OCTAHEDRAL TILTING DISTORTIONS IN THE PEROVSKITE STRUCTURE. Patrick M. Woodward, Arthur W. Sleight, Department of Chemistry and Center for Advanced Materials Research, Gilbert Hall 153, Oregon State University, Corvallis, OR 97331~003

Distortions of the AMO₃ perovskite structure that can be described by tilting of essentially rigid octahedra have been investigated. Earlier work by Glazer, which showed that such distortions can be classified into 23 different tilt systems, has been revisited. It can be shown that in six of these tilt systems (a⁺a⁺a^-, a⁺b⁺b^-, a⁺a⁺c^-, a⁺b⁺c^-, a⁰b⁺b^-, 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. All 23 tilt systems are compared in terms of their A cation coordination. On this basis they can be divided into two categories, those in which all of the A cation sites remain crystallographically equivalent, and those in which the A cation sites become nonequivalent. For most perovskites the tilt systems with equivalent A cation sites are strongly favored. When the Goldshmidt tolerance factor becomes smaller than 0.975, the a⁺b^-b^- tilt system (GdFeO₃ structure) is found almost exclusively. Both empirical lattice energy calculations and extended Hückel calculations have been performed, both calculations show that the A-O interactions are optimized in this tilt system. The ideal cubic structure is found to be stabilized only by oversized A cations, and M-O pi bonding interactions. Tilt systems with nonequivalent A site environments are favored only when there are at least two types of cations, with different sizes and/or bonding preferences, present on the A site. In these tilt systems the ratio of large to small cations will dictate the most stable tilt system. The predicted space groups for all 23 tilt systems have been extended to ordered perovskites, A₂MM'O₆. These results should be of interest not only in understanding the behavior of known perovskite compounds, but also in searching for and correctly assigning symmetry to new compounds.