Ordering kinetics in synthetic Mg(Al,Fe3+)2O4 spinels: quantitative elucidation of the whole Al-Mg-Fe partitioning, rate constants, activation energies

A novel procedure, based on the application of the kinetics simulator Gepasi, has been successfully applied for modeling the cation ordering process in two synthetic Mg(Al2-yFe3+y)O4 spinels (y~ 0.39 and 0.54, samples F39 and F54, respectively). The kinetic profiles suggested a two-stage mechanism, with rapid inter-site exchange of Fe3+ with Mg followed by slow exchange of Al with Mg. The trial to apply the classical approaches, based on the explicit solutions of the differential equations corresponding to single-cation (Sha-Chappel model) or two-cation (Müller model) exchange reactions, proved not feasible in the whole time range, thus implying a lack of information about the exchange processes involving the Fe3+ cation. Therefore an alternative methodology has been here adopted. In particular, a multistep pathway has been proposed and the mechanism has been simulated by Gepasi modeling. The suggested set of reactions and the simultaneous solving of the related rate laws allowed us not only to calculate the rate constants and the corresponding activation energies for the Al/Mg cationic interchange (257 and 264 kJ/mol for the F39 and F54 samples, respectively), but also to estimate for the first time in such kind of samples (three cations - two sites) the kinetic constants and the activation energies for the Fe/Mg cationic interchange (204 and 234 kJ/mol for low- and high-Fe3+ samples, respectively). The evaluation of the significant effect of the iron content, which actually inhibits the Mg-Al exchange between T and M site, provided new insights useful for the construction of geothermometers based upon iron-bearing spinels.