Temperature dependence of the inversion degree in three-cation spinel solid solutions: experimental evaluation by XRD

Abstract

The method of degree of inversion calculation presented in the present paper was based on the determination of several temperature-dependent parameters such as: oxygen positional parameter, lattice parameter, cation site occupancies, and a cation–anion distance in tetrahedral and octahedral sites. The theoretical basis of the method as well as the required derivation of formulae and the conditions of its application has been described.The values of the measured temperature-dependent parameters were used to calculate the degree of inversion vs. temperature in the spinel structure. Initial temperatures of the order–disorder transformation were determined. The described method of investigating the order–disorder phase transformation based on three examples of spinel solid solutions: Mg(Al0.5Fe0.5)2O4, (Mg0.75Ni0.25)Al2O4, and (Mg0.75Co0.25)Al2O4 has been presented. Investigations by means of the high-temperature X-ray diffraction method at temperatures ranging from 25 to 1100 °C were carried out. It has been shown that using the present method, it is possible to determine the distribution of each cation in tetrahedral and octahedral sites at each temperature. In consequence, the unidirectional order–disorder phase transformation as well the bidirectional transformation in the spinel structure can be investigated. The advantages and disadvantages of the method have been discussed and its uncertainties presented.