Experimental and theoretical study of (Fe2+, Mg)(Al,Fe3+)2O4 spinels: Activity-composition relationships,miscibility gaps,vacancy contents

The compositions of (Fe²⁺, Mg)(Al, Fe³⁺)₂O₄ spinels equilibrated with a l M (Fe²⁺, Mg)Cl₂ aqueous solution at 800°C, 4 kbars were determined. General considerations of reciprocal systems allow derivation of the exchange isotherm between a chloride aqueous solution and (Mg, Fe²⁺)Al₂O₄ spinels. They enable calculation of ΔG of the reaction: FeCl₂ + MgAl₂O₄ = MgCl₂ + FeAl₂O₄ΔG = 2.9 kcal at 800°C, 4 kbars and provide the activity-composition relationships for the binary join FeAl₂O₄-MgAl₂O₄, which shows a substantial positive deviation from ideality. Some tie-lines between coexisting aluminous and ferric spinels were also obtained in the (Fe²⁺, Mg)(Al, Fe³⁺)₂O₄ system.These experimental data are modeled by a Gibbs free energy formulation of the spinel solid solution (Lehmann and Roux, 1984), where the corrective function g₂, necessary to reproduce the deviations from ideality, is artificially split into two parts:

• 1.(1) A homogeneous second degree polynomial in the composition variables, containing only the terms specific to the reciprocal nature of the system, whose coefficients are deduced from ΔG of the exchange reaction: MgAl₂O₄ + FeFe₂O₄ = MgFe₂O₄ + FeAl₂O₄ΔG = 4.5 kcal at 800°C, 4 kbars
• 2.(2) A homogeneous second degree polynomial in the site occupancy fractions, to model the non-ideal behavior of the (Fe²⁺, Mg)Al₂O₄ and (Fe₂₊, Mg)Fe₂O₄ spinels and the miscibility gap along the Fe(Al, Fe³⁺)₂O₄ join.

A model of reciprocal spinel solution involving defect end-members is used to estimate the vacancy contents of the spinels in equilibrium with sesquioxides. In this case, the corrective function necessary to take into account the reciprocal nature of the system is no longer a second degree polynomial, but a rational fraction.