Barium titanate and phase changes

The temperature at which the spontaneous polarisation disappears is called the Curie temperature, T_C.

Above 120°C, barium titanate has a cubic structure. It is therefore centro-symmetric and possesses no spontaneous dipole. With no spontaneous dipole the material behaves like a simple dielectric, such that its polarisation varies linearly with field. T_C for barium titanate is 120°C.

Below 120°C, it changes to a tetragonal phase, with an accompanying movement of the atoms. The movement of Ti atoms inside the O₆ octahedra may be considered to be significantly responsible for the dipole moment:

Cooling through 120°C causes the cubic phase of barium titanate to transform to a tetragonal phase with the lengthening of the c lattice parameter (and a corresponding reduction in a and b). The dipole moment may be considered to arise primarily due to the movement of Ti atoms with respect to the O atoms in the same plane, but the movement of the other O atoms (i.e. those O atoms above and below Ti atoms) and the Ba atoms is also relevant.

The diagram below shows the BaTiO₃ structure with an O₆ octahedron surrounding the Ti atom.

The switching to a cubic structure is the reason for the polarisation spontaneously disappearing above 120°C. Barium titanate has two other phase transitions on cooling further, each of which enhances the dipole moment:

The phase which is reached after cooling to ~ 0°C from tetragonal is orthorhombic.

And then rhombohedral below -90°C:

All of these ferroelectric phases have a spontaneous polarisation based to a significant extent on movement of the Ti atom in the O₆ octahedra in the following way (using pseudo-cubic notation):