  A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is
presented, which enables the thermodynamic description of dense laminar
polydomain states in epitaxial ferroelectric thin films. The theory explicitly
takes into account the mechanical substrate effect on the polarizations and
lattice strains in dissimilar elastic domains (twins). Numerical calculations
are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic
substrates. The "misfit strain-temperature" phase diagrams are developed for
these films, showing stability ranges of various possible polydomain and
single-domain states. Three types of polarization instabilities are revealed
for polydomain epitaxial ferroelectric films, which may lead to the formation
of new polydomain states forbidden in bulk crystals. The total dielectric and
piezoelectric small-signal responses of polydomain films are calculated,
resulting from both the volume and domain-wall contributions. For BaTiO3 films,
strong dielectric anomalies are predicted at room temperature near special
values of the misfit strain.
