Unit cell caesium chloride

Q Use atom counting to determine the number of formula units of caesium chloride per unit cell, and hence determine the lattice type. 

Caesium chloride is not body-centered cubic, but cubic primitive. A structure is body centered only if for every atom in the position x, y, z there is another symmetry-equivalent atom in the position x+ j,y+ j,z+ j in the unit cell. The atoms therefore must be of the same kind. It is unfortunate to call a cluster with an interstitial atom a centered cluster because this causes a confusion of the well-defined term centered with a rather blurred term. Do not say, the 04 tetrahedron of the sulfate ion is centered by the sulfur atom. 

A unit cell of the caesium chloride structure is shown in Figure 1.30. It shows a caesium ion, Cs, at the centre of the cubic unit cell, surrounded by eight chloride... 

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. 

Fig. 3.03. Clinographic projection of the unit cell of the cubic structure of caesium chloride, CsCl.

It is natural to enquire why different AX compounds should possess different structures, and, in particular, why CsCl, CsBr and Csl should have a structure different from that of the other alkali halides. We can answer this question if we consider fig. 3.07a, which represents a section through the caesium chloride unit cell on a vertical diagonal plane. The ions in this diagram are shown in their correct relative sizes for Cs+ and Cl-, and anions and cations are seen to be in contact at the points P. Now let us suppose that the cations are replaced by others of... 

Fig. 3.07. Section through a unit cell of the caesium chloride structure on a vertical diagonal plane. The solid circles represent the cations. In (a) the ions are shown in their correct relative sizes for CsCl (b) corresponds to the critical radius ratio for anion-anion contact.

The second structure common to a number of T1-B1 systems is that of sodium thallide, sometimes called the Zintlphase. This structure (fig. 13.12) is closely related to that of caesium chloride in that the pattern of sites occupied forms a cubic body-centred lattice. The distribution of the atoms, however, is such that each atom has four neighbours of each kind, and the true cell is therefore the larger unit shown, containing sixteen instead of only two atoms. Some phases in which the sodium thallide structure occurs are LiZn, LiCd, LiAl, LiGa, Liln, Naln and NaTl. It is a characteristic feature of all of these phases that in them the alkali metal atom appears to have a radius considerably smaller than in the structure of the element (even when allowance is made for the change in co-ordination number), suggesting that this atom is present in a partially ionized condition and that forces other than purely metallic bonds are operative in the structure. 

Show that the structure of the unit cell for caesium chloride (Figure 5.16) is consistent with the formula CsCl. 

---