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.