Core-mantle equilibrium - Comments on a paper by R. Brett
Critique of paper on earth core-mantle chemical equilibrium, considering upper mantle element abundance, oxidation state and volatiles nature
Ringwood, A. E.↗
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Molybdenum Valence in Basaltic Silicate Melts: Effects of Temperature and Pressure
The metal-silicate partitioning behavior of molybdenum has been used as a test for equilibrium core formation hypotheses [for example, 1-6]. However, current models that apply experimental data to equilibrium core-mantle differentiation infer the oxidation state of molybdenum from solubility data or from multivariable coefficients from metal-silicate partitioning data [1,3,7]. Molybdenum, a multi-valent element with a valence transition near the fO2 of interest for core formation (approx.IW-2) will be sensitive to changes in fO2 of the system and silicate melt structure. In a silicate melt, Mo can occur in either 4+ or 6+ valence state, and Mo(6+) can be either octahedrally or tetrahedrally coordinated. Here we present X-ray absorption near edge structure (XANES) measurements of Mo valence in basaltic run products at a range of P, T, and fO2 and further quantify the valence transition of Mo.
Danielson, L. R.↗
Sulfur in Earth's Mantle and Its Behavior During Core Formation
The density of Earth's outer core requires that about 5-10% of the outer core be composed of elements lighter than Fe-Ni; proposed choices for the "light element" component of Earth's core include H, C, O, Si, S, and combinations of these elements [e.g. 1]. Though samples of Earth's core are not available, mantle samples contain elemental signatures left behind from the formation of Earth's core. The abundances of siderophile (metal-loving) elements in Earth's mantle have been used to gain insight into the early accretion and differentiation history of Earth, the process by which the core and mantle formed, and the composition of the core [e.g. 2-4]. Similarly, the abundance of potential light elements in Earth's mantle could also provide constraints on Earth's evolution and core composition. The S abundance in Earth's mantle is 250 ( 50) ppm [5]. It has been suggested that 250 ppm S is too high to be due to equilibrium core formation in a high pressure, high temperature magma ocean on early Earth and that the addition of S to the mantle from the subsequent accretion of a late veneer is consequently required [6]. However, this earlier work of Li and Agee [6] did not parameterize the metalsilicate partitioning behavior of S as a function of thermodynamic variables, limiting the different pressure and temperature conditions during core formation that could be explored. Here, the question of explaining the mantle abundance of S is revisited, through parameterizing existing metal-silicate partitioning data for S and applying the parameterization to core formation in Earth.
Chabot, Nancy L.↗
Implications for Core Formation of the Earth from High Pressure-Temperature Au Partitioning Experiments
Siderophile elements in the Earth.s mantle are depleted relative to chondrites. This is most pronounced for the highly siderophile elements (HSEs), which are approximately 400x lower than chondrites. Also remarkable is the relative chondritic abundances of the HSEs. This signature has been interpreted as representing their sequestration into an iron-rich core during the separation of metal from silicate liquids early in the Earth's history, followed by a late addition of chondritic material. Alternative efforts to explain this trace element signature have centered on element partitioning experiments at varying pressures, temperatures, and compositions (P-T-X). However, first results from experiments conducted at 1 bar did not match the observed mantle abundances, which motivated the model described above, a "late veneer" of chondritic material deposited on the earth and mixed into the upper mantle. Alternatively, the mantle trace element signature could be the result of equilibrium partitioning between metal and silicate in the deep mantle, under P-T-X conditions which are not yet completely identified. An earlier model determined that equilibrium between metal and silicate liquids could occur at a depth of approximately 700 km, 27(plus or minus 6) GPa and approximately 2000 (plus or minus 200) C, based on an extrapolation of partitioning data for a variety of moderately siderophile elements obtained at lower pressures and temperatures. Based on Ni-Co partitioning, the magma ocean may have been as deep as 1450 km. At present, only a small range of possible P-T-X trace element partitioning conditions has been explored, necessitating large extrapolations from experimental to mantle conditions for tests of equilibrium models. Our primary objective was to reduce or remove the additional uncertainty introduced by extrapolation by testing the equilibrium core formation hypothesis at P-T-X conditions appropriate to the mantle.
Danielson, L. R.↗
Protostellar formation in rotating interstellar clouds. IV Nonisothermal collapse
Radiative transfer in the Eddington approximation is included in a multidimensional, self-gravitational, hydrodynamical computer code. Details of the numerical solution and thermodynamic relations are given. Comparison calculations with previous spherically symmetrical models of protostellar collapse are used to validate the basic approach and the artifices which allow the explicit hydrodynamics code to follow the accretion of gas onto a quasi-equilibrium core. A series of axisymmetric models is used to investigate the importance of rotation in collapsing clouds, as the initial amount of angular momentum is lowered, with an emphasis on the possible formation of rings. Rings readily form even in the nonisothermal regime except for very low initial angular momenta; even these clouds may experience ring formation prior to reaching stellar densities. The models imply that other effects (such as gravitational torques or turbulent viscosity) may be necesary to avoid binary formation and thus result in a presolar nebula consistent with the assumptions of either Safronov or Cameron.
Boss, A. P.↗
Metal-Silicate Partitioning of Bi, In, and Cd as a Function of Temperature and Melt Composition
The origin of volatile elements in the Earth, Moon and Mars is not known; however, several theories have been proposed based on volatile elements such as In, As, Se, Te and Zn which are in lower concentration in the Earth, Moon, and Mars than in chondrites. Explanations for these low concentrations are based on two contrasting theories for the origin of Earth: equilibrium core formation versus late accretion. One idea is that the volatiles were added during growth of the planets and Moon, and some mobilized into the metallic core while others stayed in the mantle (e.g., [1]). The competing idea is that they were added to the mantles after core formation had completed (e.g., [2]). Testing these ideas involves quantitative modeling which can only be performed after data is obtained on the systematic metal-silicate partitioning behavior of volatile elements with temperature, pressure and melt composition. Until now, such data for Bi, In, and Cd has been lacking. After conducting a series of high pressure, high temperature experiments, the metal-silicate partition coefficients of Bi, In, and Cd as a function of temperature and melt composition can be used to evaluate potential conditions under which terrestrial planets differentiated into core and mantle, and how they acquired volatiles.
Marin, Nicole↗
Experiments on Lunar Core Composition: Phase Equilibrium Analysis of A Multi-Element (Fe-Ni-S-C) System
Previous geochemical and geophysical experiments have proposed the presence of a small, metallic lunar core, but its composition is still being investigated. Knowledge of core composition can have a significant effect on understanding the thermal history of the Moon, the conditions surrounding the liquid-solid or liquid-liquid field, and siderophile element partitioning between mantle and core. However, experiments on complex bulk core compositions are very limited. One limitation comes from numerous studies that have only considered two or three element systems such as Fe-S or Fe-C, which do not supply a comprehensive understanding for complex systems such as Fe-Ni-S-Si-C. Recent geophysical data suggests the presence of up to 6% lighter elements. Reassessments of Apollo seismological analyses and samples have also shown the need to acquire more data for a broader range of pressures, temperatures, and compositions. This study considers a complex multi-element system (Fe-Ni-S-C) for a relevant pressure and temperature range to the Moon's core conditions.
Go, B. M.↗
Evolution of primoridal gas clouds
The dynamical, chemical, and thermal evolution of zero-metal gas clouds was modeled to study conditions of star formation in the early universe. Numerical results are given for the collapse of spherical clouds of mass 1000 and 50000 solar mass. Cooling by H2 lines and by photons emitted in H + e(-) yields H(-) = h (sup nu) maintains collapse until formation of an equilibrium protostellar core of mass 0.02 solar mass. The cooling by photons produced with H is essential for low mass star formation. If the cloud is fragmented, the evolution of the pieces is similar to that of the parent cloud, but the equilibrium core has larger density and mass.
Bodenheimer, P. H.↗
The earth's core - Speculations on its chemical equilibrium with the mantle
Lighter-than-iron elements in earth iron core, assuming formation timed chemical equilibrium with mantle
Brett, R.↗
Modelling of Equilibrium Between Mantle and Core: Refractory, Volatile, and Highly Siderophile Elements
Siderophile elements have been used to constrain conditions of core formation and differentiation for the Earth, Mars and other differentiated bodies [1]. Recent models for the Earth have concluded that the mantle and core did not fully equilibrate and the siderophile element contents of the mantle can only be explained under conditions where the oxygen fugacity changes from low to high during accretion and the mantle and core do not fully equilibrate [2,3]. However these conclusions go against several physical and chemical constraints. First, calculations suggest that even with the composition of accreting material changing from reduced to oxidized over time, the fO2 defined by metal-silicate equilibrium does not change substantially, only by approximately 1 logfO2 unit [4]. An increase of more than 2 logfO2 units in mantle oxidation are required in models of [2,3]. Secondly, calculations also show that metallic impacting material will become deformed and sheared during accretion to a large body, such that it becomes emulsified to a fine scale that allows equilibrium at nearly all conditions except for possibly the length scale for giant impacts [5] (contrary to conclusions of [6]). Using new data for D(Mo) metal/silicate at high pressures, together with updated partitioning expressions for many other elements, we will show that metal-silicate equilibrium across a long span of Earth s accretion history may explain the concentrations of many siderophile elements in Earth's mantle. The modeling includes refractory elements Ni, Co, Mo, and W, as well as highly siderophile elements Au, Pd and Pt, and volatile elements Cd, In, Bi, Sb, Ge and As.
Righter, K.↗
Terrestrial magma ocean and core segregation in the earth
According to the recent theories of formation of the earth, the outer layer of the proto-earth was molten and the terrestrial magma ocean was formed when its radius exceeded 3000 km. Core formation should have started in this magma ocean stage, since segregation of metallic iron occurs effectively by melting of the proto-earth. Therefore, interactions between magma, mantle minerals, and metallic iron in the magma ocean stage controlled the geochemistry of the mantle and core. We have studied the partitioning behaviors of elements into the silicate melt, high pressure minerals, and metallic iron under the deep upper mantle and lower mantle conditions. We employed the multi-anvil apparatus for preparing the equilibrating samples in the ranges from 16 to 27 GPa and 1700-2400 C. Both the electron probe microanalyzer (EPMA) and the Secondary Ion Mass spectrometer (SIMS) were used for analyzing the run products. We obtained the partition coefficients of various trace elements between majorite, Mg-perovskite, and liquid, and magnesiowustite, Mg-perovskite, and metallic iron. The examples of the partition coefficients of some key elements are summarized in figures, together with the previous data. We may be able to assess the origin of the mantle abundances of the elements such as transition metals by using the partitioning data obtained above. The mantle abundances of some transition metals expected by the core-mantle equilibrium under the lower mantle conditions cannot explain the observed abundance of some elements such as Mn and Ge in the mantle. Estimations of the densities of the ultrabasic magma Mg-perovskite at high pressure suggest existence of a density crossover in the deep lower mantle; flotation of Mg-perovskite occurs in the deep magma ocean under the lower mantle conditions. The observed depletion of some transition metals such as V, Cr, Mn, Fe, Co, and Ni in the mantle may be explained by the two stage process, the core-mantle equilibrium under the lower mantle conditions in the first stage, and subsequent downwards separation of the ultrabasic liquid (and magnesiowustite) and flotation of Mg-perovskite in the lower mantle.
Ohtani, Eiji↗
The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
Thorne, K. S.↗
Gas core reactors for actinide transmutation
The preliminary design of a uranium hexafluoride actinide transmutation reactor to convert long-lived actinide wastes to shorter-lived fission product wastes was analyzed. It is shown that externally moderated gas core reactors are ideal radiators. They provide an abundant supply of thermal neutrons and are insensitive to composition changes in the blanket. For the present reactor, an initial load of 6 metric tons of actinides is loaded. This is equivalent to the quantity produced by 300 LWR-years of operation. At the beginning, the core produces 2000 MWt while the blanket generates only 239 MWt. After four years of irradiation, the actinide mass is reduced to 3.9 metric tonnes. During this time, the blanket is becoming more fissile and its power rapidly approaches 1600 MWt. At the end of four years, continuous refueling of actinides is carried out and the actinide mass is held constant. Equilibrium is essentially achieved at the end of eight years. At equilibrium, the core is producing 1400 MWt and the blanket 1600 MWt. At this power level, the actinide destruction rate is equal to the production rate from 32 LWRs.
Clement, J. D.↗
Modified lattice-statics approach to dislocation calculations. II - Application
The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.
Esterling, D. M.↗
Osmium Solubility in Silicate Melts: New Efforts and New Results
In a recent paper, Borisov and Palme reported the first experimental results on the partitioning of Os between metal (Ni-rich OsNi alloys) and silicate melt of anorthite-diopside eutectic composition at 1400 C and 1 atm total pressure and and at function of O2 from 10(exp -8) to 10(exp -12) atm. Experiments were done by equilibrating OsNi metal loops with silicate melt. Metal and glass were analyzed separately by INAA. D(sup 0s) ranged from 10(exp 6) to 10(exp 7), which is inconsistent with core/ mantle equilibrium for HSEs and favors the late veneer hypothesis. Unfortunately, there was practically no function of O2 dependence of Os partitioning, and the scatter of experimental results was quite serious, so the formation of Os nuggets was suspected. This new set of experiments was specifically designed to avoid of at least minimize the nugget problem
Borisov, A.↗
Phase Equilibrium Experiments on Potential Lunar Core Compositions: Extension of Current Knowledge to Multi-Component (Fe-Ni-Si-S-C) Systems
Numerous geophysical and geochemical studies have suggested the existence of a small metallic lunar core, but the composition of that core is not known. Knowledge of the composition can have a large impact on the thermal evolution of the core, its possible early dynamo creation, and its overall size and fraction of solid and liquid. Thermal models predict that the current temperature at the core-mantle boundary of the Moon is near 1650 K. Re-evaluation of Apollo seismic data has highlighted the need for new data in a broader range of bulk core compositions in the PT range of the lunar core. Geochemical measurements have suggested a more volatile-rich Moon than previously thought. And GRAIL mission data may allow much better constraints on the physical nature of the lunar core. All of these factors have led us to determine new phase equilibria experimental studies in the Fe-Ni-S-C-Si system in the relevant PT range of the lunar core that will help constrain the composition of Moon's core.
Righter, K.↗
Models of the earth's core
Combined inferences from seismology, high-pressure experiment and theory, geomagnetism, fluid dynamics, and current views of terrestrial planetary evolution lead to models of the earth's core with five basic properties. These are that core formation was contemporaneous with earth accretion; the core is not in chemical equilibrium with the mantle; the outer core is a fluid iron alloy containing significant quantities of lighter elements and is probably almost adiabatic and compositionally uniform; the more iron-rich inner solid core is a consequence of partial freezing of the outer core, and the energy release from this process sustains the earth's magnetic field; and the thermodynamic properties of the core are well constrained by the application of liquid-state theory to seismic and labroatory data.
Stevenson, D. J.↗
The Combined Strength of Thermodynamics and Comparative Planetology: Application of Activity Models to Core Formation in Terrestrial Bodies
Recent models for accretion of terrestrial bodies involve metal-silicate equilibrium as the metallic core formed during growth. Most elements considered are either refractory or well studied elements for which effects of pressure, temperature, oxygen fugacity, and metallic liquid composition are well known. There are a large number of elements that are both siderophile and volatile, whose fate in such models is unknown, largely due to a lack of data at comparable conditions and com-positions (FeNi core with light elements such as S, C, Si, and O). We have focused on Ge, In, As, Sb and determined the effect of Si and C on metal-silicate partitioning, and developed a thermo-dynamic model that allows application of these new data to a wide range of planetary bodies. New experiments: We have previously carried out experiments with FeSi metallic liquid at C-saturated conditions at 1600 and 1800 C [4]. In a new series of experiments we investigate the effect of Si in carbon-free systems at 1600 C for comparison. Experiments were carried out at 1 GPa in MgO capsules using the same basaltic starting composition as in previous studies. The MgO capsule reacts with the silicate melt to form more MgO-rich liquids that have 22-26 wt% MgO. Experimental met-als and silicates were analyzed using a combination of electron microprobe analysis and laser ablation ICP-MS. Results: The new results can be interpreted by considering Ge as an example, in the simple exchange equilibrium Fe + GeO = FeO + Ge, where the equilibrium constant Kd can be examined as a function of Si content of the metal. The slope of lnKd vs. (1-XSi) for this new series allows derivation of the epsilon interaction parameter for each of these four elements and Si (both C-saturated and C-free).All four elements have positive epsilon values, indicating that Si causes a decrease in the partition coefficients; values are 6.6, 6.5, 27.8 and 25.2 for In, Ge, As, and Sb, respectively, at 1 GPa and 1600 C. As an example of how large the effect of Si can be, these epsilon values correspond to activity coefficients (gamma) for As of 0.01 when XSi = 0, and up to gamma = 23 when XSi = 0.2. Combining these new results with previous determinations [5,6] of epsilon parameters for S and C for these elements allows us calculate activity of Ge, In, As, and Sb in Fe-Ni-Si-S-C-O metallic liquids. We apply this new model to sever-al terrestrial bodies such as Earth (Si-rich core), Mars (S-rich core), Moon (S-, C-, and Si-poor core), and Vesta, and examine the resulting core and mantle concentrations of these elements. Mantle concentrations of these four elements are well explained for Earth and Mars in models that call for mid-mantle equilibration between Si-bearing and S-bearing FeNi cores, respectively. Modeling results for the Moon and Vesta will also be presented.
Righter, K.↗