Thermodynamics and kinetics of cation ordering in MgAl₂O₄ spinel up to 1600 °C from in situ neutron diffraction

The temperature dependence of the cation distribution in synthetic spinel (MgAl₂O₄) was determined using in-situ time-of-flight neutron powder diffraction. Neutron diffraction patterns of stoichiometric MgAl₂O₄ and slightly non-stoichiometric Mg_0.99Al₂O₄ samples were collected under vacuum on heating from room temperature to 1600 °C, and the cation distribution was determined directly from site occupancies obtained by Rietveld refinement. The equilibrium non-convergent ordering has been analyzed using both the O'Neill-Navrotsky and Landau thermodynamic models, both of which fit the observed behavior well over the temperature range of the measurements. Fitting the data between 560 °C and 1600 °C using the O'Neill and Navrotsky (1983) thermodynamic model yields α = 32.8 ± 0.9 kJ/mol and β = 4.7 ± 2.0 kJ/mol. The fit to the Landau expression for ordering gives values of T(c) = 445 ± 109 K and c' = 1.62 ± 0.21. This confirms suggestions that the sign of the β coefficient in FeAl₂O₄ and MgAl₂O₄ is positive, and opposite to that found in other 2-3 oxide spinels. Non-equilibrium order-disorder behavior below 600 °C has been analyzed using the Ginzburg-Landau model, and successfully explains the time-temperature dependent relaxation behavior observed in the inversion parameter. Changing the stoichiometry, even by as little as 1 mol% Mg-deficiency, significantly reduces the degree of order.