2.2 Structural Properties of Perovskites

As outlined above, perovskites form the most important class of ferroelectric materials. They are named after the mineral perovskite $\mathrm{CaTiO_3}$ (it was discovered later that $\mathrm{CaTiO_3}$ shows only a distorted perovskite structure). The perfect structure follows the formula $\mathrm{ABO_3}$, where A is a mono- or divalent and B is a tetra- or pentavalent metal [Die97]. As outlined in Fig. 2.3, the A atoms form the corners of the 'cubic' cells, B atoms are in the center and the oxygen atoms are situated in the faces' centers. As the B atoms are enclosed in $\mathrm{O_6}$ octahedra, this structure is also regarded as $\mathrm{BO_6}$.

Figure 2.3: Lattice structure of a symmetric perovskite crystal

Figure 2.4: Polarization of a tetragonally distorted crystal