This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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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. 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],

            ----------------------------- [3531]

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 0.78 < t < 1.05, a distorted perovskite structure can normally be stabilized.

[1] V. M. Goldschmidt, T. Barth, G. Lunde, and W. Zachariasen, Skrifter Norske Videnskaps-Akad. Oslo, Mat.-Nat. Kl. 2, 117 (1926).