Figure 1
From: Topological defects at octahedral tilting plethora in bi-layered perovskites
(a) Schematic diagram of possible space groups and the corresponding Glazer notations for bi-layered perovskite A3B2O7. Lines link the group–subgroup relations. The lattice directions are given with respect to the T state (I4/mmm). (b–f) In-plane projected views of various BO6 octahedral tilts/rotations. The dashed lines outline the primitive unit cells, and the red and cyan spheres represent the O and B-site ions, respectively. Black and gray arrows indicate directions of apical and basal plane oxygen displacements, respectively. (b) Un-distorted BO6 octahedron in the T state. (c) A clockwise (+) rotated BO6 in the O* and O′ states. The rotation can be also counterclockwise (−). In two adjacent layers within one bi-layer, an out-of-phase rotation (+ − or − +) along the c axis occurs in the O* state while in-phase (+ + or − −) rotation in the O′′ state. (d) Eight possible 1±, 2±, 3± and 4± apical oxygen displacements in the O state. The azimuthal angle, φ, of an apical oxygen distortion is denoted. (e) Given tilting vectors in the O′ state. (f) Four possible apical oxygen displacements (red-circled labels) along the <100>T directions in the T′ state.
