Landau–Ginzburg–Devonshire Theory for the Temperature–Grain Size Phase Diagram of BaTiO<sub>3</sub> Nanoceramics

The temperature and grain size dependences of the ferroelectric phase transitions and dielectric properties of BaTiO3 nanoceramics are described by higher-order Landau–Ginzburg–Devonshire theory. A structurally stable 8th-order Landau–Ginzburg–Devonshire potential with the 2nd- and 4th-order coefficients varying with temperature and grain size is proposed for a phenomenology of BaTiO3 nanoceramics. The temperature–grain size phase diagram constructed on the basis of this potential model describes well the experimentally observed cubic–tetragonal–orthorhombic and cubic–orthorhombic–rhombohedral triple points and ferroelectric to paraelectric to ferroelectric reentrance phenomenon. The spontaneous polarization and dielectric constant of BaTiO3 nanoceramics are calculated. It is shown that dielectric anomalies appear at the phase transitions and dielectric peaks are depressed, and diffused with decreasing grain size.