Radius Ratios and Predicting Structure

Owing to the wave nature of electrons, the ionic radius of an element is not an easily measured quantity. The numbers which appear in tables are essentially empirical values, such that when the ionic radii of an anion and cation are added together the result is the distance apart the ions would be if measured in an ionic compound. Evidence for this idea of fixed size of ions is derived from interionic distances measured by X-ray diffraction methods (Table 1.5). 

In Table 1.5, since the MX distance is simply the sum of the ionic radii, where 

The difference must just be r K ) - r(Na ), which is approximately 0.30 A. However, even though the differences can be calculated, it is not possible to calculate the absolute values. 

One strategy to solve this problem was put forward by Pauling and often forms the basis for tabulated values. Pauling argued that on theo- 

Previous work in this chapter has shown that a number of possible structures exist for a particular formula. For example, AB2 could form either the rutile or fluorite structures. Although differences between the electronegativity of the ions is important, the vital factor is the relative size of the ions. This can be used to predict which structure is most likely to form. 

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