Spontaneous Polarisation and Domains

A ferroelectric perovskite, as distinct from a normal dielectric, has a permanent spontaneous polarisation that can be switched in direction by the application of an external electric field. All ferroelectrics are also piezoelectrics and the majority of commercially important piezoelectric materials are ferroelectric perovskites. 

The fundamental cause of ferroelectricity in oxide perovskites was originally attributed to the idea that small B-site cations could rattle around inside BO, octahedra and off-centre configurations lent stability to the structure. The displaced B-site cation created an electric dipole within each octahedron. The direction of the dipole, or, equivalently, the position of the cation, could be switched from one off-centre position to another under the influence of an applied electric field. 

The deformations of the unit cell from the high-temperature cubic form are relatively small, and the structural relationships between the various crystallographic unit cells can be simplified by reference to a pseudocubic structure. Referred to such a pseudocubic unit cell, the polarisation directions in BaTlOj are then as follows tetragonal phase, [001] orthorhombic phase, [011] and rhombohedral phase, [lll]p. 

The B-site displacement idea is too simplistic to explain the behaviour of a majority of ferroelectrics, and other features of the perovskite structure must be taken into account in explaining the formation of arrays of permanent switchable dipoles. Among these additional aspects are dipoles due to A-cation displacements, especially for lone pair cations such as Pb or Bi, octahedral tilting and irregularities in the positions of the oxygen ions that make up the BOg polyhedra. 

From symmetry considerations, the ferroelectric layered perovskites, such as the Ruddlesden-Popper, Dion-Jacobson and Aurivillius phases in which the perovskite layers are an even number of octahedra in thickness, tend to have the spontaneous polarisation vector lying parallel to the perovskite sheets. In phases with an odd number of octahedra in thickness, the spontaneous polarisation can lie perpendicular to the sheets or at least have a component in this direction. Thus the n=2 Dion-Jacobson phase RbBiNbjO has the spontaneous polarisation vector lying parallel to the perovskite layers. This polarisation arises from the tilted NbOg octahedra and, more importantly, from the displaced lone pair Bi - cations that are found between the perovskite layers. 

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