Displacements of 180-degree domain walls in electroded ferroelectric single crystals: the effect of surface layers on restoring force

Macroscopic properties of ferroelectric samples, including those in form of thin films, are, to large extent, influenced by their domain structure. In this paper the free energy is calculated for a plate-like sample composed of nonferroelectric surface layers and ferroelectric central part with antiparallel domains. The sample is provided with electrodes with a defined potential difference. The effect of applied field and its small changes on the resulting domain structure is discussed. This makes it possible to determine the restoring force acting on domain walls which codetermines dielectric and piezoelectric properties of the sample. Calculations of the potential and free energy take into account interactions of opposite surfaces and are applicable also to thin films.