Stilbite-laumontite equilibrium

The reaction stilbite=laumontite+3 quartz+3 H₂O was experimentally studied using conventional hydrothermal techniques employing mineral mixtures consisting of reactants and products in 91 and 19 ratios. Equilibrium was demonstrated; the univariant curve passes through about 170° C and 2000 bars, 185°±10° C and 3000 bars, about 185° C and 4000 bars, and 183°±10° C at 5000 bars P _fluid. These results combined with published equilibria for analcime, laumontite, wairakite and prehnite permit delineation of the P-T conditions for the zeolite and prehnite-pumpellyite facies metamorphism in the Tanzawa Mountains, Japan.     

Olivine-liquid equilibrium

A number of experiments have been conducted in order to study the equilibria between olivine and basaltic liquids and to try and understand the conditions under which olivine will crystallize. These experiments were conducted with several basaltic compositions over a range of temperature (1150–1300° C) and oxygen fugacity (10^?0.68–10^?12 atm.) at one atmosphere total pressure. The phases in these experimental runs were analyzed with the electron microprobe and a number of empirical equations relating the composition of olivine and liquid were determined. The distribution coefficient 1 $$K_D = \frac{{(X_{{\text{FeO}}}^{{\text{Ol}}} )}}{{(X_{{\text{FeO}}}^{{\text{Liq}}} )}}\frac{{(X_{{\text{MgO}}}^{{\text{Liq}}} )}}{{(X_{{\text{MgO}}}^{{\text{Ol}}} )}}$$ relating the partioning of iron and magnesium between olivine and liquid is equal to 0.30 and is independent of temperature. This means that the composition of olivine can be used to determine the magnesium to ferrous iron ratio of the liquid from which it crystallized and conversely to predict the olivine composition which would crystallize from a liquid having a particular magnesium to ferrous iron ratio. A model (saturation surface) is presented which can be used to estimate the effective solubility of olivine in basaltic melts as a function of temperature. This model is useful in predicting the temperature at which olivine and a liquid of a particular composition can coexist at equilibrium.     

Garnet + liquid equilibrium

New experiments were performed to determine saturation conditions for garnet and silicate liquid. Starting compositions were natural basalt powders ranging from komatiite to nephelinite, which were partially melted at pressures between 25 and 100 kbar. Rounded grains of natural pyrope or grossular were added to some experiments to induce garnet saturation, and to aid the segregation of liquid pools for microprobe analysis. Simple expressions describing K _eq as a function of P, T and liquid composition were calibrated by linear least squares analysis of the data from this, and other, studies. Since garnets do not often occur as phenocrysts, equations were designed to predict garnet compositions when P, T and a silicate liquid composition are given. The regression data have a pressure range of 20–270 kbar, and compositions as diverse as nephelinite and komatiite. These models should thus apply to a broad range of geological problems. The majorite component in garnet was found to increase with increasing P, but compositional effects are also important. A garnet saturation surface applied to liquids with chondritic compositions shows that such liquids crystallize garnet with Mj contents of 0.27–0.42 at 200 kbar. Models of Earth differentiation thus need to account not only for fractionation of majorite, but also for Fe-, Ca-, Na- and Ti-bearing garnet components, which occur in non-trivial quantities at high pressure. Since many models of igneous petrogenesis rely on mineral-melt partition coefficients for the minor elements Na, Ti, and Cr, partition coefficients for these elements were also examined. The K _d ^gar/liq for Na was found to be P-sensitive; Na contents of basalts may thus potentially yield information regarding depths of partial melting. Received : 28 May 1997 / 25 November 1997     

The gypsum-anhydrite equilibrium by solubility measurements

Solubility measurements have been used to establish the gypsum-anhydrite equilibrium in the CaSO₄-H₂O system at atmospheric pressure. The saturation equilibrium has been approached both from undersaturated and supersaturated solutions. The invariant point temperature has been found to be 49.5 ± 2.5°C.     

Theoretical estimates of equilibrium chlorine-isotope fractionations

Equilibrium chlorine-isotope (³⁷Cl/³⁵Cl) fractionations have been determined by using published vibrational spectra and force-field modeling to calculate reduced partition function ratios for Cl-isotope exchange. Ab initio force fields calculated at the HF/6-31G(d) level are used to estimate unknown vibrational frequencies of ³⁷Cl-bearing molecules, whereas crystalline phases are modeled by published lattice-dynamics models. Calculated fractionations are principally controlled by the oxidation state of Cl and its bond partners. Molecular mass (or the absence of C-H bonds) also appears to play a role in determining relative fractionations among simple Cl-bearing organic species. Molecules and complexes with oxidized Cl (i.e., Cl⁰, Cl⁺, etc.) will concentrate ³⁷Cl relative to chlorides (substances with Cl⁻). At 298 K, ClO₂ (containing Cl⁴⁺) and [ClO₄]⁻ (containing Cl⁷⁺) will concentrate ³⁷Cl relative to chlorides by as much as 27‰ and 73‰, respectively, in rough agreement with earlier calculations. Among chlorides, ³⁷Cl will be concentrated in substances where Cl is bonded to +2 cations (i.e., FeCl₂, MnCl₂, micas, and amphiboles) relative to substances where Cl is bonded to +1 cations (such as NaCl) by ∼2 to 3‰ at 298 K; organic molecules with C-Cl bonds will be even richer in ³⁷Cl (∼5 to 9‰ at 298 K). Precipitation experiments, in combination with our results, provide an estimate for Cl-isotope partitioning in brines and suggest that silicates (to the extent that their Cl atoms are associated with nearest-neighbor +2 cations analogous with FeCl₂ and MnCl₂) will have higher ³⁷Cl/³⁵Cl ratios than coexisting brine (by ∼2 to 3‰ at room temperature). Calculated fractionations between HCl and Cl₂, and between brines and such alteration minerals, are in qualitative agreement with both experimental results and systematics observed in natural samples. Our results suggest that Cl-bearing organic molecules will have markedly higher ³⁷Cl/³⁵Cl ratios (by 5.8‰ to 8.5‰ at 295 K) than coexisting aqueous solutions at equilibrium. Predicted fractionations are consistent with the presence of an isotopically heavy reservoir of HCl that is in exchange equilibrium with Cl⁻_aq in large marine aerosols.     

Pressure and equilibrium in deforming rocks

It is widely proposed that tectonic pressure (the difference between the mean stress and the pressure arising from a lithostatic load) is large, and has a significant influence on mineral phase equilibria in deforming metamorphic rocks. The implication/assertion is that the mean stress is equivalent to the thermodynamic pressure which characterizes mineral phase equilibria and is a measure of how the energy changes as the volume changes. We distinguish two useful thermodynamic pressures. The first is an equilibrium thermodynamic pressure, characteristic of non‐dissipative systems and related directly to equilibrium values of the chemical potentials that define stable, equilibrium phase assemblages. The second is a non‐equilibrium thermodynamic pressure characteristic of dissipative systems with zero net entropy production and related to non‐equilibrium chemical potentials that define stable non‐equilibrium phase assemblages. In many dissipative metamorphic systems discussed in the literature, the concepts of thermodynamic pressure and chemical potential are not usefully defined because the system is not at equilibrium and/or no volume change is involved in the deformation. The conclusion of this note is that the influence of tectonic pressure on phase equilibria is minor. The role of tectonic pressure is an important issue but is only relevant to phase equilibrium when an equilibrium thermodynamic pressure can be defined; in such cases, the influence of tectonic pressure is small compared to many proposals in the literature. Except for elastic deformations, the mean stress is not useful in discussing mineral phase equilibrium.     

Plagioclase-aqueous solution equilibrium: Concentration dependence

The plagioclase-(NaCl + CaCl₂) exchange equilibrium was examined experimentally at 700°C, 0.5 GPa in aqueous solutions with salt concentrations from 1 to 64 m. The Ca/(Ca + Na) distribution between plagioclase and solution (salt melt) is illustrated in five diagrams constructed for concentrations of 1, 4, 8, 16, and 64 m. The elevated bulk salinity of the fluid at a constant Ca/(Ca + Na) ratio results in plagioclase albitization, with this effect reaching a maximum in relatively dilute solutions (1–4 m). In concentrated solutions (salt melts), the shift in the plagioclase composition with variations in the salinity is relatively insignificant. The simple hydration of basic rocks (purely metamorphic reaction) is associated with the albitization of plagioclase, and calculations suggest a possible shift from anorthite to oligoclase. This is also applicable to chemically more complex mineral associations: an increase in the overall salinity of the fluid should result in an increase in the activity of monovalent cations relative to that of bivalent ones and, correspondingly, stimulate reactions in which alkali earth cations (Ca + Mg + Fe) are substituted for alkalis (Na + K + Li). Although our experiments were carried out at temperatures 50°C lower than the melting point of albite under a pure water pressure (0.5 GPa), the addition of CaCl₂ solution to albite (i.e., plagioclase anorthitization and a decrease in the water activity in the salt solutions) induced the appearance of melt because of quartz formation by the reaction 2Ab + CaCl₂ → An + 2NaCl + 4Qtz and the eutectic phase proportions in the Ab + Qtz system.     

Solubility equilibrium constant of α-hopeite

The saturation curve for synthetic α-hopeite, Zn₃(PO₄)₂·4H₂O in dilute phosphoric acid solutions has been determined at 25°C as a function of pH. Interpretation of the data in terms of a model which assumes the formation of the ion-pairs ZnHPO₄⁰ and ZnH₂PO₄⁺ in these solutions resulted in the solubility product constant for α-hopeite of 10^?35.3±0.1. The data show that the formation of hopeite may influence both the availability of zinc in soils and the zinc levels in natural water systems.     

Approach to chemical equilibrium in diagenetic chlorites

Electron microprobe analyses were made on diagenetic chlorites in sandstones and mudstones from two deep wells according to the petrographic character of the chlorite occurrence: as pseudomorphic phases, rims on quartz or glauconite or as distinct phases in the clay matrix. Chlorite compositions do not depend upon crystallization site (reacting phases) making it apparent that new chlorites can form in an approach to chemical equilibrium at or near the surface (40° C, 1 km depth). Comparison of this data with that for late diagenetic and early metamorphic chlorites indicates that the compositional range for different grains in the same thin section is similar for the samples throughout the 40°–270° C temperature span. Compositional range decreases upon further metamorphism.Al content appears to be a more reliable indicator of temperature variations than other substitutions in the chlorite structure. The clay mineral assemblage which indicates sedimentary facies affects the trends in composition (Al increase or decrease) as a function of temperature. The octahedral site occupancy show a general increase in going from diagenesis to metamorphic conditions in pelitic rocks. The range of Fe-Mg ratios seems to depend more on the chemistry of each sample than the temperature of formation of the minerals.     

Sand transport model of barchan dune equilibrium

Erosion and deposition over a barchan dune near the Salton Sea, California, is modelled by book-keeping the quantity of sand in saltation following streamlines of transport. Field observations of near-surface wind velocity and direction plus supplemental measurements of the velocity distribution over a scale model of the dune are combined as input to Bagnold-type sand-transport formulae corrected for slope effects. A unidirectional wind is assumed. The resulting patterns of erosion and deposition compare closely with those observed in the field and those predicted by the assumption of equilibrium (downwind translation of the dune without change in size or geometry). Discrepancies between the simulated results and the observed or predicted erosional patterns appear to be largely due to natural fluctuation in the wind direction. Although the model includes a provision for a lag in response of the transport rate to downwind changes in applied shear stress, the best results are obtained when no delay is assumed. The shape of barchan dunes is a function of grain size, velocity, degree of saturation of the oncoming flow, and the variability in the direction of the oncoming wind. Smaller grain size or higher wind speed produce a steeper and more blunt stoss-side. Low saturation of the inter-dune sandflow produces open crescent-moon-shaped dunes, whereas high saturation produces a whaleback form with a small slip face. Dunes subject to winds of variable direction are blunter than those under unidirectional winds. The size of barchans could be proportional to natural atmospheric scales, to the age of the dune, or to the upwind roughness. The upwind roughness can be controlled by fixed elements or by the sand is saltation. In the latter case, dune scale may be proportional to wind velocity and inversely proportional to grain size. However, because the effective velocity for transport increases with grain size, dune scale may increase with grain size as observed by Wilson (1972).     

Explicit limit equilibrium solution for slope stability

Conventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non‐linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non‐convergence occasionally occurring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed‐form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern–Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley & Sons, Ltd.     

Error analysis for bracketed phase equilibrium data

The proper treatment of experimental errors associated with experimental phase boundary determinations and derived results is necessary for a full interpretation and for critical comparison with other data. In the past, mathematical approximations used in treating phase equilibrium data have overestimated standard deviations and confidence limits by as much as a factor of two, thus hindering the proper interpretation of results. We have derived the correct expressions for calculating uncertainties in the location of a phase boundary and in quantities derived from a boundary such as the free energy of formation of a phase. For the special case of a pair of experimental; points with equal errors bracketing the phase boundary, we have prepared equations and graphs which are particularly easy to use. Our approach can be extended to more problems involving the analysis of phase equilibrium experiments.     

基于活度计算的碳酸平衡研究

研究考虑活度情况下地下水开放系统在不同温度和CO₂分压下碳酸的3种存在形式与pH值之间的关系.分析地下水中CO₂分压为10～105Pa,温度为0～30℃变化时pH₀的变化情况,发现在一定CO₂分压下,pH₀值随温度的升高而降低并趋于一个稳定的值.在一定温度下,pH₀值随CO₂分压的升高而降低.但不论地下水的温度和CO₂分压如何变化,pH₀=7.92～8.60.这些结论更符合地下水实际情况,更有利于对水分析资料的审查.     

Geochemical and equilibrium trends in mine pit lakes

Chemical composition and equilibrium trends in mine pit lakes were examined to provide guidance for the application of geochemical models in predicting future lake water quality at prospective open pit mines. Composition trends show that elevated solute levels generally occur only at the extremes of acidic and alkaline pH conditions. Concentrations of cationic metals (Al, Cd, Cu, Fe, Mn, Pb, and Zn) are elevated only in acidic pit lakes, whereas anionic metalloids (As and Se) are generally elevated only in alkaline pit lakes. These trends are indicative of sulfide mineral oxidation and evapoconcentration for acidic and alkaline conditions, respectively.For nearly all pit lakes, SO₄ is the dominant solute, but is limited by gypsum solubility. Fluorite, calcite, and barite are also important solubility controls. Well-defined solubility controls exist for the major metals (Al, Fe, Mn), including jurbanite and alunite for Al, ferrihydrite for Fe, and manganite, birnessite, and, possibly, rhodochrosite for Mn. Determinations of definite controls for the minor metals are less distinct, but may include otavite for Cd, brochantite and malachite for Cu, cerrusite and pyromorphite for Pb, and hydrozincite and Zn silicates for Zn. Concentrations of As and Se appear to be limited only by adsorption, but this control is sharply diminished by increased pH and SO₄ concentration. In general, the concentrations of minor metals in pit lakes are not well represented by the theoretical solubilities of pure-phase minerals contained in the thermodynamic databases. Hence, modeling efforts will generally have to rely on empirical data on the leaching characteristics of pit wall-rocks to predict the concentrations of minor metals (Cd, Cu, Pb, Zn) in mine pit lakes.Methodologies for predicting pit lake water chemistry are still evolving. Geochemical and equilibrium trends in existing pit lakes can provide valuable information for guiding the development and application of predictive models. However, mineralogical studies of pit lake sediments, suspended particles, and alteration assemblages and studies of redox transformations are still needed to validate and refine the representations of geochemical processes in water quality models of mine pit lakes.     

上海地区首例自平衡法试桩

该文简要介绍了自平衡法试桩的原理和方法，并根据上海吴淞口大跨越工程实例总结了相关经验，以便该方法在上海地区推广应用和深入研究。     

Comparison of linear solvers for equilibrium geochemistry computations

Equilibrium chemistry computations and reactive transport modelling require the intensive use of a linear solver under very specific conditions. The systems to be solved are small or very small (4 × 4 to 20 × 20, occasionally larger) and are very ill-conditioned (condition number up to 10¹⁰⁰). These specific conditions have never been investigated in terms of the robustness, accuracy, and efficiency of the linear solver. In this work, we present the specificity of the linear system to be solved. Several direct and iterative solvers are compared using a panel of chemical systems, including or excluding the formation of mineral species. We show that direct and iterative solvers can be used for these problems and propose computational keys to improve the chemical solvers.