The temperature at which the spontaneous polarisation disappears is called the Curie temperature, TC.
Above 120°C, barium titanate has a cubic structure. This means it is centro-symmetric and possesses no spontaneous dipole. With no dipole the material behaves like a simple dielectric, giving a linear polarisation. TC 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.
This shows the BaTiO3 structure with an O6 octahedron surrounding the important Ti atom.
Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.
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):
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