Thermal and electrical conductivity of iron at Earth’s core conditions

Regionally-triggered geomagnetic reversals

Systematic studies of numerical dynamo simulations reveal that the transition from dipole-dominated non-reversing fields to models that exhibit reversals occurs when inertial effects become strong enough. However, the inertial force is expected to play a secondary role in the force balance in Earth's outer core. Here we show that reversals in numerical dynamo models with heterogeneous outer boundary heat flux inferred from lower mantle seismic anomalies appear when the amplitude of heat flux heterogeneity is increased. The reversals are triggered at regions of large heat flux in which strong small-scale inertial forces are produced, while elsewhere inertial forces are substantially smaller. When the amplitude of heat flux heterogeneity is further increased so that in some regions sub-adiabatic conditions are reached, regional skin effects suppress small-scale magnetic fields and the tendency to reverse decreases. Our results reconcile the need for inertia for reversals with the theoretical expectation that the inertial force remains secondary in the force balance. Moreover, our results highlight a non-trivial non-monotonic behavior of the geodynamo in response to changes in the amplitude of the core-mantle boundary heat flux heterogeneity.

Electron-Induced Nonmonotonic Pressure Dependence of the Lattice Thermal Conductivity of θ-TaN

Recent theoretical and experimental research suggests that θ-TaN is a semimetal with high thermal conductivity (κ), primarily due to the contribution of phonons (κ_{ph}). By using first-principles calculations, we show a nonmonotonic pressure dependence of the κ of θ-TaN. κ_{ph} first increases until it reaches a maximum at around 60 GPa, and then decreases. This anomalous behavior is a consequence of the competing pressure responses of phonon-phonon and phonon-electron interactions, in contrast to the known materials BAs and BP, where the nonmonotonic pressure dependence is caused by the interplay between different phonon-phonon scattering channels. Although TaN has phonon dispersion features similar to BAs at ambient pressure, its response to pressure is different and an overall stiffening of the phonon branches takes place. Consequently, the relevant phonon-phonon scattering weakens as pressure increases. However, the increased electronic density of states near the Fermi level, and specifically the emergence of additional pockets of the Fermi surface at the high-symmetry L point in the Brillouin zone, leads to a substantial increase in phonon-electron scattering at high pressures, driving a decrease in κ_{ph}. At intermediate pressures (∼20-70  GPa), the κ of TaN surpasses that of BAs. Our Letter provides deeper insight into phonon transport in semimetals and metals where phonon-electron scattering is relevant.

Measuring the Electrical Resistivity of Liquid Iron to 1.4 Mbar

We determined the electrical resistivity of liquid Fe to 135 GPa and 6680 K using a four-probe method in a diamond-anvil cell combined with two novel techniques: (i) enclosing a molten Fe in a sapphire capsule, and (ii) millisecond time-resolved simultaneous measurements of the resistance, x-ray diffraction, and temperature of instantaneously melted Fe. Our results show the minimal temperature dependence of the resistivity of liquid Fe and its anomalous resistivity decrease around 50 GPa, likely associated with a gradual magnetic transition, both in agreement with previous ab initio calculations.

Anomalous thermal transport under high pressure in boron arsenide

High pressure represents extreme environments and provides opportunities for materials discovery^1-8. Thermal transport under high hydrostatic pressure has been investigated for more than 100 years and all measurements of crystals so far have indicated a monotonically increasing lattice thermal conductivity. Here we report in situ thermal transport measurements in the newly discovered semiconductor crystal boron arsenide, and observe an anomalous pressure dependence of the thermal conductivity. We use ultrafast optics, Raman spectroscopy and inelastic X-ray scattering measurements to examine the phonon bandstructure evolution of the optical and acoustic branches, as well as thermal conductivity under varied temperatures and pressures up to 32 gigapascals. Using atomistic theory, we attribute the anomalous high-pressure behaviour to competitive heat conduction channels from interactive high-order anharmonicity physics inherent to the unique phonon bandstructure. Our study verifies ab initio theory calculations and we show that the phonon dynamics-resulting from competing three-phonon and four-phonon scattering processes-are beyond those expected from classical models and seen in common materials. This work uses high-pressure spectroscopy combined with atomistic theory as a powerful approach to probe complex phonon physics and provide fundamental insights for understanding microscopic energy transport in materials of extreme properties.

Electrical resistivity of the Fe–Si–S ternary system: implications for timing of thermal convection shutdown in the lunar core

The composition of the lunar core has been suggested to be Fe-rich with varying amounts of lighter elements, such as Si and S. Presence of Si and S affects electrical and thermal transport properties and thus influences core thermal processes and evolution. Paleomagnetic observations constrain a high intensity magnetic field that ceases shortly after formation of the moon (~ 3.5–4.2 Ga year ago), and thermal convection in the core may contribute to generation of this field. In this study, the electrical resistivity of Fe-14 wt% Si-3 wt% S was measured in both solid and molten states at pressures up to 5 GPa and thermal conductivity was calculated via the Wiedemann–Franz Law from the electrical measurements. The results were used to estimate the adiabatic conductive heat flux of a molten Fe-14 wt% Si-3 wt% S lunar core and compared to a Fe-2-17 wt% Si lunar core, which showed that thermal convection of either core composition shuts down within the duration of the high intensity magnetic field: (1) 3.17–3.72 Ga year ago for a Fe-14 wt% Si-3 wt% S core; and (ii) 3.38–3.86 Ga years ago for a Fe-2-17 wt% Si core. Results favouring compatibility of these core compositions with paleomagnetic observations are strongly dependent on the temperature of the core-mantle boundary and time-dependent mantle-side heat flux.

How was the Earth–Moon system formed? New insights from the geodynamo

The most widely accepted scenario for the formation of the Earth–Moon system involves a dramatic impact between the proto-Earth and some other cosmic body. Many features of the present-day Earth–Moon system provide constraints on the nature of this impact. Any model of the history of the Earth must account for the physical, geochemical, petrological, and dynamical evidence. These constraints notwithstanding, there are several radically different impact models that could in principle account for all the evidence. Thus, in the absence of further constraints, we may never know for sure how the Earth–Moon system was formed. Here, we put forward the idea that additional constraints are indeed provided by the fact that the Earth is strongly magnetized. It is universally accepted that the Earth’s magnetic field is maintained by a dynamo operating in the outer liquid core. However, because of the rapid rotation of the Earth, this dynamo has the peculiar property that it can maintain a strong field but cannot amplify a weak one. Therefore, the Earth must have been magnetized at a very early epoch, either preimpact or as a result of the impact itself. Either way, any realistic model of the formation of the Earth–Moon system must include magnetic field evolution. This requirement may ultimately constrain the models sufficiently to discriminate between the various candidates.

High geomagnetic field intensity recorded by anorthosite xenoliths requires a strongly powered late Mesoproterozoic geodynamo

Acquiring high-fidelity ancient magnetic field intensity records from rocks is crucial for constraining the long-term evolution of Earth’s core. However, robust estimates of ancient field strengths are often difficult to recover due to alteration or nonideal behavior. We use rocks known as anorthosite that formed in the deep crust and were brought to the near surface where they acquired thermal remanent magnetizations. These rocks have experienced minimal postformation alteration and yield high-quality paleointensity estimates. In contrast to scenarios of a progressively decaying field leading up to a proposed late nucleation of Earth’s inner core, these data record a strong field 1.1 Ga. A strong field that persisted over a 14-My interval indicates the existence of appreciable power sources for Earth’s dynamo at this time.

Obtaining estimates of Earth’s magnetic field strength in deep time is complicated by nonideal rock magnetic behavior in many igneous rocks. In this study, we target anorthosite xenoliths that cooled and acquired their magnetization within ca. 1,092 Ma shallowly emplaced diabase intrusions of the North American Midcontinent Rift. In contrast to the diabase which fails to provide reliable paleointensity estimates, the anorthosite xenoliths are unusually high-fidelity recorders yielding high-quality, single-slope paleointensity results that are consistent at specimen and site levels. An average value of ∼83 ZAm² for the virtual dipole moment from the anorthosite xenoliths, with the highest site-level values up to ∼129 ZAm², is higher than that of the dipole component of Earth’s magnetic field today and rivals the highest values in the paleointensity database. Such high intensities recorded by the anorthosite xenoliths require the existence of a strongly powered geodynamo at the time. Together with previous paleointensity data from other Midcontinent Rift rocks, these results indicate that a dynamo with strong power sources persisted for more than 14 My ca. 1.1 Ga. These data are inconsistent with there being a progressive monotonic decay of Earth’s dynamo strength through the Proterozoic Eon and could challenge the hypothesis of a young inner core. The multiple observed paleointensity transitions from weak to strong in the Paleozoic and the Proterozoic present challenges in identifying the onset of inner core nucleation based on paleointensity records alone.

Random-walk shielding-potential viscosity model for warm dense metals

We develop a model, called the "random-walk shielding-potential viscosity model" (RWSP-VM) that introduces the statistics of random-walk ions and the Debye shielding effect to describe the viscosities of warm dense metals. The viscosities of several metals with low to high atomic numbers (Be, Al, Fe, and U) are calculated using the analytical expression of RWSP-VM. Additionally, we simulate the viscosities of Fe and Be by employing the Langevin molecular dynamics (MD) and classical MD, while the MD data for Al and U are obtained from a previous work. The results of the RWSP-VM are in good agreement with the MD results, which validates the proposed model. Furthermore, we compare the RWSP-VM with the one-component plasma model and Yukawa viscosity model and show that the three models yield results in excellent agreement with each other in the regime where the RWSP-VM is applicable. These results indicate that the RWSP-VM is a universal, accurate, and highly efficient model for calculating the viscosity of metals in the warm dense state. The code of the proposed RWSP-VM is provided, and it is envisaged that it will have broad application prospects in numerous fields.

Electronic transport coefficients from density functional theory across the plasma plane

We investigate the thermopower and Lorenz number of hydrogen with Kohn-Sham density functional theory (DFT) across the plasma plane toward the near-classical limit, i.e., weakly degenerate and weakly coupled states. Our results are in concordance with certain limiting values for the Lorentz plasma, a model system which only considers electron-ion scattering. Thereby, we clearly show that the widely used method of calculating transport properties via the Kubo-Greenwood (KG) formalism does not capture electron-electron scattering processes. Our discussion also addresses the inadequateness of assuming a Drude-like frequency behavior for the conductivity of nondegenerate plasmas by revisiting the relaxation time approximation within kinetic theory.

Satellite magnetic data reveal interannual waves in Earth's core

SignificanceThe physics responsible for most of the interannual geomagnetic field changes, continually recorded by satellites for 20 years, is a long-standing open issue. By analyzing magnetic data, we detect Magneto-Coriolis waves in the Earth's outer core that account for a significant part of this signal. We further propose theoretical advances in the physical characterization of these waves, enabling a deeper understanding of the dynamics behind the geomagnetic signal. It should allow one to better sketch the heterogeneous magnetic field deep within the core, shedding further light on the mechanisms that sustain the geodynamo. Our interpretation does not require the presence of a stratified layer at the top of the core, with potent consequences regarding the Earth's thermal history.

Continuous Kubo-Greenwood formula: Theory and numerical implementation

In this paper, we present the so-called continuous Kubo-Greenwood formula intended for the numerical calculation of the dynamic Onsager coefficients and, in particular, the real part of dynamic electrical conductivity. In contrast to the usual Kubo-Greenwood formula, which contains the summation over a discrete set of transitions between electron energy levels, the continuous one is formulated as an integral over the whole energy range. This integral includes the continuous functions: the smoothed squares of matrix elements, D(ɛ,ɛ+ℏω), the densities of state, g(ɛ)g(ɛ+ℏω), and the difference of the Fermi weights, [f(ɛ)-f(ɛ+ℏω)]/(ℏω). The function D(ɛ,ɛ+ℏω) is obtained via the specially developed smoothing procedure. From the theoretical point of view, the continuous formula is an alternative to the usual one. Both can be used to calculate matter properties and produce close results. However, the continuous formula includes the smooth functions that can be plotted and examined. Thus, we can analyze the contributions of various parts of the electron spectrum to the obtained properties. The possibility of such analysis is the main advantage of the continuous formula. The continuous Kubo-Greenwood formula is implemented in the parallel code cubogram. Using the code we demonstrate the influence of technical parameters on the simulation results for liquid aluminum. We also analyze various methods of matrix elements computation and their effect on dynamic electrical conductivity.

Superionic iron alloys and their seismic velocities in Earth's inner core

Earth's inner core (IC) is less dense than pure iron, indicating the existence of light elements within it¹. Silicon, sulfur, carbon, oxygen and hydrogen have been suggested to be the candidates^2,3, and the properties of iron-light-element alloys have been studied to constrain the IC composition^4-19. Light elements have a substantial influence on the seismic velocities^4-13, the melting temperatures^14-17 and the thermal conductivities^18,19 of iron alloys. However, the state of the light elements in the IC is rarely considered. Here, using ab initio molecular dynamics simulations, we find that hydrogen, oxygen and carbon in hexagonal close-packed iron transform to a superionic state under the IC conditions, showing high diffusion coefficients like a liquid. This suggests that the IC can be in a superionic state rather than a normal solid state. The liquid-like light elements lead to a substantial reduction in the seismic velocities, which approach the seismological observations of the IC^20,21. The substantial decrease in shear-wave velocity provides an explanation for the soft IC²¹. In addition, the light-element convection has a potential influence on the IC seismological structure and magnetic field.

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.

Metallic Aluminum Suboxides with Ultrahigh Electrical Conductivity at High Pressure

Aluminum, as the most abundant metallic elemental content in the Earth's crust, usually exists in the form of alumina (Al₂O₃). However, the oxidation state of aluminum and the crystal structures of aluminum oxides in the pressure range of planetary interiors are not well established. Here, we predicted two aluminum suboxides (Al₂O, AlO) and two superoxides (Al₄O₇, AlO₃) with uncommon stoichiometries at high pressures using first-principle calculations and crystal structure prediction methods. We find that the P4/nmm Al₂O becomes stable above ~765 GPa and may survive in the deep mantles or cores of giant planets such as Neptune. Interestingly, the Al₂O and AlO are metallic and have electride features, in which some electrons are localized in the interstitials between atoms. We find that Al₂O has an electrical conductivity one order of magnitude higher than that of iron under the same pressure-temperature conditions, which may influence the total conductivity of giant planets. Our findings enrich the high-pressure phase diagram of aluminum oxides and improve our understanding of the interior structure of giant planets.

Gravity Variations and Ground Deformations Resulting from Core Dynamics

ABSTRACT

Fluid motion within the Earth's liquid outer core leads to internal mass redistribution. This occurs through the advection of density anomalies within the volume of the liquid core and by deformation of the solid boundaries of the mantle and inner core which feature density contrasts. It also occurs through torques acting on the inner core reorienting its non-spherical shape. These in situ mass changes lead to global gravity variations, and global deformations (inducing additional gravity variations) occur in order to maintain the mechanical equilibrium of the whole Earth. Changes in Earth's rotation vector (and thus of the global centrifugal potential) induced by core flows are an additional source of global deformations and associated gravity changes originating from core dynamics. Here, we review how each of these different core processes operates, how gravity changes and ground deformations from each could be reconstructed, as well as ways to estimate their amplitudes. Based on our current understanding of core dynamics, we show that, at spherical harmonic degree 2, core processes contribute to gravity variations and ground deformations that are approximately a factor 10 smaller than those observed and caused by dynamical processes within the fluid layers at the Earth's surface. The larger the harmonic degree, the smaller is the contribution from the core. Extracting a signal of core origin requires the accurate removal of all contributions from surface processes, which remains a challenge.

ARTICLE HIGHLIGHTS

Dynamical processes in Earth's fluid core lead to global gravity variations and surface ground deformationsWe review how these processes operate, how signals of core origin can be reconstructed and estimate their amplitudesCore signals are a factor 10 smaller than the observed signals; extracting a signal of core origin remains a challenge.

Quantitative estimates of average geomagnetic axial dipole dominance in deep geological time

A defining characteristic of the recent geomagnetic field is its dominant axial dipole which provides its navigational utility and dictates the shape of the magnetosphere. Going back through time, much less is known about the degree of axial dipole dominance. Here we use a substantial and diverse set of 3D numerical dynamo simulations and recent observation-based field models to derive a power law relationship between the angular dispersion of virtual geomagnetic poles at the equator and the median axial dipole dominance measured at Earth's surface. Applying this relation to published estimates of equatorial angular dispersion implies that geomagnetic axial dipole dominance averaged over 10⁷-10⁹ years has remained moderately high and stable through large parts of geological time. This provides an observational constraint to future studies of the geodynamo and palaeomagnetosphere. It also provides some reassurance as to the reliability of palaeogeographical reconstructions provided by palaeomagnetism.

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.

Electronic correlations and transport in iron at Earth's core conditions

The transport properties of iron under Earth’s inner core conditions are essential input for the geophysical modelling but are poorly constrained experimentally. Here we show that the thermal and electrical conductivity of iron at those conditions remains high even if the electron-electron-scattering (EES) is properly taken into account. This result is obtained by ab initio simulations taking into account consistently both thermal disorder and electronic correlations. Thermal disorder suppresses the non-Fermi-liquid behavior of the body-centered cubic iron phase, hence, reducing the EES; the total calculated thermal conductivity of this phase is 220 Wm⁻¹ K⁻¹ with the EES reduction not exceeding 20%. The EES and electron-lattice scattering are intertwined resulting in breaking of the Matthiessen’s rule with increasing EES. In the hexagonal close-packed iron the EES is also not increased by thermal disorder and remains weak. Our main finding thus holds for the both likely iron phases in the inner core.

The heat and electrical conductivity of Earth’s core matter represent key input quantities for geophysical models of the Earth’s core evolution and geodynamo. Here, the authors show how the scattering due to interactions between electrons has a relatively weak impact on the electrical and thermal conductivities of iron at core conditions.

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50  eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

Low thermal conductivity of iron-silicon alloys at Earth's core conditions with implications for the geodynamo

Earth’s core is composed of iron (Fe) alloyed with light elements, e.g., silicon (Si). Its thermal conductivity critically affects Earth’s thermal structure, evolution, and dynamics, as it controls the magnitude of thermal and compositional sources required to sustain a geodynamo over Earth’s history. Here we directly measured thermal conductivities of solid Fe and Fe–Si alloys up to 144 GPa and 3300 K. 15 at% Si alloyed in Fe substantially reduces its conductivity by about 2 folds at 132 GPa and 3000 K. An outer core with 15 at% Si would have a conductivity of about 20 W m⁻¹ K⁻¹, lower than pure Fe at similar pressure–temperature conditions. This suggests a lower minimum heat flow, around 3 TW, across the core–mantle boundary than previously expected, and thus less thermal energy needed to operate the geodynamo. Our results provide key constraints on inner core age that could be older than two billion-years.

Thermal conductivity of Earth’s core affects Earth’s thermal structure, evolution and dynamics. Based on thermal conductivity measurements of iron–silicon alloys at high pressure and temperature conditions, the authors here propose Earth’s inner core could be older than previously expected.

A silicate dynamo in the early Earth

The Earth’s magnetic field has operated for at least 3.4 billion years, yet how the ancient field was produced is still unknown. The core in the early Earth was surrounded by a molten silicate layer, a basal magma ocean that may have survived for more than one billion years. Here we use density functional theory-based molecular dynamics simulations to predict the electrical conductivity of silicate liquid at the conditions of the basal magma ocean: 100–140 GPa, and 4000–6000 K. We find that the electrical conductivity exceeds 10,000 S/m, more than 100 times that measured in silicate liquids at low pressure and temperature. The magnetic Reynolds number computed from our results exceeds the threshold for dynamo activity and the magnetic field strength is similar to that observed in the Archean paleomagnetic record. We therefore conclude that the Archean field was produced by the basal magma ocean.

Cooling of the iron core in the early Earth may have been too slow to allow for the generation of a magnetic field. Based on quantum mechanical and geodynamical modelling approaches, the authors find that the electrical conductivity of silicate liquid at high pressure and temperature conditions could have been sufficient to generate a silicate dynamo and a magnetic field in the early Earth.

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions

We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). We review in detail two particularly interesting regimes: first, a moderate pressure range up to 60 GPa and, second, the ultra-high pressure of about 360 GPa expected inside the solid inner core of Earth. Electronic correlations in iron under the moderate pressure of several tens GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced body-centered cubic α to hexagonal close-packed [Formula: see text] phase transition. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the [Formula: see text]-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in [Formula: see text]-Fe by many-electron effects; its experimental signatures are analyzed. The next section focuses on the geophysically relevant pressure-temperature regime of the Earth's inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes ([Formula: see text], [Formula: see text] and face-centered-cubic [Formula: see text]) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of [Formula: see text]-Fe and an almost perfect Fermi liquid in the case of [Formula: see text]-Fe. A recent active discussion on the electronic state and transport properties of [Formula: see text]-Fe at the EIC conditions is reviewed in details. Estimations for the dynamical many-electron contribution to the relative phase stability are presented. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework relevant for studies of iron-base systems as well as perspective directions for further development.

Fe Melting Transition: Electrical Resistivity, Thermal Conductivity, and Heat Flow at the Inner Core Boundaries of Mercury and Ganymede

The electrical resistivity and thermal conductivity behavior of Fe at core conditions are important for understanding planetary interior thermal evolution as well as characterizing the generation and sustainability of planetary dynamos. We discuss the electrical resistivity and thermal conductivity of Fe, Co, and Ni at the solid–liquid melting transition using experimental data from previous studies at 1 atm and at high pressures. With increasing pressure, the increasing difference in the change in resistivity of these metals on melting is interpreted as due to decreasing paramagnon-induced electronic scattering contribution to the total electronic scattering. At the melting transition of Fe, we show that the difference in the value of the thermal conductivity on the solid and liquid sides increases with increasing pressure. At a pure Fe inner core boundary of Mercury and Ganymede at ~5 GPa and ~9 GPa, respectively, our analyses suggest that the thermal conductivity of the solid inner core of small terrestrial planetary bodies should be higher than that of the liquid outer core. We found that the thermal conductivity difference on the solid and liquid sides of Mercury’s inner core boundary is ~2 W(mK)−1. This translates into an excess of total adiabatic heat flow of ~0.01–0.02 TW on the inner core side, depending on the relative size of inner and outer core. For a pure Fe Ganymede inner core, the difference in thermal conductivity is ~7 W(mK)−1, corresponding to an excess of total adiabatic heat flow of ~0.02 TW on the inner core side of the boundary. The mismatch in conducted heat across the solid and liquid sides of the inner core boundary in both planetary bodies appears to be insignificant in terms of generating thermal convection in their outer cores to power an internal dynamo suggesting that chemical composition is important.

Turbulent convective length scale in planetary cores

Convection is a fundamental physical process in the fluid cores of planets. It is the primary transport mechanism for heat and chemical species and the primary energy source for planetary magnetic fields. Key properties of convection-such as the characteristic flow velocity and length scale-are poorly quantified in planetary cores owing to the strong dependence of these properties on planetary rotation, buoyancy driving and magnetic fields, all of which are difficult to model using realistic conditions. In the absence of strong magnetic fields, the convective flows of the core are expected to be in a regime of rapidly rotating turbulence¹, which remains largely unexplored. Here we use a combination of non-magnetic numerical models designed to explore this regime to show that the convective length scale becomes independent of the viscosity when realistic parameter values are approached and is entirely determined by the flow velocity and the planetary rotation. The velocity decreases very rapidly at smaller scales, so this turbulent convective length scale is a lower limit for the energy-carrying length scales in the flow. Using this approach, we can model realistically the dynamics of small non-magnetic cores such as the Moon. Although modelling the conditions of larger planetary cores remains out of reach, the fact that the turbulent convective length scale is independent of the viscosity allows a reliable extrapolation to these objects. For the Earth's core conditions, we find that the turbulent convective length scale in the absence of magnetic fields would be about 30 kilometres, which is orders of magnitude larger than the ten-metre viscous length scale. The need to resolve the numerically inaccessible viscous scale could therefore be relaxed in future more realistic geodynamo simulations, at least in weakly magnetized regions.

Paramagnetic-to-Diamagnetic Transition in Dense Liquid Iron and Its Influence on Electronic Transport Properties

The electrical σ and thermal conductivity λ of liquid iron are calculated with spin-polarized density-functional-theory-based simulations over a significant pressure and temperature range using the Kubo-Greenwood formalism. We show that a paramagnetic state is stable in the liquid up to high temperatures at ambient pressure and that the discrepancy between experimental results and spin-degenerate simulations for σ and λ of more than 30% are reduced to within 10% with lower values resulting from the spin-polarized simulations. Along the 3700 K isotherm, we explore the persistence of magnetic fluctuations toward high densities, and beyond 20-50 GPa the liquid becomes diamagnetic, which suggests the existence of a continuous paramagnetic-to-diamagnetic transition. This transition exerts a significant influence on the physical properties of liquid iron, especially on σ and λ, and is potentially of high relevance for dynamo processes in Mercury and Mars.

Geomagnetic polar minima do not arise from steady meridional circulation

Observations of the Earth's magnetic field have revealed locally pronounced field minima near each pole at the core-mantle boundary (CMB). The existence of the polar magnetic minima has long been attributed to the supposed large-scale overturning circulation of molten metal in the outer core: Fluid upwells within the inner core tangent cylinder toward the poles and then diverges toward lower latitudes when it reaches the CMB, where Coriolis effects sweep the fluid into anticyclonic vortical flows. The diverging near-surface meridional circulation is believed to advectively draw magnetic flux away from the poles, resulting in the low intensity or even reversed polar magnetic fields. However, the interconnections between polar magnetic minima and meridional circulations have not to date been ascertained quantitatively. Here, we quantify the magnetic effects of steady, axisymmetric meridional circulation via numerically solving the axisymmetric magnetohydrodynamic equations for Earth's outer core under the magnetostrophic approximation. Extrapolated to core conditions, our results show that the change in polar magnetic field resulting from steady, large-scale meridional circulations in Earth's outer core is less than [Formula: see text] of the background field, significantly smaller than the [Formula: see text] polar magnetic minima observed at the CMB. This suggests that the geomagnetic polar minima cannot be produced solely by axisymmetric, steady meridional circulations and must depend upon additional tangent cylinder dynamics, likely including nonaxisymmetric, time-varying processes.

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.

Electrical resistivity of liquid Fe to 12 GPa: Implications for heat flow in cores of terrestrial bodies

Electrical and thermal transport properties of liquid Fe under high pressure have important implications for the dynamics and thermal evolution of planetary cores and the geodynamo. However, electrical resistivity (ρ) and thermal conductivity (k) of liquid Fe at high pressure still remain contentious properties. To date, only two experimental investigations of ρ of liquid Fe in the pressure region below 7 GPa are reported in literature. Here we report the results of measurements of ρ for solid and liquid Fe (inversely proportional to k through the Wiedemann-Franz law) at pressures from 3 to 12 GPa, using a large multi-anvil press. We show that ρ of liquid Fe decreases as a function of pressure up to the δ-γ-liquid triple point at ~5.2 GPa, and subsequently remains invariant from 6 to 12 GPa, which is consistent with an earlier study on liquid Ni. Our results demonstrate an important effect of solid phase on the structure and properties of liquid Fe. Our values of ρ for solid and liquid Fe are used to calculate k in Mercury’s solid inner core and along the adiabat in the liquid outer cores of Moon, Ganymede, Mercury and Mars. Our robust values of thermal conductivity place the focus on uncertainties in thermal expansion as the cause of variation in values of core conducted heat. Except for Mercury, our adiabatic heat flux values in these terrestrial cores validate the use of similar values used in several previous studies. Our high values of core adiabatic heat flux in Mercury would provide a stabilizing effect on, and lead to an increase in thickness of, the thermally stratified layer at the top of the core.

Helium-Iron Compounds at Terapascal Pressures

We investigate the binary phase diagram of helium and iron using first-principles calculations. We find that helium, which is a noble gas and inert at ambient conditions, forms stable crystalline compounds with iron at terapascal pressures. A FeHe compound becomes stable above 4 TPa, and a FeHe_{2} compound above 12 TPa. Melting is investigated using molecular dynamics simulations, and a superionic phase with sublattice melting of the helium atoms is predicted. We discuss the implications of our predicted helium-iron phase diagram for interiors of giant (exo)planets and white dwarf stars.

Snowball Earth climate dynamics and Cryogenian geology-geobiology

Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO2 was 102 PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO2 rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms.

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Liquid metallic hydrogen (LMH) is the most abundant form of condensed matter in our solar planetary structure. The electronic and thermal transport properties of this metallic fluid are of fundamental interest to understanding hydrogen's mechanism of conduction, atomic or pairing structure, as well as the key input for the magnetic dynamo action and thermal models of gas giants. Here, we report spectrally resolved measurements of the optical reflectance of LMH in the pressure region of 1.4-1.7 Mbar. We analyze the data, as well as previously reported measurements, using the free-electron model. Fitting the energy dependence of the reflectance data yields a dissociation fraction of 65 ± 15%, supporting theoretical models that LMH is an atomic metallic liquid. We determine the optical conductivity of LMH and find metallic hydrogen's static electrical conductivity to be 11,000-15,000 S/cm, substantially higher than the only earlier reported experimental values. The higher electrical conductivity implies that the Jovian and Saturnian dynamo are likely to operate out to shallower depths than previously assumed, while the inferred thermal conductivity should provide a crucial experimental constraint to heat transport models.

Thermal conductivity measurements of proton-heated warm dense aluminum

Thermal conductivity is one of the most crucial physical properties of matter when it comes to understanding heat transport, hydrodynamic evolution, and energy balance in systems ranging from astrophysical objects to fusion plasmas. In the warm dense matter regime, experimental data are very scarce so that many theoretical models remain untested. Here we present the first thermal conductivity measurements of aluminum at 0.5–2.7 g/cc and 2–10 eV, using a recently developed platform of differential heating. A temperature gradient is induced in a Au/Al dual-layer target by proton heating, and subsequent heat flow from the hotter Au to the Al rear surface is detected by two simultaneous time-resolved diagnostics. A systematic data set allows for constraining both thermal conductivity and equation-of-state models. Simulations using Purgatorio model or Sesame S27314 for Al thermal conductivity and LEOS for Au/Al release equation-of-state show good agreement with data after 15 ps. Discrepancy still exists at early time 0–15 ps, likely due to non-equilibrium conditions.

Local magnetic moments in iron and nickel at ambient and Earth's core conditions

Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron-electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth's core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.

Exploring the hidden interior of the Earth with directional neutrino measurements

Roughly 40% of the Earth's total heat flow is powered by radioactive decays in the crust and mantle. Geo-neutrinos produced by these decays provide important clues about the origin, formation and thermal evolution of our planet, as well as the composition of its interior. Previous measurements of geo-neutrinos have all relied on the detection of inverse beta decay reactions, which are insensitive to the contribution from potassium and do not provide model-independent information about the spatial distribution of geo-neutrino sources within the Earth. Here we present a method for measuring previously unresolved components of Earth's radiogenic heating using neutrino-electron elastic scattering and low-background, direction-sensitive tracking detectors. We calculate the exposures needed to probe various contributions to the total geo-neutrino flux, specifically those associated to potassium, the mantle and the core. The measurements proposed here chart a course for pioneering exploration of the veiled inner workings of the Earth.

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Kinematics and dynamics of the East Pacific Rise linked to a stable, deep-mantle upwelling

Earth's tectonic plates are generally considered to be driven largely by negative buoyancy associated with subduction of oceanic lithosphere. In this context, mid-ocean ridges (MORs) are passive plate boundaries whose divergence accommodates flow driven by subduction of oceanic slabs at trenches. We show that over the past 80 million years (My), the East Pacific Rise (EPR), Earth's dominant MOR, has been characterized by limited ridge-perpendicular migration and persistent, asymmetric ridge accretion that are anomalous relative to other MORs. We reconstruct the subduction-related buoyancy fluxes of plates on either side of the EPR. The general expectation is that greater slab pull should correlate with faster plate motion and faster spreading at the EPR. Moreover, asymmetry in slab pull on either side of the EPR should correlate with either ridge migration or enhanced plate velocity in the direction of greater slab pull. Based on our analysis, none of the expected correlations are evident. This implies that other forces significantly contribute to EPR behavior. We explain these observations using mantle flow calculations based on globally integrated buoyancy distributions that require core-mantle boundary heat flux of up to 20 TW. The time-dependent mantle flow predictions yield a long-lived deep-seated upwelling that has its highest radial velocity under the EPR and is inferred to control its observed kinematics. The mantle-wide upwelling beneath the EPR drives horizontal components of asthenospheric flows beneath the plates that are similarly asymmetric but faster than the overlying surface plates, thereby contributing to plate motions through viscous tractions in the Pacific region.

Revealing the Earth's mantle from the tallest mountains using the Jinping Neutrino Experiment

The Earth’s engine is driven by unknown proportions of primordial energy and heat produced in radioactive decay. Unfortunately, competing models of Earth’s composition reveal an order of magnitude uncertainty in the amount of radiogenic power driving mantle dynamics. Recent measurements of the Earth’s flux of geoneutrinos, electron antineutrinos from terrestrial natural radioactivity, reveal the amount of uranium and thorium in the Earth and set limits on the residual proportion of primordial energy. Comparison of the flux measured at large underground neutrino experiments with geologically informed predictions of geoneutrino emission from the crust provide the critical test needed to define the mantle’s radiogenic power. Measurement at an oceanic location, distant from nuclear reactors and continental crust, would best reveal the mantle flux, however, no such experiment is anticipated. We predict the geoneutrino flux at the site of the Jinping Neutrino Experiment (Sichuan, China). Within 8 years, the combination of existing data and measurements from soon to come experiments, including Jinping, will exclude end-member models at the 1σ level, define the mantle’s radiogenic contribution to the surface heat loss, set limits on the composition of the silicate Earth, and provide significant parameter bounds for models defining the mode of mantle convection.

An early geodynamo driven by exsolution of mantle components from Earth's core

Terrestrial core formation occurred in the early molten Earth by gravitational segregation of immiscible metal and silicate melts, stripping iron-loving elements from the silicate mantle to the metallic core1–3, and leaving rock-loving components behind. Here we performed experiments showing that at high enough temperature, Earth’s major rock-loving component, magnesium oxide, can also dissolve in core-forming metallic melts. Our data clearly point to a dissolution reaction, and are in agreement with recent DFT calculations4. Using core formation models5, we further show that a high-temperature event during Earth’s accretion (such as the Moon-forming giant impact6) can contribute significant amounts of magnesium to the early core. As it subsequently cools, the ensuing exsolution7 of buoyant magnesium oxide generates a substantial amount of gravitational energy. This energy is comparable to if not significantly higher than that produced by inner core solidification8 — the primary driver of the Earth’s current magnetic field9–11. Since the inner core is too young12 to explain the existence of an ancient field prior to ~1 billion years, our results solve the conundrum posed by the recent paleomagnetic observation13 of an ancient field at least 3.45 Gyr old.

Direct measurement of thermal conductivity in solid iron at planetary core conditions

The conduction of heat through minerals and melts at extreme pressures and temperatures is of central importance to the evolution and dynamics of planets. In the cooling Earth's core, the thermal conductivity of iron alloys defines the adiabatic heat flux and therefore the thermal and compositional energy available to support the production of Earth's magnetic field via dynamo action. Attempts to describe thermal transport in Earth's core have been problematic, with predictions of high thermal conductivity at odds with traditional geophysical models and direct evidence for a primordial magnetic field in the rock record. Measurements of core heat transport are needed to resolve this difference. Here we present direct measurements of the thermal conductivity of solid iron at pressure and temperature conditions relevant to the cores of Mercury-sized to Earth-sized planets, using a dynamically laser-heated diamond-anvil cell. Our measurements place the thermal conductivity of Earth's core near the low end of previous estimates, at 18-44 watts per metre per kelvin. The result is in agreement with palaeomagnetic measurements indicating that Earth's geodynamo has persisted since the beginning of Earth's history, and allows for a solid inner core as old as the dynamo.

Experimental determination of the electrical resistivity of iron at Earth's core conditions

Earth continuously generates a dipole magnetic field in its convecting liquid outer core by a self-sustained dynamo action. Metallic iron is a dominant component of the outer core, so its electrical and thermal conductivity controls the dynamics and thermal evolution of Earth's core. However, in spite of extensive research, the transport properties of iron under core conditions are still controversial. Since free electrons are a primary carrier of both electric current and heat, the electron scattering mechanism in iron under high pressure and temperature holds the key to understanding the transport properties of planetary cores. Here we measure the electrical resistivity (the reciprocal of electrical conductivity) of iron at the high temperatures (up to 4,500 kelvin) and pressures (megabars) of Earth's core in a laser-heated diamond-anvil cell. The value measured for the resistivity of iron is even lower than the value extrapolated from high-pressure, low-temperature data using the Bloch-Grüneisen law, which considers only the electron-phonon scattering. This shows that the iron resistivity is strongly suppressed by the resistivity saturation effect at high temperatures. The low electrical resistivity of iron indicates the high thermal conductivity of Earth's core, suggesting rapid core cooling and a young inner core less than 0.7 billion years old. Therefore, an abrupt increase in palaeomagnetic field intensity around 1.3 billion years ago may not be related to the birth of the inner core.

Powering Earth's dynamo with magnesium precipitation from the core

Earth's global magnetic field arises from vigorous convection within the liquid outer core. Palaeomagnetic evidence reveals that the geodynamo has operated for at least 3.4 billion years, which places constraints on Earth's formation and evolution. Available power sources in standard models include compositional convection (driven by the solidifying inner core's expulsion of light elements), thermal convection (from slow cooling), and perhaps heat from the decay of radioactive isotopes. However, recent first-principles calculations and diamond-anvil cell experiments indicate that the thermal conductivity of iron is two or three times larger than typically assumed in these models. This presents a problem: a large increase in the conductive heat flux along the adiabat (due to the higher conductivity of iron) implies that the inner core is young (less than one billion years old), but thermal convection and radiogenic heating alone may not have been able to sustain the geodynamo during earlier epochs. Here we show that the precipitation of magnesium-bearing minerals from the core could have served as an alternative power source. Equilibration at high temperatures in the aftermath of giant impacts allows a small amount of magnesium (one or two weight per cent) to partition into the core while still producing the observed abundances of siderophile elements in the mantle and avoiding an excess of silicon and oxygen in the core. The transport of magnesium as oxide or silicate from the cooling core to underneath the mantle is an order of magnitude more efficient per unit mass as a source of buoyancy than inner-core growth. We therefore conclude that Earth's dynamo would survive throughout geologic time (from at least 3.4 billion years ago to the present) even if core radiogenic heating were minimal and core cooling were slow.

Palaeomagnetic field intensity variations suggest Mesoproterozoic inner-core nucleation

The Earth's inner core grows by the freezing of liquid iron at its surface. The point in history at which this process initiated marks a step-change in the thermal evolution of the planet. Recent computational and experimental studies have presented radically differing estimates of the thermal conductivity of the Earth's core, resulting in estimates of the timing of inner-core nucleation ranging from less than half a billion to nearly two billion years ago. Recent inner-core nucleation (high thermal conductivity) requires high outer-core temperatures in the early Earth that complicate models of thermal evolution. The nucleation of the core leads to a different convective regime and potentially different magnetic field structures that produce an observable signal in the palaeomagnetic record and allow the date of inner-core nucleation to be estimated directly. Previous studies searching for this signature have been hampered by the paucity of palaeomagnetic intensity measurements, by the lack of an effective means of assessing their reliability, and by shorter-timescale geomagnetic variations. Here we examine results from an expanded Precambrian database of palaeomagnetic intensity measurements selected using a new set of reliability criteria. Our analysis provides intensity-based support for the dominant dipolarity of the time-averaged Precambrian field, a crucial requirement for palaeomagnetic reconstructions of continents. We also present firm evidence for the existence of very long-term variations in geomagnetic strength. The most prominent and robust transition in the record is an increase in both average field strength and variability that is observed to occur between a billion and 1.5 billion years ago. This observation is most readily explained by the nucleation of the inner core occurring during this interval; the timing would tend to favour a modest value of core thermal conductivity and supports a simple thermal evolution model for the Earth.

Saturation of electrical resistivity of solid iron at Earth's core conditions

We report on the temperature dependence of the electrical resistivity of solid iron at high pressure, up to and including conditions likely to be found at the centre of the Earth. We have extended some of the calculations of the resistivities of pure solid iron we recently performed at Earth's core conditions (Pozzo et al. in Earth Planet Sci Lett 393:159-164, 2014) to lower temperature. We show that at low temperature the resistivity increases linearly with temperature, and saturates at high temperature. This saturation effect is well known as the Mott-Ioffe-Regel limit in metals, but has been largely ignored to estimate the resistivity of iron at Earth's core conditions. Recent experiments (Gomi et al. in Phys Earth Planet Int 224:88-103, 2013) coupled new high pressure data and saturation to predict the resitivity of iron and iron alloys at Earth's core conditions, and reported values up to three times lower than previous estimates, confirming recent first principles calculations (de Koker et al. in Proc Natl Acad Sci 109:4070-4073, 2012; Pozzo et al. in Nature 485:355-358, 2012, Phys Rev B 87:014110-10, 2013, Earth Planet Sci Lett 393:159-164, 2014; Davies et al. in Nat Geosci 8:678-685, 2015). The present results support the saturation effect idea.

Pressure-induced changes in structural and dynamic properties of liquid Fe close to the melting line. An ab initio study

The static and dynamic properties of liquid Fe at high pressure and temperature have been studied using an ab initio molecular dynamics method. We have focused on four thermodynamic states at pressures of 27, 42, 50 and 58 GPa for which x-ray scattering data are available. The calculated static structure shows very good agreement with the available experimental data, including an asymmetric second peak which becomes more marked with increasing pressure. The dynamical structure reveals the existence of propagating density fluctuations and the associated dispersion relation has also been determined. The relaxation mechanisms for the density fluctuations have been analyzed in terms of a model with two decay channels (fast and slow, respectively). We found that the thermal relaxation proceeds along the slow decaying channel whereas the fast one is that of the viscoelastic relaxation. The possible coupling between longitudinal and transverse excitation modes has been investigated by looking at specific signatures in two wavevector regions: the first one is located around the position of the main peak of the structure factor, qp, as suggested by the recently reported appearance of high frequency transverse waves in liquid Li under high pressures; the second region is around qp/2, as suggested by the recent finding of transverse acoustic modes in inelastic x-ray scattering intensities of liquid Fe at ambient pressure. Finally, results are also reported for several transport coefficients.

Gyre-driven decay of the Earth's magnetic dipole

Direct observations indicate that the magnitude of the Earth's magnetic axial dipole has decreased over the past 175 years; it is now 9% weaker than it was in 1840. Here we show how the rate of dipole decay may be controlled by a planetary-scale gyre in the liquid metal outer core. The gyre's meridional limbs on average transport normal polarity magnetic flux equatorward and reverse polarity flux poleward. Asymmetry in the geomagnetic field, due to the South Atlantic Anomaly, is essential to the proposed mechanism. We find that meridional flux advection accounts for the majority of the dipole decay since 1840, especially during times of rapid decline, with magnetic diffusion making an almost steady contribution generally of smaller magnitude. Based on the morphology of the present field, and the persistent nature of the gyre, the current episode of dipole decay looks set to continue, at least for the next few decades.

The magnitude of the Earth's magnetic dipole has decreased by 9% over the past 175 years. Here, the authors suggest that the rate of dipole decay is controlled by a huge gyre in the liquid metal outer core acting on a field asymmetry, and that decay is set to continue for the next few decades.