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Engineering Physics by S. Mani Naidu

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1.4 Madelung constant

In ionic crystals, the effect of interaction of all the ions on an ion has been represented by Madelung constant, αM. 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 uij 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 rij. The ith ion makes an interaction with a number of surrounding ions in pair-wise. The net interaction energy ui is the sum of all pair-wise interaction energies with ...

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