Octahedra sharing edges and vertices

Linking of octahedra in NbOCl3 with alternating short and long Nb-O bonds 

Strands of edge-sharing octahedra running parallel to c are joined with each other in rutile and a-Pb02 via common vertices 

The zigzag chains of edge-sharing octahedra that occur among compounds MX4 can also be joined by common vertices, resulting in the a-Pb02 type (Fig. 16.12). This structure type is less frequent. 

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Exceptions to the rule are observed for compounds with low polarity, i.e. when covalent bonds predominate. Fluorides and oxides (including silicates) usually fulfill the rule, whereas it is inapplicable to chlorides, bromides, iodides, and sulfides. For instance, in metal trifluorides like FeF3 octahedra sharing vertices are present, while in most other trihalides octahedra usually share edges or even faces. 

In cubic closest-packing, consideration of the face-centered unit cell is a convenient way to get an impression of the arrangement of the interstices. The octahedral interstices are situated in the center of the unit cell and in the middle of each of its edges [Fig. 17.3(a)], The octahedra share vertices in the three directions parallel to the unit cell edges. They share edges in the directions diagonal to the unit cell faces. There are no face-sharing octahedra. 

Of Ihe indefinitely large number of structures that could be built from octahedra sharing vertices, edges, and/or faces, a large number are already known, and a complete account of octahedral structures would cover much of the structural... 

We shall see later that (i) and (ii) correspond to families of related structures while (iii) and (iv) produce a single structure in each case. In addition to these structures in which octahedra share only vertices, edges, or faces, there are structures in which vertices and edges are shared in which all the octahedra and all the X atoms are equivalent. The rutile structure is a simple example—others are described later. 

Many more structures are known in which vertices and edges of octahedral coordination groups are shared, and models of several of them are described in MSIC. A relatively simple example is the AX3 framework formed from edge-sharing pairs of octahedra which are further linked to form the 3D framework of Fig. 5.33. This framework is the basis of the structure of one form of KSb03 and of KBiOj,... 

Limits of the mutual rotation of vertex-sharing tetrahedra and of vertex-sharing octahedra and the resulting bond angles at the bridging atoms. The minimum distance between vertices of different polyhedra (dotted) was taken to be equal to the polyhedron edge... 

The linking of tetrahedra takes place predominantly by sharing vertices. Edge-sharing and especially face-sharing is considerably less frequent than among octahedra. 

The structure can be viewed as chains of linked TiOe octahedra, where each octahedron shares a pair of opposite edges, and the chains are linked by sharing vertices this is shown in Figure 1.41(b). Figure 1.41(c) shows a plan of the unit cell looking down the chains of octahedra so that they are seen in projection. 

Octahedra linked in different ways often occur when different kinds of metal atom are present. Li2ZrFg offers an example. The Li and the F atoms are arranged in layers of the same kind as in Bilj. The layers are joined by single ZrFg octahedra which are placed below and on top of the voids of the layer (Fig. 16.13). The octahedra of the Li2F layer share common edges with one another and they share vertices with the ZrFg octahedra. 

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