A Note on Good Practice: The charge number, z, is positive for cations and
negative for anions and the charge of an ion is ze. However, chemists almost
always refer to z itself as the charge, and speak of a charge of 1, 1, and
so on. ■
Each ion in a solid experiences attractions from all the other oppositely charged
ions and repulsions from all the other like-charged ions. The total potential energy
is the sum of all these contributions. Each cation is surrounded by anions, and there
is a large negative (energy-lowering) contribution from the attraction of the opposite
charges. Beyond those nearest neighbors, there are cations that contribute a
positive (repulsive, energy-raising) term to the total potential energy of the central
cation. There is also a negative contribution from the anions beyond those cations,
a positive contribution from the cations beyond them, and so on, to the edge of the
solid. These repulsions and attractions become progressively weaker as the distance
from the central ion increases, but because the nearest neighbors of an ion give rise
to a strong attraction, the net outcome of all these contributions is a lowering of
energy. Our task is to assess how far the energy is lowered by using the Coulomb
potential energy expression in Eq. 1.