ABX3-related structures

The basic perovskite structure ABX3 forms the prototype for a wide range of other structures related to it by combinations of topological distortions, substitution of the A, B and X ions, and intergrowth with other structure types. These compounds exhibit a range of magnetic, electrical, optical, and catalytic properties of potential application in solid state physics, chemistry, and materials science. 

When the A ion in an ABX3 compound is too small to form the perovskite structure, say when its radius is less than about i-o A, the alternative ilmenite arrangement sometimes occurs. This structure is closely related to that of corundum and haematite ( 8.46) and may be described as an hexagonal close-packed array of X ions (usually oxygen ions) with A and B ions each occupying one-third of the octahedrally co-ordinated interstices. Thus both A and B ions are now 6-co-ordinated by anion neighbours. 

Notwithstanding, it was foxmd that the cubic perovskite structure, or slightly distorted variants of it, was still retained in ABX3 compounds even where this relation is not exaetly obeyed. As a measure of the deviation form ideality Goldschmidt [21], introduced a tolerance factor t, deirned as,... 

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