Phase-field method of phase transitions/domain structures in ferroelectric thin films: A review

This article briefly reviews recent applications of phase-field method to ferroelectric phase transitions and domain structures in thin films. It starts with a brief introduction to the thermodynamics of coupled electromechanical systems and the Landau description of ferroelectric transitions in homogeneous ferroelectric single crystals. The thermodynamic potentials of a homogeneous crystal under different mechanical boundary conditions are presented, including the thin-film boundary conditions. The phase-field approach to inhomogeneous systems containing domain structures is then outlined. It describes a domain structure using the spatial distribution of spontaneous polarization. The evolution of a domain structure towards equilibrium is driven by the reduction in the total-free energy of an inhomogeneous domain structure including the chemical driving force, domain wall energy, electrostatic energy as well as elastic energy. A number of examples are discussed, including phase transitions and domain stability in ferroelectric thin films and superlattices. It is demonstrated that using a set of independently measured thermodynamic parameters for the corresponding bulk single crystals, the phase-field approach is able to quantitatively predict not only the strain effect on phase transition temperatures but also the correct ferroelectric domain structures for a given strain and temperature.