Total Energy
The total intensive potential energy of an ion in the lattice can therefore be expressed as the sum of the Madelung and repulsive potentials:
Minimizing this energy with respect to yields the equilibrium separation in terms of the unknown constant :
Evaluating the minimum intensive potential energy and substituting the expression for in terms of yields the Born–Landé equation:
Read more about this topic: Born–Landé Equation, Derivation
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