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) ↔ 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°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°C, while at T >580°C, these two values are essentially the same. The fO₂ dependence of the rate constant can be described by the relation K⁺ α (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 ln (C_oK⁺) = -41511 - 12600X_Fe/T(K) + 28:26 + 5:27 X_Fe, min^-1 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°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°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°C/Myr below 300°C. The inferred cooling rate is in agreement with the available geochronological constraints.