Thermodynamic modelling of sodic pyroxene solid-solution and its application in a garnet-omphacite-kyanite-coesite geothermobarometer for UHP metamorphic rocks

A garnet-omphacite-kyanite-coesite geothermobarometer is constructed to estimate the peak metamorphic pressure of ultrahigh-pressure (UHP) eclogites. For this we use a quaternary regular solution model for garnet, and propose a new model for sodic pyroxene that assumes double site solid-solution (Na,Ca)^M2(Al,Fe³⁺,Fe²⁺,Mg)^M1Si₂O₆, where cations in the M2- and the M1-sites mix randomly but with intersite interactions, not only between nearest neighboring cations but also bewteen next nearest neighboring cations. In the new model, overall excess interaction parameters are quantitatively deduced from the previous experimental data and critical temperature, and the activity of the jadeite component agrees reasonbly with that based on the Landau theory. Furthermore, the relations of the calculated order parameter to temperature and composition are consistent with other experimental works. These facts support the usefulness of the new model. Application of our geothermobarometer to kyanite eclogite gave metamorphic conditions around 3.4 GPa and 800°C for both samples from the Dora Maira Massif, Western Alps, and from Rongcheng County, in the Su-Lu region of Eastern China.