Garnet-clinopyroxene geothermometer

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({text{}}K) = frac{{8288 + 0.0276 P {text{(bar)}} + Q1 - Q2}}{{1.987 ln K_{text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{text{(}}X_{{text{Fe}}} - X_{{text{Mg}}} {text{)}} + 3,150{text{ }}X_{{text{Ca}}} + 2,600{text{ }}X_{{text{Mn}}} $$ (mole fractions in garnet) $$begin{gathered}Q2 = - 6,594[X_{{text{Fe}}} {text{(}}X_{{text{Fe}}} - 2X_{{text{Mg}}} {text{)]}} hfill {text{ }} - 12762{text{ [}}X_{{text{Fe}}} - X_{{text{Mg}}} (1 - X_{{text{Fe}}} {text{)]}} hfill {text{ }} - 11,281[X_{{text{Ca}}} (1 - X_{{text{Al}}} ) - 2X_{{text{Mg}}} 2X_{{text{Ca}}} ] hfill {text{ + 6137[}}X_{{text{Ca}}} (2X_{{text{Mg}}} + X_{{text{Al}}} )] hfill {text{ + 35,791[}}X_{{text{Al}}} (1 - 2X_{{text{Mg}}} )] hfill {text{ + 25,409[(}}X_{{text{Ca}}} )^2 ] - 55,137[X_{{text{Ca}}} (X_{{text{Mg}}} - X_{{text{Fe}}} )] hfill {text{ }} - 11,338[X_{{text{Al}}} (X_{{text{Fe}}} - X_{{text{Mg}}} )] hfill end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.