Classification of perovskite structural types with dynamical octahedral tilting

Perovskites ABX ₃ with delocalized positions of the X atoms represent a distinct class of dynamically distorted structures with peculiar structural relations and physical properties. The delocalization originates from atoms crossing shallow barriers of the potential energy surface. Quantum mechanically, they can be treated similar to light atoms in diffusive states. Many of these perovskite structures are widely used functional materials thanks to their particular physical properties, such as superconductivity, ferroelectricity and photo-activity. A number of these properties are related to static or dynamic motion of octahedral units. Yet, a full understanding of the relationships between perovskite crystal structure, chemical bonding and physical properties is currently missing. Several studies indicate the existence of dynamic disorder generated by anharmonic motion of octahedral units, e.g. in halide perovskite structures. To simplify structural analysis of such systems we derive a set of space groups for simple perovskites ABX ₃ with dynamical octahedral tilting. The derived space groups extend the well established space group tables for static tiltings by Glazer [Acta Cryst. B (1972). 28, 3384–3392], Aleksandrov [Ferroelectrics (1976). 24, 801–805] and Howard & Stokes [Acta Cryst. B (1998). 54, 782–789]. Ubiquity of dynamical tilting is demonstrated by an analysis of the structural data for perovskites reported in recent scientific publications and the signature of dynamic tilting in the corresponding structures is discussed, which can be summarized as follows: (a) volume increase upon a lowering of temperature, (b) apparent distortion of octahedra (where Jahn–Teller distortions can be ruled out), (c) mismatch between observed instantaneous symmetry and average symmetry, (d) deviation of the experimental space group from the theoretically predicted structures for static tilting, (e) inconsistency of lattice parameters with those suggested by the theory of static tilts, and (f) large displacement parameters for atoms at the X and B sites. Finally, the possible influence of dynamic disorder on the physical properties of halide perovskites is discussed.