Phenomenological theory of phase transitions in highly piezoelectric perovskites

The recently discovered fine structure of the morphotropic phase boundaries in highly piezoelectric mixture compounds PbZr_1-xTiₓO₃ (PZT), Pb(Mg1/3Nb2/3)_1-xTiₓO₃ (PMN-PT), and Pb(Zn1/3Nb2/3)_1-xTiₓO₃ (PZN-PT) demonstrates the importance of highly nonlinear interactions in these systems. We show that an adequate Landau-type description of the ferroelectric phase transitions in these compounds is achieved by the use of a twelfth-order expansion of the Landau potential in terms of the phenomenological order parameter. Group-theoretical and catastrophe-theory methods are used in constructing the appropriate Landau potential. A complete phase diagram is calculated in phenomenological parameter space. The theory describes both PZT and PZN-PT types of phase diagrams, including the newly found monoclinic and orthorhombic phases. Anomalously large piezoelectric coefficients are predicted in the vicinity of the phase transition lines.