A phenomenological treatment of cation distribution in spinels: system (Ni_1-xAl_x)_t[Ni_xAl_2-x]_OO₄

Abstract

Presented in this paper is a phenomenological model for cation distribution between crystallographically non-equivalent sites of the spinel structure at high temperature. Interactions between ions on each site are characterized by enthalpy parameters. A regular solution model is assumed for mixing of the species on tetrahedral and octahedral sites, independent of the nature of bonding in the solid. The model provides an equation which is functionally similar to that proposed by O'Neill and Navrotsky /15/ based on electrostatic considerations. However, the phenomenological model gives a more realistic interpretation of the constants involved in the equation. Recent experimental data on temperature dependence of cation distribution in NiAl₂O₄ are used to test the validity of the different models. Since Ni²⁺ ion in tetrahedral coordination exhibits Jahn-Teller distortion, an entropy corresponding to randomization of the distortion in the cubic phase has been incorporated in the model. Inclusion of the Jahn-Teller entropy in the expression for the cation distribution appears to be as important as introduction of quadratic dependence of enthalpy of disordering (ΔH_D) on cation distribution. Best statistical fit to experimental data is obtained when both Jahn-Teller entropy and energetics of interaction of ions are incorporated in the model.