Ionic crystals packing

The geometry of ionic crystals, in which there are two different kinds of ions, is more difficult to describe than that of metals. However, in many cases the packing can be visualized in terms of the unit cells described above. Lithium chloride, LiCl, is a case in point Here, the larger Cl- ions form a face-centered cubic lattice (Figure 9.18). The smaller Li+ ions fit into holes between the Cl- ions. This puts a Li+ ion at the center of each edge of the cube. 

The packing in ionic crystals requires that ions of opposite charges alternate with one another to maximize attractions among ions. A second important feature of ionic crystals is that the cations and anions usually are of different sizes. Usually the cations are smaller than the anions. Consequently, ionic compounds adopt a variety of structures that depend on the charges and sizes of the ions. One way to discuss ionic structures is to identify a crystal lattice for one set of ions, and then describe how the other ions pack within the lattice of the first set. 

In most ionic crystals, the anion is larger than the cation and, therefore, the packing of the anions determines the arrangement of ions in the crystal lattice. There are several possible arrangements for ionic crystals in which the anions are larger than cations, and cations and anions are present in equal molar amounts. For example. Figure 4.22 shows two different arrangements found in the structures of sodium chloride, NaCl, and cesium chloride, CsCl. 

To this point, all the examples presented have been ones in which the origin of the asymmetric induction has been unimolecular in nature, that is, the molecules adopt homochiral conformations in the solid state that favor the formation of one enantiomer over the other, usually through the close intramolecular approach of reactive centers bimolecular crystal packing effects appear to play little or no role in governing the stereochemical outcome of such reactions. This raises the interesting question of whether the soUd-state ionic chiral auxiUary approach to asymmetric synthesis could be made to work for conformationally unbiased reactants, i.e., those possessing symmetrical, conformationally locked structures. Two such cases are presented and discussed below. 

We know from quantum mechanics that atoms and ions do not have precisely defined radii. However, from the foregoing discussion of ionic crystal structures we have seen that ions pack together in an extremely regular fashion in crystals, and their atomic positions, and thus their interatomic distances, can be measured very accurately. It is a very useful concept, therefore, particularly for those structures based on close-packing, to think of ions as hard spheres, each with a particular radius. 

This opening chapter has introduced many of the principles and ideas that lie behind a discussion of the crystalline solid state. We have discussed in detail the structure of a number of important ionic crystal structures and shown how they can be linked to a simple view of ions as hard spheres that pack together as closely as possible, but can also be viewed as the linking of octahedra or tetrahedra in various ways. Taking these ideas further, we have investigated the size of these ions in terms of their radii, and... 

THE CLOSEST PACKING OF LARGE IONS IN IONIC CRYSTALS... 

An ionic compound typically contains a multitude of ions grouped together in a highly ordered three-dimensional array. In sodium chloride, for example, each sodium ion is surrounded by six chloride ions and each chloride ion is surrounded by six sodium ions (Figure 6.11). Overall there is one sodium ion for each chloride ion, but there are no identifiable sodium-chloride pairs. Such an orderly array of ions is known as an ionic crystal. On the atomic level, the crystalline structure of sodium chloride is cubic, which is why macroscopic crystals of table salt are also cubic. Smash a large cubic sodium chloride crystal with a hammer, and what do you get Smaller cubic sodium chloride crystals Similarly, the crystalline structures of other ionic compounds, such as calcium fluoride and aluminum oxide, are a consequence of how the ions pack together. 

If all the packing atoms are no longer neutral (e.gn half are cations and half are anions), the closest packed structures are no longer the most stable, as can be seen from the similar two-dimensional case (see above). However, these structures may still be useful when considered as limiting cases for certain ionic crystals. Consider lithium iodide, in which the iodide anions are so much larger than the lithium cations that they may be assumed to touch or nearly touch. They can be considered to provide the framework for the crystal. The much smaller lithium ions can then fit irto the small interstices between the anions. If they expand the lattice slightly to remove the anion-anion contact, the anionic repulsion will be reduced and the crystal stabilized, but the simple model based on a closest packed system of anions may still be taken as the limiting case and a useful approximation. 

COORDINATION POLYHEDRA. The arrangement of oxygen ions about the cation to which they are closely bonded in an ionic crystal, as, for example, the group SiOj which forms a tetrahedron. Such polyhedra pack as units in the crystal structure. 

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