Full-waveform tomography reveals iron spin crossover in Earth's lower mantle.

Three-dimensional models of Earth's seismic structure can be used to identify temperature-dependent phenomena, including mineralogical phase and spin transformations, that are obscured in 1-D spherical averages. Full-waveform tomography maps seismic wave-speeds inside the Earth in three dimensions, at a higher resolution than classical methods. By providing absolute wave speeds (rather than perturbations) and simultaneously constraining bulk and shear wave speeds over the same frequency range, it becomes feasible to distinguish variations in temperature from changes in composition or spin state. We present a quantitative joint interpretation of bulk and shear wave speeds in the lower mantle, using a recently published full-waveform tomography model. At all depths the diversity of wave speeds cannot be explained by an isochemical mantle. Between 1000 and 2500 km depth, hypothetical mantle models containing an electronic spin crossover in ferropericlase provide a significantly better fit to the wave-speed distributions, as well as more realistic temperatures and silica contents, than models without a spin crossover. Below 2500 km, wave speed distributions are explained by an enrichment in silica towards the core-mantle boundary. This silica enrichment may represent the fractionated remains of an ancient basal magma ocean.

Unveiling the effect of Ni on the formation and structure of Earth's inner core.

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 to 800 K higher than that of Fe at 323 to 360 GPa. hcp, bcc, and liquid phase relations 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 that Ni may substantially impact the structure and formation process of the solid inner core.

DeePMD-kit v2: A software package for deep potential models.

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

PBE-GGA predicts the B8↔B2 phase boundary of FeO at Earth's core conditions.

FeO is a crucial component 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 ~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 ab initio calculation of the B8↔B2 phase boundary in FeO at Earth's core pressures. We show that fully anharmonic free energies computed with the Perdew-Burke-Ernzerhof-generalized gradient approximation coupled with thermal electronic excitations reproduce the experimental phase boundary within uncertainties at P > 255 GPa, including the largely negative Clapeyron slope of -52 MPa/K. This study validates the applicability of a standard density functional theory functional to FeO under Earth's core conditions and demonstrates the theoretical framework that enables complex predictive studies of this region.

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

Oxygen and iron are the most abundant elements on Earth, and their compounds are key planet-forming components. While oxygen is pervasive in the mantle, its presence in the solid inner core is still debatable. Yet, this issue is critical to understanding the co-evolution and the 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 n O compounds has long been speculated. Here, we report that iron reacts with FeO and Fe2O3 at 220-260 GPa and 3000-3500 K in laser-heated diamond anvil cells. Ab initio structure searches using the adaptive genetic algorithm indicate that a series of stable stoichiometric Fe n O compounds (with n > 1) can be formed. Like ε-Fe and B8-FeO, Fe n O compounds have close-packed layered structures featuring oxygen-only single layers separated by iron-only layers. Two solid-solution models with compositions close to Fe2O, the most stable Fe-rich phase identified, explain the X-ray diffraction patterns of the experimental reaction products quenched to room temperature. These results suggest that Fe-rich Fe n O compounds with close-packed layered motifs might be stable under inner core conditions. Future studies of the elastic, rheological, and thermal transport properties of these more anisotropic Fe n O solids should provide new insights into the seismic features of the inner core, inner core formation process and composition, and the thermal evolution of the planet.

Two-step nucleation of the Earth's inner core.

The Earth's inner core started forming when molten iron cooled below the melting point. However, the nucleation mechanism, which is a necessary step of crystallization, has not been well understood. Recent studies have found that it requires an unrealistic degree of undercooling to nucleate the stable, hexagonal, close-packed (hcp) phase of iron that is unlikely to be reached under core conditions and age. This contradiction is 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 does 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 in solving the inner core nucleation paradox. The two-step nucleation scenario of the inner core also opens an avenue for understanding the structure and anisotropy of the present inner core.

Seismological expression of the iron spin crossover in ferropericlase in the Earth's lower mantle.

The two most abundant minerals in the Earth's lower mantle are bridgmanite and ferropericlase. The bulk modulus of ferropericlase (Fp) softens as iron d-electrons transition from a high-spin to low-spin state, affecting the seismic compressional velocity but not the shear velocity. Here, we identify a seismological expression of the iron spin crossover in fast regions associated with cold Fp-rich subducted oceanic lithosphere: the relative abundance of fast velocities in P- and S-wave tomography models diverges in the ~1,400-2,000 km depth range. This is consistent with a reduced temperature sensitivity of P-waves throughout the iron spin crossover. A similar signal is also found in seismically slow regions below ~1,800 km, consistent with broadening and deepening of the crossover at higher temperatures. The corresponding inflection in P-wave velocity is not yet observed in 1-D seismic profiles, suggesting that the lower mantle is composed of non-uniformly distributed thermochemical heterogeneities which dampen the global signature of the Fp spin crossover.

Author Correction: Velocity and density characteristics of subducted oceanic crust and the origin of lower-mantle heterogeneities.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Velocity and density characteristics of subducted oceanic crust and the origin of lower-mantle heterogeneities.

Seismic heterogeneities detected in the lower mantle were proposed to be related to subducted oceanic crust. However, the velocity and density of subducted oceanic crust at lower-mantle conditions remain unknown. Here, we report ab initio results for the elastic properties of calcium ferrite-type phases and determine the velocities and density of oceanic crust along different mantle geotherms. We find that the subducted oceanic crust shows a large negative shear velocity anomaly at the phase boundary between stishovite and CaCl2-type silica, which is highly consistent with the feature of mid-mantle scatterers. After this phase transition in silica, subducted oceanic crust will be visible as high-velocity heterogeneities as imaged by seismic tomography. This study suggests that the presence of subducted oceanic crust could provide good explanations for some lower-mantle seismic heterogeneities with different length scales except large low shear velocity provinces (LLSVPs).

Effects of Induced Stress on Seismic Waves: Validation Based on Ab Initio Calculations.

When a continuum is subjected to an induced stress, the equations that govern seismic wave propagation are modified in two ways. First, the equation of conservation of linear momentum gains terms related to the induced deviatoric stress, and, second, the elastic constitutive relationship acquires terms linear in the induced stress. This continuum mechanics theory makes testable predictions with regard to stress-induced changes in the elastic tensor. Specifically, it predicts that induced compression linearly affects the prestressed moduli with a slope determined by their local adiabatic pressure derivatives and that induced deviatoric stress produces anisotropic compressional and shear wave speeds. In this article we successfully compare such predictions against ab initio mineral physics calculations for NaCl and MgO.

Lattice Thermal Conductivity of MgSiO3 Perovskite from First Principles.

We investigate lattice thermal conductivity κ of MgSiO3 perovskite (pv) by ab initio lattice dynamics calculations combined with exact solution of linearized phonon Boltzmann equation. At room temperature, κ of pristine MgSiO3 pv is found to be 10.7 W/(m · K) at 0 GPa. It increases linearly with pressure and reaches 59.2 W/(m · K) at 100 GPa. These values are close to multi-anvil press measurements whereas about twice as large as those from diamond anvil cell experiments. The increase of k with pressure is attributed to the squeeze of weighted phase-spaces phonons get emitted or absorbed. Moreover, we find κ exhibits noticeable anisotropy, with κ zz being the largest component and [Formula: see text] being about 25%. Such extent of anisotropy is comparable to those of upper mantle minerals such as olivine and enstatite. By analyzing phonon mean free paths and lifetimes, we further show that the weak temperature dependence of κ observed in experiments should not be caused by phonons reaching 'minimum' mean free paths. These results clarify the microscopic mechanism of thermal transport in MgSiO3 pv, and provide reference data for understanding heat conduction in the Earth's deep interior.

A New Line Defect in NdTiO3 Perovskite.

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°. 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.

Nature of the Volume Isotope Effect in Ice.

The substitution of hydrogen (H) by deuterium (D) in ice Ih and in its H-ordered version, ice XI, produces an anomalous form of volume isotope effect (VIE), i.e., volume expansion. This VIE contrasts with the normal VIE (volume contraction) predicted in ice-VIII and in its H-disordered form, ice VII. Here we investigate the VIE in ice XI and in ice VIII using first principles quasiharmonic calculations. We conclude that normal and anomalous VIEs can be produced in ice VIII and ice XI in sequence by application of pressure (ice XI starting at negative pressures) followed by a third type-anomalous VIE with zero-point volume contraction. The latter should also contribute to the isotope effect in the ice VII → ice X transition. The predicted change between normal and anomalous VIE in ice VIII at 14.3 GPa and 300 K is well reproduced experimentally in ice VII using x-ray diffraction measurements. The present discussion of the VIE is general, and conclusions should be applicable to other solid phases of H(2)O, possibly to liquid water under pressure, and to other H-bonded materials.

Searching for high magnetization density in bulk Fe: the new metastable Fe6 phase.

We report the discovery of a new allotrope of iron by first principles calculations. This phase has Pmn2(1) symmetry, a six-atom unit cell (hence the name Fe6), and the highest magnetization density (Ms) among all the known crystalline phases of iron. Obtained from the structural optimizations of the Fe3C-cementite crystal upon carbon removal, Pmn2(1) Fe6 is shown to result from the stabilization of a ferromagnetic FCC phase, further strained along the Bain path. Although metastable from 0 to 50 GPa, the new phase is more stable at low pressures than the other well-known HCP and FCC allotropes and smoothly transforms into the FCC phase under compression. If stabilized to room temperature, for example, by interstitial impurities, Fe6 could become the basis material for high Ms rare-earth-free permament magnets and high-impact applications such as light-weight electric engine rotors or high-density recording media. The new phase could also be key to explaining the enigmatic high Ms of Fe16N2, which is currently attracting intense research activity.

Spin crossover in ferropericlase and velocity heterogeneities in the lower mantle.

Deciphering the origin of seismic velocity heterogeneities in the mantle is crucial to understanding internal structures and processes at work in the Earth. The spin crossover in iron in ferropericlase (Fp), the second most abundant phase in the lower mantle, introduces unfamiliar effects on seismic velocities. First-principles calculations indicate that anticorrelation between shear velocity (VS) and bulk sound velocity (Vφ) in the mantle, usually interpreted as compositional heterogeneity, can also be produced in homogeneous aggregates containing Fp. The spin crossover also suppresses thermally induced heterogeneity in longitudinal velocity (VP) at certain depths but not in VS. This effect is observed in tomography models at conditions where the spin crossover in Fp is expected in the lower mantle. In addition, the one-of-a-kind signature of this spin crossover in the RS/P (∂ ln VS/∂ ln VP) heterogeneity ratio might be a useful fingerprint to detect the presence of Fp in the lower mantle.

Phonon quasiparticles and anharmonic free energy in complex systems.

We use a hybrid strategy to obtain anharmonic frequency shifts and lifetimes of phonon quasiparticles from first principles molecular dynamics simulations in modest size supercells. This approach is effective irrespective of crystal structure complexity and facilitates calculation of full anharmonic phonon dispersions, as long as phonon quasiparticles are well defined. We validate this approach to obtain anharmonic effects with calculations in MgSiO3 perovskite, the major Earth forming mineral phase. First, we reproduce irregular thermal frequency shifts of well characterized Raman modes. Second, we combine the phonon gas model (PGM) with quasiparticle frequencies and reproduce free energies obtained using thermodynamic integration. Combining thoroughly sampled quasiparticle dispersions with the PGM we then obtain first-principles anharmonic free energy in the thermodynamic limit (N→∞).

Elastic anomalies in a spin-crossover system: ferropericlase at lower mantle conditions.

The discovery of a pressure induced iron-related spin crossover in Mg((1-x))Fe(x)O ferropericlase (Fp) and Mg-silicate perovskite, the major phases of Earth's lower mantle, has raised new questions about mantle properties which are of central importance to seismology. Despite extensive experimental work on the anomalous elasticity of Fp throughout the crossover, inconsistencies reported in the literature are still unexplained. Here we introduce a formulation for thermoelasticity of spin crossover systems, apply it to Fp by combining it with predictive first principles density-functional theory with on-site repulsion parameter U calculations, and contrast results with available data on samples with various iron concentrations. We explain why the shear modulus of Fp should not soften along the crossover, as observed in some experiments, predict its velocities at lower mantle conditions, and show the importance of constraining the elastic properties of minerals without extrapolations for analyses of the thermochemical state of this region.

Spin-state crossover and hyperfine interactions of ferric iron in MgSiO(3) perovskite.

Using density functional theory plus Hubbard U calculations, we show that the ground state of (Mg,Fe)(Si,Fe)O(3) perovskite, the major mineral phase in Earth's lower mantle, has high-spin ferric iron (S=5/2) at both dodecahedral (A) and octahedral (B) sites. With increasing pressure, the B-site iron undergoes a spin-state crossover to the low-spin state (S=1/2) between 40 and 70 GPa, while the A-site iron remains in the high-spin state. This B-site spin-state crossover is accompanied by a noticeable volume reduction and an increase in quadrupole splitting, consistent with recent x-ray diffraction and Mössbauer spectroscopy measurements. The anomalous volume reduction leads to a significant softening in bulk modulus during the crossover, suggesting a possible source of seismic-velocity anomalies in the lower mantle.

Body-centered tetragonal C4: a viable sp3 carbon allotrope.

We have investigated by first principles the electronic, vibrational, and structural properties of bct C4, a new form of crystalline sp{3} carbon recently found in molecular dynamics simulations of carbon nanotubes under pressure. This phase is transparent, dynamically stable at zero pressure, and more stable than graphite beyond 18.6 GPa. Coexistence of bct C4 with M carbon can explain better the x-ray diffraction pattern of a transparent and hard phase of carbon produced by the cold compression of graphite. Its structure appears to be intermediate between that of graphite and hexagonal diamond. These facts suggest that bct C4 is an accessible form of sp{3} carbon along the graphite-to-hexagonal diamond transformation path.

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.