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1.
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
2.
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
3.
Oxygen isotope fractionation between rutile and water 总被引：1，自引：0，他引：1
Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C. 相似文献
4.
Paragneisses of the Ivrea-Verbano zone exhibit over a horizontal distance of 5 km mineralogical changes indicative of the transition from amphibolite to granulite facies metamorphism. The most obvious change is the progressive replacement of biotite by garnet via the reaction: a $${\text{Biotite + sillimanite + quartz }} \to {\text{ Garnet + K - feldspar + H}}_{\text{2}} {\text{O}}$$ which results in a systematic increase in the modal ratio g = (garnet)/(garnet + biotite) with increasing grade. The systematic variations in garnet and biotite contents of metapelites are also reflected by the compositions of these phases, both of which become more magnesian with increasing metamorphic grade. The pressure of metamorphism has been estimated from the Ca3Al2Si3O12 contents of garnets coexisting with plagioclase, sillimanite and quartz. These phases are related by the equilibrium: b $$\begin{gathered} 3 CaAl_2 {\text{Si}}_{\text{2}} {\text{O}}_{\text{8}} \rightleftharpoons Ca_3 Al_2 {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} + 2 Al_2 {\text{SiO}}_{\text{5}} + {\text{SiO}}_{\text{2}} \hfill \\ plagioclase garnet sillimanite quartz \hfill \\ \end{gathered} $$ which has been applied to these rocks using the available data on the mixing properties of plagioclase and garnet solid solutions. Temperature and f H 2O estimates have been made in a similar way using thermodynamic data on the biotite-garnet reaction (a) and the approximate solidus temperatures of paragneisses. Amphibolite to granulite facies metamorphism in the Ivrea-Verbano zone took place in the P-T ranges 9–11 kb and 700–820 °C. The differences in temperature and pressure of metamorphism between g= 0 and g = 1 (5 kms horizontal distance) were less than 50° C and approximately 1 kb. Retrogression and re-equilibration of garnets and biotites in the metapelites extended to temperatures more than 50° C below and pressures more than 1.5 kb below the peak of metamorphism, the degree of retrogression increasing with decreasing grade of the metamorphic “peak”. The pressure and temperature of the peak of metamorphism are not inconsistent with the hypothesis that the Ivrea-Verbano zone is a slice of upthrusted lower crust from the crust-mantle transition region, although it appears that the thermal gradient was too low for the zone to represent a near-vertical section through the crust. The most reasonable explanation of the granulite facies metamorphism is that it arose through intrusion of mafic rocks into a region already undergoing recrystallisation under amphibolite facies conditions. 相似文献
5.
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
6.
Tjerk Peters Hans Schwander Volkmar Trommsdorff 《Contributions to Mineralogy and Petrology》1973,42(4):325-332
Reactions involving the phases quartz-rhodochrosite-tephroite-pyroxmangite-fluid have been studied experimentally in the system MnO-SiO2-CO2-H2O at a pressure of 2 000 bars and resulted in the following expressions 1 $$\begin{gathered} {\text{Rhodochrosite + Quartz = Pyroxmangite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{11.765}}{T} + 18.618. \hfill \\ {\text{Rhodochrosite + Pyroxmangite = Tephroite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{7.083}}{T} + 11.870. \hfill \\ \end{gathered}$$ which can be used to derive data for the remaining two reactions among the phases under consideration. Field data from the Alps are in agreement with the metamorphic sequence resulting from the experiments. 相似文献
7.
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
8.
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
9.
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
10.
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
11.
Gao Xuzheng 《中国地球化学学报》1986,5(3):215-225
Geochemical potential field is defined as the scope within the earth’s space where a given component in a certain phase of a certain material system is acted upon by a diffusion force, depending on its spatial coordinatesX, Y andZ. The three coordinates follow the relations: $$NF_{ix} = - \frac{{\partial \mu }}{{\partial x}}, NF_{iy} = - \frac{{\partial \mu }}{{\partial y}}, NF_{iz} = - \frac{{\partial \mu }}{{\partial z}}$$ The characteristics of such a field can be summarized as: (1) The summation of geochemical potentials related to the coordinatesX, Y, Z, or pseudo-velocity head, pseudo-pressure head and pseudo-potential head of a certain component in the earth is a constant as given by $$\mu _x + \mu _y + \mu _z = c$$ or $$\mu _{x2} + \mu _{y2} + \mu _{z2} = \mu _{x1} + \mu _{y1} + \mu _{z1} $$ Derived from these relations is the principle of geochemical potential conservation. The following relations have the same physical significance: $$\mu _k + \mu _u + \mu _p = c$$ or $$\mu _{k2} + \mu _{u2} + \mu _{p2} = \mu _{k1} + \mu _{u1} + \mu _{p1} $$ (2) Geochemical potential field is a vector field quantified by geochemical field intensity which is defined as the diffusion force applied to one molecular volume (or one atomic volume) of a certain component moving from its higher concentration phase to lower concentration phase. The geochemical potential field intensity is given by $$\begin{gathered} E = - grad\mu \hfill \\ E = \frac{{RT}}{x}i + \frac{{RT}}{y}j + \frac{{RT}}{z}K \hfill \\ \end{gathered} $$ The present theory has been inferred to interpret the mechanism of formation of some tungsten ore deposits in China. 相似文献
12.
The standard enthalpies of formation of FeS (troilite), FeS2 (pyrite), Co0.9342S, Co3S4 (linnaeite), Co9S8 (cobalt pentlandite), CoS2 (cattierite), CuS (covellite), and Cu2S (chalcocite) have been determined by high temperature direct reaction calorimetry at temperatures between 700 K and 1021 K. The following results are reported: $$\Delta {\rm H}_{f,FeS}^{tr} = - 102.59 \pm 0.20kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,FeS}^{py} = - 171.64 \pm 0.93kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_{0.934} S} = - 99.42 \pm 1.52kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_9 S_8 }^{ptl} = - 885.66 \pm 16.83kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_3 S_4 }^{In} = - 347.47 \pm 7.27kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,CoS_2 }^{ct} = - 150.94 \pm 4.85kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Cu_2 S}^{cc} = - 80.21 \pm 1.51kJ mol^{ - 1} ,$$ and $$\Delta {\rm H}_{f,CuS}^{cv} = - 53.14 \pm 2.28kJ mol^{ - 1} ,$$ The enthalpy of formation of CuFeS2 (chalcopyrite) from (CuS+FeS) and from (Cu+FeS2) was determined by solution calorimetry in a liquid Ni0.60S0.40 melt at 1100 K. The results of these measurements were combined with the standard enthalpies of formation of CuS, FeS, and FeS2, to calculate the standard enthalpy of formation of CuFeS2. We found \(\Delta {\rm H}_{f,CuFeS_2 }^{ccp} = - 194.93 \pm 4.84kJ mol^{ - 1}\) . Our results are compared with earlier data given in the literature; generally the agreement is good and our values agree with previous estimates within the uncertainties present in both. 相似文献
13.
The linear thermal expansions of åkermanite (Ca2MgSi2O7) and hardystonite (Ca2ZnSi2O7) have been measured across the normal-incommensurate phase transition for both materials. Least-squares fitting of the high temperature (normal phase) data yields expressions linear in T for the coefficients of instantaneous linear thermal expansion, $$\alpha _1 = \frac{1}{l}\frac{{dl}}{{dT}}$$ for åkermanite: $$\begin{gathered} \alpha _{[100]} = 6.901(2) \times 10^{ - 6} + 1.834(2) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 2.856(1) \times 10^{ - 6} + 11.280(1) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ for hardystonite: $$\begin{gathered} \alpha _{[100]} = 15.562(5) \times 10^{ - 6} - 1.478(3) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 11.115(5) \times 10^{ - 6} + 11.326(3) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ Although there is considerable strain for temperatures within 10° C of the phase transition, suggestive of a high-order phase transition, there appears to be a finite ΔV of transition, and the phase transition is classed as “weakly first order”. 相似文献
14.
Amy E. Hofmann Michael B. Baker John M. Eiler 《Contributions to Mineralogy and Petrology》2013,166(1):235-253
In order to evaluate the effect of trace and minor elements (e.g., P, Y, and the REEs) on the high-temperature solubility of Ti in zircon (zrc), we conducted 31 experiments on a series of synthetic and natural granitic compositions [enriched in TiO2 and ZrO2; Al/(Na + K) molar ~1.2] at a pressure of 10 kbar and temperatures of ~1,400 to 1,200 °C. Thirty of the experiments produced zircon-saturated glasses, of which 22 are also saturated in rutile (rt). In seven experiments, quenched glasses coexist with quartz (qtz). SiO2 contents of the quenched liquids range from 68.5 to 82.3 wt% (volatile free), and water concentrations are 0.4–7.0 wt%. TiO2 contents of the rutile-saturated quenched melts are positively correlated with run temperature. Glass ZrO2 concentrations (0.2–1.2 wt%; volatile free) also show a broad positive correlation with run temperature and, at a given T, are strongly correlated with the parameter (Na + K + 2Ca)/(Si·Al) (all in cation fractions). Mole fraction of ZrO2 in rutile $ \left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) $ in the quartz-saturated runs coupled with other 10-kbar qtz-saturated experimental data from the literature (total temperature range of ~1,400 to 675 °C) yields the following temperature-dependent expression: $ {\text{ln}}\left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) + {\text{ln}}\left( {a_{{{\text{SiO}}_{2} }} } \right) = 2.638(149) - 9969(190)/T({\text{K}}) $ , where silica activity $ a_{{{\text{SiO}}_{2} }} $ in either the coexisting silica polymorph or a silica-undersaturated melt is referenced to α-quartz at the P and T of each experiment and the best-fit coefficients and their uncertainties (values in parentheses) reflect uncertainties in T and $ \mathop X\nolimits_{{{\text{ZrO}}_{2} }}^{\text{rt}} $ . NanoSIMS measurements of Ti in zircon overgrowths in the experiments yield values of ~100 to 800 ppm; Ti concentrations in zircon are positively correlated with temperature. Coupled with values for $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ for each experiment, zircon Ti concentrations (ppm) can be related to temperature over the range of ~1,400 to 1,200 °C by the expression: $ \ln \left( {\text{Ti ppm}} \right)^{\text{zrc}} + \ln \left( {a_{{{\text{SiO}}_{2} }} } \right) - \ln \left( {a_{{{\text{TiO}}_{2} }} } \right) = 13.84\left( {71} \right) - 12590\left( {1124} \right)/T\left( {\text{K}} \right) $ . After accounting for differences in $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ , Ti contents of zircon from experiments run with bulk compositions based on the natural granite overlap with the concentrations measured on zircon from experiments using the synthetic bulk compositions. Coupled with data from the literature, this suggests that at T ≥ 1,100 °C, natural levels of minor and trace elements in “granitic” melts do not appear to influence the solubility of Ti in zircon. Whether this is true at magmatic temperatures of crustal hydrous silica-rich liquids (e.g., 800–700 °C) remains to be demonstrated. Finally, measured $ D_{\text{Ti}}^{{{\text{zrc}}/{\text{melt}}}} $ values (calculated on a weight basis) from the experiments presented here are 0.007–0.01, relatively independent of temperature, and broadly consistent with values determined from natural zircon and silica-rich glass pairs. 相似文献
15.
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
16.
High-precision WBVR photoelectric observations of the eclipsing binary GG Ori (B9.5V+B9.5V), which has an eccentric orbit (e=0.22), were carried out in 1988–2001 at the Moscow and high-altitude Tian-Shan Observatories of the Sternberg Astronomical Institute. The aim of these observations was investigation of the apsidal motion of the system. Analysis of the resulting 12-year series of observations enabled us for the first time to accurately (to within 11%) measure the rate of rotation of the orbit $\dot \omega _{obs} = 0.046 \pm 0.005^\circ /yr$ and to appreciably improve estimates of the photometric and absolute parameters. The observed value of $\dot \omega _{obs}$ is 28% higher than the theoretical prediction of $\dot \omega _{th} = \dot \omega _{cl} + \dot \omega _{rel} = 0.036 \pm 0.001^\circ /yr$ . The relativistic part of the apsidal motion in this system $\dot \omega _{rel}$ is a factor of 2.5 greater than the classical term $\dot \omega _{cl}$ due to the tidal and rotational deformations of the components. The interstellar extinction in the direction of the star (at a distance of r=425 pc) is very large (A v =1.75 m ). A number of recently published results (in particular, the conclusion that the components of this eclipsing binary are young) are confirmed. 相似文献
17.
M. A. Carpenter 《Physics and Chemistry of Minerals》1992,19(1):1-24
Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T tr, of ～2595 K and a jump in Q from 0 to ～0.65 at Ttr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An78 to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An50–An70 needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution. 相似文献
18.
M. A. F. Candia Tj. Peters J. V. Valarelli 《Contributions to Mineralogy and Petrology》1975,52(4):261-266
The equilibrium constants for the reaction (2) Rhodochrosite + Quartz=Pyroxmangite+CO2 obtained are:logK(2)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(9862 \pm 102)}}{T} \hfill \\+ (15.887 \pm 0.220) + (0.1037 \pm 0.0020)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ and for the reaction (3) Rhodochrosite+Pyroxmangite=Tephroite+CO2: logK(3)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(6782 \pm 205)}}{T} \hfill \\+ (11.296 \pm 0.304) + (0.0835 \pm 0.0030)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ The present data lie within reasonable limits of error of the values calculated from previous experimental results at P tot = 2000 bars. 相似文献
19.
Experimental data combined with data from natural rocks have been used to calibrate a geothermometer based on the distribution of Fe2+ and Mg between coexisting garnets and phengites. The pressure effect on the K D -value appears to be considerable. The calculated thermometer is expressed as $$T(K) = \frac{{3685 + 77.1P(kb)}}{{InK_D + 3.52}}.$$ The use of this \(K_{D_{(FeO/MgO)} }^{ga + ph}\) geothermometer on eclogites with low Fe2O3 content, gives P-T values which are in good accordance with those obtained by other methods. The problems that arise when Fe3+ is present in larger amounts, are discussed. 相似文献
20.
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