Kinetics of Fe2+–Mg order–disorder in orthopyroxene: experimental studies and applications to cooling rates of rocks

We determined the forward rate constant (K+) for the Fe2+-Mg order-disorder between the M2 and M1 sites of orthopyroxene (OPx), which is described by the homogeneous reaction Fe2+ (M2) + Mg(M1) (symbol omitted) Mg(M2) + Fe2+ (M1), by both ordering and disordering experiments at isothermal condition and also by continuous cooling experiments. The rate constant was determined as a function of temperature in the range of 550-750 degrees C, oxygen fugacity between quartz-fayalite-iron and Ni-NiO buffers, and at compositions of 16 and 50 mol% ferrosilite component. The K+ value derived from disordering experiment was found to be larger than that derived from ordering experiment at 550 degrees C, while at T>580 degrees C, these two values are essentially the same. The fO2 dependence of the rate constant can be described by the relation K+ value (fO2) n with n=5.5-6.5, which is compatible with the theoretically expected relation. The Arrhenius relation at the WI buffer condition is given by (formula omitted) where C o represents the total number of M2 + M1 sites occupied by Fe2+ and Mg per unit volume of the crystal. The above relation can be used to calculate the cooling rates of natural OPx crystals around the closure temperature (T c) of Fe-Mg ordering, which are usually below 300 degrees C for slowly cooled rocks. We determined the Fe-Mg ordering states of several OPx crystals (~Fs50) from the Central Gneissic Complex (Khtada Lake), British Columbia, which yields T c ~290 degrees C. Numerical simulation of the change of Fe2+-Mg ordering in OPx as a function of temperature using the above expression of rate constant and a non-linear cooling model yields quenched values of ordering states that are in agreement with the observed values for cooling rates of 11-17 degrees C/Myr below 300 degrees C. The inferred cooling rate is in agreement with the available geochronological constraints. [PUBLICATION ABSTRACT]