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

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.     

The magnesiowüstite: iron equilibrium and its implications for the activity-composition relations of (Mg,Fe)<Subscript>2</Subscript>SiO<Subscript>4</Subscript> olivine solid solutions

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:

Garnet-clinopyroxene geothermometer

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⁺.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

Solubility of Ca and Al in orthopyroxene from spinel peridotite: an improved version of an empirical geothermometer

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

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

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.     

Re-evaluation of lead isotopic data,southern Massif Central,France

Three independent Pb isotope homogenizing processes operating on large volumes of rock material during limited intervals in the Phanerozoic have been used to define a unique evolutionary curve for rock and ore lead isotopic compositions of the southern Massif Central, France. The model is

The ferric-ferrous ratio of natural silicate liquids equilibrated in air

Results of chemical analyses of glasses produced in 46 melting experiments in air at 1,350° C and 1,450° C on rocks ranging in composition from nephelinite to rhyolite have been combined with other published data to obtain an empirical equation relating in \((X_{{\text{Fe}}_{\text{2}} {\text{O}}_{\text{3}} }^{{\text{liq}}} /X_{{\text{FeO}}}^{{\text{liq}}} )\) to T, \(\ln f_{{\text{O}}_{\text{2}} } \) and bulk composition. The whole set of experimental data range over 1,200–1,450° C and oxygen fugacities of 10^?9.00 to 10^?0.69 bars, respectively. The standard errors of temperature and \(\log _{10} f_{{\text{O}}_{\text{2}} } \) predictions from this equation are 52° C and 0.5 units, respectively, for 186 experiments.     

Aluminum partitioning between olivine and ultrabasic silicate liquid to 6 GPa

Trace element analyses of 1-atm and high-pressure experiments show that in komatiite and peridotite, the olivine (OL)/liquid (L) distribution coefficient for Al₂O₃ ( ) increases with pressure and temperature. Olivine in equilibrium with liquid accepts as much as 0.2 wt% Al₂O₃ in solution at 6 GPa. Convergence to equilibrium compositions at this high level is shown by cation diffusion of Al into synthetic forsterite crystals of low-Al contents in the presence of melt. Convergence to low-Al equilibrium compositions at lower P and T is shown by diffusion of Al out of synthetic forsterite with high initial Al content. Isobaric and isothermal experimental data subsets reveal that temperature and pressure variations both have real effects on . Variation in silicate melt composition has no detectable effect on within the limited range of experimentally investigated mixtures. Least-squares regression for 24 experiments, using komatiite and peridotite, performed at 1 atm to 6 GPa and 1300 to 1960°C, gives the best fit equation: Increase in with increasingly higher-pressure melting is consistent with incorporation of a spinel-like component of low molar volume into olivine, although other substitutions possibly involving more complex coupling cannot be ruled out. High P-T ultrabasic melting residues, if pristine, may be recognized by the high calculated from microprobe analyses of Al₂O₃ concentrations in residual olivines and estimated Al₂O₃ concentration in the last liquid removed. In general the low levels of Al in natural olivine from mantle xenoliths suggest that pristine residues are rarely recovered.     

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

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.     

Amphibole composition in tonalite as a function of pressure: an experimental calibration of the Al-in-hornblende barometer

The Al-in-hornblende barometer, which correlates Al^tot content of magmatic hornblende linearly with crystallization pressure of intrusion (Hammarstrom and Zen 1986), has been calibrated experimentally under water-saturated conditions at pressures of 2.5–13 kbar and temperatures of 700–655°C. Equilibration of the assemblage hornlende-biotite-plagioclase-orthoclasequartz-sphene-Fe-Ti-oxide-melt-vapor from a natural tonalite 15–20° above its wet solidus results in hornblende compositions which can be fit by the equation: P(±0.6 kbar) = –3.01 + 4.76 Al _hbl ^tot r ²=0.99, where Al^tot is the total Al content of hornblende in atoms per formula unit (apfu). Al^tot increase with pressure can be ascribed mainly to a tschermak-exchange ( ) accompanied by minor plagioclase-substitution ( ). This experimental calibration agrees well with empirical field calibrations, wherein pressures are estimated by contact-aureole barometry, confirming that contact-aureole pressures and pressures calculated by the Al-in-hornblende barometer are essentially identical. This calibration is also consistent with the previous experimental calibration by Johnson and Rutherford (1989b) which was accomplished at higher temperatures, stabilizing the required buffer assemblage by use of mixed H₂O-CO₂ fluids. The latter calibration yields higher Al^tot content in hornblendes at corresponding pressures, this can be ascribed to increased edenite-exchange ( ) at elevated temperatures. The comparison of both experimental calibrations shows the important influence of the fluid composition, which affects the solidus temperature, on equilibration of hornblende in the buffering phase assemblage.     

Thermodynamics of coexisting cummingtonite-hornblende Pairs

The activity-composition relations for calcium-rich and calcium-poor amphiboles are calculated from the composition of coexisting cummingtonite-hornblende pairs from a suite of New Zealand rhyolites. The activities are formulated in terms of site occupancies and the regular solution model is used to represent non-ideal mixing of the cations on each site. The regular solution parameters for each site are calculated from the compositions of the coexisting amphiboles. The resulting activity-composition relations are used to calibrate the standard Gibbs energy change for the reaction $${\text{7MgSiO}}_{\text{3}} {\text{ + SiO}}_{\text{2}} {\text{ + H}}_{\text{2}} {\text{O = Mg}}_{\text{7}} {\text{Si}}_{\text{8}} {\text{O}}_{{\text{22}}} {\text{(OH)}}_{\text{2}} $$ assuming that the lowest temperature rhyolites in this suite crystallised at \(P_{{\text{H}}_2 {\text{O}}} = P_{{\text{total}}} \)      

Relationship between fluid-bearing and fluid-absent invariant points and a petrogenetic grid for a greenschist facies assemblage in the system CaO-MgO-Al2O3-SiO2-CO2-H2O

In the 6 component system CaO-MgO-Al₂O₃-SiO₂-CO₂-H₂ with 9 solid phases (quartz, plagioclase, epidote, tremolite, talc, chlorite, magnesite, calcite, dolomite) and a fluid phase, all 17 possible fluid-absent reactions have been set up and balanced. Using molar entropy and volume data for the solid phases, these reactions are arranged in P-T space about the 8 possible fluid-absent invariant points after the method of Schreinemakers. Field observations in Ordovician greenschist facies basic volcanics at Sofala N.S.W., indicate that neither talc+epidote nor magnesite+calcite are stable under the conditions of metamorphism. Assuming these conditions to apply to the theoretical study here, the fluid-absent invariant points are arranged in a relative fashion with fluid-absent reactions subdividing P-T space into smaller areas.A scheme which permits a fluid of composition (i.e. a fluid containing CO₂ and H₂O together with other components), is modeled by treating H₂O as a mobile component independent of CO₂, and by allowing values that lie off the locus of binary H₂O-CO₂. Taking into account that neither talc+epidote nor magnesite +calcite is to be permitted, the fluid scheme is used to set up and balance all 39 possible fluid-bearing reactions. These are then arranged about 20 valid fluid-bearing invariant points in space after the method of Korzhinskii and Sehreinemakers.A characteristic solid phase assemblage is defined for each P-T area using chemographic relations inherent from the fluid-absent boundary reactions. The fluid-bearing invariant points that have a solid assemblage compatible with the characteristic assemblage in a particular P-T area are stable within the P-T regime of that area. When these stable fluidbearing invariant points are arranged in a relative fashion in space, they outline a fluid grid which can be used to study the possible effects of local variation in X _fluid over the particular P-T regime.Symbols Used U chemical potential - S entropy - V molar volume - n coefficient of a phase in a reaction - X mole fraction - T temperature - P pressure - F number of degrees of freedom - C number of components - p number of phases - s solid - slope of reaction - 1 quartz - 2 plagioclase - 3 epidote - 4 tremolite - 5 talc - 6 chlorite - 7 dolomite - 8 magnesite - 9 calcite     

Antigorite-ophicarbonates: Phase relations in a portion of the system CaO-MgO-SiO2-H2O-CO2

The occurrence of critical assemblages among antigorite, diopside, tremolite, forsterite, talc, calcite, dolomite and magnesite in progressively metamorphosed ophicarbonate rocks, together with experimental data, permits the construction of phase diagrams in terms of the variables P, T, and composition of a binary CO₂-H₂O fluid. Equilibrium constants are given for the 30 equilibria that describe all relations among the above phases. Ophicalcite, ophidolomite, and ophimagnesite assemblages occupy partially overlapping fields in the diagram. The upper temperature limit of ophicalcite rocks lies below that of ophidolomite and ophimagnesite. The fluid phase in ophicarbonate rocks has 0.8$$ " align="middle" border="0"> , and there are indications that during their progressive metamorphism is approximately equal to P _total.     

Solubility of alumina in orthopyroxene plus spinel as a geobarometer in complex systems. Applications to spinel-bearing alpine-type peridotites

The addition of Fe and Cr to the simple system MgO-SiO₂-Al₂O₃ markedly affects the activities of phases involved in the equilibrium

Opening and resetting temperatures in heating geochronological systems

We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively,

Non-ideal mixing in the phlogopite-annite binary: constraints from experimental data on Mg−Fe partitioning and a reformulation of the biotite-garnet geothermometer

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.     

The origin of the high-K latites from Camp Creek,Arizona: constraints from experiments with variable fO2 and a_{{\text{H}}_{\text{2}} {\text{O}}}

Near-liquidus melting experiments were performed on a high-K latite at fO₂'s ranging from iron-wustite-graphite (IWG) to nickel-nickel oxide (NNO) in the presence of a C-O-H fluid phase. Clinopyroxene is a liquidus phase under all conditions. At IWG , the liquidus at 10 kb is about 1,150° C but is depressed to 1,025° C at NNO and . Phlogopite and apatite are near-liquidus phases, with apatite crystallizing first at pressures below 10 kb. Phlogopite is a liquidus phase only at NNO and high . Under all conditions the high-K latites show a large crystallization interval with phlogopite becoming the dominant crystalline phase with decreasing temperature. Increasing fO₂ affects phlogopite crystallization but the liquidus temperature is essentially a function of . The chemical compositions of the near-liquidus phases support formation of the high-K latites under oxidizing conditions (NNO or higher) and high . It is concluded from the temperature of the H₂O-saturated liquidus at 10 kb, the groundmass: crystal ratio and presence of chilled latite margins around some xenoliths that the Camp Creek high-K latite magma passed thru the lower crust at temperatures of 1,000° C or more.     

The system Fe-Si-O: Oxygen buffer calibrations to 1,500K

The five solid-phase oxygen buffers of the system Fe-Si-O, iron-wuestite (IW), wuestite-magnetite (WM), magnetite-hematite (MH), quartz-iron-fayalite (QIF) and fayalite-magnetite-quartz (FMQ) have been recalibrated at 1 atm pressure and temperatures from 800°–1,300° C, using a thermogravimetric gas mixing furnace. The oxygen fugacity, \(f_{{\text{O}}_{\text{2}} }\) was measured with a CaO-doped ZrO₂ electrode. Measurements were made also for wuestite solid solutions in order to determine the redox behavior of wuestites with O/Fe ratios varying from 1.05 to 1.17. For FMQ, additional determinations were carried out at 1 kb over a temperature range of 600° to 800° C, using a modified Shaw membrane. Results agree reasonably well with published data and extrapolations. The reaction parameters K, ΔG _r ^o , ΔH _r ^o , and ΔS _r ^o were calculated from the following log \(f_{{\text{O}}_{\text{2}} }\) /T relations (T in K): $$\begin{gathered} {\text{IW }}\log f_{{\text{O}}_{\text{2}} } = - 26,834.7/T + 6.471\left( { \pm 0.058} \right) \hfill \\ {\text{ }}\left( {{\text{800}} - 1,260{\text{ C}}} \right), \hfill \\ {\text{WM }}\log f_{{\text{O}}_{\text{2}} } = - 36,951.3/T + 16.092\left( { \pm 0.045} \right) \hfill \\ {\text{ }}\left( {{\text{1,000}} - 1,300{\text{ C}}} \right), \hfill \\ {\text{MH }}\log f_{{\text{O}}_{\text{2}} } = - 23,847.6/T + 13.480\left( { \pm 0.055} \right) \hfill \\ {\text{ }}\left( {{\text{1,040}} - 1,270{\text{ C}}} \right), \hfill \\ {\text{QIF }}\log f_{{\text{O}}_{\text{2}} } = - 27,517.5/T + 6.396\left( { \pm 0.049} \right) \hfill \\ {\text{ }}\left( {{\text{960}} - 1,140{\text{ C}}} \right), \hfill \\ {\text{FMQ }}\log f_{{\text{O}}_{\text{2}} } = - 24,441.9/T + 8.290\left( { \pm 0.167} \right) \hfill \\ {\text{ }}\left( {{\text{600}} - 1,140{\text{ C}}} \right). \hfill \\ \end{gathered}$$ These experimentally determined reaction parameters were combined with published 298 K data to determine the parameters G_f, H_f, and S_f for the phases wuestite, magnetite, hematite, and fayalite from 298 K to the temperatures of the experiments. The T? \(f_{{\text{O}}_{\text{2}} }\) data for wuestite solid solutions were used to obtain activities, excess free energies and Margules mixing parameters. The new data provide a more reliable, consistent and complete reference set for the interpretation of redox reactions at elevated temperatures in experiments and field settings encompassing the crust, mantle and core as well as extraterrestrial environments.