Phenomenological theories of ferroelectric phase transitions

parameter in the free energy expansion, phenomenological theory can also describe inhomogeneous structures appearPhenomenological theories for ferroelectrics are based ing in the ferroelectric phase transition, such as twins, on L andau–Devonshire type models, which can be conantiphase structures and domain walls. Here two examples structed based on thermodynamic principles and symwill be used to show the procedure and the power of metry relationships between parent and product phases. phenomenological theories in multidimensions for describPhenomenological theories can be directly linked to ing domain walls in ferroelectric systems and antiferroelecmeasurable macroscopic quantities and at the same tric phase transitions. time preserve microscopic information. T he competition between gradient energy and non-linear energy in Ginzburg–L andau type models provides an interpretFREE ENERGY BASED ON CRYSTAL ation of inhomogeneous structures in ferroelectrics, for SYMMETRY example twins and domain walls. Phenomenological In phenomenological theories, the key quantity is the order models can be extended to antiferroelectric systems parameter. A proper ferroelectric phase transition is driven using a multicomponent order parameter related to by a zone centre transverse optical soft mode, which is microscopic local dipoles, rather than the average related to the amplitude of the polarisation. Thus a ferropolarisation vector. Such a model can provide a more electric system is a textbook example of the Landau theory rigorous description of the antiferroelectric phase transof phase transitions.3–5 Following Landau’s ideas for a ition. BCT /704 second order phase transition,6,7 the free energy density is written in terms of a polynomial expansion of the polaris