Size effect on the dielectric properties of BaTiO3 nanoceramics in a modified Ginsburg-Landau-Devonshire thermodynamic theory

Grain size effects on the dielectric properties of BaTiO3 nanoceramics have been studied by using the modified Ginsburg-Landau-Devonshire (GLD) thermodynamic theory. Considering the existence of internal stresses, it is found that with decreasing grain size the transition temperature of cubic-tetragonal phase decreases, while those of tetragonal-orthorhombic and orthorhombic-rhombohedral phases increase. With further reducing grain size, our model predicts that the two ferroelectric structures of orthorhombic and tetragonal phases will become unstable and disappear at a critical size, leaving only one stable ferroelectric phase of rhombohedral structure. Consequently, a theoretical phase diagram of the transition temperature versus grain size is established wherein two triple points and a reentrance behavior are indicated. The results are compared with experimental data.