Quantitative description of the tilt of distorted octahedra in ABX3 structures

A description of the tilt of octahedra in ABX(3) perovskite-related structures is proposed that can be used to extract the unique values for the tilt parameters phi, theta and delta of ABX(3) structures with regular and distorted octahedra up to the point symmetry (1) over bar, from atomic coordinates and lattice parameters. The geometry of the BX6 octahedron is described by three B-X bond lengths (r(1), r(2), r(3)) and three X-B-X bond angles (12, 13 and 23) 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 ABX(3) 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 ABX(3) structures.