Statistical theory of orbital ordering in perovskites based on a three-minimum two-sublattice model

The existence of tetragonally distorted octahedra found in a high-temperature cubic phase of some perovskites (LaMnO$_{3}$, KCrF$_{3}$, etc.) and the estimations performed make it possible to consider the observed orbital orderings as order–disorder phase transitions. The conditions of formation of ferro- and antiferrodistortive phase states described by the order parameters corresponding to reciprocal lattice vectors $\mathbf k$ = 0 и $\mathbf k_{1/2}=(\mathbf b_1, \mathbf b_2, \mathbf b_3)$, have been determined using a three-minimum two-sublattice model. The model is shown to be applicable for description of phase transitions in some ion–molecular crystals.