Madelung constant
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The Madelung constant is used in determining the energy of a single ion in a crystal. It is named after Erwin Madelung, a German physicist.
An ionic solid has a certain amount of energy that is associated with it, because the ions don't want to be separated. It will take a positive energy to break apart the ionic solid. This value is known as lattice energy which is the exact negative of the energy of crystallization.
The lattice energy describes the amount of energy for a whole crystal but it doesn't describe the energy contribution of a single ion in the crystal. The energy of a specific ion would depend on how close it was to other ions, how many had the same charge, and how many had the opposite charge.
Since charges in ions are based on the electric energy of an electron, we can use the energy of the electron and then modify it to see how close the other electrons are.
- z = charge of ions
- e = 1.6022×10−19 C
- 4πEo = 1.112×10−10 C²/(J m)
- M = Madelung's constant, which is a relationship of the distance of the ions from one another due to a specific type of crystal. The Madelung's constant depends on the geometric arrangement of the constituent ions in the crystal structure.
