  Devonshire theory provides a successful phenomenological description of many
cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of
the free energy in the polar order parameter. However, the recent discovery of
a novel monoclinic ferroelectric phase in the PZT system by Noheda et al.
(Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we
confirm that the sixth-order Devonshire theory cannot support a monoclinic
phase, and consider extensions of the theory to higher orders. We show that an
eighth-order theory allows for three kinds of equilibrium phases in which the
polarization is confined not to a symmetry axis but to a symmetry plane. One of
these phases provides a natural description of the newly observed monoclinic
phase. Moreover, the theory makes testable predictions about the nature of the
phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A
ferroelectric phase of the lowest (triclinic) symmetry type, in which the
polarization is not constrained by symmetry, does not emerge until the
Devonshire theory is carried to twelfth order. A topological analysis of the
critical points of the free-energy surface facilitates the discussion of the
phase transition sequences.
