Alkali-free tourmaline in the system MgO-Al2O3-B2O3-SiO2-H2O

An end member of the tourmaline series with a structural formula □(Mg₂Al)Al₆(BO₃)₃[Si₆O₁₈](OH)₄ has been synthesized in the system MgO-Al₂O₃-B₂O₃-SiO₂-H₂O where it represents the only phase with a tourmaline structure. Our experiments provide no evidence for the substitutions Al → Mg + H, Mg → 2H, B + H → Si, and AlAl → MgSi and we were not able to synthesize a phase “Mg-aluminobuergerite” characterized by Mg in the (3a)-site and a strong (OH)-deficiency reported by Rosenberg and Foit (1975). The alkali-free tourmaline has a vacant (3a)-site and is related to dravite by the □ + Al for Na + Mg substitution. It is stable from at least 300°C to about 800°C at low fluid pressures and 100% excess B₂O₃, and can be synthesized up to a pressure of 20 kbars. At higher temperatures the tourmaline decomposes into grandidierite or a boron-bearing phase possibly related to mullite (“B-mullite”), quartz, and unidentified solid phases, or the tourmaline melts incongruently into corundum + liquid, depending on pressure. In the absence of excess B₂O₃ tourmaline stability is lowered by about 60°C. Tourmaline may coexist with the other MgO-Al₂O₃-B₂O₃-SiO₂-H₂O phases forsterite, enstatite, chlorite, talc, quartz, grandidierite, corundum, spinel, “B-mullite,” cordierite, and sinhalite depending on the prevailing PTX-conditions.The (3a)-vacant tourmaline has the space group R3m with $\text{a =15.90}\text{A}\text{?}$, $\text{c = 7.115}\text{A}\text{?}$, and $\text{V = 1557.0}\text{A}\text{?}{}^3$. However, these values vary at room temperature with the pressure-temperature conditions of synthesis by $\text{±0.015}\text{A}\text{?}\text{in a}$, $\text{±0.010}\text{A}\text{?}\text{in c}$, and $\text{±4.0}\text{A}\text{?}{}^3\text{in V}$, probably as a result of MgAl order/disorder relations in the octahedral positions. Despite these variations intensity calculations support the assumed structural formula. Refractive indices are n_o = 1.631(2), n_E = 1.610(2), Δn = 0.021. The infrared spectrum is intermediate between those of dravite and elbaite. The common alkali and calcium deficiencies of natural tourmalines may at least partly be explained by miscibilities towards (3a)-vacant end members. The apparent absence of (3a)-vacant tourmaline in nature is probably due to the lack of fluids that carry boron but no Na or Ca.     

The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C

The mineral solubility model of Harvie and Weare (1980) is extended to the eight component system, Na-K-Mg-Ca-H-Cl-SO₄-OH-HCO₃-CO₃-CO₂-H₂O at 25°C to high concentrations. The model is based on the semi-empirical equations of Pitzer (1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.     

Phase equilibria in the system CO2-H2O I: New equilibrium relations at low temperatures

Graphical analysis of free-energy relationships involving binary quadruple points and their associated univariant equilibria in the system CO₂-H₂O suggests the presence of at least 2 previously unrecognized quadruple points and a degenerate binary invariant point involving an azeotrope between CO₂-rich gas and liquid. Thermodynamic data extracted from the equilibrium involving clathrate (hydrate), gas, and ice (H = G+I) are employed along with published data to calculate the P-T range of the 3-ice equilibrium curve, S+I = H, where S is solid CO₂. This equilibrium curve intersects the H = G+I curve approximately where the latter curve intersects the S+H = G curve, thus confirming the existence of one of the inferred quadruple points involving the phases S, G, H, and I. Recognition of some binary equilibria probably have been hampered by extremely low mutual solubilities of CO₂ and H₂O in the fluids phases which, for example, render the S+H = G virtually indistinguishable from the CO₂-sublimation curve.To make the published portion of the L(liquid CO₂)-G-H equilibrium “connect” with the other new quadruple point involving S, L, G, and H, it is necessary to change the sense of the equilibrium from L = G+H at higher pressures to L+H = G at lower pressures by positing a L = G azeotrope at very low concentrations of H₂O. At the low-pressure origin of the azeotrope, which is only a few bars above the CO₂-triple point, the azeotrope curve intersects the 3-phase curve tangentially, creating a degenerate invariant point at which the 3-phase equilibrium changes from L+H = G at lower pressures to L = G+H at higher pressures. The azeotrope curve is offset at slightly lower temperature from the L = G+H curve until the 3-phase equilibrium terminates at the quadruple point involving G, L, H, and W (water). With further increase in pressure the azeotrope curve tracks the L = G+W equilibrium and apparently terminates at a critical end point in close proximity to critical endpoints for the CO₂-saturation curve and the L = G+W curve.Thermodynamic data for clathrate extracted from the slope of the H = G+I curve are consistent with a solid-state phase transformation in CO₂-clathrate between 235 and 255 K. Published work shows that the type-I clathrate phase, whose atomic structure is a framework of water molecules with CO₂ molecules situated in large “guest” sites within the framework, is variable in composition with ∼1 guest site vacancy per unit cell at the high-temperature limit of its stability; the number of water molecules, however, remains constant. The formula (CO₂)_8-y·46H₂O, where y is the number of vacancies per unit cell, is in keeping with the atomic structure, whereas the traditional formula, CO₂·nH₂O, where n (hydration number) = 5.75, is misleading.Ambient P-T conditions in the Antarctic and Greenland ice sheets are compatible with sequestering large amounts of carbon as liquid CO₂ and/or clathrate.     

Mineral-solution equilibria—III. The system Na2OAl2O3SiO2H2OHCl

Chemical equilibrium between sodium-aluminum silicate minerals and chloride bearing fluid has been experimentally determined in the range 500–700°C at 1 kbar, using rapid-quench hydrothermal methods and two modifications of the Ag + AgCl acid buffer technique. The temperature dependence of the thermodynamic equilibrium constant (K) for the reaction $\text{NaAlSi}{}_3\text{O}{}_8\text{+ HCl}{}^{\mathrm{o}}\text{= NaCl}{}^{\mathrm{o}}\text{+}\text{1}\text{2Al}{}_2\text{SiO}{}_5\text{, +}\text{5}\text{2SiO}{}_2\text{+}\text{1}\text{2H}{}_2\text{O}$ Albite Andalusite Qtz. can be described by the following equation: log k = ?4.437 + 5205.6/T(K) The data from this study are consistent with experimental results reported by Montoya and Hemley (1975) for lower temperature equilibria defined by the assemblages albite + paragonite + quartz + fluid and paragonite + andalusite + quartz + fluid. Values of the equilibrium constants for the above reactions were used to estimate the difference in Gibbs free energy of formation between NaCl^o and HCl^o in the range 400–700°C and 1–2 kbar. Similar calculations using data from phase equilibrium studies reported in the literature were made to determine the difference in Gibbs free energy of formation between KCl^o and HCl^o. These data permit modelling of the chemical interaction between muscovite + kspar + paragonite + albite + quartz assemblages and chloride-bearing hydrothermal fluids.     

The MgO-Al2O3-SiO2 system: free energy of pyrope and Al2O3-enstatite

Using the model of fictive ideal components, Gibbs free energies of formation of pyrope and Al₂O₃-enstatite have been determined from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range of 1200–1600 K. The negative free energies in kJ/mol are:

     

6.

Thermodynamics of brine-salt equilibria—I. The systems NaCl-KCl-MgCl₂-CaCl₂-H₂O and NaCl-MgSO₄-H₂O at 25°C     

James R. Wood 《Geochimica et cosmochimica acta》1975,39(8):1147-1163

A thermodynamic model for concentrated brines has been developed which is capable of predicting the solubilities of many of the common evaporite minerals in chloro-sulfate brines at 25°C and 1 atm. The model assumes that the behaviour of the mean stoichiometric ionic activity coefficient in mixtures of aqueous electrolytes can be described by the Scatchard deviation function and Harned's Rule. In solutions consisting of one salt and H₂O, the activity coefficient is described by the expression where $\text{a}\text{?}$ and B? salt specific parameters obtained from data regression. In a mixture of n electrolytes and H₂O, B? for the ith component is given by $\text{B}{}^{\mathrm{<mtext>i</mtext><mtext>?</mtext>}}{}_{\mathrm{i}}\text{=B}\text{i}\text{?}{}_{\mathrm{i}}\text{+σ α}{}_{\mathrm{ij}}\text{y}{}_{\mathrm{j}}$ where α_ij is a (constant) mixing parameter characterizing the interaction of the i and j components and y_j is the ionic strength fraction of the jth component. The activity of H₂O is obtained from a Gibbs-Duhem integration and does not require any additional parameters or assumptions. In this study, parameters have been obtained for the systems NaCl-KCl-MgCl₂-CaCl₂-H₂O and NaCl-MgSO₄-H₂O at 25°C and 1 atm. Computed solubility curves and solution compositions predicted for invariant points in these systems agree well with the experimental data. The model is flexible and easily extended to other systems and to higher temperatures.     

7.

New experimental data for the system CaO-MgO-SiO₂-H₂O and a synthesis of inferred phase relations     

Richard D. Warner 《Geochimica et cosmochimica acta》1975,39(10):1413-1421

Subsolidus and vapor-saturated liquidus phase relations for a portion of the system CaO-MgO-SiO₂-H₂O, as inferred from experimental data for the composition regions CaMgSi₂O₆-Mg₂SiO₄-SiO₂-H₂O and CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈ (merwinite)-H₂O, are presented in pressure-temperature projection. Sixteen invariant points and 39 univariant reactions are defined on the basis of the 1 atm and 10 kbar (vapor-saturated) liquidus diagrams. Lack of experimental control over many of the reactions makes the depicted relations schematic in part.An invariant point involving orthoenstatite, protoenstatite, pigeonite, and diopside (all solid solutions) occurs at low pressure (probably between 1 and 2 kbar). At pressures below this invariant point, orthoenstatite breaks down at high temperature to the assemblage diopside + protoenstatite; with increasing temperature, the latter assemblage reacts to form pigeonite. At pressures above the invariant point, pigeonite forms according to the reaction diopside + orthoenstatite = pigeonite, and the assemblage diopside + protoenstatite is not stable. At 1 atm, both pigeonite and protoenstatite occur as primary liquidus phases, but at pressures above 6–7 kbar orthoenstatite is the only Ca-poor pyroxene polymorph which appears on the vapor-saturated liquidus surface.At pressures above approximately 10.8 kbar, only diopside, forsterite, and merwinite occur as primary liquidus phases in the system CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈-H₂O, in the presence of an aqueous vapor phase. At pressures between 1 atm and 10.2 kbar, both akermanite and monticellite also occur as primary liquidus phases. Comparison of the 1 atm and 10 kbar vapor-saturated liquidus diagrams suggests that melilite basalt bears a low pressure, or shallow depth, relationship to monticellite-bearing ultrabasites.     

8.

Decomposition reactions of magnesium sulfate hydrates and phase equilibria in the MgSO₄-H₂O and Na-Mg-Cl-SO₄-H₂O systems with implications for Mars     

Michael Steiger  Kirsten Linnow  Dorothee Ehrhardt  Mandy Rohde 《Geochimica et cosmochimica acta》2011,75(12):3600-3626

We report new measurements of equilibrium relative humidities for stable and metastable hydration-dehydration equilibria involving several magnesium sulfates in the MgSO₄·nH₂O series. We also report a comprehensive thermodynamic treatment of the system including solution properties and experimental data from the published literature, i.e. solubilities, heat capacities and additional decomposition humidities. While for some magnesium sulfate hydrates solubility data in the binary system MgSO₄-H₂O are sparse, there is a reasonable database of solubility measurements of these hydrates in the ternary MgCl₂-MgSO₄-H₂O and the quaternary reciprocal Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O systems. To make these data suitable for the determination of solubility products, we parameterized a Pitzer ion interaction model for the calculation of activity coefficients and water activities in mixed solutions of these systems and report the ion interaction parameters for the Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O system. The model predicted solubilities in the reciprocal system are in very good agreement with experimental data. Using all available experimental data and the solution model an updated phase diagram of the MgSO₄-H₂O system covering the whole temperature range from about 170 to 473 K is established. This treatment includes MgSO₄·H₂O (kieserite), MgSO₄·4H₂O (starkeyite), MgSO₄·5H₂O (pentahydrite), MgSO₄·6H₂O (hexahydrite), MgSO₄·7H₂O (epsomite) and MgSO₄·11H₂O (meridianiite). It is shown that only kieserite, hexahydrite, epsomite and meridianiite show fields of stable existence while starkeyite and pentahydrite are always metastable. Due to sluggish kinetics of kieserite formation, however, there is a rather extended field of metastable existence of starkeyite which makes this solid a major product in dehydration reactions. The model predicted behavior of the magnesium sulfates is in excellent agreement with observations reported in the literature under terrestrial temperature and relative humidity conditions. We also discuss the implications of the new phase diagram for sulfates on Mars.     

9.

The measurement of sulfate mineral solubilities in the Na-K-Ca-Cl-SO₄-H₂O system at temperatures of 100, 150 and 200°C     

Daniela Freyer  Wolfgang Voigt 《Geochimica et cosmochimica acta》2004,68(2):307-318

At T > 100°C development of thermodynamic models suffers from missing experimental data, particularly for solubilities of sulfate minerals in mixed solutions. Solubilities in Na⁺-K⁺-Ca²⁺-Cl⁻-SO₄²⁻/H₂O subsystems were investigated at 150, 200°C and at selected compositions at 100°C. The apparatus used to examine solid-liquid phase equilibria under hydrothermal conditions has been described.In the system NaCl-CaSO₄-H₂O the missing anhydrite (CaSO₄) solubilities at high NaCl concentrations up to halite saturation have been determined. In the system Na₂SO₄-CaSO₄-H₂O the observed glauberite (Na₂SO₄ · CaSO₄) solubility is higher than that predicted by the high temperature model of Greenberg and Møller (1989), especially at 200°C. At high salt concentrations, solubilities of both anhydrite and glauberite increase with increasing temperature. Stability fields of the minerals syngenite (K₂SO₄ · CaSO₄ · H₂O) and goergeyite (K₂SO₄ · 5 CaSO₄ · H₂O) were determined, and a new phase was found at 200°C in the K₂SO₄-CaSO₄-H₂O system. Chemical and single crystal structure analysis give the formula K₂SO₄ · CaSO₄. The structure is isostructural with palmierite (K₂SO₄ · PbSO₄). The glaserite (“3 K₂SO₄ · Na₂SO₄”) appears as solid solution in the system Na₂SO₄-K₂SO₄-H₂O. Its solubility and stoichiometry was determined as a function of solution composition.     

10.

Complex formation in the ternary system Mg(II)-CO₂-H₂O     

Walter Riesen  Heinz Gamsjäger  Paul W. Schindler 《Geochimica et cosmochimica acta》1977,41(9):1193-1200

The carbonato and hydrogencarbonato complexes of Mg²⁺ were investigated at 25 and 50° in solutions of the constant ClO₄^? molality (3 M) consisting preponderantly of NaClO₄. The experimental data could be explained assuming the following equilibria: Mg²⁺ + CO_2B + H₂O ag MgHCO⁺₃ + H⁺, $\text{log}{}^1\text{β}{}_1\text{= ?7.64}{}_4\text{± 0.01}{}_7\text{(25°), ?7.46}{}_2\text{± 0.01}{}_1\text{(50°)}$, Mg²⁺ + 2 CO_2g + 2 H₂Oag Mg(HCO₃)⁰₂ ± 2 H⁺, $\text{log}{}^1\text{β}{}_2\text{= ?15.00 ± 0.14 (25°)}$, ?15.37 ± 0.39 (50°), Mg²⁺ + CO_2g + H₂Oag MgCO⁰₃ + 2 H⁺, $\text{log}{}^1\text{k}{}_1\text{= ?15.64 ± 0.06 (25°)}$,?15.23 ± 0.02 (50°), with the assumption γ_MgCO3⁰ = γ_Mg(HCO3)⁰2, ΔG⁰(I = 0) for the reaction MgCO⁰₃ + CO_2g + H₂O = Mg(HCO₃)⁰₂ was estimated to be ?3.9₁ ± 0.8₆ and 0.6 ± 2.4 kJ/mol at 25 and 50°C, respectively. The abundance of carbonate linked Mg(II) species in fresh water systems is discussed.     

11.

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     

Nicholas J. Tosca  Alexander Smirnov  Scott M. McLennan 《Geochimica et cosmochimica acta》2007,71(11):2680-2698

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.     

12.

The solubilities of calcite,aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C,and an evaluation of the aqueous model for the system CaCO₃-CO₂-H₂O     

L.Niel Plummer  Eurybiades Busenberg 《Geochimica et cosmochimica acta》1982,46(6):1011-1040

Calculations based on approximately 350 new measurements (Ca_T-PCO₂) of the solubilities of calcite, aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C indicate the following values for the log of the equilibrium constants K_C, K_A, and K_V respectively, for the reaction CaCO₃(s) = Ca²⁺ + CO^2?₃: $\text{Log K}{}_{\mathrm{C}}\text{= ?171.9065 ? 0.077993T +}\text{2839.319}\text{T}\text{+ 71.595 log T}$$\text{Log K}{}_{\mathrm{A}}\text{= ?171.9773 ? 0.077993T +}\text{2903.293}\text{T}\text{+71.595 log T}$$\text{Log K}{}_{\mathrm{V}}\text{= ?172.1295 ? 0.077993T +}\text{3074.688}\text{T}\text{+ 71.595 log T}$ where T is in ^oK. At 25°C the logarithms of the equilibrium constants are ?8.480 ± 0.020, ?8.336 ± 0.020 and ?7.913 ± 0.020 for calcite, aragonite and vaterite, respectively.The equilibrium constants are internally consistent with an aqueous model that includes the CaHCO⁺₃ and CaCO⁰₃ ion pairs, revised analytical expressions for CO₂-H₂O equilibria, and extended Debye-Hückel individual ion activity coefficients. Using this aqueous model, the equilibrium constant of aragonite shows no PCO₂-dependence if the CaHCO⁺₃ association constant is between 0 and 90°C, corresponding to the value logK_Cahco⁺3 = 1.11 ± 0.07 at 25°C. The CaCO⁰₃ association constant was measured potentiometrically to be between 5 and 80°C, yielding logK_CaCO⁰3 = 3.22 ± 0.14 at 25°C.The CO₂-H₂O equilibria have been critically evaluated and new empirical expressions for the temperature dependence of K_H, K₁ and K₂ are $\text{log K}{}_{\mathrm{H}}\text{= 108.3865 + 0.01985076T ?}\text{6919.53}\text{T}\text{? 40.45154 log T +}\text{669365.}\text{T}{}^2$, $\text{log K}{}_1\text{= ?356.3094 ? 0.06091964T +}\text{21834.37}\text{T}\text{+ 126.8339 log T —}\text{1684915.}\text{T}{}^2$ and logK₂ = ?107.8871 ? 0.03252849T + 5151.79/T + 38.92561 logT ? 563713.9/T² which may be used to at least 250°C. These expressions hold for 1 atm. total pressure between 0 and 100°C and follow the vapor pressure curve of water at higher temperatures.Extensive measurements of the pH of Ca-HCO₃ solutions at 25°C and 0.956 atm PCO₂ using different compositions of the reference electrode filling solution show that measured differences in pH are closely approximated by differences in liquid-junction potential as calculated by the Henderson equation. Liquid-junction corrected pH measurements agree with the calculated pH within 0.003-0.011 pH.Earlier arguments suggesting that the CaHCO⁺₃ ion pair should not be included in the CaCO₃-CO₂-H₂O aqueous model were based on less accurate calcite solubility data. The CaHCO⁺₃ ion pair must be included in the aqueous model to account for the observed PCO₂-dependence of aragonite solubility between 317 ppm CO₂ and 100% CO₂.Previous literature on the solubility of CaCO₃ polymorphs have been critically evaluated using the aqueous model and the results are compared.     

13.

Mineral-solution equilibria—IV. Solubilities and the thermodynamic properties of FeCl₂⁰ in the system Fe₂O₃-H₂-H₂O-HCl     

N.Z. Boctor  R.K. Popp  J.D. Frantz 《Geochimica et cosmochimica acta》1980,44(10):1509-1518

The solubility of hematite in chloride-bearing hydrothermal fluids was determined in the temperature range 400–600°C and at 1000 and 2000 bars using double-capsule, rapid-quench hydrothermal techniques and a modification of the Ag + AgCl buffer method (Frantz and Popp, 1979). The changes in the molalities of associated hydrogen chloride () as a function of the molality of total iron in the fluid at constant temperature and pressure were used to identify the predominant species of iron in the hydrothermal fluid. The molality of associated HCl varied from 0.01 to 0.15. Associated FeCl₂⁰ was found to be the most abundant species in equilibrium with hematite. Determination of Cl/Fe in the fluid in equilibrium with hematite yields values approximately equal to 2.0 suggesting that ferrous iron is the dominant oxidation state.The equilibrium constant for the reaction Fe₂O₃ + 4HCl⁰ + H₂ = 2FeCl₂⁰ + 3H₂O was calculated and used to estimate the difference in Gibbs free energy between FeCl₂⁰ and HCl⁰ in the temperature range 400–600°C at 1000 and 2000 bars pressure.     

14.

Crystallization of sodium sulfate phases in porous materials: The phase diagram Na₂SO₄-H₂O and the generation of stress   总被引：1，自引：0，他引：1  

Michael Steiger  Sönke Asmussen 《Geochimica et cosmochimica acta》2008,72(17):4291-4306

Mechanical disintegration by crystal growth of salts in pores is generally considered as an important mechanism of rock breakdown both on Earth and on Mars. Crystal growth is also a major cause of damage in porous building materials. Sodium sulfate is the most widely used salt in accelerated weathering tests of natural rocks and building materials. This paper provides an updated phase diagram of the Na₂SO₄-H₂O system based on a careful review of the available thermodynamic data of aqueous sodium sulfate and the crystalline phases. The phase diagram includes both the stable phases thenardite, Na₂SO₄(V), and mirabilite, Na₂SO₄·10H₂O, and, the metastable phases Na₂SO₄(III) and Na₂SO₄·7H₂O. The phase diagram is used to discuss the crystallization pathways and the crystallization pressures generated by these solids in common laboratory weathering experiments and under field conditions. New crystallization experiments carried out at different temperatures are presented. A dilatometric technique is used to study the mechanical response of sandstone samples in typical wetting-drying experiments as in the standard salt crystallization test. Additional experiments with continuous immersion and evaporation were carried out with the same type of sandstone. Both, the theoretical treatment and the results of the crystallization experiments confirm that the crystallization of mirabilite from highly supersaturated solutions is the most important cause of damage of sodium sulfate in porous materials.     

15.

Isopiestic measurement of the osmotic and activity coefficients for the NaOH-NaAl(OH)₄-H₂O system at 313.2 K     

Jun Zhou  Zhou L. Yin  Ping M. Zhang 《Geochimica et cosmochimica acta》2003,67(18):3459-3472

By using a specially designed and constructed isopiestic apparatus, we measured the osmotic coefficients at 313.2 K for the NaOH-NaAl(OH)₄-H₂O system with the total alkali molality, m_NaOHT (m_NaOH + m_NaAl[OH]4), from 0.05 mol/kg H₂O to 12 mol/kg H₂O and α_K (m_NaOHT/m_NaAl(OH)4) from 1.64 to 5.53. The mean standard deviation of the measurements is 0.0038. Several sets of the Pitzer model parameters for NaOH-NaAl(OH)₄-H₂O system were then obtained by regressing the measured osmotic coefficients with the Pitzer model and the Pitzer model parameters for NaOH(aq). One set of the results is as follows: β⁽⁰⁾_NaOH: 0.08669, β⁽¹⁾_NaOH: 0.31446, β⁽²⁾_NaOH: −0.00007367, C^Φ_NaOH: 0.003180, β⁽⁰⁾_NaAl(OH)4: 0.03507, β⁽¹⁾_NaAl(OH)4: 0.02401, C^Φ_NaAl(OH)4: −0.001066, θ_{OH⁻Al(OH)4⁻}: 0.08177, Ψ_Na⁺OH⁻_Al(OH)4⁻: −0.01162. The mean standard difference between the calculated and the measured osmotic coefficients is 0.0088. With the obtained Pitzer model parameters, we calculated the values of K = (γ_{NaAl(OH)4,cal²} · m_{Al(OH)4⁻,exp})/(γ_NaOH,cal² · m_OH⁻,exp) for the gibbsite solubility. The results show that the obtained Pitzer model parameters are reliable, and the relative error of the calculated activity coefficients should be < 2.1%. We also compared the calculated gibbsite solubility data among several activity coefficients models over a range of m_NaOHT at various temperatures. The comparison indicates that our activity coefficients model may be approximately applied in the ranges of temperature from 298.2 to 323.2 K and m_NaOHT from 0 to 8 mol/kg H₂O. We also calculated the stoichiometric activity coefficients of NaOH and NaAl(OH)₄ and the activity of H₂O for the NaOH-NaAl(OH)₄-H₂O system, and these calculations establish their variations with m_NaOHT and α_K. These variations imply that the strengths of the repulsive interactions among various anions are in the following sequence: Al(OH)₄⁻-Al(OH)₄⁻ < Al(OH)₄⁻-OH⁻ < OH⁻-OH⁻, and the attractive interaction between Al(OH)₄⁻ and H₂O is weaker than that between OH⁻ and H₂O.     

16.

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

Georg Kaufmann  Wolfgang Dreybrodt 《Geochimica et cosmochimica acta》2007,71(6):1398-1410

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.     

17.

Chemical equilibrium model of solution behavior and solubility in the H-Na-K-OH-Cl-HSO₄-SO₄-H₂O system to high concentration and temperature     

Christomir Christov  Nancy Moller 《Geochimica et cosmochimica acta》2004,68(6):1309-1331

This paper describes a chemical model that calculates solute and solvent activities and solid-liquid equilibria in the H-Na-K-OH-Cl-HSO₄-SO₄-H₂O system from dilute to high solution concentration within the 0° to 250°C temperature range. All binary and ternary subsystems are included in the model parameterization. The model is validated by comparing predictions with experimental data, primarily in higher order systems, not used in the parameterization process. Limitations of the model due to data insufficiencies are discussed.The Harvie and Weare (GCA44, 981, 1980) solubility modeling approach, incorporating their implementation of the concentration-dependent specific interaction equations of Pitzer (J. Phys. Chem.77, 268, 1973), is employed. This model expands the variable temperature Na-K-Cl-SO₄-H₂O model of Greenberg and Moller (GCA53, 2503, 1989) by including acid (H₂SO₄, HCl) and base (NaOH, KOH) species. Temperature functions for the chemical potentials of 5 acidic (sodium bisulfate, sodium sesquisulfate, mercallite, potassium sesquisulfate and misenite) and 6 basic (4 sodium hydroxide hydrates and 2 potassium hydroxide hydrates) solid phases are determined.     

18.

A chemical equilibrium model of solution behavior and solubility in the H-Na-K-Ca-OH-Cl-HSO₄-SO₄-H₂O system to high concentration and temperature     

Christomir Christov 《Geochimica et cosmochimica acta》2004,68(18):3717-3739

This paper describes a chemical model for calculating solute and solvent activities and solid-liquid equilibria in the H-Na-K-Ca-OH-Cl-HSO₄-SO₄-H₂O system from low to high solution concentration within the 0° to 250°C temperature range. The solubility modeling approach of Harvie and Weare (1980) and Harvie et al. (1984), and their implementation of the Pitzer (1973) specific interaction equations are employed. This model expands the variable temperature H-Na-K-OH-Cl-HSO₄-SO₄-H₂O model of Christov and Moller (2004) by evaluating the Ca²⁺-acid/base binary and ternary solution parameters and the chemical potentials of three basic calcium solid phases: Ca(OH)₂(s), CaCl₂.Ca(OH)₂.H₂O(s), and CaCl₂.3Ca(OH)₂.13H₂O and three calcium chloride hydrates (CaCl₂.nH₂O; n = 6, 4, 2). Comparisons of solubility and activity predictions with experimental data used and not used in model parameterization are given. Limitations of the model due to data insufficiencies are discussed.     

19.

Solubility of grossular, Ca₃Al₂Si₃O₁₂, in H₂O-NaCl solutions at 800 °C and 10 kbar, and the stability of garnet in the system CaSiO₃-Al₂O₃-H₂O-NaCl     

Robert C. Newton 《Geochimica et cosmochimica acta》2007,71(21):5191-5202

The solubility and stability of synthetic grossular were determined at 800 °C and 10 kbar in NaCl-H₂O solutions over a large range of salinity. The measurements were made by evaluating the weight losses of grossular, corundum, and wollastonite crystals equilibrated with fluid for up to one week in Pt capsules and a piston-cylinder apparatus. Grossular dissolves congruently over the entire salinity range and displays a large solubility increase of 0.0053 to 0.132 molal Ca₃Al₂Si₃O₁₂ with increasing NaCl mole fraction (X_NaCl) from 0 to 0.4. There is thus a solubility enhancement 25 times the pure H₂O value over the investigated range, indicating strong solute interaction with NaCl. The Ca₃Al₂Si₃O₁₂ mole fraction versus NaCl mole fraction curve has a broad plateau between X_NaCl = 0.2 and 0.4, indicating that the solute products are hydrous; the enhancement effect of NaCl interaction is eventually overtaken by the destabilizing effect of lowering H₂O activity. In this respect, the solubility behavior of grossular in NaCl solutions is similar to that of corundum and wollastonite. There is a substantial field of stability of grossular at 800 °C and 10 kbar in the system CaSiO₃-Al₂O₃-H₂O-NaCl. At high Al₂O₃/CaSiO₃ bulk compositions the grossular + fluid field is limited by the appearance of corundum. Zoisite appears metastably with corundum in initially pure H₂O, but disappears once grossular is nucleated. At X_NaCl = 0.3, however, zoisite is stable with corundum and fluid; this is the only departure from the quaternary system encountered in this study. Corundum solubility is very high in solutions containing both NaCl and CaSiO₃: Al₂O₃ molality increases from 0.0013 in initially pure H₂O to near 0.15 at X_NaCl = 0.4 in CaSiO₃-saturated solutions, a >100-fold enhancement. In contrast, addition of Al₂O₃ to wollastonite-saturated NaCl solutions increases CaSiO₃ molality by only 12%. This suggests that at high pH (quench pH is 11-12), the stability of solute Ca chloride and Na-Al ± Si complexes account for high Al₂O₃ solubility, and that Ca-Al ± Si complexes are minor. The high solubility and basic dissolution reaction of grossular suggest that Al may be a very mobile component in calcareous rocks in the deep crust and upper mantle when migrating saline solutions are present.     

20.

Some mineral stability relations in the system CaOMgOSiO₂H₂OHCl     

R.W Luce  G.L Cygan  J.J Hemley  W.M D&#x;angelo 《Geochimica et cosmochimica acta》1985,49(2):525-538

Mineral-aqueous solution equilibria for the assemblages talc-quartz, tremolite-talc-quartz, diopside-tremolite-quartz, wollastonite-diopside-quartz and wollastonite-quartz have been studied at 2 kb total pressure, 500° to 700°C and chloride concentrations from 0.03 to 6.0 molal. Most work was at 1 m chloride. Both buffered and unbuffered data were obtained and a recalibration of the Ag-AgCl buffer is presented. Log equilibrium quotients at 500°, 600° and 700°C are respectively: Ta-Qz () 2.57, 1.71, 0.73; Tr-Ta-Qz and Di-Tr-Qz () 4.98, 3.99, 2.21 and 7.29, 5.30, 3.56; WoDi-Qz () 3.30, 3.00, 2.79: Wo-Qz () 5.15, 3.95, 2.68. Mineral stability fields plotted in terms of these concentration data more tangibly represent the compositional character of real systems and the mass transfer capabilities of their fluids than do the analogous theoretical activity diagrams.Overall dissociation constants of MgCl₂ and CaCl₂ were calculated from the experimental data using the calculated ionic activity constants for the reactions and the established dissociation constants of HCl. The negative log values are respectively: 3.88. 6.63, 9.20 for CaCl₂ and 4.60, 7.54, 10.37 for MgCl₂ at 500°, 600° and 700°C, 2 kb. The Ca values are about an order of magnitude more positive than the conductance-derived values by Frantz and Marshall (1982).The phase relations developed in this study have application to the genesis of talc, tremolite, and diopside-bearing assemblages in some regional metamorphic rocks, but more specifically to the calcsilicate skarn assemblages of many metasomatic aureoles. The equilibrium fluids are characterized by high concentrations of Ca relative to Mg and increasing $\text{Ca}\text{Mg}$ ratios with decreasing temperatures. The stability fields of talc, tremolite, and quartz expand relative to those of diopside and wollastonite with decreasing temperature, hence their more common appearance as retrograde products in skarn systems.     

TK	1200	1300	1400	1500	1600
Pyrope	4869.92	4747.05	4614.26	4462.63	4311.00
Al2O3-enstatite	1257.25	1244.28	1191.93	1158.67	1125.64

Thermodynamics of brine-salt equilibria—I. The systems NaCl-KCl-MgCl2-CaCl2-H2O and NaCl-MgSO4-H2O at 25°C

A thermodynamic model for concentrated brines has been developed which is capable of predicting the solubilities of many of the common evaporite minerals in chloro-sulfate brines at 25°C and 1 atm. The model assumes that the behaviour of the mean stoichiometric ionic activity coefficient in mixtures of aqueous electrolytes can be described by the Scatchard deviation function and Harned's Rule. In solutions consisting of one salt and H₂O, the activity coefficient is described by the expression where $\text{a}\text{?}$ and B? salt specific parameters obtained from data regression. In a mixture of n electrolytes and H₂O, B? for the ith component is given by $\text{B}{}^{\mathrm{<mtext>i</mtext><mtext>?</mtext>}}{}_{\mathrm{i}}\text{=B}\text{i}\text{?}{}_{\mathrm{i}}\text{+σ α}{}_{\mathrm{ij}}\text{y}{}_{\mathrm{j}}$ where α_ij is a (constant) mixing parameter characterizing the interaction of the i and j components and y_j is the ionic strength fraction of the jth component. The activity of H₂O is obtained from a Gibbs-Duhem integration and does not require any additional parameters or assumptions. In this study, parameters have been obtained for the systems NaCl-KCl-MgCl₂-CaCl₂-H₂O and NaCl-MgSO₄-H₂O at 25°C and 1 atm. Computed solubility curves and solution compositions predicted for invariant points in these systems agree well with the experimental data. The model is flexible and easily extended to other systems and to higher temperatures.     

New experimental data for the system CaO-MgO-SiO2-H2O and a synthesis of inferred phase relations

Subsolidus and vapor-saturated liquidus phase relations for a portion of the system CaO-MgO-SiO₂-H₂O, as inferred from experimental data for the composition regions CaMgSi₂O₆-Mg₂SiO₄-SiO₂-H₂O and CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈ (merwinite)-H₂O, are presented in pressure-temperature projection. Sixteen invariant points and 39 univariant reactions are defined on the basis of the 1 atm and 10 kbar (vapor-saturated) liquidus diagrams. Lack of experimental control over many of the reactions makes the depicted relations schematic in part.An invariant point involving orthoenstatite, protoenstatite, pigeonite, and diopside (all solid solutions) occurs at low pressure (probably between 1 and 2 kbar). At pressures below this invariant point, orthoenstatite breaks down at high temperature to the assemblage diopside + protoenstatite; with increasing temperature, the latter assemblage reacts to form pigeonite. At pressures above the invariant point, pigeonite forms according to the reaction diopside + orthoenstatite = pigeonite, and the assemblage diopside + protoenstatite is not stable. At 1 atm, both pigeonite and protoenstatite occur as primary liquidus phases, but at pressures above 6–7 kbar orthoenstatite is the only Ca-poor pyroxene polymorph which appears on the vapor-saturated liquidus surface.At pressures above approximately 10.8 kbar, only diopside, forsterite, and merwinite occur as primary liquidus phases in the system CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈-H₂O, in the presence of an aqueous vapor phase. At pressures between 1 atm and 10.2 kbar, both akermanite and monticellite also occur as primary liquidus phases. Comparison of the 1 atm and 10 kbar vapor-saturated liquidus diagrams suggests that melilite basalt bears a low pressure, or shallow depth, relationship to monticellite-bearing ultrabasites.     

Decomposition reactions of magnesium sulfate hydrates and phase equilibria in the MgSO4-H2O and Na-Mg-Cl-SO4-H2O systems with implications for Mars

We report new measurements of equilibrium relative humidities for stable and metastable hydration-dehydration equilibria involving several magnesium sulfates in the MgSO₄·nH₂O series. We also report a comprehensive thermodynamic treatment of the system including solution properties and experimental data from the published literature, i.e. solubilities, heat capacities and additional decomposition humidities. While for some magnesium sulfate hydrates solubility data in the binary system MgSO₄-H₂O are sparse, there is a reasonable database of solubility measurements of these hydrates in the ternary MgCl₂-MgSO₄-H₂O and the quaternary reciprocal Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O systems. To make these data suitable for the determination of solubility products, we parameterized a Pitzer ion interaction model for the calculation of activity coefficients and water activities in mixed solutions of these systems and report the ion interaction parameters for the Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O system. The model predicted solubilities in the reciprocal system are in very good agreement with experimental data. Using all available experimental data and the solution model an updated phase diagram of the MgSO₄-H₂O system covering the whole temperature range from about 170 to 473 K is established. This treatment includes MgSO₄·H₂O (kieserite), MgSO₄·4H₂O (starkeyite), MgSO₄·5H₂O (pentahydrite), MgSO₄·6H₂O (hexahydrite), MgSO₄·7H₂O (epsomite) and MgSO₄·11H₂O (meridianiite). It is shown that only kieserite, hexahydrite, epsomite and meridianiite show fields of stable existence while starkeyite and pentahydrite are always metastable. Due to sluggish kinetics of kieserite formation, however, there is a rather extended field of metastable existence of starkeyite which makes this solid a major product in dehydration reactions. The model predicted behavior of the magnesium sulfates is in excellent agreement with observations reported in the literature under terrestrial temperature and relative humidity conditions. We also discuss the implications of the new phase diagram for sulfates on Mars.     

The measurement of sulfate mineral solubilities in the Na-K-Ca-Cl-SO4-H2O system at temperatures of 100, 150 and 200°C

At T > 100°C development of thermodynamic models suffers from missing experimental data, particularly for solubilities of sulfate minerals in mixed solutions. Solubilities in Na⁺-K⁺-Ca²⁺-Cl⁻-SO₄²⁻/H₂O subsystems were investigated at 150, 200°C and at selected compositions at 100°C. The apparatus used to examine solid-liquid phase equilibria under hydrothermal conditions has been described.In the system NaCl-CaSO₄-H₂O the missing anhydrite (CaSO₄) solubilities at high NaCl concentrations up to halite saturation have been determined. In the system Na₂SO₄-CaSO₄-H₂O the observed glauberite (Na₂SO₄ · CaSO₄) solubility is higher than that predicted by the high temperature model of Greenberg and Møller (1989), especially at 200°C. At high salt concentrations, solubilities of both anhydrite and glauberite increase with increasing temperature. Stability fields of the minerals syngenite (K₂SO₄ · CaSO₄ · H₂O) and goergeyite (K₂SO₄ · 5 CaSO₄ · H₂O) were determined, and a new phase was found at 200°C in the K₂SO₄-CaSO₄-H₂O system. Chemical and single crystal structure analysis give the formula K₂SO₄ · CaSO₄. The structure is isostructural with palmierite (K₂SO₄ · PbSO₄). The glaserite (“3 K₂SO₄ · Na₂SO₄”) appears as solid solution in the system Na₂SO₄-K₂SO₄-H₂O. Its solubility and stoichiometry was determined as a function of solution composition.     

Complex formation in the ternary system Mg(II)-CO2-H2O

The carbonato and hydrogencarbonato complexes of Mg²⁺ were investigated at 25 and 50° in solutions of the constant ClO₄^? molality (3 M) consisting preponderantly of NaClO₄. The experimental data could be explained assuming the following equilibria: Mg²⁺ + CO_2B + H₂O ag MgHCO⁺₃ + H⁺, $\text{log}{}^1\text{β}{}_1\text{= ?7.64}{}_4\text{± 0.01}{}_7\text{(25°), ?7.46}{}_2\text{± 0.01}{}_1\text{(50°)}$, Mg²⁺ + 2 CO_2g + 2 H₂Oag Mg(HCO₃)⁰₂ ± 2 H⁺, $\text{log}{}^1\text{β}{}_2\text{= ?15.00 ± 0.14 (25°)}$, ?15.37 ± 0.39 (50°), Mg²⁺ + CO_2g + H₂Oag MgCO⁰₃ + 2 H⁺, $\text{log}{}^1\text{k}{}_1\text{= ?15.64 ± 0.06 (25°)}$,?15.23 ± 0.02 (50°), with the assumption γ_MgCO3⁰ = γ_Mg(HCO3)⁰2, ΔG⁰(I = 0) for the reaction MgCO⁰₃ + CO_2g + H₂O = Mg(HCO₃)⁰₂ was estimated to be ?3.9₁ ± 0.8₆ and 0.6 ± 2.4 kJ/mol at 25 and 50°C, respectively. The abundance of carbonate linked Mg(II) species in fresh water systems is discussed.     

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.     

The solubilities of calcite,aragonite and vaterite in CO2-H2O solutions between 0 and 90°C,and an evaluation of the aqueous model for the system CaCO3-CO2-H2O

Calculations based on approximately 350 new measurements (Ca_T-PCO₂) of the solubilities of calcite, aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C indicate the following values for the log of the equilibrium constants K_C, K_A, and K_V respectively, for the reaction CaCO₃(s) = Ca²⁺ + CO^2?₃: $\text{Log K}{}_{\mathrm{C}}\text{= ?171.9065 ? 0.077993T +}\text{2839.319}\text{T}\text{+ 71.595 log T}$$\text{Log K}{}_{\mathrm{A}}\text{= ?171.9773 ? 0.077993T +}\text{2903.293}\text{T}\text{+71.595 log T}$$\text{Log K}{}_{\mathrm{V}}\text{= ?172.1295 ? 0.077993T +}\text{3074.688}\text{T}\text{+ 71.595 log T}$ where T is in ^oK. At 25°C the logarithms of the equilibrium constants are ?8.480 ± 0.020, ?8.336 ± 0.020 and ?7.913 ± 0.020 for calcite, aragonite and vaterite, respectively.The equilibrium constants are internally consistent with an aqueous model that includes the CaHCO⁺₃ and CaCO⁰₃ ion pairs, revised analytical expressions for CO₂-H₂O equilibria, and extended Debye-Hückel individual ion activity coefficients. Using this aqueous model, the equilibrium constant of aragonite shows no PCO₂-dependence if the CaHCO⁺₃ association constant is between 0 and 90°C, corresponding to the value logK_Cahco⁺3 = 1.11 ± 0.07 at 25°C. The CaCO⁰₃ association constant was measured potentiometrically to be between 5 and 80°C, yielding logK_CaCO⁰3 = 3.22 ± 0.14 at 25°C.The CO₂-H₂O equilibria have been critically evaluated and new empirical expressions for the temperature dependence of K_H, K₁ and K₂ are $\text{log K}{}_{\mathrm{H}}\text{= 108.3865 + 0.01985076T ?}\text{6919.53}\text{T}\text{? 40.45154 log T +}\text{669365.}\text{T}{}^2$, $\text{log K}{}_1\text{= ?356.3094 ? 0.06091964T +}\text{21834.37}\text{T}\text{+ 126.8339 log T —}\text{1684915.}\text{T}{}^2$ and logK₂ = ?107.8871 ? 0.03252849T + 5151.79/T + 38.92561 logT ? 563713.9/T² which may be used to at least 250°C. These expressions hold for 1 atm. total pressure between 0 and 100°C and follow the vapor pressure curve of water at higher temperatures.Extensive measurements of the pH of Ca-HCO₃ solutions at 25°C and 0.956 atm PCO₂ using different compositions of the reference electrode filling solution show that measured differences in pH are closely approximated by differences in liquid-junction potential as calculated by the Henderson equation. Liquid-junction corrected pH measurements agree with the calculated pH within 0.003-0.011 pH.Earlier arguments suggesting that the CaHCO⁺₃ ion pair should not be included in the CaCO₃-CO₂-H₂O aqueous model were based on less accurate calcite solubility data. The CaHCO⁺₃ ion pair must be included in the aqueous model to account for the observed PCO₂-dependence of aragonite solubility between 317 ppm CO₂ and 100% CO₂.Previous literature on the solubility of CaCO₃ polymorphs have been critically evaluated using the aqueous model and the results are compared.     

Mineral-solution equilibria—IV. Solubilities and the thermodynamic properties of FeCl20 in the system Fe2O3-H2-H2O-HCl

The solubility of hematite in chloride-bearing hydrothermal fluids was determined in the temperature range 400–600°C and at 1000 and 2000 bars using double-capsule, rapid-quench hydrothermal techniques and a modification of the Ag + AgCl buffer method (Frantz and Popp, 1979). The changes in the molalities of associated hydrogen chloride () as a function of the molality of total iron in the fluid at constant temperature and pressure were used to identify the predominant species of iron in the hydrothermal fluid. The molality of associated HCl varied from 0.01 to 0.15. Associated FeCl₂⁰ was found to be the most abundant species in equilibrium with hematite. Determination of Cl/Fe in the fluid in equilibrium with hematite yields values approximately equal to 2.0 suggesting that ferrous iron is the dominant oxidation state.The equilibrium constant for the reaction Fe₂O₃ + 4HCl⁰ + H₂ = 2FeCl₂⁰ + 3H₂O was calculated and used to estimate the difference in Gibbs free energy between FeCl₂⁰ and HCl⁰ in the temperature range 400–600°C at 1000 and 2000 bars pressure.     

Crystallization of sodium sulfate phases in porous materials: The phase diagram Na2SO4-H2O and the generation of stress

Mechanical disintegration by crystal growth of salts in pores is generally considered as an important mechanism of rock breakdown both on Earth and on Mars. Crystal growth is also a major cause of damage in porous building materials. Sodium sulfate is the most widely used salt in accelerated weathering tests of natural rocks and building materials. This paper provides an updated phase diagram of the Na₂SO₄-H₂O system based on a careful review of the available thermodynamic data of aqueous sodium sulfate and the crystalline phases. The phase diagram includes both the stable phases thenardite, Na₂SO₄(V), and mirabilite, Na₂SO₄·10H₂O, and, the metastable phases Na₂SO₄(III) and Na₂SO₄·7H₂O. The phase diagram is used to discuss the crystallization pathways and the crystallization pressures generated by these solids in common laboratory weathering experiments and under field conditions. New crystallization experiments carried out at different temperatures are presented. A dilatometric technique is used to study the mechanical response of sandstone samples in typical wetting-drying experiments as in the standard salt crystallization test. Additional experiments with continuous immersion and evaporation were carried out with the same type of sandstone. Both, the theoretical treatment and the results of the crystallization experiments confirm that the crystallization of mirabilite from highly supersaturated solutions is the most important cause of damage of sodium sulfate in porous materials.     

Isopiestic measurement of the osmotic and activity coefficients for the NaOH-NaAl(OH)4-H2O system at 313.2 K

By using a specially designed and constructed isopiestic apparatus, we measured the osmotic coefficients at 313.2 K for the NaOH-NaAl(OH)₄-H₂O system with the total alkali molality, m_NaOHT (m_NaOH + m_NaAl[OH]4), from 0.05 mol/kg H₂O to 12 mol/kg H₂O and α_K (m_NaOHT/m_NaAl(OH)4) from 1.64 to 5.53. The mean standard deviation of the measurements is 0.0038. Several sets of the Pitzer model parameters for NaOH-NaAl(OH)₄-H₂O system were then obtained by regressing the measured osmotic coefficients with the Pitzer model and the Pitzer model parameters for NaOH(aq). One set of the results is as follows: β⁽⁰⁾_NaOH: 0.08669, β⁽¹⁾_NaOH: 0.31446, β⁽²⁾_NaOH: −0.00007367, C^Φ_NaOH: 0.003180, β⁽⁰⁾_NaAl(OH)4: 0.03507, β⁽¹⁾_NaAl(OH)4: 0.02401, C^Φ_NaAl(OH)4: −0.001066, θ_{OH⁻Al(OH)4⁻}: 0.08177, Ψ_Na⁺OH⁻_Al(OH)4⁻: −0.01162. The mean standard difference between the calculated and the measured osmotic coefficients is 0.0088. With the obtained Pitzer model parameters, we calculated the values of K = (γ_{NaAl(OH)4,cal²} · m_{Al(OH)4⁻,exp})/(γ_NaOH,cal² · m_OH⁻,exp) for the gibbsite solubility. The results show that the obtained Pitzer model parameters are reliable, and the relative error of the calculated activity coefficients should be < 2.1%. We also compared the calculated gibbsite solubility data among several activity coefficients models over a range of m_NaOHT at various temperatures. The comparison indicates that our activity coefficients model may be approximately applied in the ranges of temperature from 298.2 to 323.2 K and m_NaOHT from 0 to 8 mol/kg H₂O. We also calculated the stoichiometric activity coefficients of NaOH and NaAl(OH)₄ and the activity of H₂O for the NaOH-NaAl(OH)₄-H₂O system, and these calculations establish their variations with m_NaOHT and α_K. These variations imply that the strengths of the repulsive interactions among various anions are in the following sequence: Al(OH)₄⁻-Al(OH)₄⁻ < Al(OH)₄⁻-OH⁻ < OH⁻-OH⁻, and the attractive interaction between Al(OH)₄⁻ and H₂O is weaker than that between OH⁻ and H₂O.     

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.     

Chemical equilibrium model of solution behavior and solubility in the H-Na-K-OH-Cl-HSO4-SO4-H2O system to high concentration and temperature

This paper describes a chemical model that calculates solute and solvent activities and solid-liquid equilibria in the H-Na-K-OH-Cl-HSO₄-SO₄-H₂O system from dilute to high solution concentration within the 0° to 250°C temperature range. All binary and ternary subsystems are included in the model parameterization. The model is validated by comparing predictions with experimental data, primarily in higher order systems, not used in the parameterization process. Limitations of the model due to data insufficiencies are discussed.The Harvie and Weare (GCA44, 981, 1980) solubility modeling approach, incorporating their implementation of the concentration-dependent specific interaction equations of Pitzer (J. Phys. Chem.77, 268, 1973), is employed. This model expands the variable temperature Na-K-Cl-SO₄-H₂O model of Greenberg and Moller (GCA53, 2503, 1989) by including acid (H₂SO₄, HCl) and base (NaOH, KOH) species. Temperature functions for the chemical potentials of 5 acidic (sodium bisulfate, sodium sesquisulfate, mercallite, potassium sesquisulfate and misenite) and 6 basic (4 sodium hydroxide hydrates and 2 potassium hydroxide hydrates) solid phases are determined.     

A chemical equilibrium model of solution behavior and solubility in the H-Na-K-Ca-OH-Cl-HSO4-SO4-H2O system to high concentration and temperature

This paper describes a chemical model for calculating solute and solvent activities and solid-liquid equilibria in the H-Na-K-Ca-OH-Cl-HSO₄-SO₄-H₂O system from low to high solution concentration within the 0° to 250°C temperature range. The solubility modeling approach of Harvie and Weare (1980) and Harvie et al. (1984), and their implementation of the Pitzer (1973) specific interaction equations are employed. This model expands the variable temperature H-Na-K-OH-Cl-HSO₄-SO₄-H₂O model of Christov and Moller (2004) by evaluating the Ca²⁺-acid/base binary and ternary solution parameters and the chemical potentials of three basic calcium solid phases: Ca(OH)₂(s), CaCl₂.Ca(OH)₂.H₂O(s), and CaCl₂.3Ca(OH)₂.13H₂O and three calcium chloride hydrates (CaCl₂.nH₂O; n = 6, 4, 2). Comparisons of solubility and activity predictions with experimental data used and not used in model parameterization are given. Limitations of the model due to data insufficiencies are discussed.     

Solubility of grossular, Ca3Al2Si3O12, in H2O-NaCl solutions at 800 °C and 10 kbar, and the stability of garnet in the system CaSiO3-Al2O3-H2O-NaCl

The solubility and stability of synthetic grossular were determined at 800 °C and 10 kbar in NaCl-H₂O solutions over a large range of salinity. The measurements were made by evaluating the weight losses of grossular, corundum, and wollastonite crystals equilibrated with fluid for up to one week in Pt capsules and a piston-cylinder apparatus. Grossular dissolves congruently over the entire salinity range and displays a large solubility increase of 0.0053 to 0.132 molal Ca₃Al₂Si₃O₁₂ with increasing NaCl mole fraction (X_NaCl) from 0 to 0.4. There is thus a solubility enhancement 25 times the pure H₂O value over the investigated range, indicating strong solute interaction with NaCl. The Ca₃Al₂Si₃O₁₂ mole fraction versus NaCl mole fraction curve has a broad plateau between X_NaCl = 0.2 and 0.4, indicating that the solute products are hydrous; the enhancement effect of NaCl interaction is eventually overtaken by the destabilizing effect of lowering H₂O activity. In this respect, the solubility behavior of grossular in NaCl solutions is similar to that of corundum and wollastonite. There is a substantial field of stability of grossular at 800 °C and 10 kbar in the system CaSiO₃-Al₂O₃-H₂O-NaCl. At high Al₂O₃/CaSiO₃ bulk compositions the grossular + fluid field is limited by the appearance of corundum. Zoisite appears metastably with corundum in initially pure H₂O, but disappears once grossular is nucleated. At X_NaCl = 0.3, however, zoisite is stable with corundum and fluid; this is the only departure from the quaternary system encountered in this study. Corundum solubility is very high in solutions containing both NaCl and CaSiO₃: Al₂O₃ molality increases from 0.0013 in initially pure H₂O to near 0.15 at X_NaCl = 0.4 in CaSiO₃-saturated solutions, a >100-fold enhancement. In contrast, addition of Al₂O₃ to wollastonite-saturated NaCl solutions increases CaSiO₃ molality by only 12%. This suggests that at high pH (quench pH is 11-12), the stability of solute Ca chloride and Na-Al ± Si complexes account for high Al₂O₃ solubility, and that Ca-Al ± Si complexes are minor. The high solubility and basic dissolution reaction of grossular suggest that Al may be a very mobile component in calcareous rocks in the deep crust and upper mantle when migrating saline solutions are present.     

Some mineral stability relations in the system CaOMgOSiO2H2OHCl

Mineral-aqueous solution equilibria for the assemblages talc-quartz, tremolite-talc-quartz, diopside-tremolite-quartz, wollastonite-diopside-quartz and wollastonite-quartz have been studied at 2 kb total pressure, 500° to 700°C and chloride concentrations from 0.03 to 6.0 molal. Most work was at 1 m chloride. Both buffered and unbuffered data were obtained and a recalibration of the Ag-AgCl buffer is presented. Log equilibrium quotients at 500°, 600° and 700°C are respectively: Ta-Qz () 2.57, 1.71, 0.73; Tr-Ta-Qz and Di-Tr-Qz () 4.98, 3.99, 2.21 and 7.29, 5.30, 3.56; WoDi-Qz () 3.30, 3.00, 2.79: Wo-Qz () 5.15, 3.95, 2.68. Mineral stability fields plotted in terms of these concentration data more tangibly represent the compositional character of real systems and the mass transfer capabilities of their fluids than do the analogous theoretical activity diagrams.Overall dissociation constants of MgCl₂ and CaCl₂ were calculated from the experimental data using the calculated ionic activity constants for the reactions and the established dissociation constants of HCl. The negative log values are respectively: 3.88. 6.63, 9.20 for CaCl₂ and 4.60, 7.54, 10.37 for MgCl₂ at 500°, 600° and 700°C, 2 kb. The Ca values are about an order of magnitude more positive than the conductance-derived values by Frantz and Marshall (1982).The phase relations developed in this study have application to the genesis of talc, tremolite, and diopside-bearing assemblages in some regional metamorphic rocks, but more specifically to the calcsilicate skarn assemblages of many metasomatic aureoles. The equilibrium fluids are characterized by high concentrations of Ca relative to Mg and increasing $\text{Ca}\text{Mg}$ ratios with decreasing temperatures. The stability fields of talc, tremolite, and quartz expand relative to those of diopside and wollastonite with decreasing temperature, hence their more common appearance as retrograde products in skarn systems.