The Born-Mayer equation gives the total electrostatic interaction
energy for a given structure in terms of the Madelung constant,
A, for that structure. Something else that varies from structure
to structure is the number of ions within the formula unit for
a given structure.
| Structure |
Coordination Number |
Madelung constant,
A |
A/ν |
| |
|
|
ν
is the number of ions in the formula unit |
| Sodium Chloride (NaCl) |
6:6 |
1.74756 |
0.88 |
| Cesium Chloride (CsCl) |
8:8 |
1.76267 |
0.87 |
| Zinc Blende (ZnS) |
4:4 |
1.638 |
0.82 |
| Wurtzite (ZnS) |
4:4 |
1.64132 |
0.82 |
| Fluorite (CaF2) |
8:4 |
2.51939 |
0.84 |
| Rutile (TiO2) |
6:3 |
2.408 |
0.80 |
| Corundum (Al2O3) |
6:4 |
4.1719 |
0.83 |
Kapustinskii noted that the ratio of the Madelung
constant, A, to the total number of ions per formula unit for
a series of compounds with different structures deviate by less
than 10% from 0.87, the value found for the NaCl structure.
By replacing A with 0.87ν,
taking the average value of n, and making the approximation
that the internuclear separation is the sum of the ionic radii,
he derived a new expression for the total electrostatic interaction
from the Born-Lande equation. This is known as the Kapustinskii
equation.
| The Kapustinskii Equation:
(note that r+ and r- are measured in pm) |
 |
The Kapustinskii equation predicts lattice enthalpies
to within 10% of the experimental values for most compounds.
|