The Coulomb model assumes opposing point charges in a regular arrangement, since ions are positively or negatively charged towards the outside. However, if the approach is sufficiently close, the electron shells of the ions meet and repel each other due to their identical “charge”. The size of the repulsion depends on the electron density of the ions and is measured using the Born exponent . This is determined experimentally from the compressibility of the ion crystals, but average values can also be used for the calculation.
The Madelung constant should be marked with instead of with to avoid confusion with the molar mass .
Conversion of the result to temperatures above absolute zero
The larger the covalent bond component, the worse the results will correspond to reality. This is because the model is based on the consideration of pure ions.
example
The lattice energy of barium oxide is to be calculated. Barium is twice positively charged in the crystal lattice and the oxide ions twice negative. The amounts of the ion charges are entered:
Barium oxide crystallizes in the NaCl type. Its Madelung constant is 1.7475. We also insert the numerical value of the Avogadro constant, the permittivity and the elementary charge:
We determine the equilibrium distance between the ions from the sum of the ion radii. This amounts to:
is the mean of the Born exponent of the cation and the anion:
The units are reduced to voltampereseconds (energy, joules) per mol: