Octahedral tilting in perovskites .2. Structure stabilizing forces

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 a(0)a(0)a(0) tilt system is only observed when stabilized by oversized A cations and/or M-O pi-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.