Theoretical Model for TetragonaltoCubic Phase Transformations in Transition Metal Spinels
Abstract
The origin of the large tetragonal distortions which occur in a number of transition metal oxides having the spinel structure has been examined recently by Dunitz and Orgel in terms of the crystal field theory. According to these authors the macroscopic distortions arise as a consequence of a JahnTeller type distortion in the immediate environment of certain transition metal ions. Thus, all the observed large distortions in spinels have been correlated with the results of this crystal field treatment on the basis of the spatial ordering of the local distortions. In this communication we investigate the detailed properties of the transformations from tetragonal to cubic phases which are observed at elevated temperatures. An approximate model has been constructed which explicitly takes into account the interactions between local JahnTeller distortions about neighboring octahedral site cations. The configurational energy of the model has been derived in a completely general form in terms of occupation variables, and has been used to deduce the structure of the stable lowtemperature phase. By the use of the usual methods of statistical mechanics it has proved possible to derive the thermodynamic behavior of the model, and hence to contribute to an understanding of the cooperative nature of these phase transformations. The temperature and composition dependence of the longrange order parameter, the thermodynamic functions, and the lattice parameters are calculated explicitly. The principal result of importance is the demonstration that the transformations from tetragonal to cubic spinel phases are thermodynamic transitions of the first order type. That is, a latent heat, a volume discontinuity, lattice parameter discontinuities, and a lambda anomaly in the heat capacity are to be observed at the transformation temperature. The available experimental evidence supports the conclusions drawn from the theoretical model. The agreement between theory and experiment is found to be semiquantitative in most of the cases considered.
 Publication:

Physical Review
 Pub Date:
 October 1959
 DOI:
 10.1103/PhysRev.116.32
 Bibcode:
 1959PhRv..116...32W