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We present a structural update to the thermodynamic model for calculating peridotite phase relations and melt compositions at 0·01 to 60 kbar and from 600 °C to the peridotite liquidus in the system K₂O–Na₂O–CaO–FeO–MgO–Al₂O₃–SiO₂–TiO₂–Fe₂O₃–Cr₂O₃ (KNCFMASTOCr), based on the model of [Melting of Peridotites through to Granites: A Simple Thermodynamic Model in the System KNCFMASHTOCr. Journal of Petrology 59, 881–900]. The new model is better able to predict the phase relations and melting of ultramafic rocks, in particular the abundance of orthopyroxene in the residue and the concentration of silica in the melt. In addition, improvements in modelling Cr-spinels mean that the model is now able to reproduce Cr-content of garnet and spinel above and below the solidus without modification to the knorringite free energy. Model calculations indicate that, for peridotite composition …