OCTAHEDRAL TILTING IN PEROVSKITES .1. GEOMETRICAL CONSIDERATIONS

The 23 Glazer tilt systems describing octahedral tilting in perovskite s 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 o f perfectly rigid octahedra. In these tilt systems small distortions o f 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 pre dicted space groups for ordered perovskites, A(2)MM'O-6, for all 23 ti lt systems is also given.