SIZE-INDUCED PHASE TRANSITION IN <font>BaTiO</font>₃ NANOCERAMICS DESCRIBED BY NANO-DOMAINS AND LONG-RANGE INTERACTION

Abstract

The size effect of nano-grain BaTiO 3 ceramics has been studied in this paper. We assume that the surface charge does not fully compensate long-range Coulomb interaction, so that 180 degree nano-domains still exists in small BaTiO 3 particles. We have calculated the long-range interaction in BaTiO 3 nanocrystals with 180 degree nano-domains, and obtained the relationship between grain size and domain size. The relation between transition temperature and grain size is also obtained by incorporating the domain-wall energy into the Landau–Ginzburg free-energy density. The results show that with decreasing grain size the transition temperature of cubic-tetragonal phase decreases, while those of tetragonal-orthorhombic and orthorhombic-rhombohedral phases increase. Our model predicts that with further reduction of grain size, the structures of ferroelectric phase becomes unstable and gradually disappears, leaving only one stable structure of cubic phase. In addition, an interesting conclusion is that a quadruple phase point exists in the phase diagram of the transition temperature versus grain size. The results are compared with experimental data.