Recently discovered fine structure of the morphotropic phase boundaries in highly piezoelectric mixture compounds PZT, PMN-PT, and PZN-PT demonstrates the importance of highly non-linear 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.

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preceding Comment, Phys. Rev. Lett. 62, 843 (1989). 2 V. P. Dmitriev, S. B. Rochal, Yu. M. Gufan, and P. Toledano, Phys. Rev. Lett. 60, 1958 (1988). 3 Yu. M. Gufen, V. P. Dmitriev, and P. Toledano, Fiz. Tverd. Tela 30, 1057 (1988) [Sov. Phys. Solid State 30, 613 (1988)]. 4 S. Alexander and J. McTague, Phys. Rev. Lett. 41, 702 (1978). 5 Yu. M. Gufan, V. P. Dmitriev, and P. Toledano (to be published). 844

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