The stability of the structure depends on the relative ionic radii: if the cations are too small for close packing with the oxygens, they can be displaced slightly. Since these ions carry electrical charges, such displacements can result in a net electric dipole moment (opposite charges seperated by a small distance). The material is said to be a ferro-electric by analogy with a ferro-magnet which contains magnetic dipoles.
At high temperature, the small green B-cations can "rattle around" in the larger holes between oxygen, maintaining cubic symmetry. The ¶static displacement only occurs when the structure is cooled below a certain transition temperature. We have illustrated a dispacement along the z-axis, resulting in tetragonal symmetry (z remains a 4-fold symmetry axis), but at still lower temperatures the symmetry can be lowered further by additional displacements along the x- and y-axes. We have a ¶dynamic 3D-drawing of this ferro-electric transition.
An alternative type of structural transition, called anti-ferroelectric, is also common in perovskites. If the A-cation is too large for close packing, the X-cations can be displaced instead. But since the BX6 octahedrae are relatively rigid units connected at their apexes, they twist together as in ¶NaNbO3. Again, we have a ¶dynamic 3D-drawing of this anti-ferroelectric transition. There is no net dipole moment in such anti-ferroelectric structures. Again, as the temperature is lowered, a succession of transitions can occur, with the octahedrae twisting around different axes.
Ferro-electric and other di-electric materials have important applications
as sensors, since a physical change in the dimensions of the material is
accompanied by an electric field. But so far we have concentrated on
bonding between electrically charged ions. What about the strong
covalent bonding between atoms that is
responsible for the strength of diamonds ?