A model for the mixing properties of quaternary Ca-Mg-Fe-Mn garnets is developed by mathematical programming analysis of reversed phase-equilibrium data as well as calo-rimetric and volumetric data. The positions of end-member equilibria are established by using the thermodynamic data of Berman (1988) with minor revisions. Recent phase-equilibrium and calorimetric data strongly suggest excess entropy [5.08 J/(mol K)] on the grossular-almandine join, but considerably smaller excess enthalpy than implied by the data of Cressey et al. (1978).
Near-ideal mixing is deduced for the pyrope-almandine join from an analysis of three sets of orthopyroxene-gamet Fe-Mg exchange experiments. The derived mixing properties of Fe-Mg garnets are tested by calibrating annite properties from Ferry and Spear’s (1978) experimental data on the gamet-biotite exchange equilibrium. These annite data lead to reasonable results for pressures computed from the equilibrium muscovite + almandine = annite + aluminosilicate + quartz, in contrast to results obtained with annite properties derived by using larger nonideal Fe-Mg mixing in garnet. Applications of this formulation of the gamet-biotite geothermometer yield most reasonable results when WMnMg = 0.
Excellent support for the derived mixing properties of garnet is demonstrated by (1) convergence of different equilibria involving various garnet components in a single P-T region for a two-pyroxene granulite, (2) calculating pressures with the equilibrium 3 anorthite = grossular + 2 aluminosilicate + quartz that place the observed aluminosilicate polymorph in natural assemblages within its computed stability field, and (3) computing pressures as above and gamet-biotite temperatures that place rocks with more than one aluminosilicate phase in proximity to the appropriate aluminosilicate phase boundary.