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.     

Prediction of vapor-liquid equilibrium and PVTx properties of geological fluid system with SAFT-LJ EOS including multi-polar contribution. Part I: Application to H2O-CO2 system

Molecular based equations of state (EOS) are attractive because they can take into account the energetic contribution of the main types of molecular interactions. This study models vapor-liquid equilibrium (VLE) and PVTx properties of the H₂O-CO₂ binary system using a Lennard-Jones (LJ) referenced SAFT (Statistical Associating Fluid Theory) EOS. The improved SAFT-LJ EOS is defined in terms of the residual molar Helmholtz energy, which is a sum of four terms representing the contributions from LJ segment-segment interactions, chain-forming among the LJ segments, short-range associations and long-range multi-polar interactions. CO₂ is modeled as a linear chain molecule with a constant quadrupole moment, and H₂O is modeled as a spherical molecule with four association sites and a dipole moment. The multi-polar contribution to Helmholtz energy, including the dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole contribution for H₂O-CO₂ system, is calculated using the theory of Gubbins and Twu (1978). Six parameters for pure H₂O and four parameters for pure CO₂ are needed in our model. The Van der Waals one-fluid mixing rule is used to calculate the Lennard-Jones energy parameter and volume parameter for the mixture. Two or three binary parameters are needed for CO₂-H₂O mixtures, which are evaluated from phase equilibrium data of the binary system. Comparison with the experimental data shows that our model represents the PVT properties of CO₂ better than other SAFT EOS without a quadrupole contribution. For the CO₂-H₂O system, our model agrees well with the vapor-liquid equilibrium data from 323-623 K. The average relative deviation for CO₂ solubility (expressed in mole fraction) in water is within 6%. Our model can also predict the PVTx properties of CO₂-H₂O mixtures up to 1073 K and 3000 bar. The good performance of this model indicates that: (1) taking account of the multi-polar contribution explicitly improves the agreement of calculated properties with experimental data at high temperatures and high pressures, (2) the molecular-based EOS with just a few parameters fit to data in the sub-critical region can predict the thermodynamic properties of fluids over a wide range of P-T conditions.     

Thermodynamic modeling of binary CH4-H2O fluid inclusions

This work reports the application of thermodynamic models, including equations of state, to binary (salt-free) CH₄-H₂O fluid inclusions. A general method is presented to calculate the compositions of CH₄-H₂O inclusions using the phase volume fractions and dissolution temperatures of CH₄ hydrate. To calculate the homogenization pressures and isolines of the CH₄-H₂O inclusions, an improved activity-fugacity model is developed to predict the vapor-liquid phase equilibrium. The phase equilibrium model can predict methane solubility in the liquid phase and water content in the vapor phase from 273 to 623 K and from 1 to 1000 bar (up to 2000 bar for the liquid phase), within or close to experimental uncertainties. Compared to reliable experimental phase equilibrium data, the average deviation of the water content in the vapor phase and methane solubility in the liquid phase is 4.29% and 3.63%, respectively. In the near-critical region, the predicted composition deviations increase to over 10%. The vapor-liquid phase equilibrium model together with the updated volumetric model of homogenous (single-phase) CH₄-H₂O fluid mixtures (Mao S., Duan Z., Hu J. and Zhang D. (2010) A model for single-phase PVTx properties of CO₂-CH₄-C₂H₆-N₂-H₂O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar. Chem. Geol.275, 148-160), is applied to calculate the isolines, homogenization pressures, homogenization volumes, and isochores at specified homogenization temperatures and compositions. Online calculation is on the website: http://www.geochem-model.org/.     

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.     

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.     

Residence times for protons bound to three oxygen sites in the AlO4Al12(OH)24(H2O)12 polyoxocation

Although, the kinetic reactivity of a mineral surface is determined, in part, by the rates of exchange of surface-bound oxygens and protons with bulk solution, there are no elementary rate data for minerals. However, such kinetic measurements can be made on dissolved polynuclear clusters, and here we report lifetimes for protons bound to three oxygen sites on the AlO₄Al₁₂(OH)₂₄(H₂O)₁₂⁷⁺ (Al₁₃) molecule, which is a model for aluminum-hydroxide solids in water. Proton lifetimes were measured using ¹H NMR at pH ∼ 5 in both aqueous and mixed solvents. The ¹H NMR peak for protons on bound waters (η-H₂O) lies near 8 ppm in a 2.5:1 mixture of H₂O/acetone-d₆ and broadens over the temperature range −20 to −5 °C. Extrapolated to 298 K, the lifetime of a proton on a η-H₂O is τ²⁹⁸ ∼ 0.0002 s, which is surprisingly close to the lifetime of an oxygen in the η-H₂O (∼0.0009 s), but in the same general range as lifetimes for protons on fully protonated monomer ions of trivalent metals (e.g., Al(H₂O)₆³⁺). The lifetime is reduced somewhat by acid addition, indicating that there is a contribution from the partly deprotonated Al₁₃ molecule in addition to the fully protonated Al₁₃ at self-buffered pH conditions. Proton lifetimes on the two distinct sets of hydroxyls bridging two Al(III) (μ₂-OH) differ substantially and are much shorter than the lifetime of an oxygen at these sites. The average lifetimes for hydroxyl protons were measured in a 2:1 mixture of H₂O/dmso-d₆ over the temperature range 3.7-95.2 °C. The lifetime of a hydrogen on one of the μ₂-OH was also measured in D₂O. The τ²⁹⁸ values are ∼0.013 and ∼0.2 s in the H₂O/dmso-d₆ solution and the τ²⁹⁸ value for the μ₂-OH detectable in D₂O is τ²⁹⁸ ∼ 0.013 s. The ¹H NMR peak for the more reactive μ₂-OH broadens slightly with acid addition, indicating a contribution from an exchange pathway that involves a proton or hydronium ion. These data indicate that surface protons on minerals will equilibrate with near-surface waters on the diffusional time scale.     

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).     

CO2 solubility in Martian basalts and Martian atmospheric evolution

To understand possible volcanogenic fluxes of CO₂ to the Martian atmosphere, we investigated experimentally carbonate solubility in a synthetic melt based on the Adirondack-class Humphrey basalt at 1-2.5 GPa and 1400-1625 °C. Starting materials included both oxidized and reduced compositions, allowing a test of the effect of iron oxidation state on CO₂ solubility. CO₂ contents in experimental glasses were determined using Fourier transform infrared spectroscopy (FTIR) and Fe³⁺/Fe^T was measured by Mössbauer spectroscopy. The CO₂ contents of glasses show no dependence on Fe³⁺/Fe^T and range from 0.34 to 2.12 wt.%. For Humphrey basalt, analysis of glasses with gravimetrically-determined CO₂ contents allowed calibration of an integrated molar absorptivity of 81,500 ± 1500 L mol⁻¹ cm⁻² for the integrated area under the carbonate doublet at 1430 and 1520 cm⁻¹. The experimentally determined CO₂ solubilities allow calibration of the thermodynamic parameters governing dissolution of CO₂ vapor as carbonate in silicate melt, K_II, (Stolper and Holloway, 1988) as follows: , ΔV⁰ = 20.85 ± 0.91 cm³ mol⁻¹, and ΔH⁰ = −17.96 ± 10.2 kJ mol⁻¹. This relation, combined with the known thermodynamics of graphite oxidation, facilitates calculation of the CO₂ dissolved in magmas derived from graphite-saturated Martian basalt source regions as a function of P, T, and f_O2. For the source region for Humphrey, constrained by phase equilibria to be near 1350 °C and 1.2 GPa, the resulting CO₂ contents are 51 ppm at the iron-wüstite buffer (IW), and 510 ppm at one order of magnitude above IW (IW + 1). However, solubilities are expected to be greater for depolymerized partial melts similar to primitive shergottite Yamato 980459 (Y 980459). This, combined with hotter source temperatures (1540 °C and 1.2 GPa) could allow hot plume-like magmas similar to Y 980459 to dissolve 240 ppm CO₂ at IW and 0.24 wt.% of CO₂ at IW + 1. For expected magmatic fluxes over the last 4.5 Ga of Martian history, magmas similar to Humphrey would only produce 0.03 and 0.26 bars from sources at IW and IW + 1, respectively. On the other hand, more primitive magmas like Y 980459 could plausibly produce 0.12 and 1.2 bars at IW and IW + 1, respectively. Thus, if typical Martian volcanic activity was reduced and the melting conditions cool, then degassing of CO₂ to the atmosphere may not be sufficient to create greenhouse conditions required by observations of liquid surface water. However, if a significant fraction of Martian magmas derive from hot and primitive sources, as may have been true during the formation of Tharsis in the late Noachian, that are also slightly oxidized (IW + 1.2), then significant contribution of volcanogenic CO₂ to an early Martian greenhouse is plausible.     

Application of the Pitzer ion interaction model to isopiestic data for the Fe2(SO4)3-H2SO4-H2O system at 298.15 and 323.15 K

Recent isopiestic studies of the Fe₂(SO₄)₃-H₂SO₄-H₂O system at 298.15 K are represented with an extended version of Pitzer’s ion interaction model. The model represents osmotic coefficients for aqueous {(1 − y)Fe₂(SO₄)₃ + yH₂SO₄} mixtures from 0.45 to 3.0 m at 298.15 K and 0.0435 ? y ? 0.9370. In addition, a slightly less accurate representation of a more extended molality range to 5.47 m extends over the same y values, translating to a maximum ionic strength of 45 m. Recent isopiestic data for the system at 323.15 K are represented with the extended Pitzer model over a limited range in molality and solute fraction. These datasets are also represented with the usual “3-parameter” version of Pitzer’s model so that it may be incorporated in geochemical modeling software, but is a slightly less accurate representation of thermodynamic properties for this system. Comparisons made between our ion interaction model and available solubility data display partial agreement for rhomboclase and significant discrepancy for ferricopiapite. The comparisons highlight uncertainty remaining for solubility predictions in this system as well as the need for additional solubility measurements for Fe³⁺-bearing sulfate minerals. The resulting Pitzer ion interaction models provide an important step toward an accurate and comprehensive representation of thermodynamic properties in this geochemically important system.     

Abundance of mass 47 CO2 in urban air, car exhaust, and human breath

Atmospheric carbon dioxide is widely studied using records of CO₂ mixing ratio, δ¹³C and δ¹⁸O. However, the number and variability of sources and sinks prevents these alone from uniquely defining the budget. Carbon dioxide having a mass of 47 u (principally ¹³C¹⁸O¹⁶O) provides an additional constraint. In particular, the mass 47 anomaly (Δ₄₇) can distinguish between CO₂ produced by high temperature combustion processes vs. low temperature respiratory processes. Δ₄₇ is defined as the abundance of mass 47 isotopologues in excess of that expected for a random distribution of isotopes, where random distribution means that the abundance of an isotopologue is the product of abundances of the isotopes it is composed of and is calculated based on the measured ¹³C and ¹⁸O values. In this study, we estimate the δ¹³C (vs. VPDB), δ¹⁸O (vs. VSMOW), δ47, and Δ₄₇ values of CO₂ from car exhaust and from human breath, by constructing ‘Keeling plots’ using samples that are mixtures of ambient air and CO₂ from these sources. δ47 is defined as , where is the R⁴⁷ value for a hypothetical CO₂ whose δ¹³C_VPDB = 0, δ¹⁸O_VSMOW = 0, and Δ₄₇ = 0. Ambient air in Pasadena, CA, where this study was conducted, varied in [CO₂] from 383 to 404 μmol mol⁻¹, in δ¹³C and δ¹⁸O from −9.2 to −10.2‰ and from 40.6 to 41.9‰, respectively, in δ47 from 32.5 to 33.9‰, and in Δ₄₇ from 0.73 to 0.96‰. Air sampled at varying distances from a car exhaust pipe was enriched in a combustion source having a composition, as determined by a ‘Keeling plot’ intercept, of −24.4 ± 0.2‰ for δ¹³C (similar to the δ¹³C of local gasoline), δ¹⁸O of 29.9 ± 0.4‰, δ47 of 6.6 ± 0.6‰, and Δ₄₇ of 0.41 ± 0.03‰. Both δ¹⁸O and Δ₄₇ values of the car exhaust end-member are consistent with that expected for thermodynamic equilibrium at∼200 °C between CO₂ and water generated by combustion of gasoline-air mixtures. Samples of CO₂ from human breath were found to have δ¹³C and δ¹⁸O values broadly similar to those of car exhaust-air mixtures, −22.3 ± 0.2 and 34.3 ± 0.3‰, respectively, and δ47 of 13.4 ± 0.4‰. Δ₄₇ in human breath was 0.76  ± 0.03‰, similar to that of ambient Pasadena air and higher than that of the car exhaust signature.     

Iron weathering products in a CO2 + (H2O or H2O2) atmosphere: Implications for weathering processes on the surface of Mars

Various iron-bearing primary phases and rocks have been weathered experimentally to simulate possible present and past weathering processes occurring on Mars. We used magnetite, monoclinic and hexagonal pyrrhotites, and metallic iron as it is suggested that meteoritic input to the martian surface may account for an important source of reduced iron. The phases were weathered in two different atmospheres: one composed of CO₂ + H₂O, to model the present and primary martian atmosphere, and a CO₂ + H₂O + H₂O₂ atmosphere to simulate the effect of strong oxidizing agents. Experiments were conducted at room temperature and a pressure of 0.75 atm. Magnetite is the only stable phase in the experiments and is thus likely to be released on the surface of Mars from primary rocks during weathering processes. Siderite, elemental sulfur, ferrous sulfates and ferric (oxy)hydroxides (goethite and lepidocrocite) are the main products in a water-bearing atmosphere, depending on the substrate. In the peroxide atmosphere, weathering products are dominated by ferric sulfates and goethite. A kinetic model was then developed for iron weathering in a water atmosphere, using the shrinking core model (SCM). This model includes competition between chemical reaction and diffusion of reactants through porous layers of secondary products. The results indicate that for short time scales, the mechanism is dominated by a chemical reaction with second order kinetics (k = 7.75 × 10⁻⁵ g⁻¹/h), whereas for longer time scales, the mechanism is diffusion-controlled (De_A = 2.71 × 10⁻¹⁰ m²/h). The results indicate that a primary CO₂- and H₂O-rich atmosphere should favour sulfur, ferrous phases such as siderite or Fe²⁺-sulfates, associated with ferric (oxy)hydroxides (goethite and lepidocrocite). Further evolution to more oxidizing conditions may have forced these precursors to evolve into ferric sulfates and goethite/hematite.     

Chlorine-rich metasomatic H2O-CO2 fluids in amphibole-bearing peridotites from Injibara (Lake Tana region, Ethiopian plateau): Nature and evolution of volatiles in the mantle of a region of continental flood basalts

Petrological and geochemical study of volatile bearing phases (fluid inclusions, amphibole, and nominally anhydrous minerals) in a spinel lherzolite xenolith suite from Quaternary lavas at Injibara (Lake Tana region, Ethiopian plateau) shows compelling evidence for metasomatism in the lithospheric mantle in a region of mantle upwelling and continental flood basalts. The xenolith suite consists of deformed (i.e., protogranular to porphyroclastic texture) Cl-rich pargasite lherzolites, metasomatized (LILE and Pb enrichment in clinopyroxene and amphibole) at T ? 1000 °C. Lherzolites contain chlorine-rich H₂O-CO₂ fluid inclusions, but no melt inclusions. Fluid inclusions are preserved only in orthopyroxene, while in olivine, they underwent extensive interaction with the host mineral. The metasomatic fluid composition is estimated: X_CO2 = 0.64, X_H2O = 0.33, X_Na = 0.006, X_Mg = 0.006, X_Cl = 0.018, (salinity = 14-10 NaCl eq. wt.%, a_H2O = 0.2, Cl = 4-5 mol.%). Fluid isochores correspond to trapping pressures of 1.4-1.5 GPa or 50-54 km depth (at T = 950 °C). Synchrotron sourced micro-infrared mapping (ELECTRA, Trieste) shows gradients for H₂O-distribution in nominally anhydrous minerals, with considerable enrichment at grain boundaries, along intragranular microfractures, and around fluid inclusions. Total water amounts in lherzolites are variable from about 150 up to 400 ppm. Calculated trace-element pattern of metasomatic fluid phases, combined with distribution and amount of H₂O in nominally anhydrous minerals, delineate a metasomatic Cl- and LILE-rich fluid phase heterogeneously distributed in the continental lithosphere. Present data suggest that Cl-rich aqueous fluids were important metasomatic agents beneath the Ethiopian plateau, locally forming a source of high water content in the peridotite, which may be easily melted. High Cl, LILE, and Pb in metasomatic fluid phases suggest the contribution of recycled altered oceanic lithosphere component in their source.     

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.     

A general algorithm for the O abundance correction to C/C determinations from CO2 isotopologue measurements, including CO2 characterised by ‘mass-independent’ oxygen isotope distributions

It is widely recognised that a significant limitation to the ultimate precision of carbon stable isotope ratio measurements, as obtained from dual-inlet mass spectrometric measurements of CO₂ isotopologue ion abundances at m/z 44, 45, and 46, is the correction for interference from ¹⁷O-bearing molecular ions. Two long-established, alternative procedures for determining the magnitude of this correction are in widespread use (although only one has IAEA approval); their differences lead to small but potentially significant discrepancies in the magnitude of the resulting correction. Furthermore, neither approach was designed to accommodate oxygen three-isotope distributions which do not conform to terrestrial mass-dependent behaviour. Stratospheric CO₂, for example, contains a strongly ‘mass-independent’ oxygen isotope composition. A new strategy for determining the ¹⁷O-bearing ion correction is presented, for application where the oxygen three-isotope characteristics of the analyte CO₂ are accurately known (or assigned) in terms of the slope λ of the three-isotope fractionation line and the ordinate axis intercept 10³ ln(1 + k) on a 10³ ln(1 + δ¹⁷O) versus 10³ ln(1 + δ¹⁸O) plot. At the heart of the approach is the relationship between ¹⁷R, which is the ¹⁷O/¹⁶O ratio of the sample CO₂, and other assigned or empirically determined parameters needed for the δ¹³C evaluation:

     

Evolution of the isotopic composition of carbon and oxygen in a calcite precipitating H2O-CO2-CaCO3 solution and the related isotopic composition of calcite in stalagmites

The isotopic composition of carbon and oxygen in a calcite precipitating CO₂-H₂O-CaCO₃ solution is preserved in the calcite precipitated. For the interpretation of isotopic proxies from stalagmites knowledge of the evolution of δ¹³C and δ¹⁸O in the solution during precipitation is required. A system of differential equations is presented from which this evolution can be derived. Both, irreversible loss of carbon and oxygen from the solution with precipitation time τ and exchange of oxygen in the carbonates with the oxygen in the water with exchange time T are considered. For carbon, where no exchange is active, a modified equation of Rayleigh-distillation is found, which takes into account that precipitation stops at c_eq, the saturation concentration of DIC with respect to calcite, and that c_eq as well as the precipitation time τ is slightly different for the heavy and the light isotope. This, however, requires introducing a new parameter γ = (A_eq/B_eq)/(A₀/B₀), which has to be determined experimentally. (A_eq/B_eq) is the isotopic ratio for the heavy (A) and the light isotope (B) at both chemical and isotopic equilibrium and (A₀/B₀) is the initial isotopic ratio of the solution. In the case of oxygen, where exchange is present, the isotopic shifts are reduced with increasing values of the precipitation time τ. For τ ? T the solution stays in isotopic equilibrium with the oxygen in the water during the entire time in which precipitation is active. The isotopic ratios in a calcite precipitating solution R(t)/R₀ = (1 + δ(t)/1000) for carbon are plotted versus those of oxygen. R₀ is the isotopic ratio at time t = 0, when precipitation starts and δ(t) the isotopic shift in the solution after time t. These show positive correlations for the first 50% of calcite, which can precipitate. Their slopes increase with increasing values of τ and they closely resemble Hendy-tests performed along growth layers of stalagmites. Our results show that stalagmites, which grow by high supply of water with drip times less than 50 s, exhibit positive correlations between δ¹³C and δ¹⁸O along a growth layer. But in spite of this the isotopic composition of oxygen in the solution at the apex is in isotopic equilibrium with the oxygen in the water, and therefore also that of calcite deposited at the apex.     

Calcite dissolution kinetics in the system CaCO3-H2O-CO2 at high undersaturation

Dissolution rates of limestone covered by a water film open to a CO₂-containing atmosphere are controlled by the chemical composition of the CaCO₃-H₂O-CO₂ solution at the water-mineral interface. This composition is determined by the Ca²⁺-concentration at this boundary, conversion of CO₂ into H⁺ and in the solution, and by diffusional mass transport of the dissolved species from and towards the water-limestone interface. A system of coupled diffusion-reaction equations for Ca²⁺, , and CO₂ is derived. The Ca²⁺ flux rates at the surface of the mineral are defined by the PWP-empirical rate law. These flux rates by the rules of stoichiometry must be equal to the flux rates of CO₂ across the air-water interface. In the solution, CO₂ is converted into H⁺ and . At low water-film thickness this reaction becomes rate limiting. The time dependent diffusion-reaction equations are solved for free drift dissolution by a finite-difference scheme, to obtain the dissolution rate of calcite as a function of the average calcium concentration in the water film. Dissolution rates are obtained for high undersaturation. The results reveal two regimes of linear dissolution kinetics, which can be described by a rate law F = α_i(m_ic_eq − c), where c is the calcium concentration in the water film, c_eq the equilibrium concentration with respect to calcite. For index i = 0, a fast rate law, which here is reported for the first time, is found with α₀ = 3 × 10⁻⁶ m s⁻¹ and m₀ = 0.3. For c > m₀c_eq, a slow rate law is valid with α₁ = 3 × 10⁻⁷ m  s⁻¹ and m₁ = 1, which confirms earlier work. The numbers given above are valid for film thickness of several tenths of a millimetre and at 20 °C. These rates are proven experimentally, using a flat inclined limestone plate covered by a laminar flowing water film injected at an input point with known flow rate Q and calcium concentration. From the concentration measured after flow distance x the dissolution rates are determined. These experiments have been performed at a carbon-dioxide pressure of 0.00035 atm and also of 0.01 atm. The results are in good agreement to the theoretical predictions.     

Acoustic velocity measurements on Na2O-TiO2-SiO2 liquids: Evidence for a highly compressible TiO2 component related to five-coordinated Ti

Longitudinal acoustic velocities were measured at 1 bar in 10 Na₂O-TiO₂-SiO₂ (NTS) liquids for which previous density and thermal expansion data are reported in the literature. Data were collected with a frequency-sweep acoustic interferometer at centered frequencies of 4.5, 5, and 6 MHz between 1233 and 1896 K; in all cases, the sound speeds decrease with increasing temperature. Six of the liquids have a similar TiO₂ concentration (∼25 mol %), so that the effect of varying Na/Si ratio on the partial molar compressibility of the TiO₂ component can be evaluated. Theoretically based models for β_T and (∂V/∂P)_T as a function of composition and temperature are presented. As found previously for the partial molar volume of TiO₂ in sodium silicate melts, values of (13.7-18.8 × 10⁻²/GPa) vary systematically with the Na/Si and Na/(Si + Ti) ratio in the liquid. In contrast values of for the SiO₂ and Na₂O components (6.6 and 8.0 × 10⁻²/GPa, respectively, at 1573 K) are independent of composition. Na₂O is the only component that contributes to the temperature dependence of the compressibility of NTS liquids (1.13 ± 0.04 × 10⁻⁴/GPa K). The results further indicate that the TiO₂ component is twice as compressible as the Na₂O and SiO₂ components. The enhanced compressibility of TiO₂ appears to be related to the abundance of five-coordinated Ti (^[5]Ti) in these liquids, but not with a change in Ti coordination. Instead, it is proposed that the asymmetric geometry of ^[5]Ti in a square pyramidal site promotes different topological rearrangements in alkali titanosilicate liquids, which lead to the enhanced compressibility of TiO₂.     

Molecular H2O in armenite, BaCa2Al6Si9O30·2H2O, and epididymite, Na2Be2Si6O15·H2O: Heat capacity, entropy and local-bonding behavior of confined H2O in microporous silicates

Armenite, ideal formula BaCa₂Al₆Si₉O₃₀·2H₂O, and its dehydrated analog BaCa₂Al₆Si₉O₃₀ and epididymite, ideal formula Na₂Be₂Si₆O₁₅·H₂O, and its dehydrated analog Na₂Be₂Si₆O₁₅ were studied by low-temperature relaxation calorimetry between 5 and 300 K to determine the heat capacity, C_p, behavior of their confined H₂O. Differential thermal analysis and thermogravimetry measurements, FTIR spectroscopy, electron microprobe analysis and powder Rietveld refinements were undertaken to characterize the phases and the local environment around the H₂O molecule.The determined structural formula for armenite is Ba_0.88(0.01)Ca_1.99(0.02)Na_0.04(0.01)Al_5.89(0.03)Si_9.12(0.02)O₃₀·2H₂O and for epididymite Na_1.88(0.03)K_0.05(0.004)Na_0.01(0.004)Be_2.02(0.008)Si_6.00(0.01)O₁₅·H₂O. The infrared (IR) spectra give information on the nature of the H₂O molecules in the natural phases via their H₂O stretching and bending vibrations, which in the case of epididymite only could be assigned. The powder X-ray diffraction data show that armenite and its dehydrated analog have similar structures, whereas in the case of epididymite there are structural differences between the natural and dehydrated phases. This is also reflected in the lattice IR mode behavior, as observed for the natural phases and the H₂O-free phases. The standard entropy at 298 K for armenite is S° = 795.7 ± 6.2 J/mol K and its dehydrated analog is S° = 737.0 ± 6.2 J/mol K. For epididymite S° = 425.7 ± 4.1 J/mol K was obtained and its dehydrated analog has S° = 372.5 ± 5.0 J/mol K. The heat capacity and entropy of dehydration at 298 K are Δ = 3.4 J/mol K and ΔS^rxn = 319.1 J/mol K and Δ = −14.3 J/mol K and ΔS^rxn = 135.7 J/mol K for armenite and epididymite, respectively. The H₂O molecules in both phases appear to be ordered. They are held in place via an ion-dipole interaction between the H₂O molecule and a Ca cation in the case of armenite and a Na cation in epididymite and through hydrogen-bonding between the H₂O molecule and oxygen atoms of the respective silicate frameworks. Of the three different H₂O phases ice, liquid water and steam, the C_p behavior of confined H₂O in both armenite and epididymite is most similar to that of ice, but there are differences between the two silicates and from the C_p behavior of ice. Hydrogen-bonding behavior and its relation to the entropy of confined H₂O at 298 K is analyzed for various microporous silicates.The entropy of confined H₂O at 298 K in various silicates increases approximately linearly with increasing average wavenumber of the OH-stretching vibrations. The interpretation is that decreased hydrogen-bonding strength between a H₂O molecule and the silicate framework, as well as weak ion-dipole interactions, results in increased entropy of H₂O. This results in increased amplitudes of external H₂O vibrations, especially translations of the molecule, and they contribute strongly to the entropy of confined H₂O at T < 298 K.