Thermodynamic properties in a multicomponent solid solution involving cation disorder; Fe ₃ O ₄ -MgFe ₂ O₄ -FeAl ₂ O₄ -MgAl ₂ O₄ spinels

The spinel quaternary Fe₃O₄-FeAl₂O₄-MgFe₂O₄-MgAl₂O₄ is petrologically important but difficult to deal with thermodynamically because of complex order-disorder relations. We have used our recent measurements of Fe²⁺ and Fe³⁺ site occupancies together with measured activity-composition relations, interphase cation distributions, and solvi to develop an internally consistent thermodynamic model for this system. The model is based on a second-degree Taylor series expansion of the vibrational part of the Gibbs free energy in terms of order and compositional parameters. It can readily be related to the familiar Margules parameters, $WGij$ and reciprocal interactions commonly used to represent activities in multisite solid solutions.

With appropriate simplifications, the model reduces to the Navrotsky-Kleppa (-RT ln K_D is constant) or O’Neill-Navrotsky (-RTln K_D is a function of order parameters) models of octahedral-tetrahedral disorder. Although neither of these simpler models provides a complete description of cation distributions in the quaternary, the O'Neill-Navrotsky formalism works well over wide ranges of composition.