MODELLING AMPHIBOLE THERMODYNAMICS
The model incorporates three key methodological advances. Firstly, we consider the possibility of asymmetric nonideal mixing in multicomponent systems by using the recently reformulated van Laar model. This permits the complete description of mixing between the seven amphibole endmembers in terms of 21 interaction energies and 7 asymmetry parameters. Secondly it utilises a robust nonlinear regression approach (least median of squares) for fitting noisy data typical of natural assemblages, minimising the damaging effect of outliers on regression results. Thirdly the model incorporates dependent endmember constraints for several of the interaction parameters by considering the equivalence between alternative sets of amphibole end-members (e.g. the magnesian system described above, and the corresponding ferrous system). This provides valuable constraints for several of the interaction energies which are otherwise poorly determined by the regression.
The calibration of the model is based on two large naturalassemblage datasets collected from the literature involving two different mineral assemblages. The first dataset consists of 73 pairs of coexisting amphiboles (actinolitehornblende, winchitehornblende, and barroisiteglaucophane) equilibrated over the range 250580ºC, 218 kbar. The second consists of 270 garnetamphiboleplagioclasequartz assemblages equilibrated over the range 400900ºC, 317 kbar. Simultaneously regressing two different datasets increases the quality of control available in comparison with calibrations based on a single assemblage.