A universal order-disorder mechanism of structural phase transitions in A ' A '' Bx(4) compounds

Experimental data concerning ferroelectric, ferroelastic and long-period spatially modulated phases in A'A"BX4 compounds are reviewed. It is shown that a simple statistical model wih two Ising spins on a hexagonal close-packed structure explains practically all the structural phase transitions observed in this class of compounds. The Ising variables describe four discrete orientational states of BX4 anions in the environment of A cations. Symmetrical nearest-neighbour interactions between spins stabilize various crystallographic structures with up to four formula units per elementary cell. Longer-period, as well as incommensurate modulations of the order parameter, both along the hexagonal axis and in the hexagonal plane, originate either from symmetrical next-nearest-neighbour or, competitively, antisymmetrical nearest-neighbour interactions.