Distribution of Mg2+ between olivine and silicate melt,and its implications regarding melt structure

Consideration of experimental data on the distribution of Mg²⁺ between olivine and silicate liquid clearly demonstrates that the distribution coefficient (K_Mg) is dependent upon variations in temperature, pressure and melt composition, largely because these variables control the solubility of Mg²⁺ in the melt phase. Attempts to minimize composition dependence of K_Mg, utilizing various activity-composition models for silicate melts, have been partially successful. Composition-related effects do not appear to be large, however, for melts of restricted range in composition (e.g., tholeiitic or lunar basalts) as long as the contents of alkalis and the alkali/alumina ratio are relatively small (on a molar basis). For such melts, K_Mg may be used as a reliable geothermometer. By analogy, these conclusions can be extended to the distribution of other divalent cation such as Fe²⁺, Mn²⁺, Ni²⁺ and Co²⁺.     

On type B CAI formation: experimental constraints on fO2 variations in spinel minor element partitioning and reequilibration effects

We report data from a series of dynamic crystallization experiments that focus on determining the partition coefficients (D’s) for V and Ti in the spinel + liquid system of an average type B1 CAI bulk composition for three different fO₂ conditions. Partitioning data for Ca and Si are also obtained. We show that the D’s for V and Ti are fO₂ dependent with D_Ti decreasing at low oxygen fugacity due to the presence of Ti³⁺. D_V is essentially 0 in air, rises to 2.2 at the Fe-FeO buffer and drops to 1.4 at the C-CO buffer. This indicates that V³⁺ is highly compatible in spinel and that higher and lower valence states are much less compatible. We also report data from isothermal experiments that determine diffusion times for V and Ti in same system at a temperature close to the T_max for type B1 CAIs. Diffusion of these elements between spinel and liquid is surprisingly rapid, with essentially total equilibration of Ti and V between spinel and liquid in 90 h run duration. Lack of equilibration of Cr, Si, and Ca shows that the Ti and V equilibration mechanism was diffusion and not dissolution and reprecipitation. Our experimental run durations set an upper limit of a few tens of hours on the time that type B1 CAIs were at their maximum temperature. Based on our data we argue that subsolidus reequilibration between spinel inclusion and host-silicate phases within type B CAIs likely explains the observed range of V and Ti concentrations in spinels which are inclusions in clinopyroxene.     

The solubility of TiO2 in olivine: implications for the mantle wedge environment

One characteristic of many subduction-zone garnet peridotites is that they contain titanium-bearing phases not otherwise found in mantle rocks. In particular, titanoclinohumite and/or its breakdown assemblage consisting of symplectic intergrowths of olivine and ilmenite is common in many of these bodies. The Alpe Arami garnet lherzolite of the Swiss Alps, while lacking titanoclinohumite, displays instead large numbers of FeTiO₃ rod-shaped precipitates in the oldest generation of olivine, amounting to approximately 1% by volume, indicating that at some time in its past, the peridotite experienced conditions under which the solubility of TiO₂ in olivine was >0.6 wt.%. In order to test the hypothesis that the environment of very high solubility of TiO₂ in olivine is to be found at very high pressures, we have conducted experiments on lherzolite compositions with added ilmenite at pressures between 5 and 12 GPa and temperatures of 1350–1700 K. Our results on anhydrous compositions show that whereas solubility of TiO₂ was not detected in olivine at 5 GPa, 1400 K where it coexists with rutile, when rutile disappeared from the paragenesis, the solubility climbed to 0.4 wt.% at 8 GPa, 0.5 wt.% at 10 GPa and to >1.0 wt.% at 12 GPa, 1700 K. These results support our previous interpretations from titanate morphology and abundance that the Alpe Arami massif has surfaced from P=10 GPa but remove the need to suggest a deeper origin and possible precursor phase such as wadsleyite. They also support the hypothesis that garnet peridotites with unusual Ti-bearing phases reflect a unique mantle environment occurring in the mantle wedge overlying subduction zones.     

The dependence of the Fe2+-Mg cation-partitioning between olivine and basaltic liquid on pressure,temperature and composition

The equilibrium partitioning of Fe²⁺ and Mg between olivine and liquid along a liquid line of descent has been determined for a calc-alkaline system, ranging in composition from picritic to andesitic. Experiments were conducted between 1000–1450° C and 1 bar to 30 kbar. Within the compositional range investigated and , the compositional dependence of the Fe²⁺ and Mg partitioning is a function of the Mg-content of the liquid. The Mg-content of the liquid correlates strongly with temperature. The variation of the Fe²⁺ and Mg partitioning were therefore evaluated individualy as functions of composition and temperature alone. The composition dependence of the cation-partitioning coefficients (Kd) is given by the following two equations:

Oxygen isotope exchange between H2O and CO2 at elevated CO2 pressures: Implications for monitoring of geological CO2 storage

Traditionally, the application of stable isotopes in Carbon Capture and Storage (CCS) projects has focused on δ¹³C values of CO₂ to trace the migration of injected CO₂ in the subsurface. More recently the use of δ¹⁸O values of both CO₂ and reservoir fluids has been proposed as a method for quantifying in situ CO₂ reservoir saturations due to O isotope exchange between CO₂ and H₂O and subsequent changes in δ¹⁸O_H2O values in the presence of high concentrations of CO₂. To verify that O isotope exchange between CO₂ and H₂O reaches equilibrium within days, and that δ¹⁸O_H2O values indeed change predictably due to the presence of CO₂, a laboratory study was conducted during which the isotope composition of H₂O, CO₂, and dissolved inorganic C (DIC) was determined at representative reservoir conditions (50 °C and up to 19 MPa) and varying CO₂ pressures. Conditions typical for the Pembina Cardium CO₂ Monitoring Pilot in Alberta (Canada) were chosen for the experiments. Results obtained showed that δ¹⁸O values of CO₂ were on average 36.4 ± 2.2‰ (1σ, n = 15) higher than those of water at all pressures up to and including reservoir pressure (19 MPa), in excellent agreement with the theoretically predicted isotope enrichment factor of 35.5‰ for the experimental temperatures of 50 °C. By using ¹⁸O enriched water for the experiments it was demonstrated that changes in the δ¹⁸O values of water were predictably related to the fraction of O in the system sourced from CO₂ in excellent agreement with theoretical predictions. Since the fraction of O sourced from CO₂ is related to the total volumetric saturation of CO₂ and water as a fraction of the total volume of the system, it is concluded that changes in δ¹⁸O values of reservoir fluids can be used to calculate reservoir saturations of CO₂ in CCS settings given that the δ¹⁸O values of CO₂ and water are sufficiently distinct.     

Systematics of calcium partitioning between olivine and silicate melt: implications for melt structure and calcium content of magmatic olivines

A systematic characterization of the chemical factors that control calcium partitioning between olivine and melt in a magmatic environment was undertaken using experiments performed on compositionally simple systems (CaO-MgO-SiO₂, CaO-MgO-Al₂O₃-SiO₂, CaO-MgO-Al₂O₃-SiO₂-Cr₂O₃, CaO-MgO-Al₂O₃-SiO₂-TiO₂, CaO-MgO-Al₂O₃-SiO₂-Na₂O, CaO-MgO-Al₂O₃-SiO₂-FeO, CaO-MgO-Al₂O₃-SiO₂-FeO-Na₂O) over a wide range of temperature (1050–1530 °C) at one bar pressure. The calcium concentration of olivines is shown to be dependent not only on the forsterite content of the olivine but to a large extent on melt composition. For a fixed CaO content of the melt, these results show that the CaO concentration of olivine is strongly sensitive to the amount of alumina, alkali and ferrous iron present in the coexisting melt. Oxygen fugacity and temperature are not found directly to affect Ca partitioning. It is thus proposed that the systematic variations of the calcium content of olivine may be used as an “in-situ chemical potentiometer” of the lime activity of the melt. Based upon these data in synthetic systems, an empirical model describing Ca partitioning between olivine and melt is developed. When applied to natural olivines this model reproduces their Ca content, where melt composition is known, to within ±10% relative. The model may therefore be used to predict changes in melt composition during olivine crystallization and/or to assess whether an olivine is in equilibrium with its host magma. Finally, the wide range of Ca partitioning observed at fixed crystal composition confirms that minor element partitioning between crystal and melt cannot be predicted from the physical characteristics of the crystal alone, and that the non-ideality of the melt has to be taken into account. Received: 12 June 1998 / Accepted: 1 February 1999     

Carbon-13 exchange between CO2 and CH4 under geothermal conditions

On the basis of recently reported data on the kinetics of carbon-13 exchange between CO₂ and CH₄ at temperatures above 500°C, first order rate constants $\text{log k = 11.16?10,190/T}$ were derived allowing variations in Δ, the difference in the isotopic composition of coexisting CO₂ and CH₄, to be evaluated as a function of initial composition and cooling rate of the rising geothermal fluid. Observed Δ-values in geothermal discharges are likely to represent frozen in compositions attained after minimum residence times of 20 ka at 400°C or 10 Ma at 300°C. The carbon-13 contents of any biogenic gases are unlikely to have been affected by thermal re-equilibration at temperatures below 200°C. The chemical equilibrium involving CO₂ and CH₄ can be expected to proceed about a hundred times faster than isotopic equilibration.     

Experiments and geochemical modelling of CO2 sequestration by olivine: Potential,quantification

Aqueous solutions equilibrated with supercritical CO₂ (150 °C and total pressure of 150 bar) were investigated in order to characterize their respective conditions of carbonation. Dissolution of olivine and subsequent precipitation of magnesite with a net consumption of CO₂ were expected. A quantified pure mineral phase (powders with different olivine grain diameter [20–80 μm], [80–125 μm], [125–200 μm] and [>200 μm]), and CO₂ (as dried ice) were placed in closed-batch reactors (soft Au tubes) in the presence of solutions. Different salinities (from 0 to 3400 mM) and different ratios of solution/solid (mineral phase) (from 0.1 to 10) were investigated. Experiments were performed over periods from 2 to 8 weeks. Final solid products were quantified by the Rock-Eval 6 technique, and identified using X-ray diffraction, Raman spectroscopy, electron microprobe and scanning electron microscopy. Gaseous compounds were quantified by a vacuum line equipped with a Toepler pump and identified and measured by gas chromatography (GC). Carbon mass balances were calculated.     

CO2 in haplo-phonolite melt: solubility, speciation and carbonate complexation

CO₂ solubility was measured in a synthetic iron-free phonolite (haplo-phonolite) by equilibrating melt with excess CO₂ fluid in a piston cylinder apparatus for a range of pressures (1.0- 2.5 GPa) and temperatures (1300 to 1550°C). The quenched glasses were then analysed using a bulk carbon analytical method (LECO). The measured solubilities are between 0.65 and 2.77 wt.% for the range of conditions studied and show a negative correlation with temperature as reported for most other silicate melt compositions.A range of carbonate species are present within the glass, as well as minor amounts of molecular CO₂. FTIR and NMR analyses suggest that carbonate is present as both ‘network’ and ‘depolymerised’ units as shown for relatively highly polymerised compositions in the model of Brooker et al. (2001b). The bulk CO₂ analyses were used to calibrate the IR extinction coefficient for the carbonate groups. However, the results show that the values obtained for the glasses vary with the melt equilibration conditions, presumably because the ratio of the different carbonate species changes as a complex function of run pressure, temperature and quench rate. Thus the use of IR may not be a reliable method for the quantification of dissolved CO₂ concentrations in natural glasses of ‘intermediate’ composition.     

The combined effects of ƒO2 and melt composition on SnO2 solubility and tin diffusivity in haplogranitic melts

The diffusion profile method has been employed to measure tin diffusion coefficients and SnO₂ solubility in water-saturated, peralkaline to peraluminous haplogranitic melts at 850°C, 2 kbar, and log ƒ_O2 conditions ranging from FMQ - 0.57 to FMQ + 3.49. At reduced conditions cassiterite is highly soluble and tin is present dominantly as a Sn²⁺ species, whereas at oxidized conditions SnO₂ is much less soluble, and tin is present dominantly as a Sn⁴⁺ species. There is a strong melt composition control on SnO₂ solubility; solubilities are at a minimum at the subaluminous composition, increase strongly with alkali content in peralkaline compositions and weakly with Al content in peraluminous compositions. In the case of the latter, this increase can only be distinguished at reduced conditions, e.g., at a log ƒ_O2 of FMQ - 0.57 cassiterite solubility increases from 2.78 to 4.11 wt% SnO₂ for melt with Al/(Na + K)compositions (A.S.I.) of 1.0 and 1.2, respectively. At oxidized conditions SnO₂ solubility is 500 ppm for both the A.S.I. 1.0 and 1.2 compositions. By comparison Sn0₂ solubilities in the most peralkaline composition investigated range from 3.94 wt% to -10 wt% Sn02, for the most oxidized to the most reduced conditions, respectively. Thermodynamic modelling of the data indicates that the Sn⁴⁺/ΣSn ratio in the melt is also at a minimum at the subaluminous composition, ranging from 0.4 at log ƒ_O2 of FMQ + 3.49 to 0.01 at FMQ - 0.57. Over the same log foZ range the Sn⁴⁺/ΣSn ratio for the A.S.I. 0.6 composition ranges from 0.98 to 0.4 and for the A.S.I. 1.25 composition, from 0.8 to 0.02.Tin diffusivity is dependent on both f_O2 and melt composition. The effective binary diffusion coefficient of tin at reduced conditions is approximately 10^−7.5 cm²/sec for the peraluminous compositions and 10^−8.2 cm²/sec for the peralkaline compositions. At oxidized conditions these values decrease to approximately 10^−8.2 and 10^−9.0 cm²/sec, respectively. These are interpreted to reflect relatively fast diffusion where Sn²⁺ is the dominant valence and tin in this case behaves similar to a network modifier and relatively slow diffusion where Sn⁴⁺ is dominant and tin likely has a lower coordination number. Alternatively, the coordination of Sn²⁺ and Sn⁴⁺ is the same, but the bond strengths are different. At fixed f_O2 the faster diffusivity in the peraluminous compositions reflects the lower Sn⁴⁺/Sn²⁺ ratio. The fact the Sn⁴⁺/Sn²⁺ ratio in melts varies greatly with ƒ_O2 at redox conditions near FMQ suggests that the partitioning behaviour of tin possibly changes during the evolution of an igneous suite in general and of a peraluminous granite suite in particular.     

Effects of speciation on equilibrium fractionations and rates of oxygen isotope exchange between (PO4)aq and H2O

The effects of phosphate speciation on both rates of isotopic exchange and oxygen isotope equilibrium fractionation factors between aqueous phosphate and water were examined over the temperature range 70 to 180°C. Exchange between phosphate and water is much faster at low pH than at high pH, an observation that is similar to what has been observed in the analogous sulfate-water system. Oxygen isotope fractionations between protonated species like H₃PO₄ and H₂PO₄⁻ that are dominant at relatively low pH and species like PO₄³⁻ and ion pairs like KHPO₄⁻ that are dominant at relatively high pH, range between 5 and 8‰ at the temperatures of the experiments. In aqueous phosphate systems at equilibrium, ¹⁸O/¹⁶O ratios increase with increasing degree of protonation of phosphate. This effect can be explained in part by the relative magnitudes of the dissociation constants of the protonated species. Under equilibrium conditions, carbonate in solution or in solid phases concentrates ¹⁸O relative to orthophosphate in solution or in solid phases at all temperatures, supporting the traditional view that biogenic phosphate is precipitated in near oxygen isotope equilibrium with body/ambient aqueous fluids with no attendant vital effects.     

Low-pressure granulite facies metapelitic assemblages and corona textures from MacRobertson Land, east Antarctica: the importance of Fe2O3 and TiO2 in accounting for spinel-bearing assemblages

Low-pressure granulite facies metasedimentary gneisses exposed in MacRobertson Land, east Antarctica, include hercynitic spinel-bearing metapelitic gneisses. Peak metamorphic mineral assemblages include spinel + rutile + ilmenite + sillimanite + garnet, spinel + ilmenite + sillimanite + garnet + cordierite, ortho-pyroxene + magnetite + ilmenite + garnet, spinel + cordierite + biotite + ilmenite and orthopyroxene + cordierite + biotite, each with quartz, K-feldspar and melt. The presence of garnet + biotite- and cordierite + orthopyroxene-bearing assemblages implies crossing tie-lines in AFM projection for the K₂O-FeO-MgO-Al₂O₃-SiO₂-H₂O (KFMASH) system. This apparent contradiction, and the presence of spinel, rutile and ilmenite in the assemblages, is acounted for by using the KFMASH-TiO₂-O₂ system, i.e. AFM + TiO₂+ Fe₂O₃. We derive a petrogenetic grid for this system, applicable to low-pressure granulite facies metamorphic conditions. Retrograde assemblages are interpreted from corona textures on hercynitic spinel and Fe-Ti oxides. The relative positions of the peak and retrograde metamorphic assemblages on the petrogenetic grid suggest that corona development occurred during essentially isobaric cooling.     

A high temperature equation of state for the H2O-CaCl2 and H2O-MgCl2 systems

An equation of state (EOS) is developed for salt-water systems in the high temperature range. As an example of the applications, this EOS is parameterized for the calculation of density, immiscibility, and the compositions of coexisting phases in the CaCl₂-H₂O and MgCl₂-H₂O systems from 523 to 973 K and from saturation pressure to 1500 bar. All available volumetric and phase equilibrium measurements of these binaries are well represented by this equation. This EOS is based on a Helmholtz free energy representation constructed from a reference system containing hard-sphere and polar contributions plus an empirical correction. For the temperature and pressure range in this study, the electrolyte solutes are assumed to be associated. The water molecules are modeled as hard spheres with point dipoles and the solute molecules, MgCl₂ and CaCl₂, as hard spheres with point quadrupoles. The free energy of the reference system is calculated from an analytical representation of the Helmholtz free energy of the hard-sphere contributions and perturbative estimates of the electrostatic contributions. The empirical correction used to account for deviations of the reference system predictions from measured data is based on a virial expansion. The formalism allows generalization to aqueous systems containing insoluble gases (CO₂, CH₄), alkali chlorides (NaCl, KCl), and alkaline earth chlorides (CaCl₂, MgCl₂). The program of this model is available as an electronic annex (see EA1 and EA2) and can also be downloaded at: http://www.geochem-model.org/programs.htm.     

Experimental determination of oxygen isotope fractionations between CO2 vapor and soda-melilite melt

We report results of experiments constraining oxygen isotope fractionations between CO₂ vapor and Na-rich melilitic melt at 1 bar and 1250 and 1400°C. The fractionation factor constrained by bracketed experiments, 1000^.lnα_{CO2-Na melilitic melt}, is 2.65±0.25 ‰ (±2σ; n=92) at 1250°C and 2.16±0.16 ‰ (2σ; n=16) at 1400°C. These values are independent of Na content over the range investigated (7.5 to 13.0 wt. % Na₂O). We combine these data with the known reduced partition function ratio of CO₂ to obtain an equation describing the reduced partition function ratio of Na-rich melilite melt as a function of temperature. We also fit previously measured CO₂-melt or -glass fractionations to obtain temperature-dependent reduced partition function ratios for all experimentally studied melts and glasses (including silica, rhyolite, albite, anorthite, Na-rich melilite, and basalt). The systematics of these data suggest that reduced partition function ratios of silicate melts can be approximated either by using the Garlick index (a measure of the polymerization of the melt) or by describing melts as mixtures of normative minerals or equivalent melt compositions. These systematics suggest oxygen isotope fractionation between basalt and olivine at 1300°C of approximately 0.4 to 0.5‰, consistent with most (but not all) basalt glass-olivine fractionations measured in terrestrial and lunar basalts.     

Thermodynamic modelling of the reaction muscovite+cordierite→Al2SiO5+biotite+quartz+ H2O: constraints from natural assemblages and implications for the metapelitic petrogenetic grid

The reaction muscovite+cordierite→biotite+Al₂SiO₅ +quartz+H₂O is of considerable importance in the low pressure metamorphism of pelitic rocks: (1) its operation is implied in the widespread assemblage Ms + Crd +And± Sil + Bt + Qtz, a common mineral assemblage in contact aureoles and low pressure regional terranes; (2) it is potentially an important equilibrium for pressure estimation in low pressure assemblages lacking garnet; and (3) it has been used to distinguish between clockwise and anticlockwise P–T paths in low pressure metamorphic settings. Experiments and thermodynamic databases provide conflicting constraints on the slope and position of the reaction, with most thermodynamic databases predicting a positive slope for the reaction. Evidence from mineral assemblages and microtextures from a large number of natural prograde sequences, in particular contact aureoles, is most consistent with a negative slope (andalusite and/or sillimanite occurs upgrade of, and may show evidence for replacement of, cordierite). Mineral compositional trends as a function of grade are variable but taken as a whole are more consistent with a negative slope than a positive slope. Thermodynamic modelling of reaction 1 and associated equilibria results in a low pressure metapelitic petrogenetic grid in the system K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O (KFMASH) which satisfies most of the natural and experimental constraints. Contouring of the Fe–Mg divariant interval represented by reaction 1 allows for pressure estimation in garnet‐absent andalusite+cordierite‐bearing schists and hornfelses. The revised topology of reaction 1 allows for improved analysis of P–T paths from mineral assemblage sequences and microtextures in the same rocks.     

Hydrogen isotope exchange kinetics between H2O and H4SiO4 from ab initio calculations

Hydrogen isotope exchange between water and orthosilicic acid (H₄SiO₄) was modeled using B3LYP calculations and classical transition-state theory. Configurations of 1, 2, 3 and 7 water molecules and H₄SiO₄ were used to investigate energetically viable reaction pathways. An upper-bound of 71 kJ/mol was assumed for the zero-point energy corrected barrier (ZPECB) because this is the experimentally determined activation energy for Si-O bond breaking (Rimstidt and Barnes, 1980) and ZPECB is expected to be close to this value. Long range solvation forces were accounted for using the integral equation formalism polarized continuum model (IEFPCM; Cancès et al., 1997). Primary and secondary isotope effects were computed by exchanging hydrogen atoms with deuterium. Results show that reaction mechanisms involving 3 and 7 water molecules have ZPECB of 34 to 38 kJ/mol, whereas those involving 1 and 2 water molecules have ZPECB in excess of the set upper-bound. The lower range of ZPECB with 3 or 7 water molecules is reasonable to explain rapid hydrogen isotope exchange with silicates. Rate constant calculations accounting for tunneling, anharmonicity and scaling factors indicate that the reaction is fast and equilibrium can be assumed under most geologic conditions.     

Partitioning of Ni2+, Co2+, Fe2+, Mn2+ and Mg2+ between olivine and silicate melts: compositional dependence of partition coefficient

Partitioning of Ni²⁺, Co²⁺, Fe²⁺, Mn²⁺ and Mg²⁺ between olivine and silicate melts has been determined near the join (Mg_0.5·-Fe_0.5)₂SiO₄-K₂O 4SiO₂ and for seven different basaltic compositions. The experiments were made at 1 atm total pressure, 1500-1100°C, and under moderate to reducing oxygen fugacities. The concentration factor, defined as K^MO = (MO)^ol/(MO)^liq (molar ratio), increases markedly for all the cations studied as the olivine component of the liquid decreases. Much of the increase in K^MO is considered as due to the compositional effect of the coexisting liquid: the temperature effect on K^MO is probably opposite to the compositional effect (K^MO decreases as temperature decreases).The partition coefficient K^MO-MgO = (MO/MgO)^ol/(MO/MgO)^liq for the reaction, M_ol²⁺ + Mg_liq²⁺ = M_liq²⁺ + Mg_ol²⁺. is relatively constant over a wide range of SiO₂ content of the liquid, except in the case of Ni²⁺. The partition coefficients have similar ranges both in synthetic and natural rock systems: K^NiO-MgO = 1.8–3.0, K^CoO-MgO = 0.6–0.8, K^FeO-MgO = 0.27–0.38, and K^MnO-MgO = 0.23–0.32. There is a systematic variation in the partition coefficient K^MO-MgO with the composition of liquid; K^MO-MgO increases with increasing SiO₂ content of melt. The partition coefficients for Co²⁺, Fe²⁺ and Mn²⁺ are useful to test the equilibration of olivine with magma of a wide compositional range.     

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 kinetics of oxygen exchange between the GeO4Al12(OH)24(OH2)12(aq) molecule and aqueous solutions

We report rates of oxygen exchange with bulk solution for an aqueous complex, ^IVGeO₄Al₁₂(OH)₂₄(OH₂)₁₂⁸⁺(aq) (GeAl₁₂), that is similar in structure to both the ^IVAlO₄Al₁₂(OH)₂₄(OH₂)₁₂⁷⁺(aq) (Al₁₃) and ^IVGaO₄Al₁₂(OH)₂₄(OH₂)₁₂⁷⁺(aq) (GaAl₁₂) molecules studied previously. All of these molecules have ε-Keggin-like structures, but in the GeAl₁₂ molecule, occupancy of the central tetrahedral metal site by Ge(IV) results in a molecular charge of +8, rather than +7, as in the Al₁₃ and GaAl₁₂. Rates of exchange between oxygen sites in this molecule and bulk solution were measured over a temperature range of 274.5 to 289.5 K and 2.95 < pH < 4.58 using ¹⁷O-NMR.Apparent rate parameters for exchange of the bound water molecules (η-OH₂) are k_ex²⁹⁸ = 200 (±100) s⁻¹, ΔH^‡ = 46 (±8) kJ · mol⁻¹, and ΔS^‡ = −46 (±24) J · mol⁻¹ K⁻¹ and are similar to those we measured previously for the GaAl₁₂ and Al₁₃ complexes. In contrast to the Al₁₃ and GaAl₁₂ molecules, we observe a small but significant pH dependence on rates of solvolysis that is not yet fully constrained and that indicates a contribution from the partly deprotonated GeAl₁₂ species.The two topologically distinct μ₂-OH sites in the GeAl₁₂ molecule exchange at greatly differing rates. The more labile set of μ₂-OH sites in the GeAl₁₂ molecule exchange at a rate that is faster than can be measured by the ¹⁷O-NMR isotopic-equilibration technique. The second set of μ₂-OH sites have rate parameters of k_ex²⁹⁸ = 6.6 (±0.2) · 10⁻⁴ s⁻¹, ΔH^‡ = 82 (±2) kJ · mol⁻¹, and ΔS^‡ = −29 (±7) J · mol⁻¹ · K⁻¹, corresponding to exchanges ≈40 and ≈1550 times, respectively, more rapid than the less labile μ₂-OH sites in the Al₁₃ and GaAl₁₂ molecules. We find evidence of nearly first-order pH dependence on the rate of exchange of this μ₂-OH site with bulk solution for the GeAl₁₂ molecule, which contrasts with Al₁₃ and GaAl₁₂ molecules.     

Rates of oxygen exchange between the Al2O8Al28(OH)56(H2O)26(aq) (Al30) molecule and aqueous solution

Rates of steady exchange of oxygens between bulk solution and the largest known aluminum polyoxocation: Al₂O₈Al₂₈(OH)₅₆(H₂O)₂₆¹⁸⁺(aq) (Al₃₀) are reported at pH≈4.7 and 32-40°C. The Al₃₀ molecule is a useful model for geochemists because it is ≈2 nm in length, comparable to the smallest colloidal solids, and it has structural complexity greater than the surfaces of most aluminum (hydr)oxide minerals. The Al₃₀ molecule has 15 distinct hydroxyl sites and eight symmetrically distinct bound waters. Among the hydroxyl bridges are two sets of μ₃-OH, which are not present in any of the other aluminum polyoxocations that have yet been studied by NMR methods. Rates of isotopic equilibration of the μ₂-OH and μ₃-OH hydroxyls and bound water molecules fall within the same range as we have determined for other aluminum solutes, although it is impossible to determine rate laws for exchange at the large number of individual oxygen sites. After injection of ¹⁷O-enriched water, growth of the ¹⁷O-NMR peak near 37 ppm, which is assigned to μ₂-OH and μ₃-OH hydroxyl bridges, indicates that these bridges equilibrate within two weeks at temperatures near 35°C. The peak at +22 ppm in the ¹⁷O-NMR spectra, assigned to bound water molecules (η-OH₂), varies in width with temperature in a similar fashion as for other aluminum solutes, suggesting that most of the η-OH₂ sites exchange with bulk solution at rates that fall within the range observed for other aluminum complexes. Signal from one anomalous group of four η-OH₂ sites is not observed, indicating that these sites exchange at least a factor of ten more rapidly than the other η-OH₂ sites on the Al₃₀.