Layered structures, edge-sharing octahedra

Figure 5.4 The corundum crystal structure (a) projected down the c axis showing layers of edge-shared [A106] octahedra with one octahedron vacant for every two Al3+ ions (b) section perpendicular to the c axis showing pairs of Al3+ ions in face-shared [A106] octahedra (c) configuration of the trigonally distorted [A106] octahedra with point symmetry C3 projected onto the (0001) plane.

Single crystal structure of Cdlj (a) showing its layered structure and (b) in polyhedral view as edge-shared octahedrons. 

Figure 3. Energy of Co/Mn ion along the Oh Oh transition path from an octahedral site in the TM layer, through a shared edge, to an octahedral site in the vacancy/ Li layer (top) delithiated Xu = 0 (M +), (bottom) half-lithiated Xu = 1/2 (average M +). (A (on j axis)) Layered structure with no transition metal in the empty/lithium layer (i.e., no defects). (B) A single TM atom located in the shared edge between neighboring octahedra (i.e., E in Figure 2). (C) A single TM atom defect in an empty/lithium layer octahedron.

The octahedrons surrounding the Ni " " ions in NiAs, on the other hand, are edge-shared in one direction while face-shared in another, leading to a layered structure with an ABABAB-type repeating motif. The following molecules all crystallize in the nickel arsenide structure TiS, TiSe, TiTe, CrS, CrSe, CrTe, CrSb, NiS, NiSe, NiTe, NiSb, and NiSn. 

Fig. 14. Layer structures composed of octahedra which share two edges and two corners, (a) planar single layer, opposite edges in common, VO(OH)2 structure. Above section perpendicular to the layers below part of one layer (b) adjacent edges shared, idealized M0O3 structure. In both structures neighboring layers are shifted by half an octahedron height relative to each other.

Fig. 15. Stepped layer structures derived from chains of (trans) edge-sharing octahedra by additional edge sharing, (a) The layer structure MXX2 of Figure 14a viewed perpendicular to the layers, (b) Stepped layers M2X5 built from double octahedron chains, (c) Combination M X3 , of (a) and (b) with n = 3. The octahedra of this figure are somewhat stretched, (d) Stepped double-layer structures MX2,...

The structures of CrClj and Bilj are based on cep Cl and hep T, respectively. In both structures one third of the available octahedral sites are occupied with two thirds of the sites in alternate layers filled by cations, resulting in layered structures. Each octahedron shares three edges with other octahedra (Figure 3.28). 

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