Quantitative description of the tilt of distorted octahedra in ABX₃ structures

A description of the tilt of octahedra in ABX₃ perovskite-related structures is proposed that can be used to extract the unique values for the tilt parameters φ, θ and δ of ABX₃ structures with regular and distorted octahedra up to the point symmetry , from atomic coordinates and lattice parameters. The geometry of the BX₆ octahedron is described by three B—X bond lengths (r₁, r₂, r₃) and three X—B—X bond angles (ψ₁₂, ψ₁₃ and ψ₂₃) or alternatively by a local strain tensor together with an average B—X bond length. Connections between the proposed method and Glazer's tilt system are discussed. The method is used to analyze structural transformations of I2/c, Pbnm and Immm structures. The proposed description allows the analysis of group–subgroup relations for the ABX₃ structures with distorted octahedra, in terms of octahedral deformations and tilting. The method might also be of interest in the study of the phase transitions in the family of ABX₃ structures.