Computer simulation in hydrothermal systems with allowance for nonideality of sphalerite and pyrrhotite

To enhance the computer simulation of hydrothermal processes using the HCh program package, an external ZnS_FeS module has been created on the basis of a nonideal asymmetric model of sphalerite solid solution. FeS and ZnS activity coefficients computed in line with this model within a temperature range 200?C350°C lead to the decrease in FeS mole fraction (X _FeS) in sphalerite by 3.0?C1.5 times as compared with the ideal model. The calculated data on composition of sphalerite at the pyrite-pyrrhotite buffer with allowance for pyrrhotite nonideality are consistent with experimental results within the limits of 2% X _FeS of its value (0.215). A nonlinear relationship logX _FeS versus $\left( {\log f_{S_2 } } \right)$ . has been established, involving additional calculated data on equilibria of sphalerite with pyrite and magnetite, as well as pyrite and barite. With transition from pyrrhotite to magnetite and barite, a FeS mole fraction in sphalerite decreases to 0.1 and 0.006, respectively, because of increase in sulfur fugacity. The feasibility of using the calculation results based on the nonideal model of sphalerite for interpretation of natural data is exemplified in the Rainbow ore occurrence at the Mid-Atlantic Ridge (MAR). The computed pyrite-pyrrhotite and pyrite-cubanite-chalcopyrite buffer equilibria (X _FeS = 0.215 and 0.10?C0.12, respectively) are consistent with compositions of sphalerite in the pyrrhotite-cubanite-sphalerite and sphalerite ores (X _FeS = 0.20?C0.33 and 0.05?C0.14, respectively).     

Fictive component model of pyroxenes and multicomponent phase equilibria

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G _f ⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G ^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant     

Fe-Zn mixing energetics of the Iss phase in the system Cu-Fe-Zn-S

A thermodynamic analysis of the intermediate solid solution (Iss) of near-cubanite composition has been attempted by considering an Fe–Zn exchange equilibrium between Iss and sphalerite. The interchange free-energy parameter of Fe–Zn mixing in Iss (W^Iss) and the free energy of the exchange equilibrium (G_1,T ) have been deduced at 500, 600, 700 and 723° C using the compositional data of sphalerite and Iss from phase equilibrium experiments and by the standard method of linear regression analysis. For sphalerite, two independent activity-composition models have been chosen. The extracted values of G_1,T and W^Iss, using both models, are compared. Although the values match, the errors in the extracted parameters are relatively larger when Hutcheon's model is used. Both G_1,T and W^Iss show linear variations with temperature, as given by the following relations: G^1,T = –35.41 + 0.033 T in kcal (SE=0.229)W^ISS= 48.451 – 0.041 T in kcal (SE=0.565) Activity-composition relations and different mixing parameters have been calculated for the Iss phase. A large positive deviation from ideality is observed in Iss on the join CuFe₂S₃–CuZn₂S₃. No geothermometric application has been attempted in this study, even though Iss of cubanite composition (isocubanite) in association with sphalerite, pyrite and pyrrhotite is reported from seafloor hydrothermal deposits. This is due to the fact that: (a) the temperatures of formation of these deposits are significantly lower than 500° C, the lower limit of appropriate experimental data base; (b) microprobe data of the coexisting isocubanite and sphalerite in the relevant natural assemblages are not available.Symbols a _J ⁱ activity of component i in phase J - G_{1, T} standard free energy change of reaction (cal) - G^IM free energy of ideal mixing (cal) - G^EM free energy of excess mixing (cal) - G _M ^ex free energy of mixing (cal) - G _i excess free energy of mixing at infinite dilution (cal) - _i ^J activity coefficient of component i in phase J - _i ^{J, 0} standard chemical potential of component i in phase J (cal) - ; _i ^J chemical potential of component i in phase J (cal) - R universal gas constant (1.98717 cal/K·mol) - T temperature in degree (K) - W^J interchange free energy of phase J in (cal) - X _J ⁱ mole fraction of component i in phase J     

The elastic solid solution model for minerals at high pressures and temperatures

Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order–disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.     

Evidence for aqueous activity on comet 81P/Wild 2 from sulfide mineral assemblages in Stardust samples and CI chondrites

The discovery of nickel-, copper-, and zinc-bearing iron sulfides from comet 81P/Wild 2 (Wild 2) represents the strongest evidence, in the Stardust collection, of grains that formed in an aqueous environment. We investigated three microtomed TEM sections which contain crystalline sulfide assemblages from Wild 2 and twelve thin sections of the hydrothermally altered CI chondrite Orgueil. Detailed structural and compositional characterizations of the sulfide grains from both collections reveal striking similarities. The Stardust samples include a cubanite (CuFe₂S₃) grain, a pyrrhotite [(Fe,Ni)_1−xS]/pentlandite [(Fe,Ni)₉S₈] assemblage, and a pyrrhotite/sphalerite [(Fe,Zn)S] assemblage. Similarly, the CI-chondrite sulfides include individual cubanite and pyrrhotite grains, cubanite/pyrrhotite assemblages, pyrrhotite/pentlandite assemblages, as well as possible sphalerite inclusions within pyrrhotite grains. The cubanite is the low temperature orthorhombic form, which constrains temperature to a maximum of 210 °C. The Stardust and Orgueil pyrrhotites are the 4C monoclinic polytype, which is not stable above ∼250 °C. The combinations of cubanite and pyrrhotite, as well as pyrrhotite and pentlandite signify even lower temperatures. The crystal structures, compositions, and petrographic relationships of these sulfides constrain formation and alteration conditions. Taken together, these constraints attest to low-temperature hydrothermal processing.Our analyses of these minerals provide constraints on large scale issues such as: heat sources in the comet-forming region; aqueous activity on cometary bodies; and the extent and mechanisms of radial mixing of material in the early nebula. The sulfides in the Wild 2 collection are most likely the products of low-temperature aqueous alteration. They provide evidence of radial mixing of material (e.g. cubanite, troilite) from the inner solar system to the comet-forming region and possible secondary aqueous processing on the cometary body.     

The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables

The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa₇₅, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities     

Application of the sphalerite geobarometer to some skarn-type ore deposits

Based on the equation recently determined, formation pressures of skarn-type ore deposits were estimated from the composition of sphalerite coexisting with pyrite and hexagonal pyrrhotite. As criteria for equilibrium among sphalerite, pyrite and hexagonal pyrrhotite, the following three points were carefully checked on each specimen: 1) the presence of hexagonal pyrrhotite, 2) no time sequences among the formation of sulfide minerals, and 3) no compositional variation in sphalerite. Most of the Cu-Fe skarn deposits studied were formed under pressures of more than 1 kb, whereas Zn-Pb(-Cu-Fe) deposits tend to have formed at relatively shallow environments, namely under less than 1 kb. The calculated pressures are qualitatively consistent with the depth of formation of deposits estimated from the geological evidences. The sphalerite geobarometry is quite sensitive even at low pressure ranges, and it is applicable to the deposits formed under shallow conditions.     

Low temperature,low pressure deformation and metamorphism of the Vangorda massive sulphide orebody,Yukon, Canada

The Vangorda orebody is a small stratiform massive sulphide orebody located in Anvil District, Yukon, Canada. The orebody consists of fineto medium-grained semi-massive and massive sulphides with a common sulphide mineralogy of pyrite, pyrrhotite, sphalerite, galena, and minor chalcopyrite. The host rocks and the sulphide lithofacies have been complexly deformed during two phases of deformation (D₁ and D₂) and associated metamorphism (M₁ and M₂). The effects of d₁ and M₁ are penetratively overprinted by D₂ and M₂. D₂ and M₂ resulted in tight to isoclinal F₂ folding of the orebody, remobilisation of the sulphides, recrystallisation and development of shear zones along the limbs of the F₂ folds. Chlorite thermometry and sulphide thermobarometry have been carried out on the host phyllites and on the sulphides. Chlorite was analysed from the S₁ and S₂ foliations in the phyllites to determine M₁ and M₂ temperatures, respectively. However, no difference was found between chlorite compositions in these foliations and a mean temperature of 363 °C was calculated from the tetrahedral A1_IV occupancy. Arsenopyrite thermometry yielded a comparable mean temperature of 336 °C. Sphalerite inclusions in M₂ pyrite porphyroblasts from D₂ shear zones were analysed for pressure using the sphalerite + hexagonal pyrrhotite + pyrite barometer. Inclusions were analysed in an attempt to determine if relic m₁ sphalerite, and hence pressure signature, was preserved. Inclusion compositions appear to reflect only M₂ conditions and yielded a mean pressure of 4.0 kb. Sphalerite + hexagonal pyrrhotite assemblages were analysed from D₂ shear zones to determine the M₂ pressure using the sphalerite + hexagonal pyrrhotite barometer. These calculations yielded a mean pressure of 6.1 kb. The M₂ temperatures and pressures calculated using these calibrations are in good agreement with those estimated from petrogenetic relationships.     

Silicate and sulphide thermobarometry of low- to medium-grade metamorphic rocks from Holkham Bay, south-east Alaska

ABSTRACT The western metamorphic belt of the Coast Plutonic Complex, south-east Alaska and adjacent British Columbia, contains strongly deformed rocks and a prominent topographic low: the Coast Range megalineament. Near Holkham Bay, south-east Alaska, the lineament separates the western metamorphic belt into: a western low-grade (greenschist facies) terrane, and an eastern medium-grade (amphibolite facies) terrane. Sphalerite compositions of grains in direct contact with pyrite and pyrrhotite in chlorite-muscovite zone rocks in the low-grade terrane give pressures of about 8 kbar; compatible with pressures of 8-10 kbar at 500°C calculated from plagioclase-biotite-garnet-muscovite assemblages adjacent to the Windham Bay pluton about 15 km away. A pressure of 4.8 ± 0.7 kbar was calculated from sphalerite compositions in staurolite zone rocks east of the Coast Range megalineament. This is indistinguishable from pressures of 4.8 ± 1 kbar at 585°C and 5.1 ± 1 kbar at 680°C (plagioclase-garnet-aluminum silicate-quartz equilibria), and 4.1 ± 1 kbar at 585°C (plagioclase-biotite-garnet-muscovite equilibrium) determined for the medium-grade terrane. An identical pressure of 4.8 ± 0.7 kbar was calculated from sphalerite compositions in biotite zone rocks adjacent to the lineament; this is considerably higher than a pressure of 3.1 ± 1 kbar at 525°C obtained using plagioclase-biotite-garnet-muscovite geobarometry from shear zones within the lineament. The discrepancy may be explained by later equilibration of mineral phases within the shear zones. The geothermobarometry suggests relatively low temperatures and high pressures for the low-grade terrane (6-10 kbar), and intermediate temperatures and pressures for the medium-grade terrane to the east (4-6 kbar). Comparison of the barometers indicate that sphalerite can be used to estimate metamorphic pressures, similar to those estimated from silicate mineral chemistry when pyrrhotite-sphalerite-pyrite assemblages are used.     

Some binary and ternary silicate solution models

Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G ^ex excess free energy of mixing - H ^ex excess enthalpy of mixing - S ^ex total excess entropy of mixing - S _ex ^c configurational excess entropy of mixing - W _ij interaction energy parameter between speciesi andj - X _i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi₂O₆) - En enstatite (Mg₂Si₂O₆) - Py pyrope (MgAl_2/3SiO₄) - Gr grossular (CaAl_2/3SiO₄) - CaTs Ca-Tschermak (CaAl₂SiO₆) - Ab albite (NaAlSi₃O₈) - An anorthite (CaAl₂Si₂O₈)     

A thermodynamic model for multicomponent melts,with application to the system CaO-Al2O3-SiO2

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

Partitioning of Fe and Mn between ilmenite and olivine at 1100 °C: constraints on the thermodynamic mixing properties of (Fe, Mn)TiO3 ilmenite solid solutions

The partitioning of Fe²⁺ and Mn²⁺ between (Fe, Mn)TiO₃ and (Fe, Mn)₂SiO₄ solid solutions in the system FeO-MnO-TiO₂-SiO₂ has been experimentally investigated at 1100 ^∘C and pressures of 1 bar and 25 kbar, over a wide range of Fe/Mn ratios, using electron microprobe analysis of quenched run products. The ilmenite solid solution in this system is within analytical uncertainty a simple binary between FeTiO₃ and MnTiO₃, but the olivine solid solution appears to contain up to 2.5 wt% TiO₂. The Fe-Mn partitioning results constrain precisely the difference in the thermodynamic mixing properties of the two solid solutions. If the mixing properties of (Fe, Mn)₂SiO₄ solid solutions are assumed to be ideal, as experimentally determined by Schwerdtfeger and Muan (1966), then the ilmenite is a regular, symmetric solution with W ^ilm _Fe-Mn=1.8±0.1 kJ mol⁻¹. The quoted uncertainty does not include the contribution from the uncertainty in the mixing properties of the olivine solution, which is estimated to be ±1.8 kJ mol⁻¹, and which therefore dominates the uncertainty in the present results. Nevertheless, this result is in good agreement with the previous experimental study of O'Neill et al. (1989), who obtained W ^ilm _Fe-Mn=2.2±0.3 kJ mol⁻¹ from an independent method. The results provide another item of empirical evidence supporting the proposition that solid solutions between isostructural end-members, in which order-disorder effects are not important, generally have simple thermodynamic mixing properties, with little asymmetry, modest excess entropies, and excess enthalpies approximately proportional to the difference in the molar volumes of the end-members. Received: 11 February 1998 / Accepted: 29 June 1998     

Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems

Use of simple mixing models of orthopyroxene and garnet solid solutions enables extrapolation of experimentally determined equilibria in the MgSiO₃-Al₂O₃ system to uninvestigated parts of pressure-temperature-composition space. Apparent discrepancies in the experimental data for simple and multicomponent systems may be explained by considering the effect of CaO and FeO on reducing pyrope activity in the garnet solid solutions. Equilibration pressures of natural garnet-orthopyroxene assemblages may be calculated, provided temperatures are known, from a combination of the experimental data on the MgSiO₃-Al₂O₃ system and analyses of coexisting natural phases.Despite the presence of a compositional gap in the system, the solubility of enstatite in diopside coexisting with orthopyroxene can also be approximately treated by an ideal solution model. An empirical approach has been developed to take account of Fe²⁺ on the orthopyroxene-clinopyroxene miscibility gap in natural systems in order to calculate equilibration temperatures of 2-pyroxene assemblages. The model presented reproduces almost all of the available experimental data for multicomponent systems to within 60° C.     

Rates of zinc and trace metal release from dissolving sphalerite at pH 2.0–4.0

High-Fe and low-Fe sphalerite samples were reacted under controlled pH conditions to determine nonoxidative rates of release of Zn and trace metals from the solid-phase. The release (solubilization) of trace metals from dissolving sphalerite to the aqueous phase can be characterized by a kinetic distribution coefficient, (D_tr), which is defined as [(R_tr/X(tr)_Sph)/(R_Zn/X(Zn)_Sph)], where R is the trace metal or Zn release rate, and X is the mole fraction of the trace metal or Zn in sphalerite. This coefficient describes the relationship of the sphalerite dissolution rate to the trace metal mole fraction in the solid and its aqueous concentration. The distribution was used to determine some controls on metal release during the dissolution of sphalerite. Departures from the ideal D_tr of 1.0 suggest that some trace metals may be released via different pathways or that other processes (e.g., adsorption, solubility of trace minerals such as galena) affect the observed concentration of metals.     

Thermochemistry of the tremolite-edenite amphiboles using fluorine analogues,and applications to amphibole-plagioclase-quartz equilibria

Heats of mixing of synthetic C2/m fluortremolite-fluoredenite amphiboles measured at 985 K show a systematic deviation from ideal mixing consistent with a subregular solution model. The deviations from ideal mixing are interpreted in terms of Na ordering in the A-site and Na-Al interactions in edenite-poor compositions. Enthalpies of edenite substitution reactions in amphiboles and in SiO₂-NaAlO₂ glasses and framework silicates are comparable. Gibbs free energies of formation of fluortremolite and fluoredenite at 298K are -2,821.07±3.34 kcal mol^–1 and -2,889.59±2.40 kcal mol^–1 respectively. The former value is in good agreement with values calculated from both F-OH exchange experiments and from a natural fluortremolite-bearing metamorphic rock. Least-squares fitted sub-regular heat-of-mixing parameters are poorly constrained and unrealistically high, but estimated subregular mixing parameters consistent with 95% confidence interval uncertainties in the calorimetric data and with TEM constraints give activity-composition relations in good agreement with the A-site compositions of natural metamorphic and igneous hornblendes. These relations predict unmixing in edenite-rich compositions over a wide range of temperature, but lend no support to the existence of a hornblende-actinolite miscibility gap. Calibration of the reaction tremolite+ albite=edenite+4 quartz as a function ofP,T andX _ed ^amph indicates negativedP/dT slopes and a limited range of X _ed ^amph (0.3 to 0.5) in equilibrium with plagioclase and quartz over a wide range of pressure and temperature, consistent with metamorphic hornblende-plagioclase assemblages. The energetics of this reaction suggest, however, that amphibole-plagioclase disequilibrium may be common.     

Oxidation potential and the composition of metamorphic fluid as a solution to the inverse problem of convex programming

Using the Selektor-C software program package, oxidation potential and the composition of metamorphogenic fluid were determined for mineral assemblages from nine samples of granulite-grade metamorphic rocks by solving the inverse problems of convex programming. The calculated and real mineral assemblages are in good agreement with respect to the composition and association of minerals, which is compelling evidence for the attainment of chemical equilibrium (minimum of Gibbs free energy) under given P-T conditions. Based on the dual solution of the inverse problem, a new approach was proposed for the estimation of the oxidation potential of fluid and mineral assemblages, which can be used to determine oxygen potential for almost any mineral association, independent of the presence of magnetite, ilmenite, or graphite. It was found that magnetite-free mineral associations are characterized by highly reducing conditions corresponding to oxygen potentials close to the CCO buffer. The external metamorphic fluid that was present during granulite-facies metamorphism was probably formed in the graphite stability field. The results of calculations for the model aqueous electrolyte solution-mineral assemblage suggest high SiO₂ solubility in the metamorphogenic fluid. Therefore, the process of granulite metamorphism may be a potent geochemical factor of the redistribution and transportation of silica from lower to upper crustal levels.     

Sphalerite geobarometry of deformed sulphide ores from the C. S. A. Mine,Cobar, Australia

The C. S. A. Mine is located near Cobar, central New South Wales. The copper-zinc-lead ores occur in Early Devonian rocks of the Cobar Super-Group. Lower greenschist (slate-grade) metamorphism has developed elongate lenticular ore systems parallel to the extension (down-dip) lineation in cleavage. FeS contents of sphalerites coexisting with pyrite and pyrrhotite outside and inside pressure shadows indicate much higher pressures (7.7 to 9.0 kbar) than those inferred from stratigraphic reasoning and the low metamorphic grade. The homogeneous distribution of Fe in sphalerites suggests equilibration with pyrite-pyrrhotite; and concentrations of Co and Ni in iron sulphides, and Mn, Cd and Cu in sphalerite are too low to have influenced phase relations in the FeS-ZnS pseudobinary system. The anomalously high pressures are therefore ascribed to reequilibration of sphalerite compositions with a monoclinic pyrrhotite-pyrite buffer. The FeS contents of the reequilibrated sphalerites apparently reflect the differing mean stress domains that exist outside and inside pressure shadows. This suggests that reequilibration occurred under the same stress distribution as produced the original pressure shadows, and implies FeS dissolution during the decay of the cleavage-producing structuro-metamorphic event. The commonly observed scatter of sphalerite compositions in low grade assemblages appears to record micro-scale mean stress domains, and thereby testifies to the pressure sensitivity of the mole percent FeS contents.     

Fe-Zn exchange reaction between tetrahedrite and sphalerite in natural environments

Microprobe and fluid inclusion analyses of hydrothermal ore deposits containing the subassemblage sphalerite+ tetrahedrite-tennantite [(Cu, Ag)₁₀(Fe, Zn)₂(As,Sb)₄S₁₃] reveal that the Gibbs energies of the reciprocal reaction Cu₁₀Zn₂Sb₄S₁₃ + Cu₁₀Fe₂As₄S₁₃ = Cu₁₀Fe₂Sb₄S₁₃ + Cu₁₀Zn₂As₄S₁₃ and the Fe-Zn exchange reaction 1/2Cu₁₀Fe₂Sb₄S₁₃ + ZnS = 1/2Cu₁₀Zn₂Sb₄S₁₃ + FeS are within the uncertainties of the values established by Sack and Loucks (1985) and Raabe and Sack (1984), 2.59±0.14 and 2.07±0.07 kcal/gfw. However, this study suggests that the Fe-Zn exchange reaction between sphalerite and Sb and Ag-rich tetrahedrites does not obey the simple systematics suggested by Sack and Loucks (1985) wherein tetrahedrite is assumed to behave as an ideal reciprocal solution. Instead these studies show that the configurational Gibbs energy of this exchange reaction,RTln[(X _Fe/X _Zn)^TET(X _ZnS/X _FeS)^SPH], corrected for sphalerite nonideality exhibits both a local maximum and minimum as a function of Ag/(Cu+Ag) ratio at a givenX _FeS ^SPH and temperature. The local maximum forX _FeS ^SPH 0.10 corresponds to the position of the cell edge maximum established for natural tetrahedrites by Riley (1974), Ag/(Ag+Cu)0.4. These studies and the results of structural refinements of Ag-bearing tetrahedrites suggest that in low silver tetrahedrites Ag is preferentially incorporated in trigonal-planar sites but that in tetrahedrites with intermediate and greater Ag/(Ag+Cu) ratio, Ag is preferentially incorporated in tetrahedral sites. A nonconvergent site ordering model for tetrahedrite is developed to quantify and extrapolate these predictions.     

Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.