MgAl2O4-Al8/3O4 spinels: Formulation and calibration of the low-pressure thermodynamics of mixing

Abstract

A thermodynamic model for the mixing properties of MgAl2O4–Al8/3O4 spinels is formulated, calibrated, and used to develop a closed-form polynomial for the excess Gibbs energy of mixing. The model is formulated on the assumptions that Mg, Al and vacancies exhibit long-range-ordering (LRO) between tetrahedral and octahedral sites, and that the vibrational Gibbs energy may be described by a Taylor expansion of second degree in the composition variable X ≡ 3 2 (2XAlOCT + XAlTET − 2) = (3XVacTET + 6XVacOCT) and in LRO variables s1 ≡ XAlOCT − 1 2 XAlTET and s2 ≡ 3XVacTET − 6XVacOCT. Calibration of the parameters produces a model that, in addition to being consistent with spectroscopic constraints on Mg-Al ordering in MgAl2O4-rich spinels, successfully reproduces the brackets on the compositions of MgAl2O4–Al8/3O4 spinels coexisting with corundum over the temperature range 1400 to 2200 K, employing only a few mixing parameters and making physically plausible predictions, such as random distribution of vacancies and Al between octahedral and tetrahedral sites in the metastable, cubic γ-Al8/3O4 endmember. The resulting activity–composition relations for MgAl2O4–Al8/3O4 spinels are extremely simple and show minimal (Al8/3O4) to negligible (MgAl2O4) temperature dependence.