Phase Transitions in Ferroelectric and Antiferroelectric Crystals

Group theory is applied to phase transitions in ferroelectric and antiferroelectric crystals. The procedure is given to derive for a paraelectric crystal with a given space group all possible ferroelectric states which can exist for arbitrarily small values of the polarization. A knowledge of the space groups of the crystal above and below the transition point makes it possible to predict whether a second-order phase transition is possible. The predictions made for a number of ferroelectric and antiferroelectric crystals are in agreement with available experimental data. The classification of ferroelectric phase transitions given by Aizu and Devonshire's theory for BaTi${\mathrm{O}}_3$ follow quite naturally from these symmetry considerations. In an appendix the symmetry properties of second-order phase transitions leading to structures which cannot be described by a three-dimensional space group (e.g., magnetic spirals) are discussed.