Octahedral tilting in perovskites .1. 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.