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The name “perovskite” originally refers to a type of minerals with chemical formula CaTiO₃, named after Russian mineralogist L. A. Perovski. In general, any crystals with the same structure as CaTiO₃ are categorized into the perovskite structure.

Most perovskite crystals are oxides with the general formula ABO₃, where A and B represent two different cations and O represents oxygen elements. The A-site cations are larger than B-site cations. Perovskite oxides (ABO₃) can be described as the framework of corner-shared BO₆ octahedra with 12-coordinated A cations. The unit cell of an ideal perovskite structure is a cube, where the A-site cations locate at the corners of the cube, the B-site cation sits in the body center and oxygen sits in the face centers as shown in Figure 3533a. The structure is a corner-linked oxygen octahedral network. The octahedra are linked in a regular cubic array, resulting in high-symmetry cubic m-3m prototype structure. The 6-fold-coordinated B-site in the center of the oxygen octahedron is occupied by a small highly charged cation with a valence state of 3+, 4+, 5+ or 6+, and the larger 12-fold coordinated A-site between octahedra is occupied by a larger cation with a valence state of 1+, 2+, or 3+.

The main advantage of the perovskite structures is the large flexibility in tailoring the chemical composition and lattice parameter(s) of the system by substituting the different cations that present on both the A and B sites without changing the overall structure completely.

Figure 3533a. Schematic illustration of ideal perovskite structure.

However, most perovskite structures do not have such ideal cubic symmetry and are normally distorted, even for the prototype perovskite, CaTiO₃. For instance, the properties of the cations on the A-sites and on the B-sites often induce common distortions such as cation displacements within the octahedra and tilting of the octahedra. In general, the degree of distortion in ABO₃ perovskites can be determined by [1],

            ----------------------------- [3533]

where,
          R_A, R_B and R_O -- The ionic radii of the A-site cation, B-site cation and oxygen anion, respectively.
          t -- Goldschmidt tolerance factor.

In an ideal cubic perovskite crystalline structure the A-site and B-site cations optimize their equilibrium bond distances to the oxygen elements without inducing any distortion of the unit cell at t = 1. When 0.75 < t < 1.05 (that almost all the perovskites have), a distorted perovskite structure can normally be stabilized. Note that most of the cubic perovskites have t values in between 0.8 and 0.9.

All the ferroelectric materials today are based on corner-linked oxygen octahedral structures. The simplest configuration is the well-known perovskite structure. In EELS, perovskite type ferroelectric and high-k dielectric materials, such as BaTiO₃ and SrTiO₃, normally show only one interband plasmon peak [2–5].

For perovskite cell structures, octahedral oxygen (O) bonding around the atom (Mn for LaMnO₃ as shown in Figure 3533b) in B-site generates the crystal field around the B-site atom. The valence states of the atoms (e.g. Mn) are fixed by charge neutrality. In the case of LaMnO₃, if the parent compound is doped with Sr²⁺ for La³⁺, then Mn³⁺ (d³) is replaced by Mn⁴⁺ in the lattice.

Table 3533a. Atomistic positions in cubic perovskites.

Table 3533b. Atomistic positions in orthorhombic perovskites.

Table 3533c. Atomic positions for rhombohedral perovskites.

Table 3533d. Atomic positions for hexagonal perovskites.

Table 3533e. Examples of perovskite crystals.

In Table 3533a, some dopants are introduced into the perovskite structures for different purposes. For instance, Sb, Mo or Sn are introduced [15-17] at the Co positions in SrCoO_3-δ in order to avoid the formation of the unwanted 2H-hexagonal structure. [6-8]

Table 3533f. Other characteristics of perovskite structures.

[1] V. M. Goldschmidt, T. Barth, G. Lunde, and W. Zachariasen, Skrifter Norske Videnskaps-Akad. Oslo, Mat.-Nat. Kl. 2, 117 (1926).
[2] K.S. Katti, M. Qian, F. Dogan, M. Sarikaya, J. Am. Ceram. Soc. 85 (2002) 2236–2243.
[3] K. van Benthem, C. Elsasser, R.H. French, J. Appl. Phys. 90 (2001) 6156–6164.
[4] S. Schamm, G. Zanchi, Ultramicroscopy 88 (2001) 211–217.
[5] J. Zhang, A. Visinoiu, F. Heyroth, F. Syrowatka, M. Alexe, D. Hesse, H.S. Leipner, Phys. Rev. B 71 (2005) 064108.
[6] Aguadero, A.; Pérez-Coll, D.; Alonso, J.A.; Skinner, S.J.; Kilner, J. A new family of Mo-doped SrCoO3−δ perovskites for application in reversible solid state electrochemical cells. Chem Mater 2012, 24, 2655-2663.
[7] Wang, S.F.; Hsu, Y.F.; Yeh, C.T.; Huang, C.C.; Lu, H.C. Characteristics of SrCo1−xSnxO3−δ cathode materials for use in solid oxide fuel cells. Solid State Ionics 2012, 227, 10-16.
[8] Aguadero, A.; Alonso, J.A.; Perez-Coll, D.; De la Calle, C.; Fernández-Díaz, M.T.; Goodenough, J.B. SrCo0.95Sb0.05O3-δ as cathode material for high power density solid oxide fuel cells. Chem. Mater 2010, 22, 789–798.