Madelung constant

The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. It is named after Erwin Madelung, a German physicist.

Because the anions and cations in an ionic solid are attracting each other by virtue of their opposing charges, separating the ions requires a certain amount of energy. This energy must be given to the system in order to break the anion-cation bonds. The energy required to break these bonds for one mole of an ionic solid under standard conditions is the lattice energy.

The Madelung constant allows for the calculation of the electric potential V_i of all ions of the lattice felt by the ion at position r_i

where r_ij =|r_i - r_j| is the distance between the ith and the jth ion. In addition,

If the distances r_ij are normalized to the nearest neighbor distance r₀ the potential may be written

with ${\displaystyle M_{i}}$ being the (dimensionless) Madelung constant of the ith ion

The electrostatic energy of the ion at site ${\displaystyle r_{i}}$ then is the product of its charge with the potential acting at its site

...
Wikipedia