Inter-relationship of octahedral geometry, polyhedral volume ratio and ferroelectric properties in rhombohedral perovskites

Abstract

A unifying, quantitative analytical framework has been developed for rhombohedral perovskite structures, ABO 3 . Three principal parameters are defined: polyhedral volume ratio, V A /V B , mean octahedral tilt angle, , and octahedral distortion, Δs. The first two of these parameters are directly related through the equation V A /V B =6K cos 2 -1, with K practically invariant between all crystal structures. The four permutations of zero or non-zero with zero or non-zero Δs are related to the four space groups in which rhombhedral perovskites crystallize, R3m, R3c, R3m and R3c. The most general space group is R3c, which can accommodate non-zero values of both and Δs