Mean-field theory of structural phase transitions in the A’A’’BX4-type compounds

The class of compounds with crystallographic structures incorporating slight distortions from the prototype α-${\mathrm{K}}_2$ ${\mathrm{SO}}_4$ structure is studied. Various experimentally reported ferroelectric and ferroelastic phase transitions are considered as resulting from the ordering of the orientations of the ${\mathrm{BX}}_4$ groups accompanied by ionic displacements. The four-state Hamiltonian, with no dynamics, of the orientational interactions is formulated and the possible modes of displacement are identified. The thermodynamics of a four-sublattice model is examined in the molecular-field approximation. In this model 25 different phases are possible. The three-dimensional phase diagram obtained allows a variety of sequences of successive temperature transitions. A classification of experimentally studied compounds is proposed.