Constructing Landau-Ginzburg-Devonshire type models for ferroelectric systems based on symmetry

Landau-Ginzburg-Devonshire type phenomenological models have been widely used to study ferroelectric phase transitions and domain pattern formation. By including time variation, such models become the time dependent Ginzburg-Landau (TDGL) theory, which may be used to study the kinetics of domains and predicting time variation of material properties. The model construction is straightforward for one-dimensional systems, but for multiple dimensions, more rigorous group theoretical analysis based on crystal symmetry must be used to derive the proper form of the free energy. This paper illustrates the basic procedure for the model construction and provides free energy densities for a few commonly encountered crystal symmetries in ferroelectric systems. An example is also given to illustrate how to deal with phase transitions involving unit cell change using phenomenological theory.