Contributions to Mineralogy and Petrology

, Volume 103, Issue 4, pp 423–433 | Cite as

Grossular activity-composition relationships in ternary garnets determined by reversed displaced-equilibrium experiments

  • Andrea M. Koziol
  • Robert C. Newton
Article

Abstract

Activity-composition relationships of Ca3Al2Si3O12 (grs) in ternary Ca-Mg-Fe garnets of various compositions have been determined by reversed displaced equilibrium experiments at 1000° C and 900° C and pressures of 8 to 17 kbar. The mixing of grs in garnet is nearly ideal at 30 mol% grs, with positive deviations from ideality at lower grs contents. Models of garnet mixing currently in the literature do not predict this trend. Analysis of the present reversals, in conjunction with a garnet mixing model based solely on calorimetry measurements on the binary joins, indicates that a ternary interaction constant for a ternary asymmetric Margules model (Wohl 1953) cannot be constrained. Apparently, some aspects of the garnet binary joins are still not well-known. An alternative asymmetric empirical model, based on analysis of pseudobinary joins of constant Mg/Mg + Fe(Mg #), reproduces the data well and is able to predict grs activity coefficients for garnets with grs contents between 3 and 40 mol% and Mg numbers between 0 and 0.60. The grossular activity coefficient,γgrs, is given by:
$$RT\ln \gamma _{grs} = (1 - X_{grs} )^2 [W_{Ca} + 2X_{grs} (W_{FM} - W_{Ca} )]$$
where:
$$\begin{gathered} W_{Ca} (J) = - 2060 + 3.57 \times 10^4 (Mg\# ) - 4.95 \times 10^4 (Mg\# )^2 \hfill \\ W_{FM} (J) = 3390 - 3.71 \times 10^4 (Mg\# ) + 6.49 \times 10^4 (Mg\# )^2 \hfill \\ \end{gathered} $$
These expressions are valid only over the composition range investigated. The formulation cannot be used to extract Fe and Mg activity coefficients. There appears to be no temperature or pressure dependence of theW-parameters over theP-T range investigated. The improved definition of the grossular activity coefficient which results from the present work contributes to an improved formulation of the garnet-Al2SiO5-quartz-plagioclase (GASP) geobarometer and other phase equilibria relevant to metamorphic petrology.

Keywords

Calorimetry Phase Equilibrium Empirical Model Activity Coefficient Composition Range 
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. Acree WE Jr (1984) Thermodynamic properties of non-electrolyte solutions. Academic Press, OrlandoGoogle Scholar
  2. Anovitz LM, Essene EJ (1987) Compatibility of geobarometers in the system CaO-FeO-Al2O3-SiO2-TiO2(CFAST): implications for garnet mixing models. J Geol 95:633–645Google Scholar
  3. Aranovich LY, Podlesskii KK (1980) Garnet-plagioclase barometer. Dokl Akad nauk SSSR 251:1216–1219Google Scholar
  4. Berman RG (1988) Internally-consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2. J Petrol 29:445–522Google Scholar
  5. Berman RG, Brown TH (1988) A general method for thermobarometric calculations, with a revised garnet solution model and geologic applications. Geol Soc Am Abstr Progr 20:A98Google Scholar
  6. Bohlen SR, Wall VJ, Boettcher AL (1983) Experimental investigation and application of garnet granulite equilibria. Contrib Mineral Petrol 83:52–61Google Scholar
  7. Clark SP Jr (1959) Effect of pressure on the melting points of eight alkali halides. J Chem Phys 31:1526–1531Google Scholar
  8. Cressey G (1981) Entropies and enthalpies of aluminosilicate garnets. Contrib Mineral Petrol 76:413–419Google Scholar
  9. Cressey G, Schmid R, Wood BJ (1978) Thermodynamic properties of almandine-grossular garnet solid solutions. Contrib Mineral Petrol 67:397–404Google Scholar
  10. Dahl PS (1980) The thermal-compositional dependence of Fe2+-Mg distributions between coexisting garnet and pyroxene: applications to geothermometry. Am Mineral 65:854–866Google Scholar
  11. Ellis DJ, Green DH (1979) An experimental study of the effect of Ca upon garnet-clinopyroxene Fe-Mg exchange equilibria. Contrib Mineral Petrol 71:13–22Google Scholar
  12. 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
  13. Ganguly J (1979) Garnet and clinopyroxene solid solutions, and geothermometry based on Fe-Mg distribution coefficient. Geochim Cosmochim Acta 43:1021–1029Google Scholar
  14. Ganguly J, Kennedy GC (1974) The energetics of natural garnet solid solution. I. Mixing of the aluminosilicate end-members. Contrib Mineral Petrol 48:137–148Google Scholar
  15. Ganguly J, Saxena SK (1984) Mixing properties of aluminosilicate garnets: constraints from natural and experimental data, and applications to geothermo-barometry. Am Mineral 69:88–97Google Scholar
  16. Ganguly J, Saxena SK (1987) Mixtures and mineral reactions. Springer, Berlin Heidelberg New York Tokyo, pp 14–36Google Scholar
  17. Gasparik T (1984) Experimentally determined stability of clinopyroxene + garnet + corundum in the system CaO-MgO-Al2O3-SiO2. Am Mineral 69:1025–1035Google Scholar
  18. Geiger CA (1986) Thermodynamic mixing properties of almandine garnet solid solutions. Unpub PhD thesis, University of ChicagoGoogle Scholar
  19. Geiger CA, Newton RC, Kleppa OJ (1987) Enthalpy of mixing of synthetic almandine-grossular and almandine-pyrope garnets from high-temperature solution calorimetry. Geochim Cosmochim Acta 51:1755–1763Google Scholar
  20. Gokcen NA (1986) Statistical thermodynamics of alloys. Plenum Press, New YorkGoogle Scholar
  21. Harley S (1984) An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene. Contrib Mineral Petrol 86:359–373Google Scholar
  22. Haselton HT, Newton RC (1980) Thermodynamics of pyrope-grossular garnets and their stabilities at high temperatures and high pressures. J Geophys Res 85:6973–6982Google Scholar
  23. Haselton HT Jr, Westrum EF Jr (1980) Low-temperature heat capacities of synthetic pyrope, grossular, and pyrope60grossular40. Geochim Cosmochim Acta 44:701–709Google Scholar
  24. Hensen BJ, Schmid R, Wood BJ (1975) Activity-composition relationships for pyrope-grossular garnet. Contrib Mineral Petrol 51:161–166Google Scholar
  25. Hodges KV, Spear FS (1982) Geothermometry, geobarometry and the Al2SiO5 triple point at Mt. Moosilauke, New Hampshire. Am Mineral 67:1118–1134Google Scholar
  26. Hoinkes G (1986) Effect of grossular content in garnet on the partitioning of Fe and Mg between garnet and biotite: an empirical investigation on staurolite-zone samples from the Austroalpine Schneeburg complex. Contrib Mineral Petrol 92:393–399Google Scholar
  27. Holdaway MJ (1971) Stability of andalusite and the aluminum silicate phase diagram. Amer J Sci 272:97–131Google Scholar
  28. Holland TJB, Powell R (1985) An internally consistent thermodynamic dataset with uncertainties and correlations: 2. Data and results. J Meta Petrol 3:343–353Google Scholar
  29. Johannes W, Bell PM, Mao HK, Boettcher AL, Chipman DW, Hays JF, Newton RC, Seifert F (1971) An interlaboratory comparison of piston-cylinder pressure calibration using the albitebreakdown reaction. Contrib Mineral Petrol 32:24–38Google Scholar
  30. King MB (1969) Phase equilibrium in mixtures. Pergamon, OxfordGoogle Scholar
  31. Koziol AM, Newton RC (1987) Experimental determination of spessartine-grossular solid solution relations (abs). EOS 68:460Google Scholar
  32. Koziol AM, Newton RC (1988a) Redetermination of the anorthite breakdown reaction and improvement of the plagioclase-garnet-Al2SiO3-quartz barometer. Am Mineral 73:216–223Google Scholar
  33. Koziol AM, Newton RC (1988b) Experimental determination of almandine-grossular and (Ca, Fe, Mg) ternary garnet solid solution relations (abs). EOS 69:498Google Scholar
  34. Lee HY, Ganguly J (1988) Equilibrium compositions of coexisting garnet and orthopyroxene: experimental determinations in the system FeO-MgO-Al2O3-SiO2, and applications. J Petrol 29:93–113Google Scholar
  35. Mirwald PW, Getting IC, Kennedy GC (1975) Low-friction cell for piston-cylinder high-pressure apparatus. J Geophys Res 80:1519–1525Google Scholar
  36. 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, Berlin Heidelberg New York, pp 131–147Google Scholar
  37. Newton RC, Perkins D III (1982) Thermodynamic calibration of geobarometers based on the assemblages garnet-plagioclase-orthopyroxene (clinopyroxene)-quartz. Am Mineral 67:203–222Google Scholar
  38. Newton RC, Wood BJ (1980) Volume behavior of silicate solid solutions. Am Mineral 65:733–745Google Scholar
  39. Newton RC, Charlu TV, Kleppa OJ (1977) Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2. Geochim Cosmochim Acta 41:369–377Google Scholar
  40. Newton RC, Geiger CA, Kleppa OJ, Brousse C (1986) Thermochemistry of binary and ternary garnet solid solutions. Int Mineral Assoc Abstr Progr: 186Google Scholar
  41. O'Neill H St C, Wood BJ (1979) An experimental study of Fe-Mg partitioning between garnet and olivine and its calibration as a geothermometer. Contrib Mineral Petrol 70:59–70Google Scholar
  42. Pattison DRM, Newton RC (1989) Reversed experimental calibration of the garnet-clinopyroxene Fe-Mg exchange thermometer. Contrib Mineral Petrol 101:87–103Google Scholar
  43. Perchuk LL, Lavrent'eva IV (1983) Experimental investigation of exchange equilibria in the system cordierite-garnet-biotite. In: Saxena SK (ed) Kinetics and equilibrium in mineral reactions. Springer, Berlin Heidelberg New York, pp 199–239Google Scholar
  44. Perkins D III, Chipera SJ (1985) Garnet-orthopyroxene-plagioclase-quartz barometry: refinement and application to the English River subprovince and the Minnesota River valley. Contrib Mineral Petrol 89:69–80Google Scholar
  45. Perkins D III, Holland TJB, Newton RC (1981) The Al2O3 contents of enstatite in equilibrium with garnet in the system MgO-Al2O3-SiO2 at 15–40 kbar and 900° C–1600° C. Contrib Mineral Petrol 78:99–109Google Scholar
  46. Pownceby MI, Wall VI, O'Neill H St C (1987) Fe-Mn partitioning between garnet and ilmenite: experimental calibration and applications. Contrib Mineral Petrol 97:116–126Google Scholar
  47. Prigogine I, Defay R (1954) Chemical Thermodynamics (DH Everett, trans). Langmans, LondonGoogle Scholar
  48. Råheim A, Green DH (1974) Experimental determination of the temperature and pressure dependence of the Fe-Mg partition coefficient for coexisting garnet and clinopyroxene. Contrib Mineral Petrol 48:179–203Google Scholar
  49. Redlich O, Kister AT (1948) Thermodynamics of non-electrolyte solutions. Algebraic representation of thermodynamic properties and the classification of solutions. Indus Engin Chem 40:345–348Google Scholar
  50. Schmid R, Cressey G, Wood BJ (1978) Experimental determination of univariant equilibria using divariant solid-solution assemblages. Am Mineral 63:511–515Google Scholar
  51. Skinner BJ (1956) Physical properties of end-members of the garnet group. Am Mineral 41:428–436Google Scholar
  52. Wohl K (1953) Thermodynamic evaluation of binary and ternary liquid systems. Chem Eng Prog 49:218–219Google Scholar
  53. Wood BJ (1988) Activity measurements and excess entropy-volume relationships for pyrope-grossular garnets. J Geol 96:721–729Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Andrea M. Koziol
    • 1
  • Robert C. Newton
    • 1
  1. 1.Department of the Geophysical SciencesUniversity of ChicagoChicagoUSA

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