Octahedral Tilting in Perovskites. I. Geometrical Considerations

The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. It is shown that in tilt systems a⁺a⁺a^-, a⁺b⁺b^-, a⁺a⁺c^-, a⁺b⁺c^-, a⁰b⁺b^- and a⁰b⁺c^- it is not possible to link together a three-dimensional network of perfectly rigid octahedra. In these tilt systems small distortions of the octahedra must occur. The magnitude of the distortions in the a⁺a⁺a^- and a⁰b⁺b^- tilt systems are estimated. A table of predicted space groups for ordered perovskites, A₂MM'O₆, for all 23 tilt systems is also given.