Engineering Physics

1.4 Madelung constant

In ionic crystals, the effect of interaction of all the ions on an ion has been represented by Madelung constant, α_M. In ionic crystals, individual atoms do not exist. Every ion is surrounded by some number of opposite ions, i.e., an anion is surrounded by certain number of cations and vice versa. The Madelung constant has been explained by considering one of the ionic crystals [say NaCl]. As shown in Fig. 1.5, let u_ij is the interaction energy between a particular ion ‘i’ and another ion ‘j’ [j is a variable], so that the separation between these ions is r_ij. The i^th ion makes an interaction with a number of surrounding ions in pair-wise. The net interaction energy u_i is the sum of all pair-wise interaction energies with ...