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:

from which Δ‎H_L can be found. It is named after Max Born and the German chemist Fritz Haber (1868–1934).