Geometrical and structural relations in the rhombohedral perovskites

Abstract

The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaA103, PrA103) and for their ferroelectric properties (e.g. LiNbO3, PbZr/TiO3). In this paper, data scattered through the literature are correlated, with correction of some misleading mistakes of calculation. Geometrical descriptions are put in a form allowing comparisons. The structures, classified by their space groups, are described in terms of four structural parameters, the octahedron tilt co, octahedron distortion d, and A-and B-cation displacements s and t, together with an elongation or flattening ~ of the octahedron, deducible with the help of co from the interaxial angle a,h. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the R-3e structures a correlation not previously noted in the literature is found between the tilt angle co and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3e structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.

General Rules for Predicting Phase Transitions in Perovskites due to Octahedral Tilting

“…This structure has Pm3m symmetry. Under ambient conditions many perovskites exhibit structures with lower symmetries that can be derived from the cubic aristotype structure through the tilting of essentially rigid BX 6 octahedra [5][6][7][8][9]. While we restrict ourselves in this Letter to structures in which tilting alone is the symmetry-breaking process, we note that many other perovskites, including CaTiO 3 itself, exhibit structures and symmetries that result from cation displacements in addition to tilting of the octahedra.…”

Ferroelectric-Paraelectric Transition inBiFeO3: Crystal Structure of the OrthorhombicβPhase

“…1(a)) follow the same trends observed by previous authors. 12,13,16 The oxygen octahedral rotation, ω, and the 'polar' shifts of the Bi 3+ (tc) and Fe 3+ (sc) ions from their 'ideal' positions (c is the lattice parameter; t and s parameters are defined by Megaw et al 26 and Moreau et al 27 and summarised by Fischer et al 11 ) are plotted in Fig. 1.…”

Strain-controlled oxygen vacancy formation and ordering in CaMnO3

“…1), or changing the angle or pattern of rotations and tilts of the oxygen octahedra (center row of Fig. 1) [16][17][18] . Indeed first-principles electronic-structure calculations within this approximation have proven successful in predicting and explaining many of the observed novel behaviors 14,19,20 ; for a review see Ref.…”