A STATISTICAL-MODEL OF THERMODYNAMIC MIXING PROPERTIES OF CA-MG-FE2+ GARNETS

At present the most widely used models of thermodynamic mixing propert ies of garnet are those that are optimized to fit the experimental pha se-equilibrium data along various binary garnet joins using the method of mathematical programming. We conducted a thorough weighted regress ion analysis of the available volumetric, calorimetric, and phase equi librium data. This resulted in a much improved set of a-X relationship s with the following Margules parameters (in joules, kelvins, bars). W -FeMg(G) = -24166 + 22.09T - 0.034P, WGMgFe = 22265 = 12.40T + 0.050P, W-FeCa(G) = 17526 = 14.51T + 0.135P, W-CaFe(G) = -18113 + 15.51T + 0. 040P, W-MgCa(G) = 14306 - 2.49T + 0.140P, W-CaMg(G) = 65182 - 20.82T 0.068P (all pfu containing 12 O atoms). The robust regression analyse s allowed us to obtain the uncertainties associated with each of the p arameters, quantities not available by mathematical programming analys is of phase-equilibrium data. Uncertainty estimates are essential for rigorous quantification of errors associated with mineralogic thermoba rometers. From the probabilistic model developed here, we present deta iled formulations for ascertaining errors of activity coefficients of the end-member components in any garnet solid solution. This provides an opportunity to evaluate the uncertainties in mineralogic thermobaro meters involving garnets of compositions dissimilar to those used in t he experiments on which the garnet mixing models are based. The result s of this study elicit several significant points. The analysis strong ly suggests that there is an excess entropy of mixing along the Fe-Mg join because Fe-Mg mixing in garnet is substantially nonideal. The exc ess entropy of mixing along the Ca-Mg and Ca-Fe joins is asymmetric an d therefore assumption of a large symmetric entropy parameter or no en tropy along these joins is an oversimplification. Large uncertainty in the mixing properties exists for Ca-rich garnets. There should be a C a-Mg-Fe ternary interaction parameter (7110 J/mol).