Ferroelectric domain structures of epitaxial films, investigated using both transmission electron microscopy and phase-field simulations, are reported. Experiment and numerical simulation both reveal that the domain structures consist of irregularly shaped domains with curved domain walls. It is shown that the elastic contribution to domain structures can be neglected in due to its small ferroelastic distortion, less than 0.0018%. Two-beam dark-field imaging using reflections unique to domains of each of the two 90° polarization axes reveal the domain structure. Phase-field simulation is based on the elastic and electrostatic solutions obtained for thin films under different mechanical and electric boundary conditions. The effects of ferroelastic distortion and dielectric constant on ferroelectric domains are systematically analyzed. It is demonstrated that electrostatic interactions which favor straight domain walls are not sufficient to overcome the domain wall energy which favors curved domains in
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