Thermal conductivity of Fe-Si alloys and thermal stratification in Earth's core.

Light elements in Earth's core play a key role in driving convection and influencing geodynamics, both of which are crucial to the geodynamo. However, the thermal transport properties of iron alloys at high-pressure and -temperature conditions remain uncertain. Here we investigate the transport properties of solid hexagonal close-packed and liquid Fe-Si alloys with 4.3 and 9.0 wt % Si at high pressure and temperature using laser-heated diamond anvil cell experiments and first-principles molecular dynamics and dynamical mean field theory calculations. In contrast to the case of Fe, Si impurity scattering gradually dominates the total scattering in Fe-Si alloys with increasing Si concentration, leading to temperature independence of the resistivity and less electron-electron contribution to the conductivity in Fe-9Si. Our results show a thermal conductivity of ∼100 to 110 W⋅m-1⋅K-1 for liquid Fe-9Si near the topmost outer core. If Earth's core consists of a large amount of silicon (e.g., > 4.3 wt %) with such a high thermal conductivity, a subadiabatic heat flow across the core-mantle boundary is likely, leaving a 400- to 500-km-deep thermally stratified layer below the core-mantle boundary, and challenges proposed thermal convection in Fe-Si liquid outer core.

Ultrahigh-pressure disordered eight-coordinated phase of Mg2GeO4: Analogue for super-Earth mantles.

Mg2GeO4 is important as an analog for the ultrahigh-pressure behavior of Mg2SiO4, a major component of planetary interiors. In this study, we have investigated magnesium germanate to 275 GPa and over 2,000 K using a laser-heated diamond anvil cell combined with in situ synchrotron X-ray diffraction and density functional theory (DFT) computations. The experimental results are consistent with the formation of a phase with disordered Mg and Ge, in which germanium adopts eightfold coordination with oxygen: the cubic, Th3P4-type structure. DFT computations suggest partial Mg-Ge order, resulting in a tetragonal [Formula: see text] structure indistinguishable from [Formula: see text] Th3P4 in our experiments. If applicable to silicates, the formation of this highly coordinated and intrinsically disordered phase may have important implications for the interior mineralogy of large, rocky extrasolar planets.

Computational Screening and Stabilization of Boron-Substituted Type-I and Type-II Carbon Clathrates.

Boron substitution represents a promising approach to stabilize carbon clathrate structures, but no thermodynamically stable substitution schemes have been identified for frameworks other than the type-VII (sodalite) structure type. To investigate the possibility for additional tetrahedral carbon-based clathrate networks, more than 5000 unique boron decoration schemes were investigated computationally for type-I and type-II carbon clathrates with a range of guest elements including Li, Na, K, Rb, Cs, Mg, Ca, Sr, and Ba. Density functional theory calculations were performed at 10 and 50 GPa, and the stability and impact of boron substitution were evaluated. The results indicate that the boron-substituted carbon clathrates are stabilized under high-pressure conditions. Full cage occupancies of intermediate-sized guest atoms (e.g., Na, Ca, and Sr) are the most favorable energetically. Clathrate stability is maximized when the boron atoms are substituted within the hexagonal rings of the large [51262]/[51264] cages. Several structures with favorable formation enthalpies <-200 meV/atom were predicted, and type-I Ca8B16C30 is on the convex hull at 50 GPa. This structure represents the first thermodynamically stable type-I clathrate identified and suggests that boron-substituted carbon clathrates may represent a large family of diamond-like framework materials with a range of structure types and guest/framework substitutions.

Effects of electron correlations on transport properties of iron at Earth's core conditions.

Earth's magnetic field has been thought to arise from thermal convection of molten iron alloy in the outer core, but recent density functional theory calculations have suggested that the conductivity of iron is too high to support thermal convection, resulting in the investigation of chemically driven convection. These calculations for resistivity were based on electron-phonon scattering. Here we apply self-consistent density functional theory plus dynamical mean-field theory (DFT + DMFT) to iron and find that at high temperatures electron-electron scattering is comparable to the electron-phonon scattering, bringing theory into agreement with experiments and solving the transport problem in Earth's core. The conventional thermal dynamo picture is safe. We find that electron-electron scattering of d electrons is important at high temperatures in transition metals, in contrast to textbook analyses since Mott, and that 4s electron contributions to transport are negligible, in contrast to numerous models used for over fifty years. The DFT+DMFT method should be applicable to other high-temperature systems where electron correlations are important.

Prediction of an Extended Ferroelectric Clathrate.

Using first-principles calculations, we predict a lightweight room-temperature ferroelectric carbon-boron framework in a host-guest clathrate structure. This ferroelectric clathrate, with composition ScB_{3}C_{3}, exhibits high polarization density and low mass density compared with widely used commercial ferroelectrics. Molecular dynamics simulations show spontaneous polarization with a moderate above-room-temperature T_{c} of ∼370 K, which implies large susceptibility and possibly large electrocaloric and piezoelectric constants at room temperature. Our findings open the possibility for a new class of ferroelectric materials with potential across a broad range of applications.

Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo.

We measure the electrical resistivity of hcp iron up to ∼170 GPa and ∼3000 K using a four-probe van der Pauw method coupled with homogeneous flattop laser heating in a DAC, and compute its electrical and thermal conductivity by first-principles molecular dynamics including electron-phonon and electron-electron scattering. We find that the measured resistivity of hcp iron increases almost linearly with temperature, and is consistent with our computations. The results constrain the resistivity and thermal conductivity of hcp iron to ∼80±5 µΩ cm and ∼100±10 W m^{-1} K^{-1}, respectively, at conditions near the core-mantle boundary. Our results indicate an adiabatic heat flow of ∼10±1 TW out of the core, supporting a present-day geodynamo driven by thermal and compositional convection.

Polar Metallocenes.

Crystalline polar metallocenes are potentially useful active materials as piezoelectrics, ferroelectrics, and multiferroics. Within density functional theory (DFT), we computed structural properties, energy differences for various phases, molecular configurations, and magnetic states, computed polarizations for different polar crystal structures, and computed dipole moments for the constituent molecules with a Wannier function analysis. Of the systems studied, Mn2(C9H9N)2 is the most promising as a multiferroic material, since the ground state is both polar and ferromagnetic. We found that the predicted crystalline polarizations are 30⁻40% higher than the values that would be obtained from the dipole moments of the isolated constituent molecules, due to the local effects of the self-consistent internal electric field, indicating high polarizabilities.

Thermal Conductivity and Electrical Resistivity of Solid Iron at Earth's Core Conditions from First Principles.

We compute the thermal conductivity and electrical resistivity of solid hcp Fe to pressures and temperatures of Earth's core. We find significant contributions from electron-electron scattering, usually neglected at high temperatures in transition metals. Our calculations show a quasilinear relation between the electrical resistivity and temperature for hcp Fe at extreme high pressures. We obtain thermal and electrical conductivities that are consistent with experiments considering reasonable error. The predicted thermal conductivity is reduced from previous estimates that neglect electron-electron scattering. Our estimated thermal conductivity for the outer core is 77±10 W m^{-1} K^{-1} and is consistent with a geodynamo driven by thermal convection.

Origin of Negative Longitudinal Piezoelectric Effect.

Piezoelectrics with negative longitudinal piezoelectric coefficients will contract in the direction of an applied electric field. Such piezoelectrics are thought to be rare, but there is no fundamental physics preventing the realization of negative longitudinal piezoelectric effect in a single-phase material. Using first-principles calculations, we demonstrate that several hexagonal ABC ferroelectrics possess significant negative longitudinal piezoelectric effects. The data mining of a first-principles-based database of piezoelectrics reveals that this effect is a general phenomenon. The origin of this unusual piezoelectric response relies on the strong ionic bonds associated with small effective charges and rigid potential energy surfaces. Moreover, ferroelectrics with negative longitudinal piezoelectric coefficients show anomalous pressure-enhanced ferroelectricity. Our results offer design principles to aid the search for new piezoelectrics for novel electromechanical device applications.

Improving the Functional Control of Aged Ferroelectrics Using Insights from Atomistic Modeling.

We provide a fundamental insight into the microscopic mechanisms of the aging processes. Using large-scale molecular dynamics simulations of the prototypical ferroelectric material PbTiO_{3}, we demonstrate that the experimentally observed aging phenomena can be reproduced from intrinsic interactions of defect dipoles related to dopant-vacancy associates, even in the absence of extrinsic effects. We show that variation of the dopant concentration modifies the material's hysteretic response. We identify a universal method to reduce loss and tune the electromechanical properties of inexpensive ceramics for efficient technologies.

Raman measurements of phase transitions in dense solid hydrogen and deuterium to 325 GPa.

Raman spectroscopy of dense hydrogen and deuterium performed to 325 GPa at 300 K reveals previously unidentified transitions. Detailed analysis of the spectra from multiple experimental runs, together with comparison with previous infrared and Raman measurements, provides information on structural modifications of hydrogen as a function of density through the I-III-IV transition sequence, beginning near 200 GPa at 300 K. The data suggest that the transition sequence at these temperatures proceeds by formation of disordered stacking of molecular and distorted layers. Weaker spectral changes are observed at 250, 285, and 300 GPa, that are characterized by discontinuities in pressure shifts of Raman frequencies, and changes in intensities and linewidths. The results indicate changes in structure and bonding, molecular orientational order, and electronic structure of dense hydrogen at these conditions. The data suggest the existence of new phases, either variations of phase IV, or altogether new structures.

Electronic excitations and metallization of dense solid hydrogen.

Theoretical calculations and an assessment of recent experimental results for dense solid hydrogen lead to a unique scenario for the metallization of hydrogen under pressure. The existence of layered structures based on graphene sheets gives rise to an electronic structure related to unique features found in graphene that are well studied in the carbon phase. The honeycombed layered structure for hydrogen at high density, first predicted in molecular calculations, produces a complex optical response. The metallization of hydrogen is very different from that originally proposed via a phase transition to a close-packed monoatomic structure, and different from simple metallization recently used to interpret recent experimental data. These different mechanisms for metallization have very different experimental signatures. We show that the shift of the main visible absorption edge does not constrain the point of band gap closure, in contrast with recent claims. This conclusion is confirmed by measured optical spectra, including spectra obtained to low photon energies in the infrared region for phases III and IV of hydrogen.

Chemical accuracy from quantum Monte Carlo for the benzene dimer.

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Origin of morphotropic phase boundaries in ferroelectrics.

A piezoelectric material is one that generates a voltage in response to a mechanical strain (and vice versa). The most useful piezoelectric materials display a transition region in their composition phase diagrams, known as a morphotropic phase boundary, where the crystal structure changes abruptly and the electromechanical properties are maximal. As a result, modern piezoelectric materials for technological applications are usually complex, engineered, solid solutions, which complicates their manufacture as well as introducing complexity in the study of the microscopic origins of their properties. Here we show that even a pure compound, in this case lead titanate, can display a morphotropic phase boundary under pressure. The results are consistent with first-principles theoretical predictions, but show a richer phase diagram than anticipated; moreover, the predicted electromechanical coupling at the transition is larger than any known. Our results show that the high electromechanical coupling in solid solutions with lead titanate is due to tuning of the high-pressure morphotropic phase boundary in pure lead titanate to ambient pressure. We also find that complex microstructures or compositions are not necessary to obtain strong piezoelectricity. This opens the door to the possible discovery of high-performance, pure-compound electromechanical materials, which could greatly decrease costs and expand the utility of piezoelectric materials.

Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica.

Silica (SiO(2)) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger's equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense alpha-PbO(2) structure above the core-insulating D" layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.

Giant electrocaloric effect around Tc.

We use molecular dynamics with a first-principles-based shell model potential to study the electrocaloric effect (ECE) in lithium niobate, LiNbO(3), and find a giant electrocaloric effect along a line passing through the ferroelectric transition. With an applied electric field, a line of maximum ECE passes through the zero field ferroelectric transition, continuing along a Widom line at high temperatures with increasing fields, and along the instability that leads to homogeneous ferroelectric switching below T(c) with an applied field antiparallel to the spontaneous polarization. This line is defined as the minimum in the inverse capacitance under an applied electric field. We investigate the effects of pressure, temperature and an applied electric field on the ECE. The behavior we observe in LiNbO(3) should generally apply to ferroelectrics; we therefore suggest that the operating temperature for refrigeration and energy scavenging applications should be above the ferroelectric transition region to obtain a large electrocaloric response. The relationship between T(c), the Widom line, and homogeneous switching should be universal among ferroelectrics, relaxors, multiferroics, and the same behavior should be found under applied magnetic fields in ferromagnets.

Experimental and theoretical evidence for pressure-induced metallization in FeO with rocksalt-type structure.

Electrical conductivity of FeO was measured up to 141 GPa and 2480 K in a laser-heated diamond-anvil cell. The results show that rock-salt (B1) type structured FeO metallizes at around 70 GPa and 1900 K without any structural phase transition. We computed fully self-consistently the electronic structure and the electrical conductivity of B1 FeO as a function of pressure and temperature, and found that although insulating as expected at ambient condition, B1 FeO metallizes at high temperatures, consistent with experiments. The observed metallization is related to spin crossover.

Anomalous optical and electronic properties of dense sodium.

Synchrotron infrared spectroscopy on sodium shows a transition from a high reflectivity, nearly free-electron metal to a low-reflectivity, poor metal in an orthorhombic phase at 118 GPa. Optical spectra calculated within density functional theory (DFT) agree with the experimental measurements and predict a gap opening in the orthorhombic phase at compression beyond its stability field, a state that would be experimentally attainable by appropriate choice of pressure-temperature path. We show that a transition to an incommensurate phase at 125 GPa results in a partial recovery of good metallic character up to 180 GPa, demonstrating the strong relationship between structure and electronic properties in sodium.

Measuring the melting curve of iron at super-Earth core conditions.

The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth's interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth's inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth's mass have the longest dynamos, which provide important shielding against cosmic radiation.

Fundamental high-pressure calibration from all-electron quantum Monte Carlo calculations.

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We compute the static contribution to the free energy with the QMC method and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We compute the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy.