Composition of coexisting ortho- and Ca-pyroxene or pigeonite may be used to estimate the temperature of crystallization at low to moderate pressures by solving the equation:
where R is gas constant, T temperature in °K to be estimated, XcpxMg−M1 the site of occupancy of Mg on the site Ml or М2 in clinopyroxene (Cpx), γ the М2 site activity coefficient and aMg-opx the activity of Mg in orthopyroxene. A non-ideal model for the М2 site in both the pyroxenes is used to obtain the activity composition relations. The site occupancy data in orthopyroxene are available in the literature. The site occupancy data in clinopyroxene are obtained by using compositional data on three coexisting pyroxenes by using the condition that in such coexisting pyroxenes the intracrystalline equilibrium constants are simply related. Using the activity-composition data, equation (16) may be solved graphically or by using a computer to match the two sides of the equation at various assumed temperatures. The temperature estimates must be based on an accurate compositional analysis of several samples. It is expected that further work on the solution parameters and determination of site occupancies as a function of temperature and composition will be actively pursued to improve temperature estimates. The proposed geothermometer is recommended as a relative temperature scale to test models of chemical equilibrium and differentiation in metamorphic and igneous rocks.