A new generalised petrological mixing model

Abstract

A generalised petrological mixing model is described, which can estimate the proportions required to minimise the sum of squares of the differences between the bulk compositions of the reactants and the products in a reaction of the type biotite+sillimanite+quartz =garnet+K-feldspar+water therby providing a good indication of whether the reaction is isochemical or not. This model supercedes the existing simple mixing models, which have previously been applied to such problems, as it is mathematically more rigorous and provides the simple mixing model as a special case. A numerical example is given using the above reaction with data from N. Italy, which indicate that the reaction is far from isochemical. The addition of magnetite to the reactants, however, considerably improves the fit.