Thermodynamic properties of andradite and application to skarn with coexisting andradite and hedenbergite     

Zheru Zhang  S. K. Saxena 《Contributions to Mineralogy and Petrology》1991,107(2):255-263

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   

Non-ideal Mg-Fe binary mixing in cordierite: Constraints from experimental data on Mg-Fe partitioning in garnet and cordierite and a reformulation of garnet-cordierite geothermometer     

S. B. Dwivedi 《Journal of Earth System Science》1996,105(4):365-377

The non-ideal regular Mg-Fe binary in cordierite has been derived through multivariate linear regression of the expressionRT InK_D +(P- 1)ΔVK ₁ ⁰ , 298 along with updated subfegular mixing parameter of almandine-pyrope solution (Hackler and Wood 1989; Berman 1990). The data base used for multivariate analyses consists of published experimental data (n = 177) on Mg-Fe partitioning between garnet and cordierite in theP-T range 650–1050°C and 4–12 K bar. The non-ideality can be approximated by temperature-dependent Margules parameters. The retrieved values of ΔH_<T> ^o and ΔH_<T> ^o of exchange reaction between garnet and cordierite and enthalpy and entropy of mixing of Mg-Fe cordierite were combined with recent quaternary (Fe-Mg-Ca-Mn) mixing data in garnet to obtain the geothermometric expressions to determine temperature (T Kelvin): $$\begin{gathered} T(WH) = 6832 + 0.031(P - 1) - \{ 166(X_{Mg}^{Gt} )^2 - 506(X_{Fe}^{Gt} )^2 + 680X_{Fe}^{Gt} X_{Mg}^{Gt} + 336(X_{Ca} + X_{Mn} ) \hfill \\ (X_{Mg} - X_{Fe} )^{Gt} - 3300X_{Ca}^{Gt} - 358X_{Mn}^{Gt} \} + 954(X_{Fe} - X_{Mg} )^{Crd} /1.987\ln K_D + 3.41 + 1.5X_{Ca}^{Gt} \hfill \\ + 1.23(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ \end{gathered} $$ $$\begin{gathered} T(Br) = 6920 + 0.031(p - 1) - \{ 18(X_{Mg}^{Gt} )^2 - 296(X_{Fe}^{Gt} )^2 + 556X_{Fe}^{Gt} X_{Mg}^{Gt} - 6339X_{Ca}^{Gt} X_{Mg}^{Gt} \hfill \\ - 99(X_{Ca}^{Gt} )^2 + 4687X_{Ca}^{Gt} (X_{Mg} - X_{Fe}^{Gt} ) - 4269X_{Ca}^{Gt} X_{Fe}^{Gt} - 358X_{Mn}^{Gt} \} + 640(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ + 1.90X_{Ca}^{Gt} (X_{Mg} - X_{Ca} )^{Gt} . \hfill \\ \end{gathered} $$   相似文献   

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder     

Paula M. Davidson  John Grover  Donald H. Lindsley 《Contributions to Mineralogy and Petrology》1982,80(1):88-102

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.  相似文献   

Enstatite-diopside solvus and geothermometry     

S. K. Saxena  C. E. Nehru 《Contributions to Mineralogy and Petrology》1975,49(3):259-267

The enstatite-diopside solvus presents certain interesting thermodynamic and crystal-structural problems. The solvus may be considered as parts of two solvi one with the ortho-structure and the other with clino-structure. By assuming the standard free energy change for the two reactions (MgMgSi₂O₆)opx ? (MgMgSi₂O₆)cpx and (CaMgSi₂O₆) opx ? (CaMgSi₂O₆) cpx as 500 and 1 000 to 3 000 cal/mol respectively, it is possible to calculate the regular solution parameter W for orthopyroxene and clinopyroxene. These W's essentially refer to mixing on M2 sites. The expression for the equilibrium constant by assuming ideal mixing for Fe-Mg, Fe-Ca and non-ideal mixing for Ca-Mg on binary M1 and ternary M2 sites is given by 1 $$K_a = \frac{{X_{{\text{Mg - cpx}}}^{{\text{M1}}} X_{{\text{Mg - cpx}}}^{{\text{M2}}} \exp \left[ {\frac{{W_{{\text{cpx}}} }}{{RT}}\left\{ {X_{{\text{Ca - cpx}}}^{{\text{M2}}} \left( {X_{{\text{Ca - cpx}}}^{{\text{M2}}} + X_{{\text{Fe - cpx}}}^{{\text{M2}}} } \right)} \right\}} \right]}}{{X_{{\text{Mg - cpx}}}^{{\text{M1}}} X_{{\text{Mg - opx}}}^{{\text{M2}}} \exp \left[ {\frac{{W_{{\text{cpx}}} }}{{RT}}\left\{ {X_{{\text{Ca - opx}}}^{{\text{M2}}} \left( {X_{{\text{Ca - opx}}}^{{\text{M2}}} + X_{{\text{Fe - opx}}}^{{\text{M2}}} } \right)} \right\}} \right]}}$$ where X's are site occupancies, R is 1.987 and T is temperature in ^oK. Temperature of pyroxene crystallization may be estimated by substituting for T in the above equation until the equation ?RT In K _a=500 is satisfied. The shortcomings of this method are the incomplete standard free energy data on the end member components and the absence of site occupancy data in pyroxenes at high temperatures. The assumed free energy data do, however, show the possible extent of inaccuracy in temperature estimates resulting from the neglect of Mg-Ca non ideality.  相似文献   

The reversed alumina contents of orthopyroxene in equilibrium with spinel and forsterite in the system MgO-Al2O3-SiO2     

T. Gasparik  R. C. Newton 《Contributions to Mineralogy and Petrology》1984,85(2):186-196

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   

From the simplest chemical system to the natural one: garnet peridotite barometry     

P. Bertrand  C. Sotin  J.-C. C. Mercier  E. Takahashi 《Contributions to Mineralogy and Petrology》1986,93(2):168-178

The available experimental data on garnet-bearing-assemblages for synthetic chemical systems (MAS, FMAS, CMAS) have been used to calibrate consistent models for the Al-solubility in orthopyroxene coexisting with garnet, on the basis of equilibrium reaction Py(opx) ? Py(gt). The alternative reaction En(opx)+MgTs(opx) ? Py(gt) is discarded as it yields larger a-posteriori uncertainties. To provide a reliable equation, directly applicable to natural garnet lherzolites, each successive synthetic-system calibration is tested against Mori and Green's (1978) natural-system reequilibration data. For the MAS system, an ideal solution model with constant ΔH°, ΔV° and ΔS° based on 12-oxygen structural formulae for aluminous pyroxenes yields the best fit (GPa, K), $${\text{25,134 + 9,941 }}P - 23.177{\text{ }}T{\text{ + }}RT{\text{ ln (}}X_{{\text{Al}}}^{TB'} {\text{) = 0}}$$ . The MAS synthetic-system calibration can be directly applied to the FMAS system by adding an empirical correction term (20,835 [X _Fe ^gt ]²) independent of either pressure and temperature. However, this correction term is not important because of the limited Fe content of mantle peridotites. When calcium is added to the MAS system, the equilibrium constant is calculated as: $$K_{{\text{CMAS}}} = {{[(1 - X_{{\text{Ca}}}^{M2} )^2 (X_{{\text{Al}}}^{TB'} )]} \mathord{\left/ {\vphantom {{[(1 - X_{{\text{Ca}}}^{M2} )^2 (X_{{\text{Al}}}^{TB'} )]} {[(1 - X_{{\text{Ca}}}^X )^3 (X_{{\text{Al}}}^Y )^2 ]}}} \right. \kern-\nulldelimiterspace} {[(1 - X_{{\text{Ca}}}^X )^3 (X_{{\text{Al}}}^Y )^2 ]}}$$ where M2 and TB′ are pyroxene sites and X and Y are garnet sites. Up to 5 GPa, X _Ca ^X ～ and the CMAS experimental data agree well with the MAS model, but for Yamada and Takahashi's (1983) higher pressure experiments (up to 10 GPa), this no longer holds. Indeed, the garnet solid solution does not behave ideally and an asymmetric regular solution model is needed for application to the deepest natural samples available (>7GPa). Calibration based on new high pressure data yields, $$\begin{gathered} \Delta G_{{\text{CMAS}}}^{XS} = (X_{{\text{Ca}}}^X )(1 - X_{{\text{Ca}}}^X )(0.147 - X_{{\text{Ca}}}^X ) \hfill \\ {\text{ }} \cdot {\text{(6,440,535 - 1,490,654 }}P{\text{)}} \hfill \\ \end{gathered}$$ . According to tests of the inferred solution model, the CFMAS system is a good analogue of natural systems in the pressure, temperature and composition ranges covered by the natural-system reequilibration data (up to 1,500° C and 4 GPa). Simultaneous application of this thermobarometer and of the two-pyroxene mutual solubility thermometer (Bertrand and Mercier 1985) to the phases of the garnet-peridotite xenoliths from Thaba Putsoa, Lesotho, yields a refined paleogeotherm for southern Africa strongly contrasting with previous results. The “granular” nodules yield a thermal gradient of about 8 K/km characteristic of a lithospheric-type environment, whereas the “sheared” ones show a lower gradient of about 1 K/km. This is a typical geotherm expected for a steady thermal state with an inflexion point at the depth of about 160 km corresponding to the lithosphere/asthenosphere boundary.  相似文献   

Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2     

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   

F-OH substitution in natural tremolite,talc, and phlogopite     

H. J. Abercrombie  G. B. Skippen  D. D. Marshall 《Contributions to Mineralogy and Petrology》1987,97(3):305-312

The distribution of F between tremolite and talc has been determined in metamorphosed siliceous carbonates from the Grenville Province, Ontario. Wavelength dispersive electron microprobe analyses of contiguous, texturally compatible tremolite-talc pairs indicate that the substitution of F for OH is the most significant deviation from end-member stoichiometry in the samples studied. Mixing of F and OH components has been represented by an ideal solution model for F in tremolite and an asymmetric model for F in talc. Both linear and nonlinear regression techniques have been used to derive activity coefficients for the exchange of one equivalent of OH and F components in talc. The following expressions are the result of nonlinear regression of 32 analyses from coexisting mineral pairs: $$\begin{gathered} \ln \gamma _{TC(OH)} = X_{TC(F)}^2 [2.447 - 2.845X_{TC(OH)} ] \hfill \\ \ln \gamma _{TC(F)} = X_{TC(OH)}^2 [1.024 + 2.845X_{TC(F} ] \hfill \\ \end{gathered} $$ Isobaric \(T - X_{CO_2 } \) sections constructed using these equations show an enhanced stability for the assemblages talc+calcite and phlogopite+quartz+calcite with F substituting for OH. Projection of isothermal invariant points into P-T space predicts a shift in the stability of the assemblage talc-calcite from lower grade into the sillimanite field with increasing substitution of F for OH in talc.  相似文献   

Energetics of hydration of cordierite and water barometry in cordierite-granulites     

A. Bhattacharya  S. K. Sen 《Contributions to Mineralogy and Petrology》1985,89(4):370-378

The Gibbs free energy and volume changes attendant upon hydration of cordierites in the system magnesian cordierite-water have been extracted from the published high pressure experimental data at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P _total, assuming an ideal one site model for H₂O in cordierite. Incorporating the dependence of ΔG and ΔV on temperature, which was found to be linear within the experimental conditions of 500°–1,000°C and 1–10,000 bars, the relation between the water content of cordierite and P, T and \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) has been formulated as $$\begin{gathered} X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} = \hfill \\ \frac{{f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }}{{\left[ {{\text{exp}}\frac{1}{{RT}}\left\{ {64,775 - 32.26T + G_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{1, }}T} - P\left( {9 \times 10^{ - 4} T - 0.5142} \right)} \right\}} \right] + f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }} \hfill \\ \end{gathered} $$ The equation can be used to compute H₂O in cordierites at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) <1. Our results at different P, T and partial pressure of water, assuming ideal mixing of H₂O and CO₂ in the vapour phase, are in very good agreement with the experimental data of Johannes and Schreyer (1977, 1981). Applying the formulation to determine \(X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} \) in the garnet-cordierite-sillimanite-plagioclase-quartz granulites of Finnish Lapland as a test case, good agreement with the gravimetrically determined water contents of cordierite was obtained. Pressure estimates, from a thermodynamic modelling of the Fe-cordierite — almandine — sillimanite — quartz equilibrium at \(P_{{\text{H}}_{\text{2}} {\text{O}}} = 0\) and \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P_total, for assemblages from South India, Scottish Caledonides, Daly Bay and Hara Lake areas are compatible with those derived from the garnetplagioclase-sillimanite-quartz geobarometer.  相似文献   

Calcic amphibole equilibria and a new amphibole-plagioclase geothermometer   总被引：13，自引：4，他引：9  

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 Al^iv 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, RTlnγ_ab, 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   

The thermodynamic properties of reciprocal solid solutions     

Bernard J. Wood  J. Nicholls 《Contributions to Mineralogy and Petrology》1978,66(4):389-400

A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: $$\Delta G^0 = (\mu _{AX}^0 + \mu _{BY}^0 - \mu _{AY}^0 - \mu _{BX}^0 = 0$$ applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG ⁰ contributes terms of the following form to the activity coefficients of the constituent components: $$RT\ln \gamma _{AX} = - X_{B_1 } X_{Y_2 } \Delta G^0$$ (X _Ji refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the “cross-site” or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: $$\Delta G^0 \ll zn_1 RT$$ where z is the number of nearest-neighbour (X, Y) sites around A and n ₁ is the number of (A, B) sites in the formula unit. If ΔG ⁰ is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): $$\gamma _{AX} = \left( {\frac{{1 - X'_{Y_2 } }}{{1 - X_{Y_2 } }}} \right)^{zn_1 }$$ where X′_Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved.  相似文献   

Garnet-clinopyroxene geothermometer     

S. K. Saxena 《Contributions to Mineralogy and Petrology》1979,70(3):229-235

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.  相似文献   

Oxygen isotope fractionation between rutile and water   总被引：1，自引：0，他引：1  

Sunit K. Addy  G. D. Garlick 《Contributions to Mineralogy and Petrology》1974,45(2):119-121

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   

Ca-Fe-Mg olivines: phase relations and a solution model     

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   

Experimental investigation of the metamorphism of siliceous dolomites     

Hans -Rolf Käse  Paul Metz 《Contributions to Mineralogy and Petrology》1980,73(2):151-159

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 K_14b: (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   

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties     

Udo Warhus  Niranjan D. Chatterjee 《Contributions to Mineralogy and Petrology》1984,85(1):74-79

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   

Olivine-liquid equilibrium   总被引：6，自引：5，他引：6  

P. L. Roeder  R. F. Emslie 《Contributions to Mineralogy and Petrology》1970,29(4):275-289

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

Crystal chemistry and reaction relations of piemontites and thulites from highly oxidized low grade metamorphic rocks at Vitali,Andros Island,Greece     

Thomas Reinecke 《Contributions to Mineralogy and Petrology》1986,93(1):56-76

Piemontite- and thulite-bearing assemblages from highly oxidized metapelitic and metacalcareous schists associated with braunite quartzites at Vitali, Andros island, Greece, were chemically investigated. The Mn-rich metasediments are intercalated in a series of metapelitic quartzose schists, marbles, and basic metavolcanites which were affected by a regional metamorphism of the highP/T type (T=400–500° C,P>9 kb) and a later Barrovian-type greenschist metamorphism (T=400–500° C,P～-5–6 kb). Texturally and chemically two generations of piemontite (I and II) can be distinguished which may show complex compositional zoning. Piemontite I coexisted at highP/T conditions with braunite, manganian phengite (alurgite), Mn³⁺-Mn²⁺-bearing Na-pyroxene (violan), carbonate, quartz, hollandite, and hematite. Zoned grains generally exhibit a decreasing Mn³⁺ and an increasing Fe³⁺ and Al content towards the rim. Chemical compositions of piemontite I range from 2.0 to 32.1 mole % Mn³⁺, 0 to 25.6 mole % Fe³⁺, and 60.2 to 81.2 mole % Al. Up to 12.5 mole % Ca on the A(2) site can be substituted by Sr. Piemontites formed in contact or close to braunite (±hematite) attained maximum (Mn³⁺+Fe³⁺)Al_?1 substitution corrresponding to about 33 mole % Mn³⁺+Fe³⁺ in lowiron compositions and up to about 39 mole % Mn³⁺+ Fe³⁺ at intermediate Fe³⁺/(Fe³⁺+Mn³⁺) ratios. Piemontite II which discontinuously overgrows piemontite I or occurs as separate grains may have been formed by greenschist facies decomposition of manganian Na-pyroxenes according to the reaction: (1) $$\begin{gathered} {\text{Mn}}^{{\text{3 + }}} - Mn^{2 + } - bearing omphacite/chloromelanite \hfill \\ + CO_2 + H_2 O + HCl \pm hermatite \hfill \\ = piemontite + tremolite + albite + chlorite \hfill \\ + calcite + quartz + NaCl \pm O_2 . \hfill \\ \end{gathered} $$ Thulites crystallized in coexistence with Al-rich piemontite II. All thulites analysed are low-Fe³⁺ manganian orthozoisites with Mn^tot～-Mn³⁺ substituting for Al on the M(3) site. Their compositions range from 2.9 to 7.2 mole % Mn³⁺, 0 to 1.2 mole % Fe³⁺, and 91.8 to 96.7 mole % Al. Piemontites II in thulite-bearing assemblages range from 5.8 to 15.9 mole % Mn³⁺, 0 to 3.7 mole % Fe³⁺, and 83.7 to 93.6 mole % Al. By contrast, piemontites II in thulite-free assemblages are similarly enriched in Mn³⁺ + Fe³⁺ — and partially in Sr²⁺ — as core compositions of piemontite I (21.1 to 29.6 mole % Mn³⁺, 2.0 to 16.5 mole % Fe³⁺, 60.6 to 68.4 mole % Al, 0 to 29.4 mole % Sr in the A(2) site). The analytical data presented in this paper document for the first time a continuous low-Fe³⁺ piemontite solid solution series from 5.8 to 32.1 mole % Mn³⁺. Aluminous piemontite II is enriched by about 3 mole % Mn³⁺+Fe³⁺ relative to coexisting thulite in Fe³⁺-poor samples and by about 6 mole % Mn³⁺+Fe³⁺ in more Fe³⁺-rich samples. Mineral pairs from different samples form a continuous compositional loop. Compositional shift of mineral pairs is attributed to the effect of a variable fluid composition at constantP _fluid andT on the continuous reaction: (2) $$\begin{gathered} piemontite + CO_2 \hfill \\ = thulite + calcite + quartz \hfill \\ + Mn^{2 + } Ca_{ - 1} [calcite] + H{_2} O + O{_2} \hfill \\ \end{gathered} $$ Further evidence for a variable \(x_{H_2 O} \) and/or \(f_{O_2 } \) possibly resulting from fluid infiltration and local buffering during the greenschist metamorphism is derived from the local decomposition of piemontite, braunite, and rutile to form spessartine, calcite, titanite, and hematite by the reactions: (3) $$\begin{gathered} piemontite + braunite + CO_2 \hfill \\ = sperssartine + calcite + quartz \pm hermatite \hfill \\ + H{_2} O + O{_2} \hfill \\ \end{gathered} $$ and more rarely: (4) $$\begin{gathered} piemontite + quartz + rutile + braunite \hfill \\ = spessartine + titanite + hematite + H{_2} O + O{_2} . \hfill \\ \end{gathered} $$   相似文献   

Distribution of Al between coexisting micas in metamorphic rocks from the Central Alps     

Eduard Wenk 《Contributions to Mineralogy and Petrology》1970,26(1):50-61

In 61 pairs of coexisting biotites and muscovites from the Central Alps total Al scatters considerably, but in both series a gradual increase is noticed with increasing metamorphic grade. The ratio Al _Mu ^tot /Al _Bi ^tot remains virtually constant (1.61 average for greenschist facies, 1.57 for amphibolite facies). Tetrahedral Al varies little in biotites and increases in muscovites-phengites with rising metamorphic grade; accordingly the ratio Al _Mu ^IV /Al _Bi ^IV increases slightly with grade. Far the best control of metamorphism is evidenced by octahedral Al. In the muscovite series, and still more pronounced in the biotite series, Al^VI increases with increasing metamorphic grade. Consequently 1 $$K_D = \frac{{Al_{Mu}^{VI} }}{{Al_{Bl}^{VI} }}$$ decreases from 14 to 3. A map (Fig. 6) representing the regional distribution of the K_D values locates a 100 km long and 23 km broad central zone with low K_D. The outline of this central core almost coincides with the isograds anorthite-diopside-calcite and labradorite-pyroxene-hornblende of the Tertiary regional metamorphism; with some deviations this core also agrees with the zone in which phenomena of partial anatexis are observed. The K_D values of micas from anateotic pegmatites agree with those of associated gneisses and schists. The study demonstrates that in the course of progressive regional metamorphism equilibrium has been approached to an unexpected extent and that the two micas coexisted in a strict sense.  相似文献   

Equilibrium thermodynamics of Al/Si ordering in anorthite     

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 T_tr. 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