A micromechanics-based thermodynamic model for the domain switch in ferroelectric crystals

In this work we take the view that domain switch in ferroelectric crystals is a thermodynamics-driven process. In this light we first consider the micromechanics of domain switch to derive the Gibbs free energy of the heterogeneous system and the corresponding thermodynamic driving force at a given level of switched domain concentration fp, applied stress σ-barij, and applied electric field E-bari. Then in conjunction with Miller and Weinreich's [Phys. Rev. 117 (1960) 1460] resistance force for the sidewise motion of 180 deg. domain walls, a kinetic equation is established to calculate the evolution of new domains under a reversed electric field for a BaTiO3 crystal. The calculated results show that, as the field increases, the switching process is initially rapid, and then becomes quite slow as it approaches the saturation state. The calculated polarization versus the electric field relation (P-E relation) is found to agree with the measured characteristics. The effect of porosity on the switching processes is also examined. It is found that, due to the lower level of Gibbs free energy in the presence of pores, a higher field is required to overcome the energy resistance of domain switch. On the other hand, due to the lower initial parent domain concentration, the level of electric field to cause a complete reversal of the domains decreases with porosity