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1.
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   

2.
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   

3.
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   

4.
Geothermometric equations for spinel peridotites by Fujii (1976), Gasparik and Newton (1984), and Chatterjee, and Terhart (1985) based on the reaction enstatite (en)+spinel (sp)Mg–Tschermaks (mats)+forsterite (fo) were tested using a nearly isothermal suite of mantle xenoliths from the Eifel, West Germany. In spite of using activities of MgAl2O4, en, and mats to allow for the non-ideal solution behaviour of the constituent phases, temperatures calculated from these equations systematically change as a function of Cr/(Cr+AL+Fe3+) in spinel. We propose an improved version of the empirical geothermometer for spinel peridotites of Sachtleben and Seck (1981) derived from the evaluation of the solubilities of Ca and Al in orthopyroxene from more than 100 spinel peridotites from the Rhenish Volcanic Province. A least squares regression yielded a smooth correlation between
  相似文献   

5.
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   

6.
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 \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =Ptotal, 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   

7.
River, rain and spring water samples from a region covered in “Shirasu” ignimbrite were collected on Kyushu Island, Japan. The analytical results were subjected to multivariate statistical analysis and stoichiometric calculation to understand the geographical distribution of chemical components in water and to extract geochemical underlying factors. The multivariate statistical analysis showed that the river-water chemistry is only slightly influenced by hot springs or polluted waters, but is highly controlled by weathering of ignimbrite. On the basis of the stoichiometric calculation based on water–rock interaction, the water chemistry was successfully estimated by a simple equation:\({\left[ {{\text{Si}}} \right]}{\text{ = 2}}{\left[ {{\text{Na}}^{{\text{ + }}} } \right]}{\text{ + }}{\left[ {{\text{Mg}}^{{{\text{2 + }}}} } \right]}\) in the upstream area, complemented by \({\left[ {{\text{Si}}} \right]}{\text{ = }}{\left[ {{\text{Na}}^{{\text{ + }}} } \right]}{\text{ - 3}}{\left[ {{\text{K}}^{{\text{ + }}} } \right]}{\text{ + }}{\left[ {{\text{Mg}}^{{{\text{2 + }}}} } \right]}{\text{ - 2}}{\left[ {{\text{Ca}}^{{{\text{2 + }}}} } \right]}\) in the downstream area.  相似文献   

8.
The chemical potential of oxygen (µO2) in equilibrium with magnesiowüstite solid solution (Mg, Fe)O and metallic Fe has been determined by gas-mixing experiments at 1,473 K supplemented by solid-cell EMF experiments at lower temperatures. The results give:
where IW refers to the Fe-"FeO" equilibrium. The previous work of Srecec et al. (1987) and Wiser and Wood (1991) agree well with this equation, as does that of Hahn and Muan (1962) when their reported compositions are corrected to a new calibration curve for lattice parameter vs. composition. The amount of Fe3+ in the magnesiowüstite solid solution in equilibrium with Fe metal was determined by Mössbauer spectroscopy on selected samples. These data were combined with literature data from gravimetric studies and fitted to a semi-empirical equation:
These results were then used to reassess the activity-composition relations in (Mg, Fe)2SiO4 olivine solid solutions at 1,400 K, from the partitioning of Mg and Fe2+ between olivine and magnesiowüstite in equilibrium with metallic Fe experimentally determined by Wiser and Wood (1991). The olivine solid solution is constrained to be nearly symmetric with , with a probable uncertainty of less than ±0.5 kJ/mol (one standard deviation). The results also provide a useful constraint on the free energy of formation of Mg2SiO4.Editorial responsibility: B. Collins  相似文献   

9.
Olivine-liquid equilibrium   总被引：6，自引：5，他引：6  
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   

10.
The existing experimental data [Ferry and Spear 1978; Perchuk and Lavrent'eva 1983] on Mg?Fe partitioning between garnet and biotite are disparate. The underlying assumption of ideal Mg?Fe exchange between the minerals has been examined on the basis of recently available thermochemical data. Using the updated mixing parameters for the pyrope-almandine asymmetric regular solution as inputs [Ganguly and Saxena 1984; Hackler and Wood 1984], thermodynamic analysis points to non-ideal mixing in the phlogopite-annite binary in the temperature range of 550°C–950°C. The non-ideality can be approximated by a temperature-independent, one constant Margules parameter. The retrieved values for enthalpy of mixing for Mg?Fe biotites and the standard state enthalpy and entropy changes of the exchange reaction were combined with existing thermochemical data on grossular-pyrope and grossular-almandine binaries to obtain geothermometric expressions for Mg?Fe fractionation between biotite and garnet. [T in K] $$\begin{gathered} {\text{T(HW) = [20286 + 0}}{\text{.0193P - \{ 2080(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} {\text{ - 6350(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 8540(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{)}} \hfill \\ {\text{ + 4215(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)\} + 4441}}{{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[13}}{\text{.138}}}}} \right. \kern-\nulldelimiterspace} {{\text{[13}}{\text{.138}}}} \hfill \\ {\text{ + 8}}{\text{.3143 InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ {\text{T(GS) = [13538 + 0}}{\text{.0193P - \{ 837(X}}_{{\text{Mg}}}^{{\text{Gt}}} )^{\text{2}} {\text{ - 10460(X}}_{{\text{Fe}}}^{{\text{Gt}}} )^2 \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 19246(X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} ) \hfill \\ {\text{ }}{{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[6}}{\text{.778}}}}} \right. \kern-\nulldelimiterspace} {{\text{[6}}{\text{.778}}}} \hfill \\ {\text{ + 8}}{\text{.3143InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ \end{gathered} $$ The reformulated geothermometer is an improvement over existing biotite-garnet geothermometers because it reconciles the experimental data sets on Fe?Mg partitioning between the two phases and is based on updated activity-composition relationship in Fe?Mg?Ca garnet solid solutions.  相似文献   

11.
A thermodynamic formulation of hydrous Mg-cordierite (Mg2Al4Si5O18·nH2O) has been obtained by application of calorimetric and X-ray diffraction data for hydrous cordierite to the results of hydrothermal syntheses. The data include measurements of the molar heat capacity and enthalpy of hydration and the molar volume. The synthesis data are consistent with a thermodynamic formulation in which H2O mixes ideally on a single crystallographic site in hydrous cordierite. The standard molar Gibbs free energy of hydration is-9.5±1.0 kJ/mol (an average of 61 syntheses). The standard molar entropy of hydration derived from this value is-108±3 J/mol-K. An equation providing the H2O content of cordierite as a function of temperature and fugacity of H2O is as follows (n moles of H2O per formula unit, n<1): $$\begin{gathered}n = {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } \mathord{\left/{\vphantom {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}}} \right.\kern-\nulldelimiterspace} {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}} \hfill \\{\text{ }}\left. {\left. { - {\text{ln}}\left( {\frac{T}{{{\text{298}}{\text{.15}}}}} \right) - \left( {\frac{{298.15}}{T} - 1} \right)} \right]} \right) \hfill \\\end{gathered}$$ Application of this formulation to the breakdown reaction of Mg-cordierite to an assemblage of pyrope-sillimanite-quartz±H2O shows that cordierite is stabilized by 3 to 3.5 kbar under H2O-saturated conditions. The thermodynamic properties of H2O in cordierite are similar to those of liquid water, with a standard molar enthalpy and Gibbs free energy of hydration that are the same (within experimental uncertainty) as the enthalpy and Gibbs free energy of vaporization. By contrast, most zeolites have Gibbs free energies of hydration two to four times more negative than the corresponding value for the vaporization of water.  相似文献   

12.
A mineralogic geobarometer based on the reaction garnet+clinopyroxene+quartz=2 orthopyroxene+anorthite is proposed. The geobarometric formulations for the Fe- and Mg- end member equilibria are $$\begin{gathered} P_{({\text{Fe}})} {\text{ }}({\text{bars}}){\text{ = 32}}{\text{.097 }}T{\text{ }} - {\text{ 26385 }} - {\text{ 22}}{\text{.79 (}}T - 848 - T1{\text{n(}}T/848{\text{))}} \hfill \\ {\text{ }} - (3.655 + 0.0138T){\text{ }}\left( {\frac{{{\text{(}}T - 848{\text{)}}^{\text{2}} }}{T}} \right) \hfill \\ {\text{ }} - {\text{(3}}{\text{.123) }}T1{\text{n }}\frac{{(a_{a{\text{n}}}^{{\text{Plag}}} )(a_{{\text{fs}}}^{{\text{P}}\ddot u{\text{x}}} )^2 }}{{(a_{{\text{alm}}}^{{\text{Gt}}} )(a_{{\text{hed}}}^{{\text{Opx}}} )}} \hfill \\ P_{({\text{Mg}})} {\text{ (bars) = 9}}{\text{.270 }}T + 4006 - 0.9305{\text{ }}(T - 848 - T1{\text{n (}}T/848{\text{)}}) \hfill \\ {\text{ }} - (1.1963{\text{ }} - {\text{ }}6.0128{\text{ x 10}}^{ - {\text{3}}} T)\left( {\frac{{(T - 848)^2 }}{T}} \right) \hfill \\ {\text{ }} - 3.489{\text{ }}T1{\text{n }}\frac{{(a_{an}^{{\text{Plag}}} ){\text{ }}(a_{{\text{ens}}}^{{\text{Opx}}} )}}{{{\text{(}}a_{{\text{pyr}}}^{{\text{Gt}}} {\text{) (}}a_{{\text{diop}}}^{{\text{Cpx}}} {\text{)}}}}. \hfill \\ \end{gathered}$$ The end member thermodynamic data have been taken from the data base of Helgeson et al. (1978) and Saxena and Erikson (1983). The activities of pyroxene components and anorthite in plagioclase have been modelled after Wood and Banno (1973) and Newton (1983) respectively. The activities of pyrope and almandine are calculated from the binary interaction parameters for garnet solid solutions proposed by Saxena and Erikson (1983). Pressures computed from these equations for fifty sets of published mineral data from several granulite areas are comparable with those obtained from dependable geobarometers. The pressure values determined from the Fe-end member equilibrium appear to be more reasonable than those from the Mg-end member reaction. It is likely that the difference in pressures computed from the Fe- and Mg-end members, ΔP *, have been caused by non-ideal mixing in the phases, especially in garnets.  相似文献   

13.
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   

14.
The effective binary diffusion coefficient (EBDC) of silicon has been measured during the interdiffusion of peralkaline, fluorine-bearing (1.3 wt% F), hydrous (3.3 and 6 wt% H2O), dacitic and rhyolitic melts at 1.0 GPa and temperatures between 1100°C and 1400°C. From Boltzmann-Matano analysis of diffusion profiles the diffusivity of silicon at 68 wt% SiO2 can be described by the following Arrhenius equations (with standard errors): $$\begin{gathered} {\text{with 1}}{\text{.3 wt\% F and 3}}{\text{.3\% H}}_{\text{2}} {\text{O:}} \hfill \\ {\text{D}}_{{\text{Si}}} = \begin{array}{*{20}c} { + {\text{3}}{\text{.59}}} \\ {{\text{3}}{\text{.66}} \times {\text{10}}^{ - {\text{9}}} } \\ { - {\text{1}}{\text{.86}}} \\ \end{array} {\text{exp}}\left( {{{ - {\text{86}}{\text{.1}} \pm {\text{8}}{\text{.9}}} \mathord{\left/ {\vphantom {{ - {\text{86}}{\text{.1}} \pm {\text{8}}{\text{.9}}} {{\text{RT}}}}} \right. \kern-\nulldelimiterspace} {{\text{RT}}}}} \right) \hfill \\ {\text{with 1}}{\text{.3 wt\% F and 6}}{\text{.0\% H}}_{\text{2}} {\text{O:}} \hfill \\ {\text{D}}_{{\text{Si}}} = \begin{array}{*{20}c} { + {\text{3}}{\text{.59}}} \\ {{\text{3}}{\text{.51}} \times {\text{10}}^{ - {\text{8}}} } \\ { - {\text{1}}{\text{.77}}} \\ \end{array} {\text{exp}}\left( {{{ - {\text{109}}{\text{.5}} \pm {\text{8}}{\text{.9}}} \mathord{\left/ {\vphantom {{ - {\text{109}}{\text{.5}} \pm {\text{8}}{\text{.9}}} {{\text{RT}}}}} \right. \kern-\nulldelimiterspace} {{\text{RT}}}}} \right) \hfill \\ \end{gathered} $$ where D is in m2s?1 and activation energies are in kJ/mol. Diffusivities measured at 64 and 72 wt% SiO2 are only slightly different from those at 68 wt% SiO2 and frequently all measurements are within error of each other. Silicon, aluminum, iron, magnesium, and calcium EBDCs were also calculated from diffusion profiles by error function inversion techniques assuming constant diffusivity. With one exception, silicon EBDCs calculated by error function techniques are within error of Boltzmann-Matano EBDCs. Average diffusivities of Fe, Mg, and Ca were within a factor of 2.5 of silicon diffusivities whereas Al diffusivities were approximately half those of silicon. Alkalies diffused much more rapidly than silicon and non-alkalies, however their diffusivities were not quantitatively determined. Low activation energies for silicon EBDCs result in rapid diffusion at magmatic temperatures. Assuming that water and fluorine exert similar effects on melt viscosity at high temperatures, the viscosity can be calculated and used in the Eyring equation used to determine diffusivities, typically to within a factor of three of those measured in this study. This correlation between viscosity and diffusivity can be inverted to calculate viscosities of fluorine- and water-bearing granitic melts at magmatic temperatures; these viscosities are orders of magnitude below those of hydrous granitic melts and result in more rapid and effective separation of granitic magmas from partially molten source rocks. Comparison of Arrhenius parameters for diffusion measured in this study with Arrhenius parameters determined for diffusion in similar compositions at the same pressure demonstrates simple relationships between Arrhenius parameters, activation energy-Ea, kJ/mol, pre-exponential factor-Do, m2s?1, and the volatile, X=F or OH?, to oxygen, O, ratio of the melt {(X/X+O)}: $$\begin{gathered} {\text{E}}a = - {\text{1533\{ }}{{\text{X}} \mathord{\left/ {\vphantom {{\text{X}} {\left( {{\text{X}} + {\text{O}}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\text{X}} + {\text{O}}} \right)}}{\text{\} }} + {\text{213}}{\text{.3}} \hfill \\ {\text{D}}_{\text{O}} = {\text{2}}{\text{.13}} \times {\text{10}}^{ - {\text{6}}} {\text{exp}}\left[ { - {\text{6}}{\text{.5\{ }}{{\text{X}} \mathord{\left/ {\vphantom {{\text{X}} {\left( {{\text{X}} + {\text{O}}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\text{X}} + {\text{O}}} \right)}}{\text{\} }}} \right] \hfill \\ \end{gathered} $$ These relationships can be used to estimate diffusion in various melts of dacitic to rhyolitic composition containing both fluorine and water. Calculations for the contamination of rhyolitic melts by dacitic enclaves at 800°C and 700°C provide evidence for the virtual inevitability of diffusive contamination in hydrous and fluorine-bearing magmas if they undergo magma mixing of any form.  相似文献   

15.
The diffusion rates of carbon and oxygen in two calcite crystals of different Mn contents have been studied between 500° and 800° C in a CO2-H2O atmosphere (P CO 2=1?5 bars, P H2O=0.02?24 bars) labeled with 13C and 18O. Isotope concentration gradients within annealed specimens were measured using a secondary ion microprobe by depth profiling parallel and perpendicular to the c axis. Despite the anisotropic structure of calcite, the diffusion of carbon and oxygen are both very nearly isotropic. Least-squares fitting of the carbon data to an Arrhenius relation gives an activation energy of 87±2 kcal/mole, with D 0 terms dependent only slightly upon direction: 1 $$D_{\text{0}} {\text{(}}\parallel c{\text{) = }}\left( {9\frac{{ + 12}}{{ - 5}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ , 2 $$D_{\text{0}} {\text{(}} \bot c{\text{) = }}\left( {5\frac{{ + 6}}{{ - 3}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ . These results are in close agreement with previous determinations. Results for oxygen diffusion, however, give D values much larger than those previously reported for dry conditions; at 650° to 800° C the D values are two orders of magnitude larger. The diffusion of oxygen, unlike carbon, is strongly dependent on water pressure, as well as Mn content, and does not fit an Arrhenius relation over the entire temperature range. On the basis of these observations and considerations of the defect chemistry of calcite, it is proposed that carbon migrates as a Frenkel pair. The diffusion of oxygen, however, appears to be more complicated and may depend upon several simultaneous mechanisms.  相似文献   

16.
Solubility of hydrogen in olivine: dependence on temperature and iron content   总被引：11，自引：0，他引：11  
  相似文献   

17.
The carbon dioxide solubility in alkali basalts: an experimental study   总被引：1，自引：1，他引：0  
Experiments were conducted to determine CO2 solubilities in alkali basalts from Vesuvius, Etna and Stromboli volcanoes. The basaltic melts were equilibrated with nearly pure CO2 at 1,200°C under oxidizing conditions and at pressures ranging from 269 to 2,060 bars. CO2 solubility was determined by FTIR measurements. The results show that alkalis have a strong effect on the CO2 solubility and confirm and refine the relationship between the compositional parameter Π devised by Dixon (Am Mineral 82:368–378, 1997) and the CO2 solubility. A general thermodynamic model for CO2 solubility in basaltic melts is defined for pressures up to 2 kbars. Based on the assumption that O2− and CO32− mix ideally, we have:
_boxclose_3^2 - ^m (P,T)X_^2 - ^m f__2 (P,T) K(P,T) = X__3^2 - ^m (P,T) ( X_^2 - ^m f__2 (P,T) ). \begin{gathered} K(P,T) = {\frac{{X_{{{\text{CO}}_{3}^{2 - } }}^{m} (P,T)}}{{X_{{{\text{O}}^{2 - } }}^{m} \times f_{{{\text{CO}}_{2} }} (P,T)}}} \hfill \\ K(P,T) = {{X_{{{\text{CO}}_{3}^{2 - } }}^{m} (P,T)} \mathord{\left/ {\vphantom {{X_{{{\text{CO}}_{3}^{2 - } }}^{m} (P,T)} {\left( {X_{{{\text{O}}^{2 - } }}^{m} \times f_{{{\text{CO}}_{2} }} (P,T)} \right).}}} \right. \kern-\nulldelimiterspace} {\left( {X_{{{\text{O}}^{2 - } }}^{m} \times f_{{{\text{CO}}_{2} }} (P,T)} \right).}} \hfill \\ \end{gathered}  相似文献   

18.
A statistical mechanical analysis of the limiting laws for coupled solid solutions shows that the random model, in which the configurational entropy is calculated as if atoms mix randomly on each crystallographic site, is correct as a first approximation. In coupled solid solutions, since atoms of different valence substitute on the same sites, significant short-range order which reduces the entropy can be expected. A first-order correction is rigorously obtained for the entropy in dilute binary short-range ordered coupled solid solutions: $$\bar S^{{\text{XS}}} {\text{/R = }}Q\left( {{\text{e}}^{--H_{\text{A}} /{\text{R}}T} \left( {\frac{{H_{\text{A}} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_2^a N_4^b ,$$ where Q is the number of positions an associated cation pair can assume per formula unit, H A is the association energy per formula unit, and N 2 a and N 4 b are the site occupancy fractions for atoms 2 and 4 that are dilute on sites a and b. S XS is the configurational entropy minus the random model entropy. Aluminous pyroxenes on the joints diopside-jadeite and diopside-CaTs are examined as examples. A generalization for dilute multiple component solutions, including possible long-range ordering variations is given by: $$\frac{{\bar S^{{\text{XS}}} }}{{\text{R}}}{\text{ = }}\sum\limits_i {\sum\limits_j {\sum\limits_k {Q_i } } \left( {{\text{e}}^{--H_{\text{A}}^{j{\text{ }}k{\text{, }}i} /{\text{R}}T} \left( {\frac{{H_{\text{A}}^{j{\text{ }}k{\text{, }}i} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_j^l N_k^m ,} $$ where i labels each crystallographically distinct pair, j and k label atomic species, l and m label crystallographic sites, and the N's are site occupancy fractions for the solute atoms. A total association model is examined as well as the partial association and random models. Real solution behavior must lie between the total association model and the random model. Molecular models in which the ideal activity is proportional to a mole fraction, which in itself is not always unambiguously defined, do not lie in this range and furthermore have no physical justification.  相似文献   

19.
The iron-magnesium distribution coefficient, $$K'_D = (X_{\Sigma {\text{FeO}}} /X_{{\text{MgO}}} )^{{\text{olivine}}} (X_{{\text{MgO}}} /X_{\Sigma {\text{FeO}}} )^{{\text{liquid}}} ,$$ has frequently been used as a means of testing whether experimental and natural silicate liquids could have been in equilibrium with olivine of mantle composition. It is shown here that this K′ D decreases with increasing oxygen fugacity (xxx) for a hydrous partial melt in equilibrium with a natural spinel peridotite assemblage under pressure and temperature conditions corresponding to those of the upper mantle (from 0.52 at the xxx of the iron-wüstite buffer to 0.04 at the xxx of the magnetite-hematite buffer). K′ D also increases with increasing pressure, with decreasing temperature, and probably with increasing Mg/(Mg+∑ Fe) of the parental peridotite, suggesting that $$K_D = (X_{{\text{FeO}}} /X_{{\text{MgO}}} )^{{\text{olivine}}} (X_{{\text{MgO}}} /X_{{\text{FeO}}} )^{{\text{liquid}}}$$ also increases with increasing pressure and decreasing temperature. Thus, unless these four variables (P, T, xxx, silicate composition) are known for a natural magma, K′ D and probably K D are variables, and the Mg/(Mg+∑ Fe) of such a magma cannot be correlated to that of the parent. The K D determined at 1 atm pressure by Roeder and Emslie has frequently been used to test whether the Mg/(Mg+∑ Fe) ratios of experimentally formed liquids at high pressure in equilibrium with olivine of known Fo content represent the equilibrium Mg/(Mg+Fe2+) of this liquid, assuming that ∑Fe=Fe2+ and that K′ D does not vary with P, T, and composition of the system. Published data demonstrate that the oxygen fugacities of the experimental designs employed by different laboratories vary between those of the magnetite-hematite and magnetite-wüstite buffers (6 orders of magnitude), resulting in K′ D between 0.04 and 0.31 at 1050° C and 15 kbar, for example. Thus, published arguments as to whether the quenched liquids represent equilibrium compositions based on iron-magnesium partitioning are inadequate. The effects of P, T, xxx, and the composition of the starting material must also be considered.  相似文献   

20.
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