Structural and Electronic Transitions in Liquid FeO Under High Pressure

FeO represents an important end-member for planetary interiors mineralogy. However, its properties in the liquid state under high pressure are poorly constrained. Here, in situ high-pressure and high-temperature X-ray diffraction experiments, ab initio simulations, and thermodynamic calculations are combined to study the local structure and density evolution of liquid FeO under extreme conditions. Our results highlight a strong shortening of the Fe-Fe distance, particularly pronounced between ambient pressure and ∼40 GPa, possibly related with the insulator to metal transition occurring in solid FeO over a similar pressure range. Liquid density is smoothly evolving between 60 and 150 GPa from values calculated for magnetic liquid to those calculated for non-magnetic liquid, compatibly with a continuous spin crossover in liquid FeO. The present findings support the potential decorrelation between insulator/metal transition and the high-spin to low-spin continuous transition, and relate the changes in the microscopic structure with macroscopic properties, such as the closure of the Fe-FeO miscibility gap. Finally, these results are used to construct a parameterized thermal equation of state for liquid FeO providing densities up to pressure and temperature conditions expected at the Earth's core-mantle boundary.

Electron Density Changes across the Pressure-Induced Iron Spin Transition

High-pressure single-crystal x-ray diffraction is used to experimentally map the electron-density distribution changes in (Fe,Mg)O as ferrous iron undergoes a pressure-induced transition from high- to low-spin states. As the bulk density and elasticity of magnesiowüstite-one of the dominant mineral phases of Earth's mantle-are affected by this electronic transition, our results have applications to geophysics as well as to validating first-principles calculations. The observed changes in diffraction intensities indicate a spin-transition-induced change in orbital occupancies of the Fe ion in general accord with crystal-field theory, illustrating the use of electron density measurements for characterizing high-pressure d-block chemistry and motivating further studies characterizing chemical bonding under pressure.

Structural transition and re-emergence of iron's total electron spin in (Mg,Fe)O at ultrahigh pressure

Fe-bearing MgO [(Mg_1−xFe_x)O] is considered a major constituent of terrestrial exoplanets. Crystallizing in the B1 structure in the Earth’s lower mantle, (Mg_1−xFe_x)O undergoes a high-spin (S = 2) to low-spin (S = 0) transition at ∼45 GPa, accompanied by anomalous changes of this mineral’s physical properties, while the intermediate-spin (S = 1) state has not been observed. In this work, we investigate (Mg_1−xFe_x)O (x ≤ 0.25) up to 1.8 TPa via first-principles calculations. Our calculations indicate that (Mg_1−xFe_x)O undergoes a simultaneous structural and spin transition at ∼0.6 TPa, from the B1 phase low-spin state to the B2 phase intermediate-spin state, with Fe’s total electron spin S re-emerging from 0 to 1 at ultrahigh pressure. Upon further compression, an intermediate-to-low spin transition occurs in the B2 phase. Depending on the Fe concentration (x), metal–insulator transition and rhombohedral distortions can also occur in the B2 phase. These results suggest that Fe and spin transition may affect planetary interiors over a vast pressure range.

Iron spin transition occurs at ultrahigh pressure. The total electron spin increases from 0 to 1 as the structural transition of (Mg,Fe)O occurs (~0.6 TPa) and drops back to 0 at higher pressure. Its effects on exoplanet interiors are anticipated.

New dynamic diamond anvil cells for tera-pascal per second fast compression x-ray diffraction experiments

Fast compression experiments performed using dynamic diamond anvil cells (dDACs) employing piezoactuators offer the opportunity to study compression-rate dependent phenomena. In this paper, we describe an experimental setup which allows us to perform time-resolved x-ray diffraction during the fast compression of materials using improved dDACs. The combination of the high flux available using a 25.6 keV x-ray beam focused with a linear array of compound refractive lenses and the two fast GaAs LAMBDA detectors available at the Extreme Conditions Beamline (P02.2) at PETRA III enables the collection of x-ray diffraction patterns at an effective repetition rate of up to 4 kHz. Compression rates of up to 160 TPa/s have been achieved during the compression of gold in a 2.5 ms fast compression using improved dDAC configurations with more powerful piezoactuators. The application of this setup to low-Z compounds at lower compression rates is described, and the high temporal resolution of the setup is demonstrated. The possibility of applying finely tuned pressure profiles opens opportunities for future research, such as using oscillations of the piezoactuator to mimic propagation of seismic waves in the Earth.

Effects of iron spin transition on the electronic structure, thermal expansivity and lattice thermal conductivity of ferropericlase: a first principles study

The effects of the spin transition on the electronic structure, thermal expansivity and lattice thermal conductivity of ferropericlase are studied by first principles calculations at high pressures. The electronic structures indicate that ferropericlase is an insulator for high-spin and low-spin states. Combined with the quasiharmonic approximation, our calculations show that the thermal expansivity is larger in the high-spin state than in the low-spin state at ambient pressure, while the magnitude exhibits a crossover between high-spin and low-spin with increasing pressure. The calculated lattice thermal conductivity exhibits a drastic reduction upon the inclusion of ferrous iron, which is consistent with previous experimental studies. However, a subsequent enhancement in the thermal conductivity is obtained, which is associated with the spin transition. Mechanisms are discussed for the variation in thermal conductivity by the inclusion of ferrous iron and the spin transition.

Determination of elastic moduli from measured acoustic velocities

Methods are evaluated in solution of the inverse problem associated with determination of elastic moduli for crystals of arbitrary symmetry from elastic wave velocities measured in many crystallographic directions. A package of MATLAB functions provides a robust and flexible environment for analysis of ultrasonic, Brillouin, or Impulsive Stimulated Light Scattering datasets. Three inverse algorithms are considered: the gradient-based methods of Levenberg-Marquardt and Backus-Gilbert, and a non-gradient-based (Nelder-Mead) simplex approach. Several data types are considered: body wave velocities alone, surface wave velocities plus a side constraint on X-ray-diffraction-based axes compressibilities, or joint body and surface wave velocities. The numerical algorithms are validated through comparisons with prior published results and through analysis of synthetic datasets. Although all approaches succeed in finding low-misfit solutions, the Levenberg-Marquardt method consistently demonstrates effectiveness and computational efficiency. However, linearized gradient-based methods, when applied to a strongly non-linear problem, may not adequately converge to the global minimum. The simplex method, while slower, is less susceptible to being trapped in local misfit minima. A "multi-start" strategy (initiate searches from more than one initial guess) provides better assurance that global minima have been located. Numerical estimates of parameter uncertainties based on Monte Carlo simulations are compared to formal uncertainties based on covariance calculations.

Investigation of iron spin crossover pressure in Fe-bearing MgO using hybrid functional

Pressure-induced spin crossover behaviors of Fe-bearing MgO were widely investigated by using an LDA  +  U functional for describing the strongly correlated Fe-O bonding. Moreover, the simulated spin crossover pressures depend on the applied U values, which are sensitive to environments and parameters. In this work, the spin crossover pressures of (Mg_1-x ,Fe _x )O are investigated by using the hybrid functional with a uniform parameter. Our results indicate that the spin crossover pressures increase with increasing iron concentration. For example, the spin crossover pressure of (Mg_0.03125,Fe_0.96875)O and FeO was 56 GPa and 127 GPa, respectively. The calculated crossover pressures agreed well with the experimental observations. Therefore, the hybrid functional should be an effective method for describing the pressure-induced spin crossover behaviors in transition metal oxides.

Pressure dependence of transverse acoustic phonon energy in ferropericlase across the spin transition

We investigated transverse acoustic (TA) phonons in iron-bearing magnesium oxide (ferropericlase) up to 56 GPa using inelastic x-ray scattering (IXS). The results show that the energy of the TA phonon far from the Brillouin zone center suddenly increases with increasing pressure above the spin transition pressure of ferropericlase. Ab initio calculations revealed that the TA phonon energy far from the Brillouin zone center is higher in the low-spin state than in the high spin state; that the TA phonon energy depend weakly on pressure; and that the energy gap between the TA and the lowest-energy-optic phonons is much narrower in the low-spin state than in the high-spin state. This allows us to conclude that the anomalous behavior of the TA mode in the present experiments is the result of gap narrowing due to the spin transition and explains contradictory results in previous experimental studies.

Stability of ferrous-iron-rich bridgmanite under reducing midmantle conditions

Our current understanding of the electronic state of iron in lower-mantle minerals leads to a considerable disagreement in bulk sound speed with seismic measurements if the lower mantle has the same composition as the upper mantle (pyrolite). In the modeling studies, the content and oxidation state of Fe in the minerals have been assumed to be constant throughout the lower mantle. Here, we report high-pressure experimental results in which Fe becomes dominantly Fe²⁺ in bridgmanite synthesized at 40-70 GPa and 2,000 K, while it is in mixed oxidation state (Fe³⁺/∑Fe = 60%) in the samples synthesized below and above the pressure range. Little Fe³⁺ in bridgmanite combined with the strong partitioning of Fe²⁺ into ferropericlase will alter the Fe content for these minerals at 1,100- to 1,700-km depths. Our calculations show that the change in iron content harmonizes the bulk sound speed of pyrolite with the seismic values in this region. Our experiments support no significant changes in bulk composition for most of the mantle, but possible changes in physical properties and processes (such as viscosity and mantle flow patterns) in the midmantle.

Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth's Lower Mantle

Brillouin light scattering and impulsive stimulated light scattering have been used to determine the full elastic constants of magnesiosiderite [(Mg_{0.35}Fe_{0.65})CO_{3}] up to 70 GPa at room temperature in a diamond-anvil cell. Drastic softening in C_{11}, C_{33}, C_{12}, and C_{13} elastic moduli associated with the compressive stress component and stiffening in C_{44} and C_{14} moduli associated with the shear stress component are observed to occur within the spin transition between ∼42.4 and ∼46.5  GPa. Negative values of C_{12} and C_{13} are also observed within the spin transition region. The Born criteria constants for the crystal remain positive within the spin transition, indicating that the mixed-spin state remains mechanically stable. Significant auxeticity can be related to the electronic spin transition-induced elastic anomalies based on the analysis of Poisson's ratio. These elastic anomalies are explained using a thermoelastic model for the rhombohedral system. Finally, we conclude that mixed-spin state ferromagnesite, which is potentially a major deep-carbon carrier, is expected to exhibit abnormal elasticity, including a negative Poisson's ratio of -0.6 and drastically reduced V_{P} by 10%, in Earth's midlower mantle.

High-pressure studies with x-rays using diamond anvil cells

Pressure profoundly alters all states of matter. The symbiotic development of ultrahigh-pressure diamond anvil cells, to compress samples to sustainable multi-megabar pressures; and synchrotron x-ray techniques, to probe materials' properties in situ, has enabled the exploration of rich high-pressure (HP) science. In this article, we first introduce the essential concept of diamond anvil cell technology, together with recent developments and its integration with other extreme environments. We then provide an overview of the latest developments in HP synchrotron techniques, their applications, and current problems, followed by a discussion of HP scientific studies using x-rays in the key multidisciplinary fields. These HP studies include: HP x-ray emission spectroscopy, which provides information on the filled electronic states of HP samples; HP x-ray Raman spectroscopy, which probes the HP chemical bonding changes of light elements; HP electronic inelastic x-ray scattering spectroscopy, which accesses high energy electronic phenomena, including electronic band structure, Fermi surface, excitons, plasmons, and their dispersions; HP resonant inelastic x-ray scattering spectroscopy, which probes shallow core excitations, multiplet structures, and spin-resolved electronic structure; HP nuclear resonant x-ray spectroscopy, which provides phonon densities of state and time-resolved Mössbauer information; HP x-ray imaging, which provides information on hierarchical structures, dynamic processes, and internal strains; HP x-ray diffraction, which determines the fundamental structures and densities of single-crystal, polycrystalline, nanocrystalline, and non-crystalline materials; and HP radial x-ray diffraction, which yields deviatoric, elastic and rheological information. Integrating these tools with hydrostatic or uniaxial pressure media, laser and resistive heating, and cryogenic cooling, has enabled investigations of the structural, vibrational, electronic, and magnetic properties of materials over a wide range of pressure-temperature conditions.

Condensed-matter equation of states covering a wide region of pressure studied experimentally

The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α1(PV) + α2(PV)2 + α3(PV)3, in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1 − α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.

Elasticity of Ferropericlase across the Spin Crossover in the Earth's Lower Mantle

Knowing the elasticity of ferropericlase across the spin transition can help explain seismic and mineralogical models of the lower-mantle including the origin of seismic heterogeneities in the middle to lowermost parts of the lower mantle1234. However, the effects of spin transition on full elastic constants of ferropericlase remain experimentally controversial due to technical challenges in directly measuring sound velocities under lower-mantle conditions12345. Here we have reliably measured both V_P and V_S of a single-crystal ferropericlase ((Mg_0.92,Fe_0.08)O) using complementary Brillouin Light Scattering and Impulsive Stimulated Light Scattering coupled with a diamond anvil cell up to 96 GPa. The derived elastic constants show drastically softened C₁₁ and C₁₂ within the spin transition at 40–60 GPa while C₄₄ is not affected. The spin transition is associated with a significant reduction of the aggregate V_P/V_S via the aggregate V_P softening because V_S softening does not visibly occur within the transition. Based on thermoelastic modelling along an expected geotherm, the spin crossover in ferropericlase can contribute to 2% reduction in V_P/V_S in a pyrolite mineralogical model in mid lower-mantle. Our results imply that the middle to lowermost parts of the lower-mantle would exhibit enhanced seismic heterogeneities due to the occurrence of the mixed-spin and low-spin ferropericlase.

Spin crossover in ferropericlase from first-principles molecular dynamics

Ferropericlase, (Mg,Fe)O, is the second-most abundant mineral of Earth's lower mantle. With increasing pressure, the Fe ions in the material begin to collapse from a magnetic to nonmagnetic spin state. We present a finite-temperature first-principles phase diagram of this spin crossover, finding a broad pressure range with coexisting magnetic and nonmagnetic ions due to favorable enthalpy of mixing of the two. Furthermore, we find the electrical conductivity of the mineral to reach semimetallic values inside Earth.

Hidden carbon in Earth's inner core revealed by shear softening in dense Fe7C3

Earth's inner core is known to consist of crystalline iron alloyed with a small amount of nickel and lighter elements, but the shear wave (S wave) travels through the inner core at about half the speed expected for most iron-rich alloys under relevant pressures. The anomalously low S-wave velocity (vS) has been attributed to the presence of liquid, hence questioning the solidity of the inner core. Here we report new experimental data up to core pressures on iron carbide Fe7C3, a candidate component of the inner core, showing that its sound velocities dropped significantly near the end of a pressure-induced spin-pairing transition, which took place gradually between 10 GPa and 53 GPa. Following the transition, the sound velocities increased with density at an exceptionally low rate. Extrapolating the data to the inner core pressure and accounting for the temperature effect, we found that low-spin Fe7C3 can reproduce the observed vS of the inner core, thus eliminating the need to invoke partial melting or a postulated large temperature effect. The model of a carbon-rich inner core may be consistent with existing constraints on the Earth's carbon budget and would imply that as much as two thirds of the planet's carbon is hidden in its center sphere.

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.

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.

A perovskitic lower mantle inferred from high-pressure, high-temperature sound velocity data

The determination of the chemical composition of Earth's lower mantle is a long-standing challenge in earth science. Accurate knowledge of sound velocities in the lower-mantle minerals under relevant high-pressure, high-temperature conditions is essential in constraining the mineralogy and chemical composition using seismological observations, but previous acoustic measurements were limited to a range of low pressures and temperatures. Here we determine the shear-wave velocities for silicate perovskite and ferropericlase under the pressure and temperature conditions of the deep lower mantle using Brillouin scattering spectroscopy. The mineralogical model that provides the best fit to a global seismic velocity profile indicates that perovskite constitutes more than 93 per cent by volume of the lower mantle, which is a much higher proportion than that predicted by the conventional peridotitic mantle model. It suggests that the lower mantle is enriched in silicon relative to the upper mantle, which is consistent with the chondritic Earth model. Such chemical stratification implies layered-mantle convection with limited mass transport between the upper and the lower mantle.

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.

Anomalous compressibility of ferropericlase throughout the iron spin cross-over

The thermoelastic properties of ferropericlase Mg(1-x)Fe(x)O (x = 0.1875) throughout the iron high-to-low spin cross-over have been investigated by first principles at Earth's lower mantle conditions. This cross-over has important consequences for elasticity such as an anomalous bulk modulus (K(S)) reduction. At room temperature the anomaly is somewhat sharp in pressure but broadens with increasing temperature. Along a typical geotherm it occurs across most of the lower mantle with a more significant K(S) reduction at approximately 1,400-1,600 km depth. This anomaly might also cause a reduction in the effective activation energy for diffusion creep and lead to a viscosity minimum in the mid-lower mantle, in apparent agreement with results from inversion of data related with mantle convection and postglacial rebound.