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Contributions to Mineralogy and Petrology

, Volume 104, Issue 2, pp 225–234 | Cite as

Empirical calibration of six geobarometers for the mineral assemblage quartz+muscovite+biotite+plagioclase+garnet

  • Thomas D. Hoisch
Article

Abstract

Six equilibria among quartz, plagioclase, biotite, muscovite, and garnet were empirically calibrated using mineral composition data from 43 samples having the assemblage quartz+muscovite+biotite+garnet+plagioclase+Al2SiO5 (sillimanite or kyanite). Pressures and temperatures in the data set used for calibration were determined through the simultaneous application of garnet-biotite geothermometry and garnet-quartz-plagioclase-Al2SiO5 geobarometry. Thermodynamic expressions for four of the six equilibria incorporate interaction parameters that model non-ideality in the mixing of cations in the octahedral sites of both muscovite and biotite. With pressure chosen as the dependent variable, multiple regression was used to solve for unknowns in the equilibrium thermodynamic expressions. The regressions yielded multiple correlation coefficients ranging from 0.983 to 0.999, with corresponding standard deviations of 338 and 92 bars in the residuals. The standard deviations in the residuals may be explained largely or entirely by the propagation of errors associated with electron microprobe analysis. These equilibria enable the determination of pressures from equilibrium assemblages of quartz+garnet+plagioclase+muscovite+biotite, and give results closely comparable to the experimentally calibrated garnet-quartz-plagioclase-Al2SiO5 geobarometer. Geobarometric applications should be restricted to rocks in which equilibrium constants and compositional variables fall within the same ranges as those used for calibration.

Keywords

Mineral Composition Mineral Assemblage Electron Microprobe Microprobe Analysis Compositional Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Anderson GM (1976) Error propagation by the Monte Carlo method in geochemical calculations. Geochim Cosmochim Acta 40:1533–1538Google Scholar
  2. Anderson GM (1977) Uncertainties in calculations involving thermodynamic data. In: Greenwood HJ (ed) Short course in application of thermodynamics to petrology and ore deposits. Mineral Assoc Canada, Toronto, pp 199–215Google Scholar
  3. Demarest HH Jr, Haselton HT Jr (1981) Error analysis for bracketed phase equilibrium data. Geochim Cosmochim Acta 45:217–224Google Scholar
  4. Devore JL (1982) Probability & Statistics for Engineering and the Sciences. Brooks/Cole, Monterey, p 640Google Scholar
  5. Ferry JM, Spear FS (1978) Experimental calibration of the partitioning of Fe and Mg between biotite and garnet. Contrib Mineral Petrol 66:113–117Google Scholar
  6. Fletcher CJN, Greenwood HJ (1979) Metamorphism and structure of the Penfold Creek area, near Quesnel Lake, British Columbia. J Petrol 20:743–794Google Scholar
  7. Ganguly J, Kennedy GC (1974) The energetics of natural garnet solid solution. Contrib Mineral Petrol 48:137–148Google Scholar
  8. Ghent ED, Stout MZ (1981) Geobarometry and geothermometry of plagioclase-biotite-garnet-muscovite assemblages. Contrib Mineral Petrol 76:92–97Google Scholar
  9. Graham CM, Powell R (1984) A garnet-biotite geothermometer: calibration, testing, and application to the Pelona Schist, southern California. J Meta Geol 2:13–21Google Scholar
  10. Hodges KV, Crowley PD (1985) Error estimation for empirical geothermometry for pelitic systems. Am Mineral 70:702–709Google Scholar
  11. Hodges KV, McKenna LW (1987) Realistic propagation of uncertainties in geologic thermobarometry. Am Mineral 72:671–680Google Scholar
  12. Hodges KV, Spear FS (1982) Geothermometry, geobarometry and the Al2SiO5 triple point at Mt Moosilauke, New Hampshire. Am Mineral 67:1118–1134Google Scholar
  13. Hoisch TD (1989) A muscovite-biotite geothermometer. Am Mineral 74:565–572Google Scholar
  14. Kohn MJ, Spear FS (1989) Empirical calibration of geobarometers for the assemblage garnet+hornblende+plagioclase+quartz. Am Mineral 74:77–84Google Scholar
  15. Koziol AM, Newton RC (1988) Redetermination of the anorthite breakdown reaction and improvement of the plagioclase-garnet-Al2SiO5-quartz geobarometer. Am Mineral 73:216–223Google Scholar
  16. McKenna LW, Hodges KV (1988) Accuracy versus precision in locating reaction boundaries: implications for the garnet-plagioclase-aluminum silicate-quartz geobarometer. Am Mineral 73:1205–1208Google Scholar
  17. Newton RC, Charlu TV, Kleppa OJ (1980) Thermochemistry of the high structural state plagioclases. Geochim Cosmochim Acta 44:933–941Google Scholar
  18. Newton RC, Haselton HT (1981) Thermodynamics of the garnet-plagioclase-Al2SiO5-quartz geobarometer. In: Newton RC, Navrotsky A, Wood BJ (eds) Thermodynamics of minerals and melts. Springer, New York Berlin Heidelberg, pp 131–147Google Scholar
  19. Pigage LC (1982) Linear regression analysis of sillimanite-forming reactions at Azure Lake, British Columbia. Can Mineral 20:405–421Google Scholar
  20. Pigage LC (1976) Metamorphism of the Settler Schist, southwest of Yale, British Columbia. Can J Earth Sci 13:405–421Google Scholar
  21. Price JG (1985) Ideal site mixing in solid solutions, with an application to two-feldspar geothermometry. Am Mineral 70:696–701Google Scholar
  22. Powell R (1978) Equilibrium thermodynamics in petrology. Harper and Row, New York, p 284Google Scholar
  23. Tracy RJ (1978) High grade metamorphic reactions and partial melting in pelitic schist, west central Massachussetts. Am J Sci 278:150–178Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Thomas D. Hoisch
    • 1
  1. 1.Department of GeologyNorthern Arizona UniversityFlagstaffUSA

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