deviations in Bullen's parameter due to the spin crossover in ferropericlase for geophysically relevant compositions may be sufficiently large to resolve in accurate seismic inversions of this parameter, and could shed light on both the lateral variations in temperature at depth within the lower mantle, and the amount of ferropericlase at depth.

There has been growing interest in perovskite BaSnO3 due to its desirable properties for oxide electronic devices including high electron mobility at room temperature and optical transparency. As these electronic and optical properties originate largely from the electronic structure of the material, here the basic electronic structure of epitaxially-grown BaSnO3 films is studied using high-energy-resolution electron energy-loss spectroscopy in a transmission electron microscope and ab initio calculations. This study provides a detailed description of the dielectric function of BaSnO3, including the energies of bulk plasmon excitations and critical interband electronic transitions, the band structure and partial densities of states, the measured band gap, and more. To make the study representative of a variety of deposition methods, results from BaSnO3 films grown by both hybrid molecular beam epitaxy and high pressure oxygen sputter deposition are reported., Comment: 23 pages, 7 figures, 3 tables

The iron spin crossover in ferropericlase introduces anomalies in its thermodynamics and thermoelastic properties. Here we investigate how these anomalies can affect the lower mantle geotherm. The effect is examined in mantle aggregates consisting of mixtures of bridgmanite, ferropericlase, and CaSiO$_3$ perovskite, with different Mg/Si ratios varying from harzburgitic to perovskitic (Mg/Si$\sim$1.5 to 0.8). We find that the anomalies introduced by the spin crossover increase the isentropic gradient and thus the geotherm proportionally to the amount of ferropericlase. The geotherms can be as much as $\sim$ 200K hotter than the conventional adiabatic geotherm at deep lower mantle conditions. Aggregate elastic moduli and seismic velocities are also sensitive to the spin crossover and the geotherm, which impacts analyses of lower mantle velocities and composition.

We examine the challenge of performing accurate electronic structure calculations at high pressures by comparing the results of all-electron full potential linearized augmented-plane-wave calculations with those of the projector augmented wave (PAW) method. In particular, we focus on developing an automated and consistent way of generating transferable PAW data-sets that can closely produce the all electron equation of state defined from zero to arbitrary high pressures. The technique we propose is an evolutionary search procedure that exploits the ATOMPAW code to generate atomic data-sets and the Quantum ESPRESSO software suite for total energy calculations. We demonstrate different aspects of its workability by optimizing PAW basis functions of some elements relatively abundant in planetary interiors. In addition, we introduce a new measure of atomic data-set goodness by considering their performance uniformity over an enlarged pressure range.

Perovskite oxides form an eclectic class of materials owing to their structural flexibility in accommodating cations of different sizes and valences. They host well known point and planar defects, but so far no line defect has been identified other than dislocations. Using analytical scanning transmission electron microscopy (STEM) and ab initio calculations we have detected and characterized the atomic and electronic structures of a novel line defect in NdTiO3 perovskite. It appears in STEM images as a perovskite cell rotated by 45 degrees. It consists of self-organized Ti-O vacancy lines replaced by Nd columns surrounding a central Ti-O octahedral chain containing Ti4+ ions, as opposed to Ti3+ in the host. The distinct Ti valence in this line defect introduces the possibility of engineering exotic conducting properties in a single preferred direction and tailoring novel desirable functionalities in this Mott insulator., Comment: 24 pages, 5 figures

The spin crossover of iron in Fe$^{3+}$-bearing bridgmanite, the most abundant mineral of the Earth's lower mantle, is by now a well-established phenomenon, though several aspects of this crossover remain unclear. Here we investigate effects of disorder, iron concentration, and temperature on this crossover using ab initio LDA + U$_{sc}$ calculations. The effect of concentration and disorder are addressed using complete statistical samplings of coupled substituted configurations in super-cells containing up to 80 atoms. Vibrational/thermal effects on the crossover are addressed within the quasiharmonic approximation. The effect of disorder seems quite small, while increasing iron concentration results in considerable increase in crossover pressure. Our calculated compression curves for iron-free, Fe$^{2+}$-, and Fe$^{3+}$-bearing bridgmanite compare well with the latest experimental measurements. The comparison also suggests that in a close system, Fe$^{2+}$ present in the sample may transform into Fe$^{3+}$ by introduction of Mg and O vacancies with increasing pressure. As in the spin crossover in ferropericlase, this crossover in bridgmanite is accompanied by a clear volume reduction and an anomalous softening of the bulk modulus throughout the crossover pressure range. These effects reduce significantly with increasing temperature. Though the concentration of [Fe$^{3+}$]$_{Si}$ in bridgmanite may be small, related elastic anomalies may impact the interpretation of radial and lateral velocity structures of the Earth's lower mantle., Comment: Under review with Earth and Planetary Science Letters

We report \textit{ab initio} (LDA + U$_{sc}$) calculations of thermoelastic properties of ferric iron (Fe$^{3+}$)- and aluminum (Al)-bearing bridgmanite (MgSiO$_3$ perovskite), the main Earth forming phase, at relevant pressure and temperature conditions and compositions. Three coupled substitutions, namely, [Al]$_{Mg}$-[Al]$_{Si}$, [Fe$^{3+}$]$_{Mg}$-[Fe$^{3+}$]$_{Si}$, and [Fe$^{3+}$]$_{Mg}$-[Al]$_{Si}$ have been investigated. Aggregate elastic moduli and sound velocities are successfully compared with limited experimental data available. In the case of the [Fe$^{3+}$]$_{Mg}$-[Fe$^{3+}$]$_{Si}$ substitution, the high-spin (S=5/2) to low-spin (S=1/2) crossover in [Fe$^{3+}$]$_{Si}$ induces a volume collapse and elastic anomalies across the transition region. However, the associated anomalies should disappear in the presence of aluminum in the most favorable substitution, i.e., [Fe$^{3+}$]$_{Mg}$-[Al]$_{Si}$. Calculated elastic properties along a lower mantle model geotherm suggest that the elastic behavior of bridgmanite with simultaneous substitution of Fe$_{2}$O$_3$ and Al$_{2}$O$_3$ in equal proportions or with Al$_{2}$O$_3$ in excess should be similar to that of (Mg,Fe$^{2+}$)SiO$_3$ bridgmanite. Excess Fe$_{2}$O$_3$ should produce elastic anomalies though., Comment: Under review with Geophysical Research Letters