bei48482_FM

The Solid State 341

B r 0 n^1 (10.4)

The total potential energy at the equilibrium separation is therefore given by

U 0   1   (10.5)

We must add this amount of energy per ion pair to separate an ionic crystal into

individual ions (Fig. 10.7). For the cohesive energy, which corresponds to separating

the crystal into atoms, we must take into account the energy involved in shifting an

electron from a Na atom to a Cl atom to give a Na-Clion pair.

The exponent ncan be found from the observed compressibilities of ionic crystals.

The average result is n9, which means that the repulsive force varies sharply with r.

The ions are “hard” rather than “soft” and strongly resist being packed too tightly. At

the equilibrium ion spacing, the mutual repulsion due to the exclusion principle (as

1



n

e^2



4  0 r 0

Total

potential

energy

e^2



4  0 n

r 0

r

U 0

U

Utotal

Urepulsive

Ucoulomb

Figure 10.7How the ionic potential energies in an ionic crystal vary with ionic separation r. The

minimum value U 0 of Utotaloccurs at an equilibrium separation of r 0.

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