Energies of Ion Systems and the Born Treatment

According to the Born picture, then, the potential energy (En), of a 

The summation of repulsion forces on a single ion (due to electron-cloud overlapping) is simpler for, unless there is appreciable anion-anion repul- 

The total potential energy (PE) for a sodium ion in a crystal of NaF is then  

Now any ion within a crystal will be at its position of greatest stability when its potential energy is a minimum. The most stable interionic distance may then be determined by differentiating Equation (5) with respect to r, equating to 0, and solving for r. In Exercise 4, the student will show that the interionic distance associated with maximum stability is  

For compounds in which the radius ratio is small, another term may be added to (5) to include also the appreciable effect of anion-anion repulsion. Pauling has indeed proposed such a treatment, analogous to Born s, but refined to include radius-ratio effects in doing so, he has been able to predict just how much the interionic distances in each of the alkali halides should depart from strict additivity. In using his modified treatment further for calculation of lattice energies, he has been able to show that the anomalies in melting points and boiling points, mentioned earlier in this chapter, may be correlated, at least semiquantitatively, with the radius ratios. 

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