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


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:
$$RT\ln \gamma _{grs} = (1 - X_{grs} )^2 [W_{Ca} + 2X_{grs} (W_{FM} - W_{Ca} )]$$
$$\begin{gathered} W_{Ca} (J) = - 2060 + 3.57 \times 10^4 (Mg\# ) - 4.95 \times 10^4 (Mg\# )^2 \hfill \\ W_{FM} (J) = 3390 - 3.71 \times 10^4 (Mg\# ) + 6.49 \times 10^4 (Mg\# )^2 \hfill \\ \end{gathered} $$
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.


Calorimetry Phase Equilibrium Empirical Model Activity Coefficient Composition Range 
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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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