The shift of Curie temperature and evolution of ferroelectric domain in ferroelectric crystals

A micromechanics-based thermodynamic model for the phase transition of ferroelectric crystals is developed and, with it, the shift of Curie temperature and evolution of ferroelectric phase upon cooling are examined. This approach differs from the classical phenomenological one in that the evolution of new domain concentration can be predicted. We start out by formulating the Gibbs free energy of a generic, two-phase crystal consisting of the parent paraelectric phase and the transformed ferroelectric phase, at a given level of temperature, stress, and electric field. The thermodynamic driving force for domain growth is then derived and, together with the resistance force, a kinetic equation is established. The derived driving force is found to arise from three different sources of Gibbs free energy: (i) the interaction energy due to the heterogeneity of electromechanical moduli of the parent and product phases, (ii) the energy dissipation due to spontaneous polarization, and (iii) the self-energy of the dual-phase system due to the existence of polarization strain and electric polarization. For a BaTiO₃ crystal the electromechanical heterogeneity is found to play a rather significant role that seems not to have been recognized before. The derived shift recovers to the Clausius-Clapeyron relation if such heterogeneity disappears. We have examined in detail several factors that affect the shift of Curie temperature, and calculated the evolution of overall polarization and dielectric constant of a BaTiO₃ crystal. The results are found to be consistent with available test data.