Quantitative description of the tilt of distorted octahedra in ABX 3 structures

• Published in: Acta crystallographica. Section B, Structural science Structural science, 2007-04, Vol.63 (2), p.190-200
• Main Authors: Tamazyan, Rafael, van Smaalen, Sander
• Format: Article
• Language: English
• ISSN: 0108-7681
• DOI: 10.1107/S010876810605244X

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 φ, θ and δ of ABX 3 structures with regular and distorted octahedra up to the point symmetry \bar 1, from atomic coordinates and lattice parameters. The geometry of the BX 6 octahedron is described by three B — X bond lengths ( r 1 , r 2 , r 3 ) and three X — B — X bond angles (ψ 12 , ψ 13 and ψ 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 I 2/ 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.