Fe²⁺-Mg order-disorder in orthopyroxene: Equilibrium fractionation between the octahedral sites and thermodynamic analysis

The equilibrium intracrystalline distribution coefficient, k(D)(*), of Fe(*) (i.e. Fe²⁺ + Mn) and Mg between the M1 and M2 sites of three natural nearly binary Fe²⁺-Mg orthopyroxene crystals (Fs₁₄, Fs₁₅ and Fs₄₉) were determined by annealing experiments at several temperatures between 550 and 1000 °C and single crystal X-ray structure refinements. In addition, the X-ray data of an orthopyroxene crystal (Fs₂₃), which were collected earlier by Molin et al. (1991) between 700 and 1000 °C, were re-refined. The data were processed through two different refinement programs (SHELXL93 and RFINE90) using both unit and individual weights and also both ionic and atomic scattering factors. The calculated site occupancies were found to agree within their estimated standard errors. However, the use of ionic scattering factors led to significantly better goodness of fit and agreement index, and smaller standard deviations of the site occupancies than those obtained from the use of atomic scattering factors. Furthermore, the weighted refinements yielded significantly smaller standard deviations of the site occupancies than the unweighted refinements even when the same set of reflections was used in the two procedures. The site occupancy data from this study were combined with selected published data to develop expressions of k(D)(*) as a function of temperature and composition. Calculation of the excess configurational entropy, ΔS(XS), suggests that orthopyroxene should be treated as a two parameter symmetric solution instead of as a 'simple mixture'. The calculated ΔS(XS) values and the excess Gibbs free energy of mixing suggested by available cation exchange data lead to a slightly negative enthalpy of mixing in the orthopyroxene solid solution.