Contributions to Contrib Mineral Petrol (1988) 100:92-106 Mineralogyand Petrology Springer-Verlag1988 Calculation and application of clinopyroxene-garnet-plagioclase-quartz geobarometers* D.P. Moecher, E.J. Essene, and L.M. Anovitz** Department of Geological Sciences, University of Michigan, Ann Arbor, MI 48109-1063, USA Abstract. Recently published thermodynamic and experi- ter) if not extrapolated to mineral assemblages whose com- mental data in a variety of chemical systems have been positions are extremely far removed from the end member evaluated to derive Gibbs free energies for hedenbergite and system for which the barometers were calibrated. pyrope. These were used to calculate the geobarometric equilibria Hedenbergite + Anorthite = Grossular + Almandine + Quartz: "HD barometer", Introduction Diopside + Anorthite = Grossular + Pyrope + Quartz: Major advances in the accuracy and precision of geobar- "DI barometer". ometers have been made in the last decade, in part a result of careful experimental reversal of pressure dependent equi- We have compared the pressures obtained from these equi- libria (Bohlen et al. 1980; Bohlen and Boettcher 1982; Boh- libria for garnet-clinopyroxene-orthopyroxene-plagioclase- len et al. 1983a, 1983b; Gasparik 1984a, 1984b; Gasparik quartz assemblages with the geobarometer and Newton 1984; Bohlen and Liotta 1986; Koziol and Ferrosilite + Anorthite = Almandine + Grossular + Quartz: Newton 1988), more precise thermodynamic data (e.g. Ha- "FS barometer". selton and Newton 1980; Metz et al. 1983; Bohlen et al. 1983; Robie and Hemingway 1984; Haselton et al. 1987; Pressures calculated for 68 samples containing the above Robie et al. 1987), and more accurate modeling of activity- assemblage from a variety of high grade metamorphic ter- composition relations for mineral phases involved in geo- ranes indicate that, in general, the HD and DI barometers barometric equilibria (e.g., Newton et al. 1980; Newton and yield values that are in good agreement with the FS barome- Haselton 1981; Ganguly and Saxena 1984; Davidson and ter, and that the three barometers are generally consistent Lindsley 1985; Anovitz and Essene 1987a). Reasonably ac- with constraints from aluminosilicate occurrences. How- curate and precise geobarometers now exist for most granu- ever, in some samples the HD barometer yields pressures lite facies metabasites, charnockites and high grade metape- up to 2 kbar greater than constraints imposed by the pres- lites, and for some upper amphibolite facies metabasites ence of an aluminosilicate phase. Relative to the FS barome- and metapelites. The above experiments also serve as impor- ter, the HD barometer overestimates pressure by an average tant constraints on thermodynamic data for mineral phases of 0.2_+ 1.0 (1 a)kbar and the DI barometer underestimates involved in the particular reaction. In concert with precise pressure by an average of 0.6 4-1.6 (1 o-) kbar. The pressure thermodynamic data for other phases, the experimentally discrepancies for the HD and DI barometers are likely to constrained thermodynamic data may be used to calculate be a result of imprecision in thermodynamic data and activi- geobarometers that are not easily reversed experimentally. ty models for silicates, and not a result of resetting of the Using this approach we have calculated the location of the clinopyroxene equilibria. The relative imprecision of the DI pressure dependent reactions barometer relative to the FS barometer results from overes- timates of pressure by the DI and FS barometers in Fe-rich Hedenbergite + Anorthite = Grossular + Almandine and Mg-rich systems, respectively. Application of the HD + Quartz and DI barometers to high grade Cpx-Gt-Pg-Qz as- 3 CaFeSizO6 + 3 CaA12Si~Os = 2 Ca3A12Si3012 semblages yields pressures that are generally consistent with other petrologic constraints and geobarometers. It is con- + F%AIzSi3012 + 3 SiOz (1) cluded that the HD and DI barometers can place reasonable (the "Hedenbergite (HD) barometer") and, constraints on pressure (+ 1 kbar relative to the FS barome- Diopside + Anorthite = Grossular + Pyrope + Quartz * Contribution No. 447 from the Mineralogical Laboratory of 3 CaMgSi206 + 3 CaA12Si2Os = 2 Ca3A12Si3012 the University of Michigan + Mg3AI2Si3012 + 3 SiO2 (2) ** Present address: Department of Geosciences, University of Ari- zona, Tucson, AZ 85721 USA (the "Diopside (DI) barometer"), in order to expand the Offprint requests to: D.P. Moecher range of assemblages for which there exist reasonably pre- 93 cise geobarometers. Because garnet, plagioclase and quartz Almandine+ Grossular + Rutile = Ilmenite + Anorthite + Quartz are phases common to both barometers we have chosen 2 F%AlzSi~Ola + Ca3AlzSi3Olz + 6 TiOz to distinguish them on the basis of the particular pyroxene = 6 FeTiO 3 + 3 CaAlzSi20 s + 3 SiO 2 (8) present. Reaction 2 was previously calculated by Newton and Perkins (1982) based on the best available thermoehem- (Bohlen et al. 1983b, 1983c; Bohlen and Liotta 1986) ical data. Their version of Reaction 2 typically underesti- mated pressure by an average of 2.2 kbar relative to their Anorthite = Grossular + Kyanite + Quartz orthopyroxene geobarometer (Newton and Perkins 1982), 3 CaAlzSi20 s = Ca3A12SizO12+ 2 A12SiOs + SiO2 (9) which was ascribed to imprecise thermodynamic data. This paper presents calculations of new calibrations for (Koziol and Newton 1988) and clinopyroxene-garnet-plagioclase-quartz geobarometers in Wollastonite + Anorthite = Grossular + Quartz the system CaO-A1203-FeO-MgO-SiO2, based on thermodynamic data derived from a number of sources and 2 CaSiO 3 + CaAI2Si208 = Ca3A12Si3012 + SiO2 (10) constrained by a variety of experimental equilibria. The pre- cision and accuracy of these calibrations are tested by com- (Newton 1966; Hays 1967; Boettcher 1970; Huckenholz et al. 1975) paring pressures obtained for Reactions 1 and 2 against combined with heat capacity functions and volume data serve to constrain the 1 bar Gibbs free energy (A G~gs) of fayalite, ferrosilite, the equilibrium kyanite, grossular, almandine and anorthite. The latter data were compiled by Anovitz and Essene (1987a; Table 1) from a number Ferrosilite + Anorthite = Almandine + Grossular + Quartz of sources and comprise part of an internally consistent thermody- namic data set for selected phases in the system CaO-FeO 6 FeSiO3 + 3 CaAlaSi20 s =2 Fe3A12Si3012 -A1203 -SiO2(-TiO2) (Table 1 and 2). Thermodynamic data for + Ca3A12Si3012 + 3 SiO2 (3) diopside (Tables 1 and 2) have been compiled and evaluated by Sharp et al. (1986) from various sources and experiments in the (the "Ferrosilite (FS) barometer"), and the location of the system CaO-MgO-SiO2-CO2. The reader is referred to these polymorphic transition sources for a detailed discussion of the methods used in deriving the respective data. Thermodynamic data for enstatite are taken Sillimanite = Kyanite (4) from Robinson et al. (1982), and derivation of thermodynamic data for pyrope and hedenbergite is described below. (Richardson et al. 1968; Holdaway 1971; Robie and Hem- There has been considerable discussion concerning the pres- ingway 1984). Reaction 3 is derived by addition of the ex- ence of AI-Si disorder in synthetic anorthite produced in phase perimentally reversed reactions equilibrium experiments such as Reaction 9, and the necessity of adding a eonfigurational entropy term to $29s of anorthite in order Fayalite + Quartz = 2 Ferrosilite to fit the experimental reversals (e.g., Gasparik 1984a; Wood and Holloway 1984; Koziol and Newton 1988). Anovitz and Essene Fe2SiO~ + SiO 2 = FeSiO3 (5) (1987a) also address this problem, concluding that use of different values for S~98 of grossular, and lack of application of thermal (Bohlen et al. 1980) and expansion and compressibility in phase equilibrium calculations may require an So term of anorthite in order to fit the reversals. Fayalite + Anorthite = Almandine + Grossular However, the thermodynamic data set derived by Anovitz and Es- 3 Fe2SiO 4 + 3 CaAlzSi20 8 sene (1987a: Tables 1 and 2 of this study) uses an alternative $298 for grossular and includes the effects of expansivity and compressi- = (2 Fe3A12Si3012 + Ca3AlzSi3012)ss (6) bility of solids, providing an adequate fit to the reversals for Reac- tion 9 and other equilibria. Following their conclusion we do not (where SS is a 2/3 almandine + 1/3 grossular solid solution believe a configurational entropy term is warranted for anorthite. produced in the experiments, Bohlen et al. 1983 a), and has The loci of relevant equilibria were calculated with a computer program (EQUILI, Wall and Essene unpubl) that solves the rela- proven to be an extremely useful geobarometer for granu- tion lites. Calculations of Reaction 3 as a geobarometer have P2 T2 been presented by Bohlen et al. (1983a), Perkins and Chi- P2 Pl -- pera (1985), and Anovitz and Essene (1987a) that differ in AGr2-AGrl- ~ AVdP- ~ ASdT P1 TI the choice of thermodynamic data and garnet mixing model used to calculate the position of the end member reaction with an experimental reversal or a known Gibbs free energy of (Reaction 3). For these purposes we have used the garnet reaction as the starting point for the calculation. Using EQUILI, reactions are then calculated at 1 bar, 298 K in order to obtain mixing model of Ganguly and Saxena (1984) with Ca- Fe the Gibbs free energy (A G~9s) of each reaction. Algebraic combina- mixing parameters derived by Anovitz and Essene (1987a). tion of the reactions allows calculation of the AG~gs of each