Phase-field simulation study on size effect of the microstructure evolution of a single-domain barium titanate 2D lattice square

Abstract

Microstructure evolution and size effect of a two-dimensional barium titanate lattice sqaure have been studied using phase-field simulation. Based on the Landau phenomenological model, we calculated the microstructure evolution of the tetragonal and orthorhombic ferroelectric BaTiO3 started from a single domain with various lattice sizes. A direction-dependent hysteresis loop can be quantitatively described. The results show that both the phase transition with temperature and polarization switching under an external electric field are accompanied by multidomain and multiphase production in a large single-domain lattice, but synchronous changes in polarization in small lattice; As the grain size decreases, the orthorhombic → tetragonal phase-transition temperature increased, while the tetragonal → cubic, cubic → tetragonal, and tetragonal → orthorhombic phase-transition temperatures decrease. An interesting conclusion is that it shows triple hysteresis loops along the [11]-direction when the lattice size decreases to a certain size. The simulations of microstructure evolutions not only produce a good domain-switching process under various electric fields, but also provide a comprehensive microstructure evolution in the vicinity of the phase-transition points. The physics underlying the continuous evolution of microstructure with electric field and temperature is discussed.