Silicate solid solutions and geothermometry

Principal component analysis, using eigenvalues and eigenvectors, of the encountered variation in the chemistry of 153 garnets indicates the following: (1) In low grade metamorphic rocks, spessertite and almandine are distinctly isomorphous. The variability of pyrope content does not influence the binary Fe-Mn relationship. However there may be some influence of the grossularite content. (2) In high grade metamorphic rocks, pyrope and almandine are distinctly isomorphous. Variability of grossularite content does not affect the binary Mg-Fe relationship. However, variability in spessertite content may influence the linearity particularly when there is little pyrope.Similar statistical analysis of the chemical data on 119 samples of clinopyroxenes indicates that only significant changes in the concentrations of Al in octahedral and/or of Al in tetrahedral sites and Ti could cause some change in the FeMg ratio in the mineral.Principal component analysis of the data on coexisting garnet and clinopyroxene could be used to classify rocks into their petrogenetic types.Distribution coefficient calculated by assuming ideal binary solution of Mg and Fe members in pyroxene and garnet is useful to indicate the P-T of the formation of the rocks.