research papers
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 π-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.