MgAl₂O₄–Al_8/3O₄ spinels: Formulation and calibration of the low-pressure thermodynamics of mixing

Abstract

A thermodynamic model for the mixing properties of MgAl₂O₄–Al_8/3O₄ 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 ≡ (2X_Al^OCT + X_Al^TET − 2) = (3X_Vac^TET + 6X_Vac^OCT) and in LRO variables s₁ ≡ X_Al^OCT − X_Al^TET and s₂ ≡ 3X_Vac^TET − 6X_Vac^OCT. 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–Al_8/3O₄ 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-Al_8/3O₄ endmember. The resulting activity–composition relations for MgAl₂O₄–Al_8/3O₄ spinels are extremely simple and show minimal (Al_8/3O₄) to negligible (MgAl₂O₄) temperature dependence.