Lattice energy

Definition: “The Lattice enthalpy change is the standard molar enthalpy change for the formation of an ionic compound (at 0K) from it gaseous ions.” [2]

+ ‐ 0 M (gas) + X (gas) Æ MX(solid) ∆H L

Since it is impossible to produce a sufficient amount of such gaseous ions, and to work at 0K, it is impossible to measure the lattice energy directly in a certain experiment. Therefore there exist only two possibilities to quantify the lattice energy; either indirectly (via Born Haber cycle), or theoretically.

Theoretical calculation of the lattice energy

The two major parts of the calculation, concerning the lattice energy, are the Born repulsion and the Coulomb attraction. This is of cause only true for ionic compounds; the more covalent the compound the less valid is the calculation. The Coulomb attraction describes the force that interacts between two charged particles (attractive between opposite charged particles, etc.). The closer two different ions get together, the higher is the coulomb force, i.e. the potential energy of such a bonding decreases . The Born repulsion on the other hand takes into account that positive ions as they are treated like a single point charge are still surrounded by several electrons (e.g. 10 e‐, for Na+‐ion), who interact with the negative charged ion and produce a repulsive force .

Madelung constant

The lattice energy is calculated from the sum of all interactions between the ions in a crystal. To do so, you have to simplify the calculation by adding the Madelung constant (A). This constant is evaluated in the simple crystal structure by focusing at just one fix ion, sum up all different charged ions divided by there distance (in multiples of the atom distances; rAB) and subtract all same charged ions. For the simple rock‐salt structure:

Since the constant diverge to a certain value, which is the same for all compounds with that particular unit cell, it reduces the calculation to a more simple formula. For the final calculation of 0 ∆H L you have to multiply the Coulomb potential energy with the Avogadro constant (NA) and the Madelung constant (A), add the potential of the Born repulsion, set the first derivative zero and then you can rearrange it to:

The given formula allows to predict which structure type is favoured by a certain compound or can give for example some information about the solubility in water.

Lit.: [1] U. Müller, Anorganische Strukturchemie, 2. Auflage,Teubner, Stuttgart, 1992 [2] D. Shriver, P. Atkins, Inorganic Chemistry, 3rd ed., Oxford University Press, 2002 [3] E. Riedel, Anorganische Chemie, 4. Auflage, Walter de Gryter, Berlin, 1999