Anthony R. West - Solid State Chemistry and its Applications

The octahedral sites between two cp layers in an ideal hcp anion array are shown in the projection in Fig. 1.38(a). While all these sites are occupied in NiAs [Fig. 1.35(h)], only half are occupied in rutile and in such a manner that alternate horizontal rows of octahedral sites are full and empty. The orientation of the tetragonal unit cell in rutile is shown. Parallel to the tetragonal c axis, horizontally, the TiO 6octahedra share edges. This is shown in Fig. 1.38(b) for two octahedra with oxygens 1 and 2 forming the common edge.

An alternative, and more accurate, way to describe the packing arrangement of oxide ions in rutile is as a slightly distorted version of a different type of packing called tetragonal packing ( tp ), characterised by a sphere coordination number of 11 which contrasts with hcp and ccp which have a packing sphere coordination number of 12. The symmetry of tp is quite different to that of hcp since tp is characterised by fourfold rotational symmetry without any threefold symmetry whereas hcp has no fourfold symmetry but is characterised by threefold (or sixfold) symmetry. An [001] projection of the rutile structure is shown in Fig. 1.37(f); the fourfold symmetry shown is not a simple rotation axis but is a fourfold screw axis in which the structure rotates by 90° and translates by half the unit cell in the [001] direction.

The bond lengths in TiO 2may be calculated readily; for the Ti–O bond between Ti at and O at (0.3, 0.3, 0) the difference in both x and y coordinates of Ti and O is . From a right‐angled triangle calculation, the Ti–O distance in projection down c [Fig. 1.37(a)] is . However, Ti and O have a difference in c height of and the Ti–O bond length is therefore equal to . The axial Ti–O bond length between, for example, and O (0.8, 0.2, 0.5) is easier to calculate because both atoms are at the same c height. It is equal to .

Figure 1.38 (a) Octahedral sites in an ideal hcp array; (b) edge‐sharing octahedra.

Table 1.15 Some compounds with the rutile structure

R. W. G. Wyckoff, Crystal Structures , Vols 1 to 6, Wiley (1971).

Two main groups of compounds exhibit the rutile structure, Table 1.15: oxides of tetravalent metals and fluorides of divalent metals. In both cases, the metals are too small to have eight coordination and form the fluorite structure. The rutile structure may be regarded as essentially ionic.

The CdI 2structure is nominally similar to that of rutile because it has an hcp anion array with also, half of the octahedral sites occupied by M 2+ions. The manner of occupancy of the octahedral sites is quite different, however; entire layers of octahedral sites are occupied and these alternate with layers of empty sites, Fig. 1.39. CdI 2is therefore a layered material in both its crystal structure and properties, in contrast to rutile, which has a more rigid, 3D character.

Two I layers in a hcp array are shown in Fig. 1.39(a) with the octahedral sites in between occupied by Cd. To either side of the I layers, the octahedral sites are empty. Compare this with NiAs [Fig. 1.35(d) and (h)] which has the same anion arrangement but with all octahedral sites occupied. The layer stacking sequence along c in CdI 2is shown schematically in Fig. 1.39(b) and emphasises the layered nature of the CdI 2structure: I layers form an … ABABA … stacking sequence. Cd occupies octahedral sites which may be regarded as the C positions relative to the AB positions for I. The CdI 2structure is, effectively, a sandwich structure in which Cd 2+ions are sandwiched between layers of I –ions; adjacent sandwiches are held together by weak van der Waals bonds between the I layers. In this sense, CdI 2has certain similarities to molecular structures. For example, solid CCl 4has strong C–Cl bonds within the molecule but only weak Cl–Cl bonds between adjacent molecules. Because the intermolecular forces are weak, CCl 4is volatile with low melting and boiling points. In the same way, CdI 2may be regarded as an infinite sandwich ‘molecule’ in which there are strong Cd–I bonds within the molecule but weak van der Waals bonds between adjacent molecules.

The coordination of I in CdI 2is shown in Fig. 1.39(c). An I at (shaded) has three close Cd neighbours to one side at c = 0. The next nearest neighbours are 12 I that form the hcp array: six are in the same plane, forming a hexagonal ring, at ; three are at and three at .