Madelung Constants^†

Madelung constants are simple numbers which depend on the type of structure investigated. They are needed for the calculation (using the Born-Haber cycle) of lattice energies and enthalpies of formation of ionic compounds. Each Madelung constant is the sum of partial Madelung constants which represent the contributions of the individual ions to the total lattice energy. The partial Madelung constants depend on the ionic charge and, clearly though not stringently, on the coordination number. On the other hand, each Madelung constant can be represented by a sum of Madelung constants for related simple primitive AB structures. Surprisingly, these Madelung constants are numerically interrelated in a simple manner, and are related to the partial Madelung constants of interstitial sites. – Madelung constants of parameter-dependent structures (e.g. of the rutile or anatase type) and their variations with the structure-determining quantities are of particular interest. Madelung constants also yield information in the case of complex compounds and – surprisingly – of non-metal compounds (e.g. XeF₂, XeF₄, XeF₂·XeF₄).