Acta Cryst. (1997). B53, 44-66 [ doi:10.1107/S0108768196012050 ]
Abstract: The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. The various tilt systems have been compared in terms of their A-cation coordination and it is shown that those tilt systems in which all the A-cation sites remain crystallographically equivalent are strongly favored, when all the A sites are occupied by the same ion. Calculations based on both ionic and covalent models have been performed to compare the seven equivalent A-site tilt systems. Both methods predict that when the tilt angles become large, the orthorhombic a+b-b- tilt system will result in the lowest energy structure. This tilt system gives the lowest energy structure because it maximizes the number of short A-O interactions. The rhombohedral a-a-a- tilt system gives a structure with a slightly lower Madelung energy, but increased ion-ion repulsions destabilize this structure as the tilt angles increase. Consequently, it is stabilized by highly charged A cations and small to moderate tilt angles. The ideal cubic a0a0a0 tilt system is only observed when stabilized by oversized A cations and/or M-O ![[pi]](/logos/entities/pi_rmgif.gif)
-bonding. Tilt systems with nonequivalent A-site environments are observed when at least two A cations with different sizes and/or bonding preferences are present. In these compounds the ratio of large-to-small cations dictates the most stable tilt system.
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