A theory of triple hysteresis in ferroelectric crystals

In the vicinity of the transition temperature between two ferroelectric states, a ferroelectric crystal could exhibit a triple hysteresis under an ac field. For a BaTiO3 with the c-plate configuration slightly below this temperature, the middle loop is caused by the 0 degrees -> 180 domain switch in the orthorhombic phase, whereas the upper and lower loops are the result of orthorhombic-to-tetragonal phase transition, and vice versa. In this article we first develop a micromechanics-based thermodynamic model to determine the thermodynamic driving force for phase transition and for domain switch as a function of electric field and temperature, and in the latter case, further supplement it with a kinetic equation and a homogenization scheme. The dependence of dielectric constant of the orthorhombic and tetragonal phases on temperature and electric field are also established. The developed theory is then applied to calculate the triple hysteresis loops of BaTiO3 at several levels of temperature. The calculated results for the triple loops, and for the variation of dielectric constant, are found to be in full accord with the test data of Huibregtse and Young [Phys. Rev. 103, 1705 (1956)]. (C) 2009 American Institute of Physics. [doi:10.1063/1.3243084]