MODELLING AMPHIBOLE THERMODYNAMICS

Quantitative mineral equilibria modelling in metabasic rocks has long been intractable because the activity–composition (a–X) relationships in amphiboles are poorly understood. We present a powerful new a–X model for clinoamphiboles in the system Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2–H2O–O2 in terms of the independent set of end–members tremolite, tschermakite, pargasite, glaucophane, ferro–actinolite, K–pargasite and ferri–tschermakite. The model is calibrated by regressing natural assemblage data from well characterised rocks.

The model incorporates three key methodological advances. Firstly, we consider the possibility of asymmetric non–ideal mixing in multicomponent systems by using the recently reformulated van Laar model. This permits the complete description of mixing between the seven amphibole end–members in terms of 21 interaction energies and 7 asymmetry parameters. Secondly it utilises a robust non–linear 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 end–member 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 natural–assemblage datasets collected from the literature involving two different mineral assemblages. The first dataset consists of 73 pairs of coexisting amphiboles (actinolite–hornblende, winchite–hornblende, and barroisite–glaucophane) equilibrated over the range 250–580ºC, 2–18 kbar. The second consists of 270 garnet–amphibole–plagioclase–quartz assemblages equilibrated over the range 400–900ºC, 3–17 kbar. Simultaneously regressing two different datasets increases the quality of control available in comparison with calibrations based on a single assemblage.