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.     

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

Oxygen isotope exchange between H₂O and H₄SiO₄ was modeled with ab initio calculations on H₄SiO₄ + 7H₂O. Constrained optimizations were performed with the B3LYP/6-31+G(d,p) method to determine reactants, transition states, and intermediates. Long-range solvation was accounted for using self-consistent reaction field calculations. The mechanism for exchange involves two steps, a concerted proton transfer from H₄SiO₄ forming a 5-coordinated Si followed by a concerted proton transfer from the 5-coordinated Si forming another H₄SiO₄. The 5-coordinated Si intermediate is C2 symmetric. At 298K and with implicit solvation included, the Gibbs free energy of activation from transition state theory is 66 kJ/mol and the predicted rate constant is 16 s⁻¹. Equilibrium calculations between 298K and 673K yield α_H4SiO4-H2O that are uniformly less than, but similar to, α_qtz-H2O, and therefore α_qtz-H4SiO4 is expected to be relatively small in this temperature range.     

Calorimetric measurements of fusion enthalpies for Ni2SiO4 and Co2SiO4 olivines and application to olivine-liquid partitioning

Calorimetric measurements of fusion enthalpies for Ni₂SiO₄ and Co₂SiO₄ olivines were carried out using a high-temperature calorimeter, and Ni and Co partitioning between olivine and silicate liquid was analyzed using the measured heats of fusion. The fusion enthalpy of Co₂SiO₄ olivine measured by transposed-temperature drop calorimetry was 103 ± 15 kJ/mol at melting point (1688 K). The fusion enthalpy of Ni₂SiO₄ olivine was calculated based on the enthalpies of liquids in the system An₅₀Di₅₀-Ni₂SiO₄ measured by transposed-temperature drop calorimetry at 1773 K, and was 221 ± 26 kJ/mol at its metastable melting point (1923 K). The fusion enthalpy of Ni₂SiO₄ is the largest among those of olivine group, this is caused by the large crystal field stabilization energy of six-coordinated Ni²⁺ in olivine. The larger fusion enthalpy of Ni₂SiO₄ can account for the large and variable partition coefficient of Ni between olivine and silicate liquid. Based on the comparison between partition coefficients calculated from thermodynamic data and those observed in partition experiments, it is considered that the magnitude of partition coefficients is primarily dependent on the heats of fusion of the components. Furthermore, the activity coefficients for Ni-, Co- and Mn-bearing components in magmatic liquid are nearly of the same magnitude.     

First-principles study of (MgH2SiO4)? n (Mg2SiO4) hydrous olivine structures. I. Crystal structure modelling of hydrous olivine Hy-2 a (MgH2SiO4) ? 3(Mg2SiO4)

 Recently, the Hy-2a hydrous olivine (MgH₂ SiO₄)·3(Mg₂SiO₄) occurring as nanometre-sized inclusions in mantle olivines has been found by TEM, and has been suggested to be a new DHMS phase (Khisina et al. 2001). A model of the crystal structure of Hy-2a has been proposed as a 2a-superstructure of olivine with one Me²⁺ -vacant octahedral layer in the (1 0 0) plane per Hy-2a unit cell (Khisina and Wirth 2002). In the present study the crystal structure of Hy-2a hydrous olivine is optimized by ab initio calculations. The aims of this study are: (1) verification of the suggested models of Hy-2a hydrous olivine structure; (2) calculation of the most stable configurations for Hy-2a structure with minimum static lattice energy, by assuming a possible formation of Me²⁺ vacancies in either M1 or M2 octahedral sites; (3) determination of the position of protons and hydrogen bonds in the Hy-2a structure. Several different possible configurations of the Hy-2a structure are optimized. The results support the idea of a stable olivine structure with ordered planar-segregated OH-bearing defects oriented parallel to (1 0 0). The data obtained indicate a preferred stability of the Hy-2a structure with the protons associated with M1 vacancies and bonded with O1 and O2 oxygen sites. The relative energy values of the optimized Hy-2a structure configurations correlate as a rule with the average shifts of atoms from their positions in pure forsterite structure. Received: 7 February 2002 / Accepted: 23 October 2002     

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.     

Diffusion and viscosity of Mg2SiO4 liquid at high pressure from first-principles simulations

We investigate two key transport properties, self-diffusion and viscosity, of Mg₂SiO₄ liquid as a function of temperature and pressure using density functional theory-based molecular dynamics method. Liquid dynamics in a 224-atom supercell was captured in equilibrium simulations of relatively long durations (50-300 ps) to obtain an acceptable convergence. Our results show that Mg and Si are, respectively, the most and least mobile species at most conditions studied and all diffusivities become similar at high pressure. With increasing temperature from 2200 to 6000 K at ambient pressure, the self-diffusivities increase by factors of 25 (Mg), 80 (Si) and 65 (O), and the viscosity decreases by a factor of 30. The predicted temperature variations of all transport coefficients closely follow the Arrhenian law. However, their pressure variations show a significant non-Arrhenian behavior and also are sensitive to temperature. At 3000 K, the diffusivity (viscosity) decreases (increases) by more than one order of magnitude between 0 and 50 GPa with their activation volumes increasing on compression. Over the entire mantle pressure range, the variations at 4000 K are of two orders of magnitude with nearly constant activation volumes whereas the variations at 6000 K are within one order of magnitude with decreasing activation volumes. The predicted complex dynamical behavior of Mg₂SiO₄ liquid can be associated with the structural changes occurring on compression. We also estimate the diffusivity and viscosity profiles along a magma ocean isentrope, which suggest that the melt transport properties vary modestly over the relevant magma ocean depth ranges.     

Methane: An equation of state with application to the ternary system H2O-CO2-CH4

The following hardsphere modified Redlich-Kwong (HSMRK) equation of state was obtained by least squares fitting to available P-V-T data for methane (P in bars; T in Kelvins; v in cm³ mol^?1; b = 60.00 cm³ mol^?1; R = 83.14 cm³barmol^?1K^?1): $\text{P}\text{RT(1 + y + y}{}^2\text{?y}{}^3\text{v(1?y)}{}^3\text{)}\text{-}\text{c(T) + d(T)}\text{v}\text{+}\text{e(T)}\text{v}{}^2\text{/v(v + b)T}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$$\text{y =}\text{b}\text{4v}$c(T) = 13.403 × 10⁶ + (9.28 × 10⁴)T + 2.7 T²d(T) = 5.216 × 10⁹ ? (6.8 × 10⁶)T + (3.28 × 10³)T²e(T) = (?2.3322 × 10¹¹) + (6.738 × 10⁸)T + (3.179 × 10⁵)T² For the P-T range of experimental data used in the fit (50 to 8600 bars and from 320 to 670 K), calculated volumes and fugacity coefficients for CH₄ relative to experimentally determined volumes and fugacity coefficients have average percent deviations of 0.279 and 1.373, respectively. The HSMRK equation, which predicts linear isochores over a wide P-T range, should yield reasonable estimates of fugacity coefficients for CH₄ to pressures and temperatures well outside the P-T range of available P-V-T data. Calculations for the system H₂O-CO₂-CH₄, using the HSMRK equations for H₂O and CO₂ of Kerrick and Jacobs (1981) and the HSMRK equation for CH₄ of this study, indicate that compared to the binary H₂O-CO₂ system, small amounts of CH₄ in the ternary system H₂O-CO₂-CH₄ slightly increases the activity of H₂O, and significantly decreases the activity of CO₂.     

橄榄岩-卤水反应实验生成富烷氢流体

<正>1研究目的(Objective)利用地球化学动力学实验室流动反应装置(国家发明专利)探索高温高压下水(卤水)与橄榄岩相互作用产出氢气和甲烷的生成机制。实验发现:400℃反应时释放很高浓度氢气和甲烷等可燃气,同时橄榄岩发生蛇纹石化。实验表明氢和甲烷可能来自地下深处,这是蛇绿岩与油气有关的实验依据。近年来发现:大西洋中脊的一些水热活动地区,热水与超镁铁岩石反应。喷口流体富含甲烷、氢和     

An investigation into thermodynamic consistency of data for the olivine, wadsleyite and ringwoodite form of (Mg,Fe)2SiO4

We have performed a thermodynamic analysis to determine the internal consistency of state-of-the-art experimental data for olivine, wadsleyite, and ringwoodite solid solutions. The analysis has been carried out between 200 and 2200 K and 0 and 20 GPa. We conclude that the volume-pressure-temperature data of wadsleyite and ringwoodite show very large inconsistencies, which hamper the accurate prediction of bulk sound velocities in the transition zone to within tomographic accuracy. Owing to the compositional effect in two-phase regions, thermodynamic properties, crucial for geodynamic modeling, differ up to an order of magnitude relative to values in single-phase regions at conditions prevailing in the earth’s transition zone. Thermal expansivity in the olivine-wadsleyite two-phase region is ∼23 times larger than that in the olivine region. For the wadsleyite-ringwoodite two-phase region, thermal expansivity is ∼6 times larger than that in the wadsleyite region. It may be anticipated that this differential thermal expansivity significantly affects future geodynamic model calculations.     

The bearing of the system CaMgSi2O6CaAl2SiO6CaFeAlSiO6 on fassaitic pyroxene

The system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi₂O₆-rich portion is Cpx + An + Mel and that in the CaMgSi₂O₆-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO₆ component of the system. The Al₂O₃ content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al₂O₃ with 3.9 wt.% Fe₂O₃. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO₆ content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl₂SiO₆ and CaFeAlSiO₅ components as crystallization proceeds. These results agree with those obtained in the experimental study.     

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).     

Rhondonite solubility and thermodynamic properties of aqueous MnCl2 in the system MnOSiO2HClH2O

The solubility of rhodonite, represented by the reaction MnSiO₃ (rhodonite) + 2HCl⁰ = MnCl₂⁰ + SiO₂ (quartz) + H₂O, was investigated experimentally in the temperature range 400°–700°C at 1 and 2 kbar by rapid-quench hydrothermal techniques and the Ag-AgCl buffer methods. Variations in the molalities of associated hydrogen chloride (m_HCl⁰) as a function of the molalities of total Mn indicate that Mn in the fluid in equilibrium with the assemblage rhodonite + quartz is predominantly associated as MnCl₂⁰. The Mn:Cl in the fluid ?2, indicating that Mn⁺² is the dominant oxidation state.The solubility data were used to calculate the equilibrium constant of the above reaction as a function of temperature, pressure, and the difference in Gibbs free energy of formation between MnCl₂⁰ and HCl⁰. The equilibrium constants of solubility for Mn minerals for which thermochemical data are available were also calculated. Calculated mineral solubilities were used in conjunction with the data of Frantz et al. (1981) to calculate the composition of supercritical fluids in equilibrium with Mn-bearing phases and assemblages. At 400°C and 1000 bars, supercritical fluids in equilibrium with olivines of compositions similar to those present in MORB tend to be enriched in Mn, despite the low mole fraction of tephroite in the olivine. Supercritical fluids in equilibrium with the assemblage quartz-hematite-rhodonite at 500° and 400°C and 1000 bars show high concentrations of Mn relative to Fe. Manganese concentrations in the fluids increase with decrease in the mole fraction of H, whereas Fe concentrations decrease. The data indicate that H fugacity plays a significant role in the separation of Mn from Fe in chloride-bearing hydrothermal fluids at supercritical temperatures.     

The noble gas systematics of late-orogenic H2O-CO2 fluids, Mt Isa, Australia

The noble gases (He, Ne, Ar, Kr and Xe) are powerful geochemical tracers because they have distinctive isotopic compositions in the atmosphere, crust and mantle. This study illustrates how noble gases can be used to trace fluid origins in high-temperature metamorphic and mineralising environments; and at the same time provides new information on the composition of noble gases in deeper parts of the crust than have been sampled previously.We report data for H₂O and CO₂ fluid inclusions trapped at greenschist to amphibolite facies metamorphic conditions associated with three different styles of mineralisation and alteration in the Proterozoic Mt Isa Inlier of Australia. Sulphide fluid inclusions are dominated by crustal ⁴He. However, co-variations in fluid inclusion ²⁰Ne/²²Ne, ²¹Ne/²²Ne, ⁴⁰Ar/³⁶Ar and ¹³⁶Xe/¹³⁰Xe indicate noble gases were derived from three or more reservoirs. In most cases, the fluid inclusions elemental noble gas ratios (e.g. Ne/Xe) are close to the ranges expected in sedimentary and crystalline rocks. However, the elemental ratios have been modified in some of the samples providing evidence for independent pulses of CO_2, and interaction of CO₂ with high-salinity aqueous fluids.Compositional variation is attributed to mixing of: (i) magmatic fluids (or deeply sourced metamorphic fluids) characterised by basement-derived noble gases with ²⁰Ne/²²Ne ∼ 8.4, ²¹Ne/²²Ne ∼ 0.4, ⁴⁰Ar/³⁶Ar ∼ 40,000 and ¹³⁶Xe/¹³⁰Xe ∼ 8; (ii) basinal-metamorphic fluids with a narrow range of compositions including near-atmospheric values and (iii) noble gases derived from the meta-sedimentary host-rocks with ²⁰Ne/²²Ne ∼ 8-9.8, ²¹Ne/²²Ne < 0.1, ⁴⁰Ar/³⁶Ar < 2500 and ¹³⁶Xe/¹³⁰Xe ∼ 2.2.These data provide the strongest geochemical evidence available for the involvement of fluids from two distinct geochemical reservoirs in Mt Isa’s largest ore deposits. In addition the data show how noble gases in fluid inclusions can provide information on fluid origins, the composition of the crust’s major lithologies, fluid-rock interactions and fluid-fluid mixing or immiscibility processes.     

Theoretical exploration of the water exchange mechanism of the polyoxocation GaO4Al12(OH)24(H2O)12 in aqueous solution

Reaction pathways, solvent effects and energy barriers have been investigated for the water exchange of the polyoxocation GaO₄Al₁₂(OH)₂₄(H₂O)₁₂⁷⁺ (K-GaAl₁₂) in aqueous solution by means of supermolecule density functional theory calculations. In the proposed reaction pathway, the supermolecular reactant K-GaAl₁₂15H₂O first loses a water ligand to form an intermediate with a five-coordinated aluminum atom, and then the incoming water molecule in the second coordination sphere attacks the intermediate with a five-coordinated aluminum atom to produce the reaction product. Our calculated results indicate that the water exchange of K-GaAl₁₂ proceeds via a dissociative mechanism, and that the reverse reaction of Step II is the most favorable dissociative pathway, with a barrier height of 31.3 kJ mol⁻¹. The calculated transition-state rate for the favorable dissociative pathway is much larger than the experimental rate constant, but is close to the data calculated for Al₃₀ by molecular dynamics. The transmission coefficient was also predicted on the basis of both the calculated transition-state rate and the experimental rate. Our calculated results also indicate that both the explicit solvent effect and the bulk solvent effect have obvious effects on the barrier heights of the water exchange reaction of K-GaAl₁₂. By comparison, the water exchange mechanism for K-GaAl₁₂ was found to be more similar to that for mineral surfaces than that for monomeric aluminum species.     

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.     

Equations of state for the NaCl-H2O-CH4 system and the NaCl-H2O-CO2-CH4 system: Phase equilibria and volumetric properties above 573 k

An equation of state (EOS) based on thermodynamic perturbation theory is presented for the NaCl-H₂O-CH₄ system. This equation consistently reproduces PvTX properties and phase equilibria with an accuracy close to that of data in the temperature, pressure and concentration ranges from 648 K to 873 K, 0 to 2500 bar and up to 2.37 mol % NaCl. Good agreement with recent ternary immiscibility data from 673 K to 873 K suggests that the EOS may provide accurate predictions for NaCl concentrations as high as 40 mol %. We could not find any experimental data above 873 K that can be used to validate the predictions of the EOS inside the ternary. However, parameters for the mixed ternary system were established from parameters evaluated for pure and binary systems and accurate combination rules. Therefore, predictions in the ternary should be reliable to the high temperatures and pressures where the EOS for the lower order systems are valid (about 1300 K and 5000 bar). Using the same combining approach, an EOS for the quaternary NaCl-H₂O-CO₂-CH₄ is constructed on the basis of parameters from our earlier model for the NaCl-H₂O-CO₂ system and the present NaCl-H₂O-CH₄ model. This suggests that predictions of the quaternary EOS are reliable also to about 1300 K and 5000 bar.