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1.
Jonathan D. Blundy Timothy J. B. Holland 《Contributions to Mineralogy and Petrology》1990,104(2):208-224
There is currently a dearth of reliable thermobarometers for many hornblende and plagioclase-bearing rocks such as granitoids and amphibolites. A semi-empirical thermodynamic evaluation of the available experimental data on amphibole+plagioclase assemblages leads to a new thermometer based on the Aliv content of amphibole coexisting with plagioclase in silica saturated rocks. The principal exchange vector in amphiboles as a function of temperature in both the natural and experimental studies is \(\left( {Na\square _{ - 1} } \right)^A \left( {AlSi_{ - 1} } \right)^{T1}\) . We have analysed the data using 3 different amphibole activity models to calibrate the thermometer reactions 1. $$1. Edenite + 4 Quartz = Tremolite + Albite$$ 2. $$2. Pargasite + 4 Quartz = Hornblende + Albite.$$ The equilibrium relation for both (1) and (2) leads to the proposed new thermometer $$T = \frac{{0.677P - 48.98 + Y}}{{ - 0.0429 - 0.008314 ln K}} and K = \left( {\frac{{Si - 4}}{{8 - Si}}} \right)X_{Ab}^{Plag} ,$$ where Si is the number of atoms per formula unit in amphiboles, with P in kbar and T in K; the term Y represents plagioclase non-ideality, RTlnγab, from Darken's Quadratic formalism (DQF) with Y=0 for X ab>0.5 and Y=-8.06+25.5(1-X ab)2 for X ab<0.5. The best fits to the data were obtained by assuming complete coupling between Al on the T1 site and Na in the A site of amphibole, and the standard deviation of residuals in the fit is ±38°C. The thermometer is robust to ferric iron recalculation procedures from electron probe data and should yield temperatures of equilibration for hornblende-plagioclase assemblages with uncertainties of around ±75° C for rocks equilibrated at temperatures in the range 500°–1100° C. The thermometer should only be used in this temperature range and for assemblages with plagioclase less calcic than An92 and with amphiboles containing less than 7.8 Si atoms pfu. Good results have been attained on natural examples from greenschist to granulite facies metamorphic rocks as well as from a variety of mafic to acid intrusive and extrusive igneous rocks. Our analysis shows that the pressure dependence is poorly constrained and the equilibria are not suitable for barometry. 相似文献
2.
Roger L. Nielsen Paula M. Davidson Timothy L. Grove 《Contributions to Mineralogy and Petrology》1988,100(3):361-373
An updated model for pyroxene-melt equilibria at 1 atm has been developed and calibrated using new and existing experimental data in order to refine calculations of liquid lines of descent, which simulate the effect of igneous differentiation processes. We combine the Davidson and Lindsley (1985) model for activities of components in clinopyroxene and orthopyroxene solid solutions, a i p , where i represents a quadrilateral endmember, with the Nielsen and Drake (1979) expressions for component activities in the melt, a i L (two-lattice melt model). The chemical potential differences for pyroxene-melt equilibria are expressed in the form: $$\Delta \mu _{\iota } = 0 = In \left( {{{a_i^p } \mathord{\left/{\vphantom {{a_i^p } {a_i^L }}} \right.\kern-\nulldelimiterspace} {a_i^L }}} \right) + A_i + {{B_i } \mathord{\left/{\vphantom {{B_i } T}} \right.\kern-\nulldelimiterspace} T}$$ Pyroxene compositions were projected to quadrilateral compositions with the method of Lindsley and Anderson (1983). The regression constants A i and B i were calculated from experimental data that consists of 282 pyroxene-melt pairs, including 83 orthopyroxene-melt pairs. These experiments were all performed at 1 atm and represent compositions ranging from basalts (alkali to lunar) to dacites (42–66 wt% SiO2). The model is calibrated for 1000相似文献
3.
The equilibrium position of the reaction $$\begin{gathered} 1.5 KAlSi_3 O_8 + HCl = 0.5 KAl_3 Si_3 O_{10} (OH)_2 \hfill \\ + 3SiO_2 + KCl \hfill \\ \end{gathered} $$ has been located at 1 and 2 kb pressure and temperatures between 600° and 670° C using the Ag-AgCl buffer. These data can be combined with information on the dissociation of KC1, HC1 and H2O to determine species abundances in supercritical aqueous fluids in equilibrium with muscovite — K-feldspar — quartz assemblages. Chloride species become increasingly associated with increasingT, increasing total molality, (m tot or \(m_{Cl_{tot} } \) ), and decreasing \(P_{H_2 O} \) . Master variable diagrams indicate that the pH of the solutions may vary from near neutral to quite acid. Published data on the paragonite-albite-quartz reaction and exchange reactions involving feldspars and micas were included to calculate speciation in mica-feldspar-NaCl-KCl-HCl-H2O fluids at 2kb pressure and temperatures between 300° and 600° C. The data are not accurate enough to distinguish different feldspar structural states. Concentration gradients were calculated for individual species between K-feldspar+quartz, muscovite+quartz and andalusite+quartz assemblages at 500° C, 2 kb. Assuming that the proton diffuses most rapidly and that there are no [H+] gradients, the molality of the solution must vary 30-fold, with feldspar+quartz at the more concentrated side. The data on mica-feldspar-chloride equilibria are used to interpret the spacial distribution of micas, feldspar and quartz in microfolds. This distribution can be accounted for by pressure solution, due to the fact that non-hydrostatic pressure affects congruently dissolving minerals, auch as quartz, differently from minerals which dissolve incongruently, such as micas and feldspars. We postulate, that during folding at constant \(P_{H_2 O} \) ,T and \(m_{Cl - } \) , gradients in KC1 and SiO2 are created by stress differences between hinge and limb of a microfold, such that both migrate to the hinge area where quartz precipitates and muscovite is converted to K-felspar, thus accounting for the observed mineral distribution. 相似文献
4.
Ephesite, Na(LiAl2) [Al2Si2O10] (OH)2, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M1 polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M1 polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M1 poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M1 ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H f,298.15 0 =-6237372 J/mol, S 298.15 0 =300.455 J/K·mol, G 298.15 0 =-5851994 J/mol, and V 298.15 0 =13.1468 J/bar·mol. 相似文献
5.
Tibor Gasparik 《Contributions to Mineralogy and Petrology》1985,89(4):346-357
In the system Na2O-CaO-Al2O3-SiO2 (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase. 相似文献
6.
Equilibrium alumina contents of orthopyroxene coexisting with spinel and forsterite in the system MgO-Al2O3-SiO2 have been reversed at 15 different P-T conditions, in the range 1,030–1,600° C and 10–28 kbar. The present data and three reversals of Danckwerth and Newton (1978) have been modeled assuming an ideal pyroxene solid solution with components Mg2Si2O6 (En) and MgAl2SiO6 (MgTs), to yield the following equilibrium condition (J, bar, K): $$\begin{gathered} RT{\text{ln(}}X_{{\text{MgTs}}} {\text{/}}X_{{\text{En}}} {\text{) + 29,190}} - {\text{13}}{\text{.42 }}T + 0.18{\text{ }}T + 0.18{\text{ }}T^{1.5} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [0.013 + 3.34 \times 10^{ - 5} (T - 298) - 6.6 \times 10^{ - 7} P]P. \hfill \\ \end{gathered} $$ The data of Perkins et al. (1981) for the equilibrium of orthopyroxene with pyrope have been similarly fitted with the result: $$\begin{gathered} - RT{\text{ln(}}X_{{\text{MgTs}}} \cdot X_{{\text{En}}} {\text{) + 5,510}} - 88.91{\text{ }}T + 19{\text{ }}T^{1.2} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [ - 0.832 - 8.78{\text{ }} \times {\text{ 10}}^{ - {\text{5}}} (T - 298) + 16.6{\text{ }} \times {\text{ 10}}^{ - 7} P]{\text{ }}P. \hfill \\ \end{gathered} $$ The new parameters are in excellent agreement with measured thermochemical data and give the following properties of the Mg-Tschermak endmember: $$H_{f,970}^0 = - 4.77{\text{ kJ/mol, }}S_{298}^0 = 129.44{\text{ J/mol}} \cdot {\text{K,}}$$ and $$V_{298,1}^0 = 58.88{\text{ cm}}^{\text{3}} .$$ The assemblage orthopyroxene+spinel+olivine can be used as a geothermometer for spinel lherzolites, subject to a choice of thermodynamic mixing models for multicomponent orthopyroxene and spinel. An ideal two-site mixing model for pyroxene and Sack's (1982) expressions for spinel activities provide, with the present experimental calibration, a geothermometer which yields temperatures of 800° C to 1,350° C for various alpine peridotites and 850° C to 1,130° C for various volcanic inclusions of upper mantle origin. 相似文献
7.
Data systematization using the constraints from the equation $$Cp = Cv + \alpha _P {}^2V_T K_T T$$ where C p, C v, α p, K T and V are respectively heat capacity at constant pressure, heat capacity at constant volume, isobaric thermal expansion, isothermal bulk modulus and molar volume, has been performed for tungsten and MgO. The data are $$K_T (W) = 1E - 5/(3.1575E - 12 + 1.6E - 16T + 3.1E - 20T^2 )$$ $$\alpha _P (W) = 9.386E - 6 + 5.51E - 9T$$ $$C_P (W) = 24.1 + 3.872E - 3T - 12.42E - 7T^2 + 63.96E - 11T^3 - 89000T^{ - 2} $$ $$K_T (MgO) = 1/(0.59506E - 6 + 0.82334E - 10T + 0.32639E - 13T^2 + 0.10179E - 17T^3 $$ $$\alpha _P (MgO) = 0.3754E - 4 + 0.7907E - 8T - 0.7836/T^2 + 0.9148/T^3 $$ $$C_P (MgO) = 43.65 + 0.54303E - 2T - 0.16692E7T^{ - 2} + 0.32903E4T^{ - 1} - 5.34791E - 8T^2 $$ For the calculation of pressure-volume-temperature relation, a high temperature form of the Birch-Murnaghan equation is proposed $$P = 3K_T (1 + 2f)^{5/2} (1 + 2\xi f)$$ Where $$K_T = 1/(b_0 + b_1 T + b_2 T^2 + b_3 T^3 )$$ $$f = (1/2)\{ [V(1,T)/V(P,T)]^{2/3} - 1\} $$ $$\xi = ({3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4})[K'_0 + K'_1 \ln ({T \mathord{\left/ {\vphantom {T {300}}} \right. \kern-\nulldelimiterspace} {300}}) - 4]$$ where in turn $$V(1,T) = V_0 [\exp (\int\limits_{300}^T {\alpha dT)]} $$ . The temperature dependence of the pressure derivative of the bulk modulus (K′1) is estimated by using the shock-wave data. For tungsten the data are K′0 = 3.5434, K′1 = 0.032; for MgO K′0 = 4.17 and K′1 = 0.1667. For calculating the Gibbs free energy of a solid at high pressure and at temperatures beyond that of melting at 1 atmosphere, it is necessary to define a high-temperature reference state for the fictive solid. 相似文献
8.
The high-grade assemblage Cd-Ga-Si-Qz can be thermodynamically modelled from available calorimetric data on the metastable reaction: (I) $$3 MgCd \rightleftarrows 2 Py + 4 Si + 5 Qz$$ naturalK D Fe-Mg between garnet and cordierite and experimental results on cordierite hydration. In the system SiO2-Al2O3-MgO-H2O, reaction (I) becomes (II) $$3 MgCd \cdot nH_2 O \rightleftarrows 2 Py + 4 Si + 5 Qz + 3 nH_2 O$$ . However, hydrous cordierite is neither a hydrate nor a solid solution between water and anhydrous cordierite and when nH2O (number of moles of H2O in Cd) is plotted against \(P_{H_2 O} \) , the resulting isotherms are similar to adsorption isotherms characteristic of zeolitic minerals. Reaction (II) can thus be considered as a combination of reaction (I) with a physical equilibrium of the type nH2O (in Cd)?nH2O (in vapor phase). Starting from a point on equilibrium (I), introduction of H2O into anhydrous Mg-cordierite lowers the chemical potential of MgCd and hence stabilizes this mineral to higher pressure relative to the right-hand assemblage in reaction (I). The pressure increment of stabilization,ΔP, above the pressure limit of anhydrous cordierite stability at constantT, has been calculated using the standard thermodynamics of adsorption isotherms. Cordierite is regarded as a mixture of Mg2Al4Si5O18 and H2O. The activity of H2O in the cordierite is evaluated relative to an hypothetical standard state extrapolated from infinite H2O dilution, by using measured hydration data. The activity of Mg2Al4Si5O18 in the cordierite is then obtained by integration of the Gibbs-Duhem equation, and the pressure stabilization increment,ΔP, computed by means of the relation: $$\Delta V_s \Delta P \cong - RT\ln a_{MgCd}^{MgCd \cdot nH2O} \left( {\Delta V indepentdent of P and T} \right)$$ . Thus, one may contour theP-T plane in isopleths of nH2O=constant within the area of Mg-cordierite stability allowed by the hydration data for \(P_{H_2 O} = P_{total} \) . The present model indicates greater stabilization of cordierite by H2O than the model of Newton and Wood (1979) and the calculated curve for metastable breakdown of hydrous MgCd is consistent with experimental data on cordierite breakdown at \(P_{H_2 O} = P_{total} \) . Mg/(Mg+Fe) isopleths have been derived for cordierites of varying nH2O in the SiO2-Al2O3-MgO-FeO-H2O system using the additional assumptions that (Fe, Mg) cordierite and (Fe, Mg) garnet behave as ideal solutions, and that typical values of the distribution coefficient of Fe and Mg between coexisting garnet and cordierite observed in natural parageneses can be applied to the calculations. The calculated stable breakdown curve of Fe-cordierite under conditions of \(P_{H_2 O} = P_{total} \) to almandine, sillimanite, quartz and vapor has a positive slope (dP/dT) apparently in contrast to the experimental negative slope. This may be explained by hydration kinetics, which could have allowed systematic breakdown of cordierites of metastable hydration states in the experiments. The bivariant Cd-Ga fields calibrated from the present model are, potentially, good petrogenetic indicators, as, given the iron-magnesium ratio of garnet and cordierite and the hydration number of cordierite, the temperature, pressure and water fugacity are uniquely determined. As this geothermobarometer is in part based on the water content of cordierite, it can be used only if there is some assurance that the actual hydration is inherited from high-grade metamorphic conditions. Such conditions could be realised if the slope of unloading-cooling retrograde metamorphism is more or less parallel to a cordierite isohydron. 相似文献
9.
T. L. Grove 《Contributions to Mineralogy and Petrology》1982,78(3):298-304
Theoretical and practical considerations are combined to place limits on the iron content of an FePt alloy that is in equilibrium with silicate melt, olivine and a gas phase of known \(f_{{\text{O}}_{\text{2}} }\) . Equilibrium constants are calculated for the reactions: (1) $$2{\text{Fe}}^{\text{o}} + {\text{SiO}}_{\text{2}} + {\text{O}}_{\text{2}} \rightleftharpoons {\text{Fe}}_{\text{2}} {\text{SiO}}_{\text{4}}$$ (2) $${\text{Fe}}^{\text{o}} + \frac{1}{2}{\text{O}}_{\text{2}} \rightleftharpoons {\text{FeO}}$$ . These equilibria may be used to choose an appropriate iron activity for the FePt alloy of an experiment. The temperature dependence of the equilibrium constants is calculated from experimental data. The Gibbs free energy of reaction (1) obtained using thermochemical data is in close agreement with ΔGrxn calculated from the experimental data. Reaction (1) has the advantage that it is independent of the Fe2+/Fe3+ ratio of the melt, but is limited to applications where olivine is a crystallizing phase and requires a formulation for \(a_{{\text{SiO}}_{\text{2}} }^{{\text{liq}}}\) . Reaction (2) uses an empirical approximation for the FeO/Fe2O3 ratio of the liquid, and is independent of olivine saturation. However, it requires a formulation for a FeO liq . Either equilibrium constant may be used to calculate the appropriate FePt alloy in equilibrium with a silicate melt. If experiments are conducted at an \(f_{{\text{O}}_{\text{2}} }\) parallel that of a buffer assemblage, a small range of FePt alloys may be used over a large temperature interval. For example, an alloy containing from 6 % to 9 % Fe by weight is in equilibrium with olivine-saturated tholeiites and komatiites at the quartzfayalite-magnetite buffer over the temperature interval 1,400° C to 1,100° C. Lunar basalt liquids in equilibrium with olivine at 1/2 log unit below the iron-wüstite buffer require an FePt alloy that contains 30–50 wt. % iron over a similar temperature interval. 相似文献
10.
An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene 总被引：1，自引：0，他引：1
Simon L. Harley 《Contributions to Mineralogy and Petrology》1984,86(4):359-373
The partitioning of Fe and Mg between garnet and aluminous orthopyroxene has been experimentally investigated in the pressure-temperature range 5–30 kbar and 800–1,200° C in the FeO-MgO-Al2O3-SiO2 (FMAS) and CaO-FeO-MgO-Al2O3-SiO2 (CFMAS) systems. Within the errors of the experimental data, orthopyroxene can be regarded as macroscopically ideal. The effects of Calcium on Fe-Mg partitioning between garnet and orthopyroxene can be attributed to non-ideal Ca-Mg interactions in the garnet, described by the interaction term:W CaMg ga -W CaFe ga =1,400±500 cal/mol site. Reduction of the experimental data, combined with molar volume data for the end-member phases, permits the calibration of a geothermometer which is applicable to garnet peridotites and granulites: $$T(^\circ C) = \left\{ {\frac{{3,740 + 1,400X_{gr}^{ga} + 22.86P(kb)}}{{R\ln K_D + 1.96}}} \right\} - 273$$ with $$K_D = {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } \mathord{\left/ {\vphantom {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}$$ and $$X_{gr}^{ga} = (Ca/Ca + Mg + Fe)^{ga} .$$ The accuracy and precision of this geothermometer are limited by largerelative errors in the experimental and natural-rock data and by the modest absolute variation inK D with temperature. Nevertheless, the geothermometer is shown to yield reasonable temperature estimates for a variety of natural samples. 相似文献
11.
The data of Reed (1983) are analysed to produce the following empirical equations for the amplitude p 0 (overall fluctuation) in Pascals of the air pressure wave associated with a volcanic eruption of volume V km3 or a nuclear explosion of strength M Mt: Here s is the distance from the source in km. $$\begin{gathered} \log _{10} p_0 = 4.44 + \log _{10} V - 0.84\log _{10} s \hfill \\ {\text{ }} = 3.44 + \log _{10} M - 0.84\log _{10} s. \hfill \\ \end{gathered} $$ Garrett's (1970) theory is examined on the generation of water level fluctuations by an air pressure wave crossing a water depth discontinuity such as a continental shelf. The total amplitude of the ocean wave is determined to be where c 2 1 = gh 1, c 2 2 = gh 2, g is acceleration of gravity, h 1 and h 2 are the water depths on the ocean and shore side of the depth discontinuity, c is the speed of propagation of the air pressure wave, and ? is the water density. $$B = \left[ {\frac{{c_2^2 }}{{c^2 - c_2^2 }} + \frac{{c^2 (c_1 - c_2 )}}{{(c - c_1 )(c^2 - c_2^2 )}}} \right]\frac{{p_0 }}{{g\varrho }}$$ It is calculated that a 10 km3 eruption at Mount St. Augustine would cause a 460 Pa air pressure wave and a discernible water level fluctuation at Vancouver Island of several cm amplitude. 相似文献
12.
Niranjan D. Chatterjee Ludger Terhart 《Contributions to Mineralogy and Petrology》1985,89(2-3):273-284
The system MgO-Al2O3-SiO2(MAS) comprises 88–90% of the bulk composition of an average peridotite. The MAS ternary is thus a suitable starting point for exploring peridotite phase relations in multicomponent natural systems. The basic MAS phase relations may be treated in terms of the reactions (see list of symbols etc).
- py (in Gt)=en (in Opx)+mats (in Opx),
- en (in Opx)+sp (in Sp)=mats (in Opx)+fo (in Ol), and
- py (in Gt)+fo (in Ol)=en (in Opx)+sp (in Sp).
- binary Sp (sp-pc) crystalline solution (Oka et al. 1984),
- ternary Opx (en-mats-mcts) crystalline solution (this study), and
- binary Gt (py-kn) crystalline solution (this study).
- With increasing incorporation of Cr+3 into Sp and Gt, the X mats isopleths of the reactions (1) and (2) are shifted to higher temperatures (Fig. 3a); simultaneously, the spinel-peridotite to garnet-peridotite phase transition is moved to higher pressures (Fig. 3b).
- At identical P and T, the X mats values of Opx coexisting in equilibrium with Ol and Sp is strongly dependent upon the X pc value in the latter phase (Figs. 4a and b). Accurate correction for the composition of Sp is, therefore, a necessary precondition for geothermometry of the spinelperidotites.
- The discrepant temperatures reported by Sachtleben und Seck (1981, Fig. 5) from the spinel-peridotites of the Eifel area (systematically too high temperatures as a function of X pc in Sp) are demonstrated to be the result of ignoring the nonideality in the chromian spinels.
13.
Paula M. Davidson Dilip K. Mukhopadhyay 《Contributions to Mineralogy and Petrology》1984,86(3):256-263
Reversed phase equilibrium experiments in the system (Ca, Mg, Fe)2SiO4 provide four tielines at P?1 bar and 1 kbar and 800° C–1,100° C. These tielines have been used to model the solution properties of the olivine quadrilateral following the methods described by Davidson et al. (1981) for quadrilateral clinopyroxenes. The discrepancy between the calculated phase relations and the experimentally determined tielines is within the uncertainty of the experiments. The solution properties of quadrilateral olivines can be described by a non-convergent site-disorder model that allows for complete partitioning of Ca on the M2 site, highly disordered Fe-Mg cation distributions and limited miscibility between high-Ca and low-Ca olivines. The ternary data presented in this paper together with binary solution models for the joins Fo-Mo and Fa-Kst have been used to evaluate two solution parameters: $$\begin{gathered} F^0 \equiv 2(\mu _{{\rm M}o}^0 - \mu _{{\rm K}st}^0 ) + \mu _{Fa}^0 - \mu _{Fo}^0 = 12.660 (1.6) kJ, \hfill \\ \Delta G_*^0 \equiv \mu _{{\rm M}gFe}^0 + \mu _{FeMg}^0 - \mu _{Fo}^0 - \mu _{Fa}^0 = 7.030 (3.9) kJ. \hfill \\ \end{gathered} $$ . Ternary phase quilibrium data for olivines tightly constrain the value of F0, but not that for ΔG * 0 which describes nonideality in Fe-Mg mixing. From this analysis, we infer a function for the apparent standard state energy of Kst: $$\begin{gathered} \mu _{{\rm K}st}^0 = - 102.79 \pm 0.8 - (T - 298)(0.137026) \hfill \\ + (T - 298 - T1n(T/298))(0.155519) \hfill \\ + (T - 298)^2 (2.8242E - 05)/2 \hfill \\ + (T - 298)^2 (2.9665E + 03)/(2T(298)^2 ) kJ \hfill \\ \end{gathered} $$ where T is in Kelvins and the 298 K value is relative to oxides. 相似文献
14.
The biotite zone assemblage: calcite-quartz-plagioclase (An25)-phengite-paragonite-chlorite-graphite, is developed at the contact between a carbonate and a pelite from British Columbia. Thermochemical data for the equilibrium paragonite+calcite+2 quartz=albite+ anorthite+CO2+H2O yields: $$\log f{\text{H}}_{\text{2}} {\text{O}} + \log f{\text{CO}}_{\text{2}} = 5.76 + 0.117 \times 10^{ - 3} (P - 1)$$ for a temperature of 700°K and a plagioclase composition of An25. By combining this equation with equations describing equilibria between graphite and gas species in the system C-H-O, the following partial pressures: \(P{\text{H}}_2 {\text{O}} = 2572{\text{b, }}P{\text{CO}}_2 = 3162{\text{b, }}P{\text{H}}_2 = 2.5{\text{b, }}P{\text{CH}}_4 = 52.5{\text{b, }}P{\text{CO}} = 11.0{\text{b}}\) are obtained for \(f{\text{O}}_2 = 10^{ - 26}\) . If total pressure equals fluid pressure, then the total pressure during metamorphism was approximately 6 kb. The total fluid pressure calculated is extremely sensitive to the value of \(f{\text{O}}_2\) chosen. 相似文献
15.
A great wealth of analytical data for fluid inclusions in minerals indicate that the major species of gases in fluid inclusions are H2O, CO2, CO, CH4, H2 and O2. Three basic chemical reactions are supposed to prevail in rock-forming and ore-forming fluids: $$\begin{gathered} H_2 + 1/2{\text{ O}}_{\text{2}} = H_2 O, \hfill \\ CO + 1/2{\text{ O}}_{\text{2}} = CO_2 , \hfill \\ CH_4 + 2{\text{O}}_{\text{2}} = CO_2 + 2H_2 O, \hfill \\ \end{gathered} $$ and equilibria are reached among them. \(\lg f_{O_2 } - T,{\text{ }}\lg f_{CO_2 } - T\) and Eh-T charts for petrogenesis and minerogenesis in the supercritical state have been plotted under different pressures. On the basis of these charts \(f_{O^2 } ,{\text{ }}f_{CO_2 } \) , Eh, equilibrium temperature and equilibrium pressure can be readily calculated. In this paper some examples are presented to show their successful application in the study of the ore-forming environments of ore deposits. 相似文献
16.
For the reaction: 1 diopside+3 dolomite ?2 forsterite+4 calcite+2 CO2 (14) the following P total?T-brackets have been determined experimentally in the presence of a gasphase consisting of 90 mole%CO2 and 10 mole%H2O∶1 kb, 544°±20° C; 3kb, 638°±15° C; 5kb, 708°±10° C; 10kb, 861°±10° C. The determination was carried out with well defined synthetic minerals in the starting mixture. The MgCO3-contents of the magnesian calcites formed by the reaction in equilibrium with dolomite agree very well with the calcite-dolomite miscibility gap, which can be recalculated from the activities and the activity coefficients of MgCO3 as given by Gordon and Greenwood (1970). The equilibrium constant K 14b was calculated with respect to the reference pressure P 0=1 bar using the experimentally determined \(P_{total} TX_{CO_2 }\) brackets, the activities of MgCO3 and CaCO3 (Gordon and Greenwood 1970; Skippen 1974) and the fugacities of CO2 Holloway (1977) considering the correction of Flowers (1979). Results are plotted as function of the absolute reciprocal temperature in Fig. 1. For the temperature range of 530° to 750° C the following linear expression can be given for the natural logarithm of K14b: (g) $$[ln K_{14b} ]_T^P = - \frac{{18064.43}}{{T\left( {^\circ K} \right)}} + 38.58 + \frac{{0.308(P - 1 bar)}}{{T\left( {^\circ K} \right)}}$$ where P is the total pressure in bars and T the temperature in degrees Kelvin. Combining Equation (g) with the activities of MgCO3 and CaCO3 gives the equilibrium fugacity \(f_{CO_2 }\) : (i) $$[ln f_{CO_2 } ]_T^P = - \frac{{11635.44}}{{T\left( {^\circ K} \right)}} + 21.09 + \frac{{0.154(P - 1 bar)}}{{T\left( {^\circ K} \right)}}$$ Equation (i) and the fugacities of CO2 permit to calculate the equilibrium data in terms of \(P_{CO_2 }\) and T (see Fig. 3) or P total, T and \(X_{CO_2 }\) (see Fig. 5). Combining the \(P_{total} TX_{CO_2 }\) equilibrium data of the above reaction with those of the previously investigated reaction (Metz 1976): 1 tremolite+11 dolomite ?8 forsterite+13 calcite+9 CO2+1 H2O yields the stability conditions of the four-mineral assemblage: diopside+calcian dolomite+forsterite +magnesian calcite and the stability conditions of the five-mineral assemblage: tremolite+calcian dolomite+forsterite +magnesian calcite+diopside both shown in Fig. 6. Since these assemblages are by no means rare in metamorphic siliceous dolomites (Trommsdorff 1972; Suzuki 1977; Puhan 1979) the data of Fig. 6 can be used to determine the pressure of metamorphism and to estimate the composition of the CO2-H2O fluid provided the temperature of the metamorphic event was determined using the calcite-dolomite geothermometer. 相似文献
17.
Niranjan D. Chatterjee Klaus Miller Walter Olbricht 《Physics and Chemistry of Minerals》1994,21(1-2):50-62
Internally consistent thermodynamic data, including their uncertainties and correlations, are reported for 22 phases of the quaternary system CaO-Al2O3-SiO2-H2O. These data have been derived by simultaneous evaluation of the appropriate phase properties (PP) and reaction properties (RP) by the novel technique of Bayes estimation (BE). The thermodynamic model used and the theory of BE was expounded in Part I of this paper. Part II is the follow-up study illustrating an application of BE. The input for BE comprised, among others, the a priori values for standard enthalpy of formation of the i-th phase, Δf H i 0 , and its standard entropy, S i 0 , in addition to the reaction reversal constraints for 33 equilibria involving the relevant phases. A total of 269 RP restrictions have been processed, of which 107 turned out to be non-redundant. The refined values for Δf H i 0 and S i 0 obtained by BE, including their 2σ-uncertainties, appear in Table 4; the Appendix reproduces the corresponding correlation matrix. These data permit generation of computed phase diagrams with 2σ-uncertainty envelopes based on conventional error propagation; Fig. 3 depicts such a phase diagram for the system CaO-Al2O3-SiO2. It shows that the refined dataset is capable of yielding phase diagrams with uncertainty envelopes narrow enough to be geologically useful. The results in Table 4 demonstrate that the uncertainties of the prior values for Δf H i Emphasis>0 , given in Table 1, have decreased by up to an order of magnitude, while those for S i 0 improved by a factor of up to two. For comparison, Table 4 also lists the refined Δf H i 0 and S i 0 data obtained by mathematical programming (MAP), minimizing a quadratic objective function used earlier by Berman (1988). Examples of calculated phase diagrams are given to demonstrate the advantages of BE for deriving internally consistent thermodynamic data. Although P-T curves generated from both MAP and BE databases will pass through the reversal restrictions, BE datasets appear to be better suited for extrapolations beyond the P-T range explored experimentally and for predicting equilibria not constrained by reversals. 相似文献
18.
A number of experimental CO2 solubility data for silicate and aluminosilicate melts at a variety of P- T conditions are consistent with solution of CO2 in the melt by polymer condensation reactions such as SiO 4(m 4? +CO2(v)+Si n O 3n+1(m) (2n+1) ?Si n+1O 3n+4(m) (2n+4)? +CO 3(m )2? . For various metalsilicate systems the relative solubility of CO2 should depend markedly on the relative Gibbs free change of reaction. Experimental solubility data for the systems Li2O-SiO2, Na2O-SiO2, K2O-SiO2, CaO-SiO2, MgO-SiO2 and other aluminosilicate melts are in complete accord with predictions based on Gibbs Free energies of model polycondesation reactions. A rigorous thermodynamic treatment of published P- T-wt.% CO2 solubility data for a number of mineral and natural melts suggests that for the reaction CO2(m) ? CO2(v)
- CO2-melt mixing may be considered ideal (i.e., { \(a_{{\text{CO}}_{\text{2}} }^m = X_{{\text{CO}}_{\text{2}} }^m \) );
- \(\bar V_{{\text{CO}}_{\text{2}} }^m \) , the partial molal volume of CO2 in the melt, is approximately equal to 30 cm3 mole?1 and independent of P and T;
- Δ C p 0 is approximately equal to zero in the T range 1,400° to 1,650 °C and
- enthalpies and entropies of the dissolution reaction depend on the ratio of network modifiers to network builders in the melt. Analytic expressions which relate the CO2 content of a melt to P, T, and \(f_{{\text{CO}}_{\text{2}} } \) for andesite, tholeiite and olivine melilite melts of the form
19.
The enthalpy of formation of andradite (Ca3Fe2Si3O12) has been estimated as-5,769.700 (±5) kJ/mol from a consideration of the calorimetric data on entropy (316.4 J/mol K) and of the experimental phaseequilibrium data on the reactions: 1 $$\begin{gathered} 9/2 CaFeSi_2 O_6 + O_2 = 3/2 Ca_3 Fe_2 Si_3 O_{12} + 1/2 Fe_3 O_4 + 9/2 SiO_2 (a) \hfill \\ Hedenbergite andradite magnetite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 4 CaFeSi_2 O_6 + 2 CaSiO_3 + O_2 = 2 Ca_3 Fe_2 Si_3 O_{12} + 4 SiO_2 (b) \hfill \\ Hedenbergite wollastonite andradite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 18 CaSiO_3 + 4 Fe_3 O_4 + O_2 = 6Ca_3 Fe_2 Si_3 O_{12} (c) \hfill \\ Wollastonite magnetite andradite \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} Ca_3 Fe_2 Si_3 O_{12} = 3 CaSiO_3 + Fe_2 O_3 . (d) \hfill \\ Andradite pseudowollastonite hematite \hfill \\ \end{gathered} $$ and $$log f_{O_2 } = E + A + B/T + D(P - 1)/T + C log f_{O_2 } .$$ Oxygen-barometric scales are presented as follows: $$\begin{gathered} E = 12.51; D = 0.078; \hfill \\ A = 3 log X_{Ad} - 4.5 log X_{Hd} ; C = 0; \hfill \\ B = - 27,576 - 1,007(1 - X_{Ad} )^2 - 1,476(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite (Ad)-hedenbergite (Hd)-magnetite-quartz: $$\begin{gathered} E = 13.98; D = 0.0081; \hfill \\ A = 4 log(X_{Ad} / X_{Hd} ); C = 0; \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-quartz: 1 $$\begin{gathered} E = 13.98;{\text{ }}D = 0.0081; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 0;}} \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-calcitequartz: 1 $$\begin{gathered} E = - 1.69;{\text{ }}D = - 0.199; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 2;}} \hfill \\ B = - 20,441 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-calcite: 1 $$\begin{gathered} E = - 17.36;{\text{ }}D = - 0.403; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 4;}} \hfill \\ B = - 11,720 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 \hfill \\ \end{gathered} $$ The oxygen fugacity of formation of those skarns where andradite and hedenbergite assemblage is typical can be calculated by using the above equations. The oxygen fugacity of formation of this kind of skarn ranges between carbon dioxide/graphite and hematite/magnetite buffers. It increases from the inside zones to the outside zones, and appears to decrease with the ore-types in the order Cu, Pb?Zn, Fe, Mo, W(Sn) ore deposits. 相似文献
20.
Given the direction cosines a i ′ = (a 1 i , a 2 i , a 3 i )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x1, x2, x3, x4)for the angular radius x4,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking xj+1 = xj + Δxwhere xj is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements. 相似文献