Theoretical Model for Cubic-to-Tetragonal Phase Transformations in Transition Metal Spinels

Abstract

According to Dunitz and Orgel, the large tetragonal distortions which occur in a number of transition metal oxides having the spinel structure are presumed to arise as a consequence of a Jahn‐Teller type distortion in the immediate environment of certain transition metal ions. All the observed large distortions can be 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 Jahn‐Teller distortions about neighboring $\mathrm{B‐}\mathrm{site}$ transition metal cations. By the use of the usual method of statistical mechanics it has proved possible to derive the thermodynamic behavior of this model, and hence to contribute to an understanding of the cooperative nature of these transformations. The principal result of importance is the demonstration that the transformations from tetragonal to cubic spinel phases are thermodynamically of the first order. 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 evidence seems to support the conclusions drawn from the model.