Study of ferroelectric nanodomains and the effect of grain size in BaTiO3 ceramics

Nanodomains and grain-size effects in BaTiO₃ have been studied theoretically. In this article, we have calculated the long-range Coulomb interaction between ferroelectric nanodomains in a single BaTiO₃ grain, and obtained information on the domain structure at various temperatures and grain sizes. The relation between transition temperature and the grain size is obtained by incorporating the domain-wall energy, the surface energy, and the stress energy into the Landau–Ginzburg free-energy density. The results show that 180° domains exist in ferroelectric BaTiO₃ nanoceramics. At room temperature, with the decreasing grain size, the domain width does not decrease monotonically; when the grain size reduces to 18?nm, the grain becomes a single domain, and when less than 12?nm, the ferroelectric phase disappears. With the decreasing grain size the temperature of the cubic-tetragonal phase transition is reduced, while the temperatures of the tetragonal–orthorhombic and orthorhombic–rhombohedral phase transitions reach a maximum when the grain sizes are in the vicinity of 200?nm. The theoretical results are compared with experimental data.