In a ferroelectric crystal, it is likely that the alignment of dipoles in one of the polar directions extends only over a region of the crystal and there can be different regions in the crystal with aligned dipoles which are oriented in many different directions with respect to one another.

Regions of uniform polarization are called domains, separated by a boundary called domain wall.  You should not confuse ferroelectric domain walls with the grain boundaries. Depending upon the grain size, one grain can have more than one or more domains.

The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structure and symmetry of both paraelectric and ferroelectric phases.  For instance, rhombohedral phase of lead zirconate titanate, Pb(Zr,Ti)O₃ has P_s vector along [111]-direction which gives eight possible directions of spontaneous polarization with 180^o , 71^o and 109^o domain walls. On the other hand, a tetragonal perovskite like PbTiO₃ has P_s along the [001]-axis and here domain walls are either 180° or 90° domain walls.

Formation of the domains may also be the result of mechanical constraints associated with the stresses created by the ferroelectric phase transition e.g. from cubic paraelectric phase to tetragonal paraelectric phase in PbTiO₃.  Both 180° and 90° domains minimize the energy associated with the depolarizing field but elastic energy is minimized only by the formation of 90° domains. Combination of both effects leads to a complex domain structure in the material with both 90° and 180° domain walls.

Now the question is: Why is there a domain wall?

The driving force for the formation of domain walls is the minimization of the electrostatic energy of the depolarizing field (E_d), due to surface charges due to polarization, and the elastic energy associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transition. This electrostatic energy associated with the depolarizing field can be minimized by

• splitting of the material into oppositely oriented domains or

• compensation of the electrical charge via electrical conduction through the crystal.

Domains can also be seen by microscopy. The following is an image of domains in BaTiO₃ as seen by transmission electron microscopy.

Figure 5. 12   Domains in BaTiO3 samples as seen by TEM (Courtesy: DoITPoMS Micrograph Library, University of Cambridge, UK).