Cooperative PJTE in BaTiO 3 -type crystals and ferroelectricity. In crystals with PJTE centers the interaction between the local distortions may lead to their ordering to produce a phase transition to a regular crystal phase with lower symmetry. Such cooperative PJTE is quite similar to the cooperative JTE; it was shown in one of the first studies of the PJTE in solid state systems that in the case of ABO 3 crystals with perovskite structure the local dipolar PJTE distortions at the transition metal B center and their cooperative interactions lead to ferroelectric phase transitions. Provided the criterion for PJTE is met, each [BO 6 ] center has an APES with eight equivalent minima along the trigonal axes, six orthorhombic, and (higher) twelve tetragonal saddle-points between them. With temperature, the gradually reached transitions between the minima via the different kind of saddle-points explains the origin of all the four phases (three ferroelectric and one paraelectric) in perovskites of the type BaTiO 3 and their properties. The predicted by the theory trigonal displacement of the Ti ion in all four phases, the fully disordered PJTE distortions in the paraelectric phase, and their partially disordered state in two other phases was confirmed by a variety of experimental investigations (see in ).