C- and S-rich molten alloy immiscibility and core formation of planetesimals

We present the results of melting experiments to 7.7 GPa and 2200 °C on a synthetic ‘chondrite-like’ composition suitable to model early planetesimal differentiation. Our principal observation is that two immiscible liquid alloys coexist to about 5.5 GPa in Fe-Ni-S-C-O compositional space, with one liquid alloy being enriched in S and the other enriched in C. The chemical distinctions between the two liquid alloys progressively weaken as pressure increases. This is related to the contraction of the miscibility gap with increasing pressure. With the moderately C- and S-depleted composition used in this study, we observed closure of the miscibility gap at about 5.5 GPa. Our results have implications for core formation on planetary bodies that have undergone extensive melting. Because of the characteristics of the immiscibility region, core formation and differentiation histories would have been largely dependent on the size of these bodies and their C and S contents. Our results indicate that relatively small bodies with elevated S and C contents would have likely experienced significant core stratification.     

Melting relationships in the system Fe-Feo at high pressures: Implications for the composition and formation of the earth's core

A reconnaissance investigation has been carried out on melting relationships in the system Fe-FeO at pressures up to 25 GPa and temperatures up to 2200° C using an MA-8 apparatus. Limited studies were also made of the Co-CoO and Ni-NiO systems. In the system FeFeO, the rapid exsolution of FeO from liquids during quenching causes some difficulties in interpretation of textures and phase relationships. The Co-CoO and Ni-NiO systems are more tractable experimentally and provide useful analogues to the Fe-FeO system. It was found that the broad field of liquid immiscibility present at ambient pressure in the Co-CoO system had disappeared at 18 GPa, 2200° C and that the system displayed complete miscibility between molten Co and CoO, analogous to the behaviour of the Ni-NiO system at ambient pressure. The phase diagram of the system Fe-FeO at 16 GPa and from 1600–2200° C was constructed from interpretations based on the textures of quenched run products. The solubility of FeO in molten iron is considerably enhanced by high pressures. At 16 GPa, the Fe-FeO eutectic contains about 10–15 mol percent FeO and the eutectic temperature in this iron-rich region of the system occurs at 1700±25° C, some 350° C below the melting point of pure iron at the same pressure. The solubility of FeO in molten Fe increases rapidly as temperature increases from 1700 to 2200° C. A relatively small liquid immiscibility field is present above 1900° C but is believed to be eliminated above 2200° C. This inference is supported by thermodynamic calculations on the positions of key phase boundaries. A single run carried out on an Fe₅₀ FeO₅₀ composition at 25 GPa and 2200° C demonstrated extensive and probably complete miscibility between Fe and FeO liquids under these conditions. The melting point of iron is decreased considerably by solution of FeO at high pressures; moreover, the melting point gradient (dP/dT) of the Fe-FeO eutectic is much smaller than that of pure iron and is also smaller than that of mantle pyrolite under the P, T conditions studied. These characteristics make it possible for melting of metal phase and segregation of the core to proceed within the Earth under conditions where most of the mantle remains below solidus temperatures. Under these conditions, the core would inevitably contain a large proportion of dissolved FeO. It is concluded therefore, that oxygen is likely to be the principal light element in the core. The inner core may not be composed of pure iron, as often proposed. Instead, it may consist of a crystalline oxide solid solution (Ni, Fe)₂O.     

High-pressure melting relations in Fe-C-S systems: Implications for formation, evolution, and structure of metallic cores in planetary bodies

We present new high-pressure temperature experiments on melting phase relations of Fe-C-S systems with applications to metallic core formation in planetary interiors. Experiments were performed on Fe-5 wt% C-5 wt% S and Fe-5 wt% C-15 wt% S at 2-6 GPa and 1050-2000 °C in MgO capsules and on Fe-13 wt% S, Fe-5 wt% S, and Fe-1.4 wt% S at 2 GPa and 1600 °C in graphite capsules. Our experiments show that: (a) At a given P-T, the solubility of carbon in iron-rich metallic melt decreases modestly with increasing sulfur content and at sufficiently high concentration, the interaction between carbon and sulfur can cause formation of two immiscible melts, one rich in Fe-carbide and the other rich in Fe-sulfide. (b) The mutual solubility of carbon and sulfur increases with increasing pressure and no super-liquidus immiscibility in Fe-rich compositions is likely expected at pressures greater than 5-6 GPa even for bulk compositions that are volatile-rich. (c) The liquidus temperature in the Fe-C-S ternary is significantly different compared to the binary liquidus in the Fe-C and Fe-S systems. At 6 GPa, the liquidus of Fe-5 wt% C-5 wt% S is 150-200 °C lower than the Fe-5 wt% S. (d) For Fe-C-S bulk compositions with modest concentration of carbon, the sole liquidus phase is iron carbide, Fe₃C at 2 GPa and Fe₇C₃ at 6 GPa and metallic iron crystallizes only with further cooling as sulfur is concentrated in the late crystallizing liquid. Our results suggest that for carbon and sulfur-rich core compositions, immiscibility induced core stratification can be expected for planets with core pressure less than ∼6 GPa. Thus planetary bodies in the outer solar system such as Ganymede, Europa, and Io with present day core-mantle boundary (CMB) pressures of ∼8, ∼5, and 7 GPa, respectively, if sufficiently volatile-rich, may either have a stratified core or may have experienced core stratification owing to liquid immiscibility at some stage of their accretion. A similar argument can be made for terrestrial planetary bodies such as Mercury and Earth’s Moon, but no such stratification is predicted for cores of terrestrial planets such as Earth, Venus, and Mars with the present day core pressure in the order ?136 GPa, ?100 GPa, and ?23 GPa. (e) Owing to different expected densities of Fe-rich (and carbon-bearing) and sulfur-rich metallic melts, their settling velocities are likely different; thus core formation in terrestrial planets may involve rain of more than one metallic melt through silicate magma ocean. (f) For small planetary bodies that have core pressures <6 GPa and have a molten core or outer core, settling of denser carbide-rich liquid or flotation of lighter, sulfide-rich melt may contribute to an early, short-lived geodynamo.     

Thermodynamics, structure, dynamics, and freezing of Mg2SiO4 liquid at high pressure

We perform first principles molecular dynamics simulations of Mg₂SiO₄ liquid and crystalline forsterite. On compression by a factor of two, we find that the Grüneisen parameter of the liquid increases linearly from 0.6 to 1.2. Comparison of liquid and forsterite equations of state reveals a temperature-dependent density crossover at pressures of ∼12-17 GPa. Along the melting curve, which we calculate by integration of the Clapeyron equation, the density crossover occurs within the forsterite stability field at P = 13 GPa and T = 2550 K. The melting curve obtained from the root mean-square atomic displacement in forsterite using the Lindemann law fails to match experimental or calculated melting curves. We attribute this failure to the liquid structure that differs significantly from that of forsterite, and which changes markedly upon compression, with increases in the degree of polymerization and coordination. The mean Si coordination increases from 4 in the uncompressed system to 6 upon twofold compression. The self-diffusion coefficients increase with temperature and decrease monotonically with pressure, and are well described by the Arrhenian relation. We compare our equation of state to the available highpressure shock wave data for forsterite and wadsleyite. Our theoretical liquid Hugoniot is consistent with partial melting along the forsterite Hugoniot at pressures 150-170 GPa, and complete melting at 170 GPa. The wadsleyite Hugoniot is likely sub-liquidus at the highest experimental pressure to date (200 GPa).     

Evidence for high-pressure core-mantle differentiation from the metal-silicate partitioning of lithophile and weakly-siderophile elements

Liquid Fe metal-liquid silicate partition coefficients for the lithophile and weakly-siderophile elements Ta, Nb, V, Cr, Si, Mn, Ga, In and Zn have been measured in multianvil experiments performed from 2 to 24 GPa, 2023-2873 K and at oxygen fugacities of −1.3 to −4.2 log units relative to the iron-wüstite buffer. Compositional effects of light elements dissolved in the metal liquid (S, C) have been examined and experiments were performed in both graphite and MgO capsules, specifically to address the effect of C solubility in Fe-metal on siderophile element partitioning. The results were used to examine whether there is categorical evidence that a significant portion of metal-silicate equilibration occurred under very high pressures during core-mantle fractionation on Earth. Although the depletion of V from the mantle due to core formation is significantly greater than that of Nb, our results indicate that both elements have similar siderophile tendencies under reducing conditions at low pressures. With increasing pressure, however, Nb becomes less siderophile than V, implying that average metal-silicate equilibration pressures of at least 10-40 GPa are required to explain the Nb/V ratio of the mantle. Similarly the moderately-siderophile, volatile element ratios Ga/Mn and In/Zn are chondritic in the mantle but both volatility and core-mantle equilibration at low pressure would render these ratios strongly sub-chondritic. Our results indicate that pressures of metal-silicate partitioning exceeding 30-60 GPa would be required to render these element ratios chondritic in the mantle. These observations strongly indicate that metal-silicate equilibration must have occurred at high pressures, and therefore support core-formation models that involve deep magma oceans. Moreover, our results allow us to exclude models that envisage primarily low-pressure (<1 GPa) equilibration in relatively small planetary bodies. We also argue that the core cannot contain significant U as this would require metal-silicate equilibration at oxygen fugacities low enough for significant amounts of Ta to have also been extracted from the mantle. Likewise, as In is more siderophile than Pb but similarly volatile and also quite chalcophile it would have been difficult for Pb to enter the core without reversing the relative depletions of these elements in the mantle unless metal-silicate equilibration occurred at high pressures >20 GPa.     

Liquid immiscibility between nephelinite and carbonatite from 1.0 to 2.5 GPa compared with mantle melt compositions

In order to define the conditions for the formation of immiscible carbonatite magmas in the lithosphere and in the crust, we have conducted phase equilibrium experiments to determine the effect of pressure and temperature on the silicate-carbonate liquid miscibility gap in bulk compositions appropriate for magmas in the upper mantle. A primitive (magnesian) nephelinite (NEPH) was used as a starting material, mixed with carbonates. Experiments were made with mixtures in the joins NEPH-dolomite-Na₂CO₃ (NEPH-Dol-NC) at 1.0 to 2.5 GPa, and NEPH-calcite (NEPH-CC) at 1.0 GPa. The miscibility gap was intersected by the join NEPH-Dol-NC (liquids with olivine), but not by NEPH-CC. Together with previous results for the Mg-free system (Na₂O-CaO-Al₂O₃-SiO₂-CO₂), it was established that the size of the miscibility gap for magnesian compositions increases with decreasing pressures from depths of ˜100 km to ˜ 35 km; it increases further as compositions are changed by decreasing Mg/Ca. The maximum CaCO₃ in liquids associated with the miscibility gap is 50 wt % for Mg-bearing liquids, and 80 wt % for Mg-free liquids. There is no experimental evidence for nearly pure-CaCO₃ immiscible liquids, but abundant evidence for the precipitation of rounded calcite crystals from carbonate-rich liquids. The join NEPH-CC locates a piercing point on the liquidus field boundary for coprecipitation of olivine and calcite at NEPH₅₀CC₅₀ (wt %), part of the silicate-carbonate liquidus field boundary which defines the locus of liquids formed from carbonate-peridotites. The miscibility gap results are compared with magmas formed during partial fusion of CO₂-bearing mantle peridotites, and during fractional crystallization of mantle-derived magmas. None of the probable magma paths in mantle processes intersects the miscibility gap. CO₂-bearing mantle-derived alkalic magmas such as nephelinites and melilitites may fractionate during uprise through the mantle and crystallization within the crust. The compositions of these evolved nephelinites and phonolites approach the silicate side of the miscibility gap, confirming the probable generation of immiscible, alkalic carbonate-rich liquids at crustal pressures. Received: 29 January 1996 / Accepted: August 14, 1996     

Structure, thermodynamics, and diffusion in CaAl2Si2O8 liquid from first-principles molecular dynamics

We have performed first-principles molecular dynamics simulations of CaAl₂Si₂O₈ (anorthite) liquid at pressures up to 120 GPa and temperatures of 3000, 4000 and 6000 K. At the lowest degrees of compression the liquid is seen to accommodate changes in density through decreasing the abundance of 3- and 4-membered rings, while increases in coordination of network forming cations take effect at somewhat higher degrees of compression. Results are fit to a fundamental thermodynamic relation with 4th order finite strain and 1st order thermal variable expansions. Upon compression by a factor of two, the Grüneisen parameter (γ) is found to increase continuously from 0.35 to 1.10. Weak temperature dependence in γ is thermodynamically consistent with a slight decrease in isochoric heat capacity (C_V), for which values of between 4.4 and 5.2 Nk_B are obtained, depending on the temperature. Pressure and temperature dependence of self-diffusivities is found to be well represented by an Arrhenius relation, except at 3000 K and pressures lower than 5 GPa, where self-diffusivities of Si, Al, and O increase with pressure. Analysis of the lifetimes of individual coordination species reveals that this phenomenon arises due to the disproportionately high stability of 4-fold coordinated Si, and to a lesser extent 4-fold coordinated Al. Our results represent a marked improvement in accuracy and reliability in describing the physics of CaAl₂Si₂O₈ liquid at deep mantle pressures, pointing the way to a general thermodynamic model of melts at extreme pressures and temperatures relevant to planetary-scale magma oceans and deep mantle partial melting.     

The Fe-rich liquidus in the Fe-FeS system from 1 bar to 10 GPa

The composition and evolution of a metallic planetary core is determined by the behavior with pressure of the eutectic and the liquidus on the Fe-rich side of the Fe-FeS eutectic. New experiments at 6 GPa presented here, along with existing experimental data, inform a thermodynamic model for this liquidus from 1 bar to at least 10 GPa. Fe-FeS has a eutectic that becomes more Fe-rich but remains constant in T up to 6 GPa. The 1 bar, 3 GPa, and 6 GPa liquidi all cross at a pivot point at 1640 ± 5 K and FeS_37 ± 0.5. This liquid/crystalline metal equilibrium is T-x-fixed and pressure independent through 6 GPa. Models of the 1 bar through 10 GPa experimental liquidi show that with increasing P there is an increase in the T separation between the liquidus and the crest of the metastable two-liquid solvus. The solvus crest decreases in T with increasing P. The model accurately reproduces all the experimental liquidi from 1 bar to 10 GPa, as well as reproducing the 0-6 GPa pivot point. The 14 GPa experimental liquidus ( [Chen et al., 2008a] and Chen et al., 2008b) deviates sharply from the lower pressure trends indicating that the 0-10 GPa model no longer applies to this 14 GPa data.     

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

We have investigated the thermodynamics of mixing between aragonite (orthorhombic CaCO₃) and strontianite (SrCO₃). In agreement with experiment, our simulations predict that there is a miscibility gap between the two solids at ambient conditions. All Sr_xCa_1−xCO₃ solids with compositions 0.12 < x < 0.87 are metastable with respect to separation into a Ca-rich and a Sr-rich phase. The concentration of Sr in coral aragonites (x ∼ 0.01) lies in the miscibility region of the phase diagram, and therefore formation of separated Sr-rich phases in coral aragonites is not thermodynamically favorable. The miscibility gap disappears at around 380 K. The enthalpy of mixing, which is positive and nearly symmetric with respect to x = 0.5, is the dominant contribution to the excess free energy, while the vibrational and configurational entropic contributions are small and of opposite sign. We provide a detailed comparison of our simulation results with available experimental data.     

Structure, thermodynamic and transport properties of liquid MgSiO3: Comparison of molecular models and laboratory results

Liquid MgSiO₃ is a model for the Earth’s magma ocean and of remnant melt present near the core-mantle boundary. Here, models for molten MgSiO₃ are computed employing empirical potential molecular dynamics (EPMD) and results are compared to published results including two EPMD studies and three first-principles molecular dynamics (FPMD) models and to laboratory data. The EPMD results derived from the Oganov (OG) potential come closest to the density of MgSiO₃ liquid at the 1-bar melting point inferred from the melting curve. At higher P, EPMD densities calculated from the OG potential and FPMD broadly match shock wave studies, with the OG potential yielding the better comparison. Matsui (M) potential results deviate from other studies above ∼50 GPa. Overall, results based on the OG potential compare best to experimental densities over the P-T range of the mantle. Isothermally, upon increasing P the mean coordination numbers () of oxygen around Si and Mg monotonically increase with pressure. Tetrahedral Si and octahedral Si monotonically increase and decrease, respectively, whereas pentahedral Si maximizes at 10-20 GPa. Tetrahedral Mg decreases monotonically as P increases whereas pentahedral, octahedral and higher coordination polyhedra each show similar behavior first increasing and then decreasing after attaining a maximum; the P of the maximum for each polyhedra type migrates to higher P as the CN increases. Free oxygen and oxygen with one nearest neighbor of either Si or Mg decreases whereas Si or Mg with two or three nearest oxygens (i.e., tricluster oxygen) increases with increasing P isothermally. The increase of tricluster oxygen is consistent with spectroscopy on MgSiO₃ glass quenched from 2000 K and 0-40 GPa and high-energy X-ray studies constraining the coordination of O around Mg and around Si at 2300 K and 1 bar. Coordination statistics from FPMD studies for O around Si and Si around O are in agreement with the EPMD results based on the M and OG potentials. Mg self-diffusivity is greater than O and Si self-diffusivities for both the M and OG potentials. All D values monotonically decrease with increasing pressure isothermally and all atoms are more diffusive in the M liquid compared to the OG liquid except at T > ∼5000 K and P > 100 GPa. Previously published EPMD diffusivities fall between values given by the M and OG potentials, at least up to 45 GPa. The M liquid is generally less viscous than the OG liquid except at P > ∼80 GPa. Activation energy and volume are around 96 kJ/mol and 1.5 cm³/mol, respectively. The FPMD viscosity results at 120 GPa and 4000 and 4500 K are essentially identical to the values from the M and OG potentials. FPMD viscosity results are similar to the OG results for P < 60 GPa; at higher P, the FPMD viscosities are higher. At 4000 K and 100 GPa the shear viscosity of liquid MgSiO₃ is ∼0.1 Pa s. More extensive laboratory results are required to better define the thermodynamic, transport and structural properties of MgSiO₃ liquids and for comparison with computational studies.     

Majoritic garnet: A new approach to pressure estimation of shock events in meteorites and the encapsulation of sub-lithospheric inclusions in diamond

A means for estimating pressures in natural samples based on both the coupled substitution (Na+)^[1+] (Ti + ^[VI]Si)^[4+] = (M)^[2+] (Al + Cr)^[3+], and the classic pyroxene-stoichiometry majorite-substitution into garnet at high-pressure, is derived for garnets with majoritic chemistry. The technique is based on a compilation of experimental data for different bulk compositions. It is compositionally and thermally robust and can be used to estimate pressures experienced by natural materials during formation of majoritic garnet. In addition, it can be used either retrospectively, or in new experimental studies to establish the pressures of crystallization of reaction products, and determine if disequilibrium is recorded by the chemistries of majoritic garnets. Pressures are calculated based on majoritic chemistries in chondritic meteorites and diamond inclusions. Majoritic garnets associated with Mg perovskite in shocked L chondrites (n = 4) yield uniform pressures of 23.8 ± 0.2 GPa that are slightly higher than pressures recorded by majoritic garnet in shock-derived melt veins in L chondrites (22.4 ± 0.6 GPa; n = 5). Similar pressures are also exhibited by shock-derived majoritic garnets in H chondrites (22.2 ± 1.1 GPa; n = 3). Diamond inclusions with eclogitic and peridotitic majoritic garnet chemistries exhibit mean pressures of 10.7 ± 2.7 GPa (n = 30) and 8.3 ± 1.6 GPa (n = 15) respectively, consistent with a sub-lithospheric origin. However, pressures defined by majoritic diamond inclusions from Jagersfontein (22.3 ± 0.8 GPa and 16.9 ± 1 GPa), Monastery (15.7 ± 7 GPa) and Kankan (15.5 ± 0.2 GPa) show that these inclusions originated from the mantle transition zone. Thus, this new single-phase method for pressure estimation has unmatched potential to map the depth of formation of garnets with majoritic chemistries that occur as diamond inclusions in all parageneses except those that include Ca silicate perovskite. The derived pressures confirm the sub-lithospheric origin of eclogitic majoritic diamond inclusions, and thus provide a more comprehensive picture of the important role of storage of oceanic lithosphere in the transition zone.     

Pressure dependence of viscosity of rhyolitic melts

Viscosity of silicate melts is a critical property for understanding volcanic and igneous processes in the Earth. We investigate the pressure effect on the viscosity of rhyolitic melts using two methods: indirect viscosity inference from hydrous species reaction in melts using a piston cylinder at pressures up to 2.8 GPa and direct viscosity measurement by parallel-plate creep viscometer in an internally-heated pressure vessel at pressures up to 0.4 GPa. Comparison of viscosities of a rhyolitic melt with 0.8 wt% water at 0.4 GPa shows that both methods give consistent results. In the indirect method, viscosities of hydrous rhyolitic melts were inferred based on the kinetics of hydrous species reaction in the melt upon cooling (i.e., the equivalence of rheologically defined glass transition temperature and chemically defined apparent equilibrium temperature). The cooling experiments were carried out in a piston-cylinder apparatus using hydrous rhyolitic samples with 0.8-4 wt% water. Cooling rates of the kinetic experiments varied from 0.1 K/s to 100 K/s; hence the range of viscosity inferred from this method covers 3 orders of magnitude. The data from this method show that viscosity increases with increasing pressure from 1 GPa to 3 GPa for hydrous rhyolitic melts with water content ?0.8 wt% in the high viscosity range. We also measured viscosity of rhyolitic melt with 0.13 wt% water using the parallel-plate viscometer at pressures 0.2 and 0.4 GPa in an internally-heated pressure vessel. The data show that viscosity of rhyolitic melt with 0.13 wt% water decreases with increasing pressure. Combining our new data with literature data, we develop a viscosity model of rhyolitic melts as a function of temperature, pressure and water content.     

The effect of Si on metal-silicate partitioning of siderophile elements and implications for the conditions of core formation

We have determined the liquid metal-liquid silicate partitioning of Ni, Co, Mo, W, V, Cr and Nb at 1.5 GPa/1923 K and 6 GPa/2123 K under conditions of constant silicate melt composition with variable amounts of Si in the Fe-rich metallic liquid. Partitioning of Ni, Co, Mo, W and V is sensitive to the Si content of the metal with, in all five cases, increasing Si tending to make the element more lithophile than for conditions where the metal is Si-free. In contrast, metal-silicate partitioning of Cr and Nb is, at constant silicate melt composition, insensitive to the Si content of the metal.The implications of our data are that if, as indicated by the Si isotopic composition of the silicate Earth ( [Georg et al., 2007] and [Fitoussi et al., 2009]), the core contains significant amounts of Si, the important siderophile elements Ni, Co, W and Mo were more lithophile during accretion and core formation than previously believed.We use our new data in conjunction with published metal-silicate partitioning results to develop a model of continuous accretion and core segregation taking explicit account of the partitioning of Si (this study) and O (from Ozawa et al., 2008) between metal and silicate and their effects on metal-silicate partitioning of siderophile elements. We find that the effect of Si on the siderophile characteristics of Ni, Co and W means that the pressures of core segregation estimated from these elements are ∼5 GPa lower than those derived from experiments in which the metal contained negligible Si (e.g., Wade and Wood, 2005). The core-mantle partitioning of Cr and Nb requires that most of Earth accretion took place under conditions which were much more reducing than those implied by the current FeO content of the mantle and that the oxidation took place late in the accretionary process. Paths of terrestrial accretion, oxidation state and partitioning which are consistent with the current mantle contents of Ni, Co, W, V, Cr and Nb lead to Si and O contents of the core of ∼4.3 wt.% and 0.15%, respectively.     

Systematics of metal-silicate partitioning for many siderophile elements applied to Earth’s core formation

Superliquidus metal-silicate partitioning was investigated for a number of moderately siderophile (Mo, As, Ge, W, P, Ni, Co), slightly siderophile (Zn, Ga, Mn, V, Cr) and refractory lithophile (Nb, Ta) elements. To provide independent constrains on the effects of temperature, oxygen fugacity and silicate melt composition, isobaric (3 GPa) experiments were conducted in piston cylinder apparatus at temperature between 1600 and 2600 °C, relative oxygen fugacities of IW−1.5 to IW−3.5, and for silicate melt compositions ranging from basalt to peridotite. The effect of pressure was investigated through a combination of piston cylinder and multi-anvil isothermal experiments between 0.5 and 18 GPa at 1900 °C. Oxidation states of siderophile elements in the silicate melt as well as effect of carbon saturation on partitioning are also derived from these results. For some elements (e.g. Ga, Ge, W, V, Zn) the observed temperature dependence does not define trends parallel to those modeled using metal-metal oxide free energy data. We correct partitioning data for solute interactions in the metallic liquid and provide a parameterization utilized in extrapolating these results to the P-T-X conditions proposed by various core formation models. A single-stage core formation model reproduces the mantle abundances of several siderophile elements (Ni, Co, Cr, Mn, Mo, W, Zn) for core-mantle equilibration at pressures from 32 to 42 GPa along the solidus of a deep peridotitic magma ocean (∼3000 K for this pressure range) and oxygen fugacities relevant to the FeO content of the present-day mantle. However, these P-T-fO₂ conditions cannot produce the observed concentrations of Ga, Ge, V, Nb, As and P. For more reducing conditions, the P-T solution domain for single stage core formation occurs at subsolidus conditions and still cannot account for the abundances of Ge, Nb and P. Continuous core formation at the base of a magma ocean at P-T conditions constrained by the peridotite liquidus and fixed fO₂ yields concentrations matching observed values for Ni, Co, Cr, Zn, Mn and W but underestimates the core/mantle partitioning observed for other elements, notably V, which can be reconciled if accretion began under reducing conditions with progressive oxidation to fO₂ conditions consistent with the current concentration of FeO in the mantle as proposed by Wade and Wood (2005). However, neither oxygen fugacity path is capable of accounting for the depletions of Ga and Ge in the Earth’s mantle. To better understand core formation, we need further tests integrating the currently poorly-known effects of light elements and more complex conditions of accretion and differentiation such as giant impacts and incomplete equilibration.     

Conditions of core formation in the earth: Constraints from Nickel and Cobalt partitioning

The abundances of Ni and Co in the Earth’s mantle are depleted relative to chondrites due to terrestrial core formation. Recently, the observed mantle depletions of these elements have been explained by liquid metal-liquid silicate equilibrium during core formation in a high pressure, high temperature magma ocean on the early Earth. However, different magma ocean models, which would be expected to give consistent results, have proposed vastly different pressures (24 to 59 GPa), temperatures (2200 to >4000 K) and oxygen fugacities (−0.15 to −2.4 ΔIW) for the Earth’s magma ocean. In an attempt to resolve the contradictory results from different magma ocean models and determine the thermodynamic conditions appropriate for core formation in the Earth, experiments were conducted to better constrain the influences of temperature and C on the partitioning behaviors of Ni and Co. Results of experiments at 7 GPa with temperatures of 1923-2673 K show that the metal-silicate partition coefficients for both Ni and Co decrease with increasing temperature, with the effect being more significant for Ni. Little change in the partitioning behaviors of either Ni or Co with varying C-content of the metallic liquid was found. By combining the new temperature data with previous results from pressure and oxygen fugacity studies, we parameterized the partitioning behavior of Ni and Co and applied the parameterizations to core formation in a terrestrial magma ocean. Multiple combinations of pressure, temperature, and oxygen fugacity can explain the observed mantle depletions of Ni and Co, and all of the very different previously proposed magma ocean conditions are generally consistent with valid solutions. By using the FeO content of the Earth’s mantle as an additional constraint on the oxygen fugacity, magma ocean conditions of 30-60 GPa, > 2000 K, and −2.2 ΔIW are suggested. Similar systematic approaches and studies of other moderately siderophile elements could further constrain the magma ocean conditions on the early Earth.     

Molecular dynamics studies of CaAl2Si2O8 liquid. Part II: Equation of state and a thermodynamic model

A thermodynamic model and equation of state (EOS) is developed from the molecular dynamics simulation experiments of Spera et al. (2009) for CaAl₂Si₂O₈ liquid over the temperature range 3500-6000 K and pressure interval 0-125 GPa. The model is constructed utilizing the isothermal Universal EOS of Vinet et al. (1986) combined with an expression for the temperature-dependence of the internal energy derived from density functional theory (Rosenfeld and Tarazona, 1998). It is demonstrated that this model is more successful at reproducing the data than the temperature-dependent Universal EOS (Vinet et al., 1987) or the volume-explicit EOS of Ghiorso (2004a). Distinct parameterizations are required to model low (<20 GPa) and high (>20 GPa) pressure regimes. This result is ascribed to the affect of liquid structure on macroscopic thermodynamic properties, specifically the interdependence of average cation-oxygen coordination number on the bulk modulus. The thermodynamic transition between the high- and low-pressure parameterizations is modeled as second order, although the nature of the transition is open to question and may well be first order or lambda-like in character.Analysis of the thermodynamic model reveals a predicted region of liquid-liquid un-mixing at low-temperatures (<1624 K) and pressures (<1.257 GPa). These pressure-temperature conditions are above the glass transition temperature but within the metastable liquid region. They represent the highest temperatures yet suggested for liquid-liquid un-mixing in a silicate bulk composition. A shock wave Hugoniot curve is calculated for comparison with the experimental data of Rigden et al. (1989) and of Asimow and Ahrens (2008). The comparison suggests that the model developed in this paper underestimates the density of the liquid by roughly 10% at pressures greater than ∼20 GPa.     

Pressure dependence of the speciation of dissolved water in rhyolitic melts

Water speciation in rhyolitic melts with dissolved water ranging from 0.8 to 4 wt% under high pressure was investigated. Samples were heated in a piston-cylinder apparatus at 624-1027 K and 0.94-2.83 GPa for sufficient time to equilibrate hydrous species (molecular H₂O and hydroxyl group, H₂O_m + O ? 2OH) in the melts and then quenched roughly isobarically. The concentrations of both hydrous species in the quenched glasses were measured with Fourier transform infrared (FTIR) spectroscopy. For the samples with total water content less than 2.7 wt%, the equilibrium constant (K) is independent of total H₂O concentration. Incorporating samples with higher water contents, the equilibrium constant depends on total H₂O content, and a regular solution model is used to describe the dependence. K changes with pressure nonmonotonically for samples with a given water content at a given temperature. The equilibrium constant does not change much from ambient pressure to 1 GPa, but it increases significantly from 1 to 3 GPa. In other words, more molecular H₂O reacts to form hydroxyl groups as pressure increases from 1 GPa, which is consistent with breakage of tetrahedral aluminosilicate units due to compression of the melt induced by high pressure. The effect of 1.9 GPa (from 0.94 to 2.83 GPa) on the equilibrium constant at 873 K is equivalent to a temperature effect of 49 K (from 873 K to 922 K) at 0.94 GPa. The results can be used to evaluate the role of speciation in water diffusion, to estimate the apparent equilibrium temperature, and to infer viscosity of hydrous rhyolitic melts under high pressure.     

Molecular dynamics simulation of the CH4 and CH4-H2O systems up to 10 GPa and 2573 K

Based on our previous study of the intermolecular potential for pure H₂O and the strict evaluation of the competitive potential models for pure CH₄ and the ab initio fitting potential surface across CH₄-H₂O molecules in this study, we carried out more than two thousand molecular dynamics simulations for the PVTx properties of pure CH₄ and the CH₄-H₂O mixtures up to 2573 K and 10 GPa. Comparison of 1941 simulations with experimental PVT data for pure CH₄ shows an average deviation of 0.96% and a maximum deviation of 2.82%. The comparison of the results of 519 simulations of the mixtures with the experimental measurements reveals that the PVTx properties of the CH₄-H₂O mixtures generally agree with the extensive experimental data with an average deviation of 0.83% and 4% in maximum, which is equivalent to the experimental uncertainty. Moreover, the maximum deviation between the experimental data and the simulation results decreases to about 2% as temperature and pressure increase, indicating that the high accuracy of the simulation is well retained in the high temperature and pressure region.After the validation of the simulation method and the intermolecular potential models, we systematically simulated the PVTx properties of this binary system from 673 K and 0.05 GPa to 2573 K and 10 GPa. In order to integrate all the simulation results and the experimental data for the calculation of thermodynamic properties, an equation of state (EOS) is developed for the CH₄-H₂O system covering 673-2573 K and 0.01-10 GPa. Isochores for compositions <4 mol% CH₄ up to 773 K and 600 MPa are also determined in this paper. The program for the EOS can be downloaded from www.geochem-model.org/programs.htm.     

Experimental study of platinum solubility in silicate melt to 14 GPa and 2273 K: Implications for accretion and core formation in Earth

We determined the solubility limit of Pt in molten haplo-basalt (1 atm anorthite-diopside eutectic composition) in piston-cylinder and multi-anvil experiments at pressures between 0.5 and 14 GPa and temperatures from 1698 to 2223 K. Experiments were internally buffered at ∼IW + 1. Pt concentrations in quenched-glass samples were measured by laser-ablation inductively coupled-plasma mass spectrometry (LA-ICPMS). This technique allows detection of small-scale heterogeneities in the run products while supplying three-dimensional information about the distribution of Pt in the glass samples. Analytical variations in ¹⁹⁵Pt indicate that all experiments contain Pt nanonuggets after quenching. Averages of multiple, time-integrated spot analyses (corresponding to bulk analyses) typically have large standard deviations, and calculated Pt solubilities in silicate melt exhibit no statistically significant covariance with temperature or pressure. In contrast, averages of minimum ¹⁹⁵Pt signal levels show less inter-spot variation, and solubility shows significant covariance with pressure and temperature. We interpret these results to mean that nanonuggets are not quench particles, that is, they were not dissolved in the silicate melt, but were part of the equilibrium metal assemblage at run conditions. We assume that the average of minimum measured Pt abundances in multiple probe spots is representative of the actual solubility. The metal/silicate partition coefficients (D^met/sil) is the inverse of solubility, and we parameterize D^met/sil in the data set by multivariate regression. The statistically robust regression shows that increasing both pressure and temperature causes D^met/silto decrease, that is, Pt becomes more soluble in silicate melt. D^met/sil decreases by less than an order of magnitude at constant temperature from 1 to 14 GPa, whereas isobaric increase in temperature produces a more dramatic effect, with D^met/sil decreasing by more than one order of magnitude between 1623 and 2223 K. The Pt abundance in the Earth’s mantle requires that D^met/sil is ∼1000 assuming core-mantle equilibration. Geochemical models for core formation in Earth based on moderately and slightly siderophile elements are generally consistent with equilibrium metal segregation at conditions generally in the range of 20-60 GPa and 2000-4000 K. Model extrapolations to these conditions show that the Pt abundance of the mantle can only be matched if oxygen fugacity is high (∼IW) and if Pt mixes ideally in molten iron, both very unlikely conditions. For more realistic values of oxygen fugacity (∼IW − 2) and experimentally-based constraints on non-ideal mixing, models show that D^met/sil would be several orders of magnitude too high even at the most favorable conditions of pressure and temperature. These results suggest that the mantle Pt budget, and by implication other highly siderophile elements, was added by late addition of a ‘late veneer’ phase to the accreting proto-Earth.     

Equation of state of the H2O, CO2, and H2O-CO2 systems up to 10 GPa and 2573.15 K: Molecular dynamics simulations with ab initio potential surface

Based on our previous development of the molecular interaction potential for pure H₂O and CO₂ [Zhang, Z.G., Duan, Z.H. 2005a. Isothermal-isobaric molecular dynamics simulations of the PVT properties of water over wide range of temperatures and pressures. Phys. Earth Planet Interiors149, 335-354; Zhang, Z.G., Duan, Z.H. 2005b. An optimized molecular potential for carbon dioxide. J. Chem. Phys.122, 214507] and the ab initio potential surface across CO₂-H₂O molecules constructed in this study, we carried out more than one thousand molecular dynamics simulations of the PVTx properties of the CO₂-H₂O mixtures in the temperature-pressure range from 673.15 to 2573.15 K up to 10.0 GPa. Comparison with extensive experimental PVTx data indicates that the simulated results generally agree with experimental data within 2% in density, equivalent to experimental uncertainty. Even the data under the highest experimental temperature-pressure conditions (up to 1673 K and 1.94 GPa) are well predicted with the agreement within 1.0% in density, indicating that the high accuracy of the simulation is well retained as the temperature and pressure increase. The consistent and stable predictability of the simulation from low to high temperature-pressure and the fact that the molecular dynamics simulation resort to no experimental data but to ab initio molecular potential makes us convinced that the simulation results should be reliable up to at least 2573 K and 10 GPa with errors less than 2% in density. In order to integrate all the simulation results of this study and previous studies [Zhang and Duan, 2005a, 2005b] and the experimental data for the calculation of volumetric properties (volume, density, and excess volume), heat properties, and chemical properties (fugacity, activity, and possibly supercritical phase separation), an equation of state (EOS) is laboriously developed for the CO₂, H₂O, and CO₂-H₂O systems. This EOS reproduces all the experimental and simulated data covering a wide temperature and pressure range from 673.15 to 2573.15 K and from 0 to 10.0 GPa within experimental or simulation uncertainty.