The activities of components in clinopyroxene and garnet solid solutions and their application to rocks

Experimental studies of equilibria in chemically simple systems may be quantitatively extrapolated to rocks provided the activities of components in the appropriate complex phases are known. For each solid-solid equilibrium extrapolated in this way a curve of fixed Ki (equilibrium constant) for the rock may be defined in pressure-temperature space. Provided crystallization of the rock takes place under equilibrium conditions, use of two such solid-solid equilibria fixes the pressure and temperature uniquely. The relations between activities of components and mineral compositions have been determined for CaAl2SiO6-CaMgSi2O6-CaFeSi2O6 clinopyroxene and Ca3Al2Si3O12- Mg3Al2Si3O12-Fe3Al2Si3O12 garnet solid solutions. These activity-composition relations, combined with thermodynamic data on simple equilibria, were then applied to the granulites of South Harris. The equilibria used were: CaAl2Si2O8 ^ CaAl2SiO6 + SiO2, plagioclase clinopyroxene quartz CaFeSi2O6 + |Mg3Al2Si3O12 ^ clinopyroxene garnet JFe3Al2Si3O12 + CaMgSi2O6, garnet clinopyroxene 3CaAl2Si2O8 ^ Ca3Al2Si3O12 + plagioclase garnet 2Al2SiO5 + SiO2. kyanite quartz The intersection of Ki curves for appropriate mineral assemblages of the South Harris granulites yield estimated metamorphic conditions of 825 °C and 13 kbar. The calculated pressure is in excellent agreement with independent estimates (10- 13 kbar) based on the presence or absence of garnet in orthogneisses. It is concluded that, for many equilibria, the thermodynamic approach should yield pressure estimates which are accurate to within ± 1-2 kbar. Temperature uncertainties, being dependent on the slopes of Ki curves in pressure-temperature space, are related to these quoted pressure uncertainties.