5.3.11 Structural change and ferroelectricity in Barium Titanate (BaTiO₃)

Barium Titanate (BaTiO₃)  has a perovskite ABO₃ type structure. As shown below, the central Ti atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio (See Module 1).

Above 120°C, cubic form of (BaTiO₃)  has regular octahedrons of O^2- ions around Ti⁴⁺ ion and has a center of symmetry. As a result, the six Ti-O dipole moments along ±x, ±y, ±z cancel each other and the material in such a state is called paraelectric.

Below 120°C, BaTiO₃ transforms to a noncentrosymmetric tetragonal phase with one of the axis becoming longer, typically referred as z-axis or [001]-direction. Unilateral displacement of the positively changed Ti⁴⁺ ions against surrounding O^2- ions occurs to give rise to net permanent dipole moment. Coupling of such displacements and the associated dipole moment is a necessity for ferroelectricity. This transformation forces Ti ions go to lower energy off center positions, giving rise to permanent dipoles (see the energy well diagram in section 5.3.6).

The crystallographic dimension of the BaTiO₃  lattice change with temperature as shown below.

Because the distorted octahedra are coupled together in ferroelectric form, there is a very large spontaneous polarization, ~25 μC/cm², giving rise to a large dielectric constant, ~160, and large temperature dependence of dielectric constant.

BaTiO₃ shows two more structural transitions when cooled further below 120°C. It transforms to orthorhombic structure at ~5°C and then again to a rhombohedral structure at ~ -90°C and as result of change in the symmetry, the polarization vector also changes from [001] for tetragonal to [110] in orthorhombic and [111] in rhombohedral structure.