Structures in terms of non-metal anion packing

The geometric problem of packing spheres is described in Section 7.2 above. In such structures, the spheres do not fill all the available volume. There are small holes between the spheres that occur in layers between the sheets of spheres. These holes, which are called interstices, interstitial sites or interstitial positions, are of two 

Consider the structures that arise from a cubic close-packed array of X anions. If every octahedral position contains an M cation, there are equal numbers of cations and anions in the structure. 

Should the anions adopt hexagonal close-packing and all of the octahedral sites contain a cation, the hexagonal analogue of the halite structure is produced. In this case, the formula of the crystal is again MX. The structure is the nicolite, (NiAs), structure, and is adopted by a number of alloys and metallic sulphides, including NiAs, CoS, VS, FeS and TiS. 

Structures containing cations in tetrahedral sites can be described in exactly the same way. In this case, there are twice as many tetrahedral sites as anions, and so if all sites are filled the formula of the solid will be M2X. When half are filled this becomes MX, and so on. 

A large number of structures can be generated by the various patterns of filling either the octahedral or tetrahedral interstices. The number can be extended if both types of position are 

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Table 7.2 Structures in terms of non-metal (anion) packing...

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