Madelung constant
![The Madelung constant being calculated for the NaCl ion labeled 0 in the expanding spheres method. Each number designates the order in which it is summed. Note that in this case, the sum is divergent, but there are methods for summing it which give a converging series.](/Images/godic/202501/12/NaCl-ionlattice-madelung1440.png")
![This graph demonstrates the non-convergence of the expanding spheres method for calculating the Madelung constant for NaCl as compared to the expanding cubes method, which is convergent.](/Images/godic/202501/12/NaClMadelungConstant1440.png")
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.