Octahedra sharing faces and edges

Linked octahedra in corundum (a-Al203) and in ilmenite (FeTi03) Fe light, Ti dark octahedra. Left Plan view of two layers (both layers are shown only in the central part). Right Side view of sections of three layers with facesharing octahedra 

Alternate layers can be occupied by two different kinds of metal atom, then every pair of the face-sharing octahedra contains two different metal atoms this is the ilmenite type (FeTi03). Ilmenite is, along with perovskite, another structure type for the composition AiiMiv03. The space for the A2+ ion is larger in perovskite. Which structure type is preferred can be estimated with the aid of the ionic radius ratio r(A2+)/r(02-) 0.7 ilmenite 

The nickel arsenide type (NiAs) is the result of linking layers of the kind as in cadmium iodide. Continuous strands of face-sharing octahedra perpendicular to the layers 

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Two-thirds of the octahedral interstices are occupied. In a way the possible structure types are the inverse of the MX3 structures, since in these two-thirds of the octahedral interstices are vacant. If we take an MX3 type, clear the occupied interstices and occupy the vacant ones, the result is an M2X3 structure. The kind of linking between the occupied octahedra, however, is different. The arrangement of the vacant octahedral interstices of the RhF3 type corresponds to the occupied interstices in corundum, A1203 its occupied octahedra share edges and faces (Fig. 16.15, p. 179). The layer sequence is ... 

The chemistry of the orihoperiodaie ion is more complicated than implied by the formula tOs . Periodic acid often behaves as a dibasic acid forming salts of HilOj. Furthermore, pyro-type salts are known with the 10 octahedra sharing edges and faces. See Wells. A. F. Siructiiral Inorgunic Chemistry, 5th ed. Oxford University London, 1984 pp 405-406. 

The coordination theory, which has been applied successfully2 to brook-ite, the orthorhombic form of titanium dioxide, is based on the assumption that the anions in a crystal are constrained to assume positions about the cations such that they indicate the corners of polyhedra of which the cations mark the centers. These polyhedra are the fundamentally important constituents of the crystal retaining their form essentially, they are combined by sharing corners, edges, and faces in such a way as to build up a crystal with the correct stoichiometrical composition. Thus in rutile, anatase, and brookite there occur octahedra of oxygen ions about titanium ions in rutile each octahedron shares two edges with adjoining octahedra, in anatase four, and in brookite three. 

NiAss octahedra share edges in one direction (the ab plane) and faces in another (along the c direction). Many transition metal chalcogenides with a 1 1 cation to anion ratio have this structure, for example, NiS, FeS, FeTe, CoTe, and CrSe. Some of these cannot possibly be considered ionic. For example, below 260 K, NiS is a semimetal (the resistivity is 10 fl cm and temperature independent) and metallic above 260 K (with a resistivity as low as 10 fl cm that increases with temperature), the transition not being accompanied by a change in the symmetry of the crystal structure (Imada et al., 1998). 

In the corundum structure, the metal atoms are in crystallographic sites with variable coordinates. Because edge and face sharing of MOe octahedra can result in an abnormally close approach of the metal atoms to one another, such interactions can be minimized if the atoms move off center away from one another. However, in Ti203, the Ti atoms are only 2.58 A apart in face-shared octahedra and the d electrons are used to form a metal-metal bond. This compound is a semiconductor, but between 125 to 325 °C a broad structural transition takes place where this bond is broken, thus providing free electrons for electrical conduction and the compound now displays metallic conductivity. V2O3 also has this structure but has a more complex temperature dependence of its conductivity. 

We noted earlier that the number of regular octahedra that can share a common vertex without sharing edges or faces is limited to two, assuming that the distance between any pair of non-bonded X atoms of different AXg groups is not less than the edge-length, X-X, taken to be the minimum van der Waals distance. If each vertex that is shared is common to two octahedra only, there is a simple relation between the formula of the structure and the number of shared vertices (X atoms) ... 

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