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Contributions to Mineralogy and Petrology

, Volume 111, Issue 1, pp 87–93 | Cite as

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

  • A. Bhattacharya
  • L. Mohanty
  • A. Maji
  • S. K. Sen
  • M. Raith
Article

Abstract

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.

Keywords

Entropy Enthalpy Fractionation Entropy Change Regular Solution 
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. Bhattacharya A, Krishnakumar K, Raith M, Sen SK (1991) An improved set of a-X parameters for pyrope-almandine binary and refinement of orthopyroxene-garnet thermometer and orthopyroxene-garnet-plagioclase-quartz barometer. J Petrol 32:629–656Google Scholar
  2. Davies OL, Goldsmith PL (1986) Statistical methods in research and production. Longman, LondonGoogle Scholar
  3. Davis JC (1986) Statistics and data analysis in Geology. John Wiley and Sons, New YorkGoogle Scholar
  4. Dymek RF (1983) Titanium, aluminium, and interlayer cation substitutions in biotite from high grade gneiss, west Greenland. Am Mineral 68:880–889Google 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. Ganguly J, Saxena SK (1984) Mixing properties of aluminosilicate garnets: constraints from natural and experimental data, and application to geothermo-barometry. Am Mineral 69:88–97Google Scholar
  7. 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
  8. Hackler RT, Wood BJ (1989) Experimental determination of Fe and Mg exchange between garnet and olivine and estimation of Fe−Mg garnet mixing properties. Am Mineral 74:994–999Google Scholar
  9. Indares A, Martignole J (1985) Biotite-garnet geothermometry in the granulite facies: the influence of Al and Ti in biotite. Am Mineral 70:272–278Google Scholar
  10. Kawasaki T, Matsui Y (1983) Thermodynamic analyses of equilibria involving olivine, orthopyroxene and garnet. Geochim Cosmochim Acta 47:1661–1679Google Scholar
  11. Korzhinskii DS (1959) Physico-chemical basis of the analysis of the paragensis of minerals. Trans Consultants Bureau, New YorkGoogle Scholar
  12. Lee SM, 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
  13. 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, pp. 129–145Google Scholar
  14. Newton RC, Charlu TV, Kleppa OJ (1980) Thermochemistry of the high state plagioclases. Geochim Cosmochim Acta 44:933–941Google Scholar
  15. 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, New York, pp 199–239Google Scholar
  16. Pownceby MI, Wall VJ, O'Neill ASC (1987) Fe−Mn partitioning between garnet and ilmenite: experimental calibration and applications. Contrib Mineral Petrol 97:116–126Google Scholar
  17. Sengupta, P, DasGupta S, Bhattacharya PK, Hariya Y (1989) Mixing behaviour in quaternary garnet solid solution and an extended Ellis and Green garnet-clinopyroxene geothermometer. Contrib Mineral Petrol 103:223–227Google Scholar
  18. Thompson AB (1976) Mineral reactions in pelitic rocks. I. Prediction of P-T-X(Fe−Mg) phase relations. II. Calculations of some P-T-X(Fe−Mg) phase relations. Am J Sci 276:401–454Google Scholar
  19. Wohl, K (1953) Thermodynamic evaluation of binary and ternary liquid systems. Chem Eng Prog 49:218–219Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. Bhattacharya
    • 1
  • L. Mohanty
    • 1
  • A. Maji
    • 1
  • S. K. Sen
    • 2
  • M. Raith
    • 3
  1. 1.Department of Geology and GeophysicsIndian Institute of TechnologyKharagpurIndia
  2. 2.Department of Geological SciencesJadavpur UniversityCalcuttaIndia
  3. 3.Mineralogisch-Petrologisches Institutder Universität BonnBonn 1Germany

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