On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10 ³ Poise     

Phase relations of iron and iron–nickel alloys up to 300 GPa: Implications for composition and structure of the Earth's inner core

We have investigated the phase relations of iron and iron–nickel alloys with 18 to 50 wt.% Ni up to over 300 GPa using a laser-heated diamond-anvil cell. The synchrotron X-ray diffraction measurements show the wide stability of hcp-iron up to 301 GPa and 2000 K and 319 GPa and 300 K without phase transition to dhcp, orthorhombic, or bcc phases. On the other hand, the incorporation of nickel has a remarkable effect on expanding the stability field of fcc phase. The geometry of the temperature–composition phase diagram of iron–nickel alloys suggests that the hcp–fcc–liquid triple point is located at 10 to 20 wt.% Ni at the pressure of the inner core boundary. The fcc phase could crystallize depending on the nickel and silicon contents in the Earth's core, both of which are fcc stabilizer.     

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.     

SNREI地球对表面负荷和引潮力的形变响应

基于PREM模型，利用非自转、球型分层、各向同性、理想弹性（SNREI）地球的形变理论，讨论了地球在不同驱动力作用下的形变特征．采用地球位移场方程的4阶Runge Kutta数值积分方法，解算了在表面负荷和日月引潮力作用下地球表面和内部形变和扰动位，并给出了地球表面的负荷Love数和体潮Love数．结果表明在固体内核中的形变很小，液核中低阶(n＜10)负荷位移随半径的变化非常复杂．当负荷阶数超过10时，地核中的形变和扰动位都很小，地球的响应主要表现为弹性地幔中的径向位移，且随深度增加急剧减弱，负荷阶数越高这种衰减的速度越快．SNREI地球的地表负荷Love数和体潮Love数与信号频率的依赖关系很弱．在计算体潮Love数的过程中，采用了SNREI地球的运动方程，同时考虑了由于地球自转和椭率引起的核幔边界附加压力，这一近似处理方法获得的结果能很好地符合地球表面重力潮汐实际观测结果．     

Immiscible two-liquid regions in the Fe-O-S system at high pressure: Implications for planetary cores

We have determined phase relations in the Fe-O and Fe-O-S systems in the range of 15-21 GPa and 1825-2300 °C. Below the liquidus temperatures, solid FeO and metallic liquids are observed in both the Fe-O and the Fe-O-S systems. An immiscible two-liquid region exists in the Fe-O binary system in the pressure range investigated, and the immiscibility gap between Fe-rich metallic liquid and FeO-rich ionic liquid does not greatly change with either pressure or temperature. On the other hand, an immiscible two-liquid region in the Fe-O-S ternary system narrows significantly with increasing pressure at constant temperature and vice versa, and it almost disappears at 21 GPa, and 2300 °C. Immiscible two-liquid regions are thus not expected to exist in the Fe-O-S system in the Earth's core, suggesting that both oxygen and sulfur can be incorporated into the core. Our results are consistent with a geochemical model for the core containing 5.8 wt.% oxygen and 1.9 wt.% sulfur as proposed by McDonough and Sun [McDonough, W.F., Sun, S.-S., 1995. The composition of the Earth. Chem. Geol. 120, 223-253].     

Potassium partitioning into molten iron alloys at high-pressure: Implications for Earth's core

The partition coefficients of potassium, D_K, between molten sanidine, KAlSi₃O₈, and molten roedderite, K₂Mg₅Si₁₂O₃₀, with FeS-rich alloy and pure Fe metal liquids have been investigated in a multi-anvil press, between 5 and 15 GPa, at a temperature of 2173 K, and at an oxygen fugacity between 0.5 and 3 log units below the iron-wüstite (IW) buffer. No pressure dependence of the D_K coefficients in sulphur-free and sulphur-bearing systems was found within the investigated pressure range. We also observed minor effect of the silicate melt composition for an nbo/t (non-bridging oxygen to tetrahedral cation ratio) higher than 0.8 ± 0.4. In contrast, the partitioning of potassium varies strongly with the metallic phase composition, with an increase of K-solubility in the metallic liquid for high sulphur and oxygen contents.We review all available high-pressure data to obtain reliable D_K coefficients for the interaction between molten silicates and Fe-alloy liquids at pressures and temperatures relevant to those of core formation in a terrestrial magma ocean. The dominant controlling parameters appear to be the temperature and the chemical composition of the metallic phase, with D_K coefficients significantly increased with temperature, and with the sulphur and oxygen contents of the Fe-alloy liquid. Our considerations distinguish two extreme cases, with an S-free or S-bearing iron core, which yield K contents of ∼25 or ∼250 ppm, respectively. These two extreme values have very different consequences for thermal budget models of the Earth's core since its formation.     

On asymptotics of low-frequency oscillations of the liquid core: 2. Frequency dependence of the inertial core-mantle coupling

New, unique information on the inertial and dissipative coupling of the liquid core and the mantle has been retrieved from modern high-precision (radiointerferometer and GPS) data on tidal variations in the rotation velocity and nutation of the Earth. Comparison of theoretical and observed data provided new estimates for the dynamic flattening of the outer liquid and the inner solid cores, mantle quality factor, viscosity of the liquid core, and electromagnetic coupling of the liquid core and the mantle [Molodensky, 2004, 2006]. As was shown in the first part of the paper [Molodensky, 2008] (further referred to as [I]), generation of eddy flows in Proudman-Taylor columns, whose orientation is controlled by the topography of the liquid core-mantle boundary, should be taken into account for correct estimation of the inertial coupling (see formulas (8) and (34) in [I]). The range of periods within which this effect plays a significant role is determined by the decay time of these flows. This time is estimated in the paper for the case where dissipation is related to viscous friction at the core-mantle boundary or with the electromagnetic coupling of the liquid core and the mantle. Because of significant uncertainties in modern data on the viscosity of the liquid core, the magnetic field intensity at the core-mantle boundary, and the electrical conductivity of the lower mantle, the dissipative coupling of the liquid core and the mantle cannot be calculated as yet. However, as shown in the paper, the decay time of eddy flows is connected with the attenuation time of subdiurnal free nutation and with the liquid core viscosity. This enables the estimation of the frequency dependence of the dissipative coupling in a fairly wide range. It is shown that the range of periods for which relations (8) and (34) in [I] are valid encompasses the best-studied length-of-day variations and, therefore, these relations are applicable to analysis of the majority of modern data.     

Electrical conductivity of molten FeNiSC core mix

The electrical conductivity of liquid (Fe₉₀Ni₁₀)₃S₂ saturated with 2.6 weight percent carbon averages 2.7·10⁵ mho/m at 1000°C and zero pressure. This may imply a slightly lower electrical conductivity for the earth's core than that obtained by extrapolating the properties of pure liquid iron and solid iron alloys to core pressures and temperatures. Although a sulphur-rich core would have a smaller proportion of sulphur, the effect of lowering the sulphur content of the FeNiSC liquid to about 15 weight percent would be unlikely to increase the conductivity above 5·10⁵ mho/m.     

Composition of the core,II. Effect of high pressure on solubility of FeO in molten iron

An experimental and theoretical investigation of the effect of pressure on the solubility of FeO in molten iron has been carried out. Analyses of shock-wave compression data on iron oxides combined with measurements of the FeO bond length in “metallic” oxides suggest that the partial molar volume of FeO(V^*) dissolved in molten iron is substantially smaller than that of molten wüstite. Hence the effect of high pressure should be to increase the solubility of FeO in molten iron at a given temperature. This inference is confirmed by an experimental investigation of the effect of pressure on the position of the FeFeO eutectic. Thermodynamic calculations based on these experiments yield an estimate forV^* which is in reasonable agreement with the theoretical estimates. The experimental value ofV^* is used to calculate the effect of high pressure upon the FeFeO phase diagram. Solubility of FeO in molten iron increases sharply with pressure, the liquid immiscibility region contracts and disappears around 20 GPa and it is predicted that the FeFeO phase diagram should resemble a simple eutectic system above about 20 GPa. Analogous calculations predict that the solubility of FeO in molten iron in equilibrium with magnesiowüstite (Mg_0.8Fe_0.2)O at 2500°C increase from 14 mol.%(P = 0) to above 25 mol.% at 20 GPa. If the core formed by segregation of metallic iron originally dispersed throughout the earth, it seems inevitable that it would dissolved large amounts of FeO, thereby accounting for the observation that the density of the outer core is substantially smaller than that of pure iron under correspondingP, T conditions.     

Phase transformations in MSiO4 compounds at high pressures and their geophysical implications

The phase behaviour of MSiO₄ compounds (MHf, Zr, U and Th0 has been investigated at high pressures and temperatures in a diamond-anvil press coupled with laser heating. All of these compounds have been found to undergo two or perhaps three phase transformations at pressures below 300 kbar. The high-pressure phase transformations of these compounds differ from one another, with the exception of HfSiO₄ and ZrSiO₄, which undergo identical phase transformations. The ultimate phase assemblages of these compounds are of dense component dioxides (although this is yet to be confirmed in ThSiO₄). It is suggested that the heat-producing elements U and Th would exist as dioxide solid solutions rather than silicates in the deep interior of the earth. Moreover, the densities of these dioxides are more than twice as great as mantle silicates and even slightly greater than pure iron under similar P, T conditions. Gravitational separation due to mandle convection may transport these dioxides to the deep interior of the earth to form deep heat sources. It is also suggested, however, that these deep heat sources are located in the inner-outer core boundary instead of in the lower mantle.     

Inner core anisotropy, anomalies in the time-averaged paleomagnetic field, and polarity transition paths

The diffusion of the dynamo-generated magnetic field into the electrically conducting inner core of the Earth may provide an explanation for several problematic aspects of long-term geomagnetic field behavior. We present a simple model which illustrates how an induced magnetization in the inner core which changes on diffusive timescales can provide a biasing field which could produce the observed anomalies in the time-averaged field and polarity reversals. The Earth's inner core exhibits an anisotropy in seismic velocities which can be explained by a preferred orientation of a polycrystalline aggregate of hexagonal close-packed (hcp) iron, an elastically anisotropic phase. Room temperature analogs of hcp iron also exhibit a strong anisotropy of magnetic susceptibility, ranging from 15 to 40% anisotropy. At inner core conditions the magnetic susceptibility of hcp iron is estimated to be between 10⁻⁴ and 10⁻³ SI. We speculate here that the anisotropy in magnetic susceptibility in the inner core could produce the observed anomalies in the time-averaged paleomagnetic field, polarity asymmetry, and recurring transitional virtual geomagnetic pole (VGP) positions.     

Another look at the core density deficit of Earth’s outer core

A constraint adopted in several geochemical studies of core composition is that the core density deficit (cdd) is 10%, with the implication that this number is based on robust geophysical evidence. The cdd is the perceived difference between the density of pure iron at core conditions and the seismically-determined density of the outer core. The importance of the cdd is that it limits the concentration of allowable light elements, such as sulfur and silicon, which, when mixed with Fe, or an Fe-Ni alloy, comprise the geochemical model of the inner core.We present evidence that the value of 10% for the cdd of the outer core is too high. Using a thermal-pressure equation-of-state, we find that for assumed melting temperatures of pure iron at the inner-outer core (ICB) pressure of 330 GPa ranging from 7500 to 4800 K, the cdd ranges from 2.9 to 7%, respectively. Reports that the cdd value of the outer core is less than 10% are found in a number of shock-wave studies, but the values reported here are apparently the lowest. Our cdd value for an assumed melting temperature of 6000 K for iron at 330 GPa is 5.4% and is compatible with proposed concentrations of Si and S impurities found from solubility studies at high P and T.     

Corrugations on the core boundary interfaces due to constitutional supercooling and effects on motion in a predominantly stratified liquid core

With the notion that interface and boundary layer phenomena play an important part in those geophysical processes which, by observation appear to be related to the earth's internal boundaries between the solid and liquid phases of its core and mantle, constitutional supercooling suggests itself as a mechanism capable of generating and maintaining inhomogeneities in concentration and density at the boundaries of the liquid core. The mechanism of constitutional supercooling requires a slow overgrowth of mantle and core, and, it implies that this growth process is associated with a selective partitioning of certain impurities shared in different concentrations by the liquid core and the solid phases of mantle and inner core. It can lead to the formation of regular (quasi-periodic) corrugations of the core-mantle and the inner-outer core boundaries with amplitudes of the order of 1 km. Mass redistributions, off-setting continually regenerated concentration and density inhomogeneities, provide a mechanism for core motion in the form of concentration currents. A regular distribution of corrugations or humps may give rise to (zonal) patterns of closed loops of concentration currents either in layers adjacent to the solid-liquid interfaces, or in loops extending through the entire outer core. The development of regular flow patterns should be enhanced if, referable to one particular constituent of the liquid phase, some parts of the solid-liquid interfaces acted as sources, others as sinks.     

Models for the origin and composition of the earth,and the hypothesis of potassium in the Earth's core

Progress in understanding the condensation of planetary constituents from a solar nebula necessitates a re-examination of models for the origin and composition of the Earth. All models which appear to be viable require the Earth to have an Fe–FeS core and the full, or nearly full, solar (i.e. chondritic) K/Si ratio. The crust and upper mantle do not contain the requisite potassium for the entire Earth to have the solar K/Si ratio. Therefore, these models require that much of the Earth's potassium, about 80–90%, must be in the deep interior—in the lower mantle or in the core.The hypothesis that a substantial fraction of the Earth's potassium is in the Fe–FeS core is based on the chalcophilic behavior of potassium. Data including the stability of K₂S, the occurrence of potassium in sulfide phases in meteorites and in metallurgical systems, and most importantly, experiments on potassium partitioning between solid silicates and Fe–FeS melts support this hypothesis. The present data appear to require at least several percent of the Earth's total potassium to be in the core. Incorporation of much larger amounts of potassium into the core, possibly most of the 80–90% of the Earth's potassium which is postulated to be in the deep interior, is not contradicted by the present data. Additional experimental data, at high pressures, are required before quantitative estimates of the core's potassium content can be made.It is likely that⁴⁰K is a significant heat source in the core. Decay of⁴⁰K is a plausible energy source to drive core convection to maintain the geomagnetic field, and to drive mantle convection and seafloor spreading.     

Self-diffusion in liquid Fe at high pressure

The self-diffusivity of liquid iron has been measured between 2 and 20 GPa and 1883 and 2393 K. There is a large pressure dependence across the pressure range studied and simple Arrhenius extrapolation to outer core conditions yields unrealistically low diffusivities. The large pressure and temperature range covered, however, allows different a priori diffusion models to be tested using the experimental results. The free volume model [J. Chem. Phys. 31 (1959) 1164] is found to be in excellent agreement with the experimental data and provides a basis for extrapolation of the results to outer core conditions. An extrapolation to core–mantle boundary (CMB) pressure at 4300 K yields a self-diffusivity for liquid iron of 2.5×10⁻⁵ cm² s⁻¹, which corresponds to a viscosity of 11 mPa s, in reasonable agreement with previous, theoretical, estimates.     

Low-frequency dilatational wave propagation through fully-saturated poroelastic media

The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.     

The effect of the electric conductivity of the Earth's mantle on the Ekman-Hartman hydromagnetic boundary layer and on the magnetic diffusion region

Summary The effect of the electrical conductivity of the Earth's mantle on the non-stationary Ekman-Hartman hydromagnetic boundary layer is investigated under the conditions in the Earth's core. It is shown that under an impulsive change of rotation of the mantle Alfvén waves can only be excited if the Ekman-Hartman hydromagnetic boundary layer is in a non-stationary state, i.e. at a time when its structure is developing. The intensity of the Alfvén waves is very small, because the excitation is more of a mechanic nature than magnetic.     

Iron content of synthetic phlogopite as a function of growth rate

During monocrystalline growth experiments of Fe-poor phlogopite from hydrothermal potash aqueous solutions, the iron content of the mica has been found to be growth-rate-dependent. It is shown that in our experimental conditions this kinetic effect dominates possible changes of equilibrium iron content connected with variations of solution composition, oxygen fugacity and growth temperature. To a lesser extent, titanium is found to follow the same trend.     

Time dependent calibration of a sediment extraction scheme

Sediment extraction methods to quantify metal concentration in aquatic sediments usually present limitations in accuracy and reproducibility because metal concentration in the supernatant is controlled to a large extent by the physico-chemical properties of the sediment that result in a complex interplay between the solid and the solution phase. It is suggested here that standardization of sediment extraction methods using pure mineral phases or reference material is futile and instead the extraction processes should be calibrated using site-specific sediments before their application. For calibration, time dependent release of metals should be observed for each leachate to ascertain the appropriate time for a given extraction step. Although such an approach is tedious and time consuming, using iron extraction as an example, it is shown here that apart from quantitative data such an approach provides additional information on factors that play an intricate role in metal dynamics in the environment. Single step ascorbate, HCl, oxalate and dithionite extractions were used for targeting specific iron phases from saltmarsh sediments and their response was observed over time in order to calibrate the extraction times for each extractant later to be used in a sequential extraction. For surficial sediments, an extraction time of 24 h, 1 h, 2 h and 3 h was ascertained for ascorbate, HCl, oxalate and dithionite extractions, respectively. Fluctuations in iron concentration in the supernatant over time were ubiquitous. The adsorption-desorption behavior is possibly controlled by the sediment organic matter, formation or consumption of active exchange sites during extraction and the crystallinity of iron mineral phase present in the sediments.     

The Effects of the Concentration of Olivine Xenocrysts on the Viscosity of Kimberlite Melts: Experimental Evidence

The study of viscosity in sub-liquidus heterogeneous media, which includes kimberlite magma at the pressures and temperatures that prevail in the mantle, is an urgent task. We have conducted experiments in the serpentine–olivine, serpentine–CaCO3?olivine, and native kimberlite–olivine systems at a pressure of 4 GPa and temperatures of 1400?1600°С in a BARS high-pressure device using the technique of a falling Pt pellet. The samples were examined after experiments to find fine-grained chilled mass of crystals where the Pt pellet was observed at the time of chilling. The concentration of the solid phase was varied in the experiments between 10 and 50 wt %. We showed that when 50 wt % of olivine grains has been introduced, it was not possible to detect the motion of the Pt pellet, while when the concentration of olivine xenocrysts reached 10 wt %, the Pt pellet very rapidly descended to the bottom of the reaction volume. Viscosity was calculated using the Stokes method. We found that the viscosity of a homogeneous kimberlite melt at 4 GPa and 1600°С is below 2 Pa s, with the viscosity of a melt that contained up to 10 wt % of the solid phase being approximately constant. A kimberlite melt that contained 30 wt % of the solid phase had a viscosity on the order of 100 Pa s, while with 50 wt % of the solid phase the relative viscosity of an ultrabasic system increased to reach values over 1000 Pa s.