Ionic Sizes and Crystal Environments

It is apparent from the data shown in Table 7.4 that there is a great difference between the sizes of some ions. For example, the ionic radius of Li+ is 60 pm, whereas that of Cs+ is 169 pm. When these ions are forming a crystal with Cl, which has a radius of 181 pm, it is easy to understand that the geometrical arrangement of ions in the crystals may be different even though both LiCl and CsCl have equal numbers of cations and anions in the formulas. 

When spherical objects are stacked to produce a three-dimensional array (crystal lattice), the relative sizes of the spheres determine what types of arrangements are possible. It is the interaction of the cations and anions by electrostatic forces that leads to stability of any ionic structure. Therefore, it is essential that each cation be surrounded by several anions and each anion be surrounded by several cations. This local arrangement is largely determined by the relative sizes of the ions. The number of ions of opposite charge surrounding a given ion in a crystal is called the coordination number. This is actually not a very good term because the bonds are not coordinate bonds (see Chapter 16). For a specific cation, there will be a limit to the number of anions that can surround the cation because 

Singly charged Doubly charged Triply charged  

Calculating the minimum size for the cation that can be in contact with the six anions as the anions are just touching each other is a simple problem. The critical factor is the relative sizes of the ions, 

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

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