Metal/silicate fractionation in the solar system

Fractionation between the metal and silicate components of objects in the inner solar system has long been recognized as a necessity in order to explain the observed density variations of the terrestrial planets and the H-group, L-group dichotomy of the ordinary chondrites. This paper discusses the densities of the terrestrial planets in light of current physical and chemical models of processes in the solar nebula. It is shown that the observed density trends in the inner solar system need not be the result of special fractionation processes, and that the densities of the planets may be direct results of simultaneous application of both physical and chemical restraints on the structure of the nebula, most notably the variation of temperature with heliocentric distance. The density of Mercury is easily attributed to accretion at temperatures so high that MgSiO₃ is only partially retained but Fe metal is condensed. The densities of the other terrestrial planets are shown to be due to different degrees of retention of S, O and H as FeS, FeO and hydrous silicates produced in chemical equilibrium between condensates and solar-composition gases. It is proposed that Mercury and Venus Have cores of Fe⁰, Earth has a core of Fe⁰ containing substantial amounts of FeS, and Mars has a quite small core of FeS with more FeO in its mantle than in Earth's. Geophysical and geochemical consequences of these conclusions are discussed.     

Chemical fractionation in the silicate vapor atmosphere of the Earth

Despite its importance to questions of lunar origin, the chemical composition of the Moon is not precisely known. In recent years, however, the isotopic composition of lunar samples has been determined to high precision and found to be indistinguishable from the terrestrial mantle despite widespread isotopic heterogeneity in the Solar System. In the context of the giant-impact hypothesis, this level of isotopic homogeneity can evolve if the proto-lunar disk and post-impact Earth undergo turbulent mixing into a single uniform reservoir while the system is extensively molten and partially vaporized. In the absence of liquid–vapor separation, such a model leads to the lunar inheritance of the chemical composition of the terrestrial magma ocean. Hence, the turbulent mixing model raises the question of how chemical differences arose between the silicate Earth and Moon. Here we explore the consequences of liquid–vapor separation in one of the settings relevant to the lunar composition: the silicate vapor atmosphere of the post-giant-impact Earth. We use a model atmosphere to quantify the extent to which rainout can generate chemical differences by enriching the upper atmosphere in the vapor, and show that plausible parameters can generate the postulated enhancement in the FeO/MgO ratio of the silicate Moon relative to the Earth's mantle. Moreover, we show that liquid–vapor separation also generates measurable mass-dependent isotopic offsets between the silicate Earth and Moon and that precise silicon isotope measurements can be used to constrain the degree of chemical fractionation during this earliest period of lunar history. An approach of this kind has the potential to resolve long-standing questions on the lunar chemical composition.     

A numerical model of the fractionation of olivine and molten sulfide from komatiite magma

A numerical model has been formulated that simulates the differentiation of mafic and ultramafic magmas by the fractionation of olivine and molten sulfide. The model is used to simulate the low-pressure differentiation of a komatiite magma series under both sulfide-undersaturated and sulfide-saturated conditions. Under sulfide-saturated conditions, the molecular ratio of olivine to sulfide removed from the silicate liquid is39 ± 2. Separation of this relatively small proportion of sulfide melt results in significantly different chemical trends in derivative liquids and fractionated material than are produced in the sulfide-undersaturated system, and this observation may be useful in mineral exploration. Comparison of the model results with published analyses of natural rocks indicate that the liquid equivalent members of the komatiite suite at Yakabindie, Western Australia, could be derivative liquids produced by fractional crystallization of olivine from a sulfide-undersaturated parental magma containing about 32 wt.% MgO. Derivation of a komatiitic pyroxenite with 20 wt.% MgO would require fractionation of 43.4 mol.% olivine whereas production of a komatiitic basalt with 12 wt.% MgO would involve removal of 58.5 mol.% olivine. Synvolcanic intrusive dunitic lenses at Yakabindie could have been produced by accumulation of material separated during about 3.8 mol.% fractionation of a similar parental magma, but the concentration of chalcophile elements in these bodies requires that the magma was sulfide-saturated.     

A lower trophic ecosystem model including iron effects in the Okhotsk Sea

We applied a three-dimensional ecosystem-physical coupled model including iron the effect to the Okhotsk Sea. In order to clarify the sources of iron, four dissolved iron compartments, based on the sources of supply, were added to Kawamiya et al.'s [1995, An ecological-physical coupled model applied to Station Papa. Journal of Oceanography, 51, 635-664] model (KKYS) to create our ecosystem model (KKYS-Fe). We hypothesized that four processes supply iron to sea water: atmospheric loadings from Northeastern Asia, input from the Amur River, dissolution from sediments and regeneration by zooplankton and bacteria. We simulated one year, from 1 January 2001 to 31 December 2001, using both KKYS-Fe and KKYS. KKYS could not reproduce the surface nitrate distribution after the spring bloom, whereas KKYS-Fe agreed well with observations in the northwestern Pacific because it includes iron limitation of phytoplankton growth. During the spring bloom, the main source of iron at the sea surface is from the atmosphere. The contribution of riverine iron to the total iron utilized for primary production is small in the Okhotsk Sea. Atmospheric deposition, the iron flux from sediment and regeneration of iron in the water column play important roles in maintaining high primary production in the Okhotsk Sea.     

High-P/T experimental studies and water in the silicate mantle

Water (or H) in the silicate mantle is a key element in influencing Earth’s climate, habitability, geochemical evolution, geophysical properties and geodynamical processes, and has received increasing attention in the past decades. Experimental work under simulated high-pressure and high-temperature conditions is a powerful tool in characterizing the species, distribution, storage capacity and various physicochemical impacts of water in the mantle. In recent years, significant approaches have been acquired about some key physical, chemical and dynamical properties of water in the mantle and their various impacts, as a result of extensive studies by high-pressure and temperature experiments, and our knowledge of Earth’s water cycle, especially the deep water cycle, on both temporal and spatial scales has been greatly enhanced. In this paper, a brief review based mainly on experimental studies is presented concerning the current understanding and some recent approaches of water in the silicate mantle, such as the possible origin, amount, storage and the effect on mantle properties.     

Zircon saturation model in silicate melts:a review and update

Zircon stability in silicate melts—which can be quantitatively constrained by laboratory measurements of zircon saturation—is important for understanding the evolution of magma.Although the original zircon saturation model proposed by Watson and Harrison(Earth Planet Sci Lett 64(2):295-304,1983) is widely cited and has been updated recently,the three main models currently in use may generate large uncertainties due to extrapolation beyond their respective calibrated ranges.This paper reviews and updates zircon saturation models developed with temperature and compositional parameters.All available data on zircon saturation ranging in composition from mafic to silicic(and/or peralkaline to peraluminous)at temperatures from 750 to 1400℃ were collected to develop two refined models(1 and 2) that may be applied to the wider range of compositions.Model 1 is given by lnC_(Zr)(melt)=(14.297±0.308)+(0.964 ± 0.066).M-(11113±374)/r,and model 2 given by lnC_(Zr)(melt)=(18.99±0.423)-(1.069±0.102)·lnG-(12288±593)/T,where C_(Zr)(melt) is the Zr concentration of the melt in ppm and parameters M [=(Na+K+2 Ca)/(Al·Si)](cation ratios) and G [=(3·Al_2 O_3+SiO_2)/(Na_(2-)O+K_2 O+CaO+MgO+FeO)](molar proportions)represent the melt composition.The errors are at one sigma,and T is the temperature in Kelvin.Before applying these models to natural rocks,it is necessary to ensure that the zircon used to date is crystallized from the host magmatic rock.Assessment of the application of both new and old models to natural rocks suggests that model 1 may be the best for magmatic temperature estimates of metaluminous to peraluminous rocks and that model 2 may be the best for estimating magmatic temperatures of alkaline to peralkaline rocks.     

Fe isotope fractionation in iron meteorites: New insights into metal-sulphide segregation and planetary accretion

Magmatic iron meteorites are considered to be remnants of the metallic cores of differentiated asteroids, and may be used as analogues of planetary core formation. The Fe isotope compositions (δ^57/54Fe) of metal fractions separated from magmatic and non-magmatic iron meteorites span a total range of 0.39‰, with the δ^57/54Fe values of metal fractions separated from the IIAB irons (δ^57/54Fe 0.12 to 0.32‰) being significantly heavier than those from the IIIAB (δ^57/54Fe 0.01 to 0.15‰), IVA (δ^57/54Fe − 0.07 to 0.17‰) and IVB groups (δ^57/54Fe 0.06 to 0.14‰). The δ^57/54Fe values of troilites (FeS) separated from magmatic and non-magmatic irons range from − 0.60 to − 0.12‰, and are isotopically lighter than coexisting metal phases. No systematic relationships exist between metal-sulphide fractionation factor (Δ^57/54Fe_M-FeS = δ^57/54Fe_metal − δ^57/54Fe_FeS) metal composition or meteorite group, however the greatest Δ^57/54Fe_M-FeS values recorded for each group are strikingly similar: 0.79, 0.63, 0.76 and 0.74‰ for the IIAB, IIIAB, IAB and IIICD irons, respectively. Δ^57/54Fe_M-FeS values display a positive correlation with kamacite bandwidth, i.e. the most slowly-cooled meteorites, which should be closest to diffusive equilibrium, have the greatest Δ^57/54Fe_M-FeS values. These observations provide suggestive evidence that Fe isotopic fractionation between metal and troilite is dominated by equilibrium processes and that the maximum Δ^57/54Fe_M-FeS value recorded (0.79 ± 0.09‰) is the best estimate of the equilibrium metal-sulphide Fe isotope fractionation factor. Mass balance models using this fractionation factor in conjunction with metal δ^57/54Fe values and published Fe isotope data for pallasites can explain the relatively heavy δ^57/54Fe values of IIAB metals as a function of large amounts of S in the core of the IIAB parent body, in agreement with published experimental work. However, sequestering of isotopically light Fe into the S-bearing parts of planetary cores cannot explain published differences in the average δ^57/54Fe values of mafic rocks and meteorites derived from the Earth, Moon and Mars and 4-Vesta. The heavy δ^57/54Fe value of the Earth's mantle relative to that of Mars and 4-Vesta may reflect isotopic fractionation due to disproportionation of ferrous iron present in the proto-Earth mantle into isotopically heavy ferric iron hosted in perovskite, which is released into the magma ocean, and isotopically light native iron, which partitions into the core. This process cannot take place at significant levels on smaller planets, such as Mars, as perovskite is only stable at pressures > 23 GPa. Interestingly, the average δ^57/54Fe values of mafic terrestrial and lunar samples are very similar if the High-Ti mare basalts are excluded from the latter. If the Moon's mantle is largely derived from the impactor planet then the isotopically heavy signature of the Moon's mantle requires that the impacting planet also had a mantle with a δ^57/54Fe value heavier than that of Mars or 4-Vesta, which then implies that the impactor planet must have been greater in size than Mars.     

Batch fractionation model for the evolution of volcanic rocks in an island arc: an example from Central Japan

Analyses of fifty-one rock samples from three stratovolcanoes in Central Japan revealed that K and Rb contents vary in a saw-toothed fashion with the growth of these volcanoes. Peaks and valleys of the saw-toothed variation pattern of Rb (and also K) increase at first and then gradually converge on constant values. This variation trend is also shown by the Rb/Sr ratio. The convergent Rb/Sr ratio (0.23–0.24) at the peaks coincides with recent estimates of the average value for continental crust. These geochemical features are well explained by the batch fractionation model. In this model, the magma reservoir lying at the top of the mantle is periodically supplied with a batch of parental magma, while the magma in it undergoes continuous crystallization and the cumulate is continuously removed by the divergent movement of the mantle. This model, working under physical conditions in the crust-mantle structure of an island arc, not only accounts for the above geochemical features, but also gives insight into the genesis of the calc-alkaline rock series and of the continental crust.     

硅酸盐熔体和液态铁的两相模拟与核幔间的氧交换

地球早期经历了很多撞击事件, 其中与地月系统形成相关的大撞击甚至造成深达核幔边界的全球规模的岩浆洋, 在此过程中的核幔分异基本确定了地幔与地核的物质组成, 也决定了地球随后的演化路径.我们采用基于量子力学理论的第一性原理方法和机器学习技术, 实现了硅酸盐熔体和液态铁的超大体系两相分子动力学模拟, 获得了核幔边界条件下的两相平衡数据, 为超深岩浆洋中的核幔分异过程提供了重要约束.基于本研究模拟结果和现有的高温高压实验数据, 我们还建立了能够准确预测核幔间元素交换的平衡模型, 利用该模型深入探讨了核幔间的氧交换问题, 并分析了其与地球生长、大撞击和岩浆洋事件、地球早期磁场等争议问题之间的关系.

     

A model for the coast-effect

A model for the coast-effect of geomagnetism is presented, in which the horizontal magnetic field induces currents in a circuit including a thin finite ocean. The currents flow horizontally across the ocean, vertically down into the earth, back through the deep interior of the earth, and vertically up to the ocean to complete the current loop. The upper layers of the earth are given non-zero conductivity, allowing the possibility of such current loops.A two-dimensional model involving such currents has been worked out analytically, and it is found that a significant induced magnetic field at the seafloor can be obtained with a reasonable conductivity in the earth's upper layers. A three-dimensional model has also been worked out numerically. It is found that the induced vertical component of magnetic field is of comparable magnitude to the horizontal component induced normal to the coast, whereas the horizontal component parallel to the coast is small. These relations are required to explain the observation of Parkinson arrows.     

A new saturated/unsaturated model for stormwater infiltration systems

Infiltration systems are widely used as an effective urban stormwater control measure. Most design methods and models roughly approximate the complex physical flow processes in these systems using empirical equations and fixed infiltration rates to calculate emptying times from full. Sophisticated variably saturated flow models are available, but rarely applied owing to their complexity. This paper describes the development and testing of an integrated one‐dimensional model of flow through the porous storage of a typical infiltration system and surrounding soils. The model accounts for the depth in the storage, surrounding soil moisture conditions and the interaction between the storage and surrounding soil. It is a front‐tracking model that innovatively combines a soil‐moisture‐based solution of Richard's equation for unsaturated flow with piston flow through a saturated zone as well as a reservoir equation for flow through a porous storage. This allows the use of a simple non‐iterative numerical solution that can handle ponded infiltration into dry soils. The model is more rigorous than approximate stormwater infiltration system models and could therefore be valuable in everyday practice. A range of test cases commonly used to test soil water flow models for infiltration in unsaturated conditions, drainage from saturation and infiltration under ponded conditions were used to test the model along with an experiment with variable depth in a porous storage over saturated conditions. Results show that the model produces a good fit to the observed data, analytical solutions and Hydrus. Copyright © 2008 John Wiley & Sons, Ltd.     

A relationship between phonon conductivity and seismic parameter Φ for silicate minerals

Summary The relationship between the phonon conductivity at room temperature (K _N ) and the seismic parameter () for silicate minerals is suggested. The considerations are based on the Debye model of thermal energy transport phenomena in solids and on the seismic equation of state for silicates and oxides given byAnderson (1967). The semiempirical relationship is the formK _N = 0.43^0.82 where is in km²/s² andK _N in mcal/cm s K, and the empirical relationship isK _N =(0.528±0.006) –(8.18±2.11). The laboratory data on thermal and elastic properties for several silicates were taken fromHorai andSimmons (1970).     

A deformation/blurring-based spatio-temporal model

A key objective in spatio-temporal modeling consists of providing an appropriate representation of complexity in interactive spatio-temporal dynamics inherent to real phenomena. Propagated effect of dynamical spatial deformation provides a meaningful way to describe certain forms of heterogeneous behaviour; in particular, in relation to processes evolving in unstable media, or to account for the possible effect of covariates, to mention some significant interpretations. In this paper, the formulation of a discrete time and continuous space spatio-temporal interaction model with autoregressive dynamics, incorporating the effect of continuous deformation of the spatial support over time, is studied. Among other fields, this approach provides a suitable representation for a variety of geophysical and environmental applications. In particular, a vast family of heterogeneous models is generated from models which display homogeneity in the absence of deformation. Structural characteristics and variability properties, as well as self-consistency conditions for a limiting continuous-time approximation, are analyzed.     

Relationship between13C and18O fractionation and changes in major element composition in a recent calcite-depositing spring — A model of chemical variations with inorganic CaCO3 precipitation

A theoretical model is derived in which isotopic fractionations can be calculated as a function of variations in dissolved carbonate species on CO₂ degassing and calcite precipitation. This model is tested by application to a calcite-depositing spring system near Westerhof, Germany. In agreement with the model,¹³C of the dissolved carbonate species changes systematically along the flow path. The difference in δ values between the upper and lower part of the stream is about 1‰. The¹³C content of the precipitated calcite is different from that expected from the theoretical partitioning. The isotopic composition of the solid CaCO₃ is similar to that of the dissolved carbonate, though in theory it should be isotopically heavier by about 2.4‰. The¹⁸O composition of dissolved carbonate and H₂O is constant along the stream. Calculated calcite-water temperatures differ by about +5°C from the observed temperatures demonstrating isotopic disequilibrium between the water and precipitated solid. This is attributed to kinetic effects during CaCO₃ deposition from a highly supersaturated solution, in which precipitation is faster than equilibration with respect to isotopes.Plant populations in the water have virtually no influence on CO₂ degassing, calcite saturation and isotopic fractionation. Measurements of P_CO2, S_C and¹³C within a diurnal cycle demonstrate that metabolic effects are below the detection limit in a system with a high supply-rate of dissolved carbonate species. The observed variations are due to differences in CO₂ degassing and calcite precipitation, caused by continuously changing hydrodynamic conditions and carbonate nucleation rates.     

A hybrid near-field/far-field thermal discharge model for coastal areas

A hybrid technique has been used to simulate the dispersion of heat from surface discharges in coastal areas. Characteristics of the near field thermal dispersion are described by the CORMIX3 model. A two-dimensional harmonic finite element hydrodynamic model (TEA) and a Eulerian–Lagrangian transport model (ELA) are applied for the far-field computation. A Gaussian puff algorithm in ELA, which represents the near field plume as a series of patches, is used to link the two regimes. The computed results are compared to available field measurements. Very reasonable agreement is observed.     

Melting relations in the chloride–carbonate–silicate systems at high-pressure and the model for formation of alkalic diamond–forming liquids in the upper mantle

The experiments in the model system CaMgSi₂O₆–(Na₂CO₃, CaCO₃)–KCl are performed at 5 GPa and 1400–1600 °C in order to study the phase relations, including liquid immiscibility, in the chloride–carbonate–silicate systems with application to alkali and chlorine-rich liquids preserved in kimberlitic diamonds. Experiments in the boundary joins of the system demonstrated that both the carbonate–silicate and chloride–carbonate melts are homogeneous; while high-temperature (above 1800 °C) liquid immiscibility is assumed for the chloride–silicate join of the above system. Addition of silicate component into the chloride–carbonate melts and chloride component into the carbonate–silicate melts results in splitting of the homogeneous liquids into the immiscible chloride–carbonate brine and carbonate–silicate melt. Carbonate–silicate and chloride–carbonate branches of the miscibility gap converge within the carbonate-rich region of the system. Regular temperature evolution of the shape and size of the miscibility gap is deduced. With decreasing temperature, the convergence point moves toward more Si-rich compositions, expanding fields of homogeneous chloride–carbonate silica-saturated melts. This effect is governed by the precipitation of the silicate phases even from silica-bearing chloride–carbonate melts. In addition, experiments revealed regular evolution of both Cl-bearing carbonate–silicate melt and Si-bearing chloride–carbonate brine toward the low-temperature chlorine–bearing carbonatitic liquid with decreasing temperature. These trends are similar to the evolution of the melt and brine inclusions in some diamonds from Botswana, Brazil, Canada, and Yakutia, indicating their growth during cooling. The model for interaction of the chloride–carbonate brine with the mantle rocks is developed on the basis of the present experimental data. This model is applied to the chlorine-enriched kimberlites of the Udachnaya–East pipe.