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 attract 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. Formal expression 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 :V_i = \frac \sum_ \frac\,\! where r_ = , r_i-r_j, is the distance between the i^ and the j^ ion. In addition, :z_j = number of charges of the j^ ion :e= 1.6022 C :4\pi \epsilon_0= . If the distances r_ are normalized to the nearest neighbor distance r_0, the potent ...
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