Caesium chloride type structure

The second common structure is the caesium chloride structure. In this structure, ions of one type are located at the corners of a cubic lattice... 

By examining Figures 3.7 and 3.32, we note that the caesium cations sit on a primitive cubic unit cell (lattice type P) with chloride anion occupying the cubic hole in the body centre. Alternatively, one can view the structure as P-type lattice of chloride anions with caesium cation in cubic hole. Keep in mind that caesium chloride does not have a body centred cubic lattice although it might appear so at a first glance. The body centred lattice has all points identical, whereas in CsCl lattice the ion at fte body centre is different from those at the comers. 

The occurrence of the NH4+ ion in the highly symmetrical sodium chloride and caesium chloride structures is seemingly inconsistent with its tetrahedral configuration and can be explained only on the assumption that the ion effectively acquires spherical symmetry by free rotation under the influence of the energy of thermal agitation. We shall encounter many other examples of structures in which ions or molecules are in free rotation, either at all temperatures or above a certain transition temperature all are examples of yet a further type of defect structure. 

The simpler of these two structures is the caesium chloride arrangement, found in the phases LiHg, LiTl, MgTl, CaTl and SrTl. This is, of course, also the structure of the / phase in the silver-cadmium system and in other electron compounds (fig. 13.11), and for this reason the systems just mentioned are sometimes quoted as exceptions to Hume-Rothery s rule. Apart from this geometrical resemblance, however, these systems have little in common with the electron compounds, and it seems preferable to regard the Hume-Rothery rule as applicable only to alloys of the T2-B1 type. 

Fig. 1.1 The three fundamental AB structure types with coordination numbers of eight (caesium chloride, (a)), six (sodium chloride, (b)), and four (zinc-blende, (c)). Because the coordinations are identical for atoms A and B, the atomic assignment to A and B may be freely chosen by the reader.

Because the Madelung constant has been computed by a summation over all lattice sites, it adopts characteristic values for all structure types [5,8]. To give a few examples, M arrives at (dimensionless) values of 1.6381 (zinc-blende-type), 1.7476 (sodium chloride-type), 1.7627 (caesium chloride-type), 5.0388 (fluorite-type), and 25.0312 (corundum-type) and does not scale with (= is independent of) the interionic distances. For the case of NaCl, the Madelung constant shows that the three-dimensional lattice surpasses the ionic pair in energy by almost 75%. This is what has made the formation of solid NaCl possible, a collective stabilization. 

The relative sizes of the cation and anion determine the type of lattice an ionic compound adopts. For example, although caesium and sodium are both in the same group of the periodic table, the chlorides crystallize with different types of lattice. Sodium chloride adopts the simple cubic structure (Chapter 4), whereas caesium chloride adopts the lattice shown in Figure 15.10. In caesium chloride, the caesium ions cannot get as close to the chloride ions as the smaller sodium ions. Eight caesium ions can pack around a chloride ion if they are positioned at the corners of a cube. The structure of ionic lattices is determined by X-ray crystallography (see Chapter 21, and Chapter 22 on the accompanying website). 

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