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 − , a 0 b + b − and a 0 b + 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 a 0 b + b − tilt systems are estimated. A table of predicted space groups for ordered perovskites, A 2 MM′ O 6 , for all 23 tilt systems is also given.