Domain patterns in epitaxial rhombohedral ferroelectric films. I. Geometry and experiments

Possible domain patterns are developed for (001) oriented (pseudocubic indexing) epitaxial rhombohedral perovskite ferroelectric (F_R) films. We assume that the films are grown above their Curie temperature (T _C) in a cubic paraelectric (P_C) state. The rhombohedral distortion consists of a "stretch" along one of the four 〈111〉 crystallographic directions of the cubic perovskite unit cell. Domain pattern formation is concurrent with the P_C→F_R transformation on cooling from the growth temperature. The domain patterns form to minimize elastic energy in the film, at the energetic expense of both forming domain boundaries and developing local stresses in the substrate. Eight possible domains may form, half of which are related by inversion, thus leading to four mechanically distinct variants. The possible domain walls are determined by mechanical and charge compatibility and follow closely from the analysis of Fousek and Janovec [J. Appl. Phys. 40, 135 (1969)]. Domain patterns may develop with either {100} or {101} boundaries. In both cases, the individual domains in the patterns are energetically degenerate and thus equal width lamellar patterns are predicted. When polarization is included in the analysis, the {100} boundary patterns have no normal component of the net polarization, whereas the {101} boundary patterns correspond to the fully poled state. We report on experimental observation of {100} domain patterns in epitaxial PbZr _0.80Ti_0.20O₃, and PbZr_0.65Ti _0.35O₃ films.