The distance between Na ⁺ and Cl ⁻ is r . Therefore, the distance between two similar ions will be √2 r . Similarly, we can find out, 6 Cl ⁻ ions at r , 12 Na ⁺ ions at √2r, 8 Cl ⁻ ions at √3 r , 6 Na ⁺ ions at 2 r and so on.

In the three dimensional lattice,

The series within the bracket converge slowly and the limiting value is 1.74758. This value changes with the arrangement of lattice and therefore, different constant value is obtained for different crystal lattice system. This constant value for different lattice indicates a different Madelung constant (A) for different type of lattices.

Madelung constants of some crystal lattice:

Returning to the equation (1), it is clear that unless there is repulsion energy to balance the coulomb attraction energy, a stable lattice cannot be formed. Born suggested the repulsion energy as;

The net stabilization energy (lattice energy, U) gained due the formation of lattice by the combination of ions in gaseous states can be represented as the sum of E _coul and E _rep.