A cycle of reactions used for calculating the lattice energies of ionic crystalline solids. For a compound MX, the lattice energy is the enthalpy of the reaction

The standard enthalpy of formation of the ionic solid is the enthalpy of the reaction

The cycle involves equating this enthalpy (which can be measured) to the sum of the enthalpies of a number of steps proceeding from the elements to the ionic solid. The steps are:

1. (1) Atomization of the metal:

   $$\text{M}(\text{s})\to \text{M}(\text{g})\Delta H_1$$

2. (2) Atomization of the nonmetal:

   $${½\text{X}}_2(\text{g})\to \text{X}(\text{g})\Delta H_2$$

3. (3) Ionization of the metal:

   $$\text{M}(\text{g})\to {\text{M}}^{+}(\text{g})+\text{e}\Delta H_3$$

   This is obtained from the ionization potential.

4. (4) Ionization of the nonmetal:

   $$\text{X}(\text{g})+\text{e}\to {\text{X}}^{-}(\text{g})\Delta H_4$$

   This is the electron affinity.

5. (5) Formation of the ionic solids:

   $${\text{M}}^{+}{(\text{g})+\text{X}}^{-}(\text{g})\to {\text{M}}^{+}{\text{X}}^{-}(\text{s})\Delta H_{\text{L}}$$

   Equating the enthalpies gives:

   $$\Delta H_{\text{f}}=\Delta H_1+\Delta H_2+\Delta H_3+\Delta H_4+\Delta H_{\text{L}}$$

   From which Δ‎H _L can be found. It is named after the German physicist Max Born (1882–1970) and Fritz Haber.