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1.
For a phase at equilibrium in which two cation species are partitioned ideally between two sub-lattice sites, the excess functions of mixing (free energy, enthalpy and entropy) are directly related to the bulk composition of the phase and ΔGE°( T, P), the standard-state intra- crystalline exchange free energy. If the phase is not at equilibrium internally, an additional ordering parameter is necessary to fix the excess free energy of mixing, GmixEX, unambiguously. Conversely, for any fixed GmixEX there exists an infinity of possible intracrystalline cation dis- tributions, only one of which is the equilibrium distribution for the specified temperature and pressure. As ideal intraphase cation ordering becomes more pronounced, GmixEX decreases. In response, the total free energy of mixing for the phase decreases progressively for non-end member compositions, approaching, at the limits of ordering, values appropriate for stabilizing compounds of intermediate composition.The model-dependent activity coefficient for component A in the phase, γ AT, can be calculated for any bulk composition, XAT, either from GmixEX directly or from more basic equations involving the interrelation of chemical potentials at equilibrium. A general form for γ AT is ln , where Xjκ denotes the mole fraction of species j in site κ. The first term on the right-hand side of this equation is the contribution to γ AT from ideal intracrystalline partitioning, and is common to the several theories lately presented to model intraphase cation partitioning. It can be shown rigorously that this term contributes to a negative deviation from ideality for the bulk phase. The second term is the contribution to the macroscopic activity coefficient from non-ideal intraphase partitioning, and is related to an enthalpy of mixing, HmixN in excess of that resulting from ideal inter-site cation ordering. While the expression represented by Y can take several functional forms, the additional enthalpy can be evaluated explicitly for specific non-ideal partitioning models from the relation .In those cases, GmixEX can also be determined exactly. 相似文献
3.
The crystallization of plagioclase feldspar from magmatic liquid has been investigated experimentally under equilibrium conditions at 1 atm total pressure in the temperature range 1400-1095°C. Natural and synthetic melts of composition basalt to rhyolite were used, crystallizing plagioclase of composition An 89-An 32.The experimental results are analyzed initially in terms of elemental plagioclase/melt partition coefficients ( D). DSi is always less than unity and is invariant with temperature. DA1 is always greater than unity and is relatively insensitive to temperature. DNa is less than unity above 1200°C and is strongly dependent upon temperature. DCa is greater than unity below 1430°C and is strongly dependent upon temperature.Analysis of the temperature-dependence of equilibrium constants for plagioclase-melt formation and exchange reactions in which several mixing models for the melt are considered, leads to the conclusion that, with appropriate choice of melt-components, the melt-components mix quasi-ideally. At fixed temperature in the absence of H 2O, the equilibrium constant for the equilibrium of albite with the melt is insensitive to changes in melt-composition, and is insensitive to changes in pressure up to at least 10 kbars. As a consequence the composition of plagioclase crystallizing at known temperature and at low total pressure from a dry melt of known composition may be predicted [ ]. However, the equilibrium constant is sensitive to changes in water pressure.The analysis further suggests that Na is intimately associated with tetrahedrally-coordinated Al in the melt, while Ca appears to be partitioned between at least two distinct melt-sites. 相似文献
4.
The stability of the amphibole pargasite [NaCa 2Mg 4Al(Al 2Si 6))O 22(OH) 2] in the melting range has been determined at total pressures ( P) of 1.2 to 8 kbar. The activity of H 2O was controlled independently of P by using mixtures of H 2O + CO 2 in the fluid phase. The mole fraction of H 2O in the fluid ( ) ranged from 1.0 to 0.2.At P < 4 kbar the stability temperature ( T) of pargasite decreases with decreasing at constant P. Above P ? 4 kbar stability T increases as is decreased below one, passes through a T maximum and then decreases with a further decrease in . This behavior is due to a decrease in the H 2O content of the silicate liquid as decreases. The magnitude of the T maximum increases from about 10°C (relative to the stability T for ) at P = 5 kbar to about 30°C at P = 8 kbar, and the position of the maximum shifts from at P = 5 kbar to at P = 8 kbar.The H 2O content of liquid coexisting with pargasite has been estimated as a function of at 5 and 8 kbar P, and can be used to estimate the H 2O content of magmas. Because pargasite is stable at low values of at high P and T, hornblende can be an important phase in igneous processes even at relatively low H 2O fugacities. 相似文献
5.
The regular geometry and completeness of the Kiglapait intrusion permit its bulk composition to be obtained by summation, and the composition of successive liquids to be obtained by subtraction. The summations for K and Rb give 1806 and 1.08 ppm, yielding R frsol| K/ Rb= 1670 for the intrusion, taken as equal to the parent magma. R increases slightly from this initial value to 2000 at the end of crystallization where MgO approaches zero in the rocks. K and Rb are therefore closely coherent and their distribution coefficients can differ only by a small amount in the Kiglapait system.Apparent feldspar/liquid distribution coefficients (D F/L) can be estimated from detailed plots of feldspar and liquid compositions against FL. The Kiglapait data imply that these coefficients are linear 1:1 functions of plagioclase composition within experimental error, having values given by DKF/ L = 1.42? XAnDRbF/ L = 1.13? XAn with minimum values of 0.75 and 0.49, respectively. The ratio lies in the range of 1.53± 0.03 for the plagioclase composition range XAn= 0.34 to 0.67 showing that high-R rocks such as anorthosite crystallized from high- R liquids.The apparent feldspar distribution coefficients are much closer to 1.0 than common literature values. They can be reduced by assuming that the cumulate pile was continuously recharged by the circulating magma until an advanced stage of differentiation was reached, and assuming that alkalies were exchanged to the feldspars from the magma. When such an ‘aquifer recharge’ model is calibrated using olivine-liquid equilibria as a time marker for the liquid, the inferred minimum equilibrium values of the distribution coefficients are = 0.42, = 0.25 at the base of the intrusion. Their variation is given by , , The equilibrium values are considered to be appropriate for deducing liquid compositions in plutonic bodies where alkali exchange can be shown or inferred to have been inhibited, such as in small intrusions. The apparent values are considered to be appropriate, even though they may be artificial, for large intrusions similar to the Kiglapait.The bulk K and Rb concentrations in the Kiglapait intrusion are consistent with a plagioclase-rich abyssal tholeiite magma. Clinopyroxene and olivine fractionation in the mantle may contribute to the production of such high- Rmagmas. 相似文献
6.
Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature Tr, is given by , where the summation is taken over all oxide components except A1 2O 3, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and is the composition-dependent apparent partial molar volume of Al 2O 3. The thermal expansion coefficient of aluminosilicate liquids is given by , where terms are constants independent of temperature and composition, and is a composition-dependent term representing the effect of Al 2O 3 on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V( T) = Vrexp[ α( T- Tr)], where Tr = 1400° C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of is discussed in terms of several possible interpretations of the structural role of Al 3+ in aluminosilicate melts. 相似文献
7.
Self-diffusion of oxygen in adularia, anorthite, albite, oligoclase and labradorite has been measured by isotope exchange of oxygen between natural feldspars and hydrothermal water enriched in 18O. The analysis consisted of measuring the 18O/ 16O gradient inward from the feldspar surface using an ion microprobe, and fitting a solution of the diffusion equation to the data. Depth of the sputtered hole was measured with an optical interferometer. Linear Arrhenius plots were obtained: | | | | | Adularia (Or98) | | 25.6 | 350–700 | | Albite (Ab97, Ab99) | | 21.3 | 350–800 | | Anorthite (An96) | | 26.2 | 350–800 | 相似文献
10.
A parameter ΔO 2?, defined as the difference between the Gibbs energy of formation of a given oxide and its aqueous cation, was used to obtain linear relationships among Gibbs energies of formation from the elements of hydroxides, oxides and aqueous metallic ions (Tardy and Garrels, 1976). Use of this parameter has now been extended to meta- and orthosilicates for which the Gibbs energies of formation of silicates from their oxides are shown to be linear functions of the ΔO 2? values of their constituent cations. The function obtained for metasilicates is: and that for orthosilicates is: in which Δ o? silicate is the Gibbs energy of formation from the elements of a silicate of a given cation and ∑ΔG o? oxides is the sum of the Gibbs energies of formation from the elements of the constituent oxides of the silicate considered.These functions can be used to test for consistency within and between various sources of thermodynamic data and to estimate free energy of formation values for previously unstudied species. 相似文献
11.
The coprecipitation of Na and K was experimentally investigated in aragonite. The distribution functions were determined at pH 6.8 and 8.8 over aqueous Na and K concentrations of between 5 × 10 ?4and 2.0 M and temperatures of between 25 and 75°C.The mole fractions of Na and K in aragonite are related to the aqueous ratios of Na and Ca by a function of the form where C0 and C1 are constants at a given temperature. This equation was derived by a statistical model assuming a heterogeneous energy distribution for the sites of incorporation. The independence of the coprecipitation process from aqueous anion activities suggests that carbonate is the only anionic species in the solid solution. 相似文献
12.
The effect of presure on the solubility of minerals in water and seawater can be estimated from In where the volume ( ΔV) and compressibility ( ΔK) changes at atmospheric pressure ( P = 0) are given by Values of the partial molal volume ( ) and compressibilty ( ) in water and seawater have been tabulated for some ions from 0 to 50°C. The compressibility change is quite large (~10 × 10 ?3 cm 3 bar ?1 mol ?1) for the solubility of most minerals. This large compressibility change accounts for the large differences observed between values of ΔV obtained from linear plots of In Ksp versus P and molal volume data (Macdonald and North, 1974; North, 1974). Calculated values of for the solubility of CaCO 3, SrSO 4 and CaF 2 in water were found to be in good agreement with direct measurements (Macdonald and North, 1974). Similar calculations for the solubility of minerals in seawater are also in good agreement with direct measurements (Ingle, 1975) providing that the surface of the solid phase is not appreciably altered. 相似文献
13.
Solubility curves were determined for a synthetic gibbsite and a natural gibbsite (Minas Gerais, Brazil) from pH 4 to 9, in 0.2% gibbsite suspensions in 0.01 M NaNO 3 that were buffered by low concentrations of non-complexing buffer agents. Equilibrium solubility was approached from oversaturation (in suspensions spiked with Al(NO 3) 3 solution), and also from undersaturation in some synthetic gibbsite suspensions. Mononuclear Al ion concentrations and pH values were periodically determined. Within 1 month or less, data from over-and undersaturated suspensions of synthetic gibbsite converged to describe an equilibrium solubility curve. A downward shift of the solubility curve, beginning at pH 6.7, indicates that a phase more stable than gibbsite controls Al solubility in alkaline systems. Extrapolation of the initial portion of the high-pH side of the synthetic gibbsite solubility curve provides the first unified equilibrium experimental model of Al ion speciation in waters from pH 4 to 9.The significant mononuclear ion species at equilibrium with gibbsite are Al 3+, AlOH 2+, Al(OH) +2 and Al(OH) ?4, and their ion activity products are , , and . The calculated standard Gibbs free energies of formation ( ΔG° f) for the synthetic gibbsite and the A1OH 2+, Al(OH) +2 and Al(OH) ?4 ions are ?276.0, ?166.9, ?216.5 and ?313.5 kcal mol ?1, respectively. These ΔG° f values are based on the recently revised ΔG° f value for Al 3+ (?117.0 ± 0.3 kcal mol ?1) and carry the same uncertainty. The ΔG° f of the natural gibbsite is ?275.1 ± 0.4 kcal mol ?, which suggests that a range of ΔG° f values can exist even for relatively simple natural minerals. 相似文献
14.
Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C: where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for p K(NaH 2BO 3°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed p K's for MgH 2BO 3+, CaH 2BO 3+ and NaH 2BO 30 yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester. 相似文献
15.
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 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. 相似文献
16.
A linear correlation exists between the standard Gibbs free energies of formation of calcite-type carbonates (MCO 3) and the corresponding conventional standard Gibbs free energies of formation of the aqueous divalent cations (M 2+) at 25 °C and 1 bar ΔGMCO30 = m( ΔGf,M2+0) ? 141,200 cal · mole?1 where m is equal to 0.9715. This relationship enables prediction of the standard free energies of formation of numerous hypothetical carbonates with the calcite structure. Associated uncertainties typically range from about ± 250 to 600 cal · mole ?1. An important consequence of the above correlation is that the thermodynamic equilibrium constant for the distribution of two trace elements M and N between carbonate mineral and aqueous solution at 25 °C and 1 bar is proportional to the free energy difference between the corresponding two aqueous ions: In Combination of predicted standard free energies, entropies and volumes of carbonate minerals at 25°C and 1 bar with standard free energies of aqueous ions and the equation of state in Helgeson et al. (1981) enables prediction of the thermodynamic equilibrium constant for trace element distribution between carbonates and aqueous solutions at elevated temperatures and pressures. Interpretation of the thermodynamic equilibrium constant in terms of concentration ratios in the aqueous phase is considerably simplified if pairs of divalent trace elements are considered that have very similar ionic radii ( e.g., , ). In combination with data for the stabilities of complex ions in aqueous solutions, the above calculations enable useful limits to be placed on the concentrations of trace elements in hydrothermal solutions. 相似文献
17.
Differences in the chemical composition of metamorphic and igneous pyroxene minerals may be attributed to a transfer reaction, which determines the Ca content of the minerals, and an exchange reaction, which determines the relative Mg:Fe 2+ ratios. Natural data for associated Ca pyroxene (Cpx) and orthopyroxene (Opx) or pigeonite are combined with experimental data for Fe-free pyroxenes, to produce the following equations for the Cpx slope of the solvus surface: , and the following equation for the temperature-dependence of the Mg-Fe distribution coefficient: , where T is absolute temperature, X is , [Ca] is in Cpx, and KD is the distribution coefficient, defined as .The transfer and exchange equations form useful temperature indicators, and when applied to 9 sets of well-studied rocks, yield pairs of temperatures that are in good agreement. For example, temperatures obtained for the Bushveld Complex are 1020°C (solvus equation) and 980°C (exchange equation), based on 7 specimens. The uncertainty in these numbers, due to precision and accuracy errors, is estimated to be ±60°. 相似文献
18.
The apparent constants ( K' i) for the ionization of carbonic acid in seawater at various salinities ( S,%.) have been fit to equations of the form ln whereKi is the thermodynamic ionization constant in water, Ai, and Bi are adjustable parameters. The temperature dependence (TK) of Ki, Ai and Bi were of the form, a0 + a1/ T + a3 ln T. Equations of similar forms have been used to analyze the ionization constants for water and boric acid and the solubility product of calcite in seawater. The effect of pressure on the apparent constants ( ) have been fit to equations of the form ln where the volume (ΔV) and compressibility (ΔK) changes are polynomial functions of temperature. The equations generated for various açids in seawater have been used to examine the carbonate system in seawater. Equations relating the NBS and Tris pH scales have been derived as well as equations of pH as a function of temperature and pressure. The equations from Hansson (1972, Ph.D. Thesis, University of Göteborg, Sweden) and Mehrbach et al. (1973, Limnol. Oceanogr.18, 897–907) have been used to examine the components of the carbonate system. At a fixed total alkalinity and total carbon dioxide, differences of ±0.01 m-equiv kg ?1 in HCO ?3 and CO 2?3 were found; however, the [CO 2] and P co2 are nearly the same. The contribution of borate ion, B(OH) ?4 determined from the equations of Hansson (1972, Ph.D. Thesis, University of Göteborg, Sweden) and Lyman (1957, Ph.D. Thesis, University of California, Los Angeles) differ by ±0.01 m-equiv kg ?1 for waters with the same salinity and temperature. 相似文献
19.
At 750°C and 4000 bar scapolite is stable relative to plagioclase + calcite over the range of plagioclase compositions An 53–An 83. The assemblage plagioclase + scapolite + calcite is stable relative to plagioclase + calcite over the ranges of plagioclase composition An 48-An 53 and An 83–An 91.5. When NaCl is present in the coexisting fluid the range of scapolite compositions stable relative to plagioclase increases. High mole fractions of NaCl in the fluid stabilize scapolite relative to plagioclases from An 25 to An 87 in the presence of excess calcite. Determination of the ratios of the synthetic scapolites shows that the range of stable scapolite compositions is significantly larger than heretofore proposed, and that even the chloride and carbonate bearing scapolites must be considered a four component solid solution. The KD for the exchange of NaCl and CaCo 3 between coexisting scapolite, fluid and carbonate is given by the equation In . This equation implies that Cl-poor natural scapolites coexisted with fluids low in NaCl, and that regional occurrences of Cl-rich scapolites are likely to represent metamorphosed evaporite sequences. 相似文献
20.
In a soil developed on the Cretaceous chalk of the Eastern Paris basin, calcite dissolution begins at the surface. The soil water is rapidly saturated in calcite. Calcite dissolution follows two different pathways according to seasonal pedoclimatic conditions.During winter: the soil is only partly saturated in water and the CO 2 partial pressure is low (Ca 10 ?3 atm.). As a consequence total inorganic dissolved carbon (TIDC) is a hundred times the carbon content of the gaseous phase. Equilibrium is usually observed between the two phases. It is a closed system. The measured carbon 14 activity (87,5%) and 13C content ( ) of the drainage water are very close to theoretical values calculated for an ideal mixing system between gaseous and mineral phases (respectively characterized by the following isotopic values: ; ; ; ).During spring and summer: the soil moisture decreases, the input of biogenic CO 2 induces an increase of the soil CO 2 partial pressure (Ca from 3.10 ?3 atm to 7.10 ?3 atm). The carbon content of the gaseous phase is higher by an order of magnitude compared to winter conditions. Therefore the aqueous phase is undersaturated in CO 2 with respect to the latter. This disequilibrium occurs as a result of unbalanced rates of CO 2 dissolution and CO 2 effusion toward atmosphère. It is an open system. The carbon isotopic ratio of the aqueous phase is regulated by that of the gaseous phase, as demonstrated by the agreement between measured and calculated isotopic compositions (respectively δL mes = from ?9,4%0 to ?11,5%0, δl calc = from ?9,8%0 to ?13,9%0 AL mes = 119%, AL calc = from 119% to 125%).The solutions originating from both systems (open and closed) move downwards without significant mixing together. It has also been observed that no significant variation of the TIDC isotopic composition occurs during precipitation of secondary calcite. 相似文献
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