Thermodynamics and kinetics of cation ordering in MgAl2O4spinel up to 1600 degrees C from in situ neutron diffraction

Abstract

The temperature dependence of the cation distribution in synthetic spinel (MgAl ₂ O ₄ ) was determined using in-situ time-of-flight neutron powder diffraction. Neutron diffraction patterns of stoichiometric MgAl ₂ O ₄ and slightly non-stoichiometric Mg (sub 0.99) Al ₂ O ₄ samples were collected under vacuum on heating from room temperature to 1600 degrees 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 degrees C and 1600 degrees C using the O'Neill and Navrotsky (1983) thermodynamic model yields alpha = 32.8+ or -0.9 kJ/mol and beta = 4.7+ or -2.0 kJ/mol. The fit to the Landau expression for ordering gives values of T _c = 445+ or -109 K and c' = 1.62+ or -0.21. This confirms suggestions that the sign of the beta coefficient in FeAl ₂ O ₄ and MgAl ₂ O ₄ is positive, and opposite to that found in other 2-3 oxide spinels. Non-equilibrium order-disorder behavior below 600 degrees 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.