The Kapustinskii Equation
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|
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.