Module 4 : Solid State Chemistry
Lecture 16 : Lattices and Unit Cells
  16.2  

Ionic lattices and Lattice Energies.

We have studied in Module 2 the details regarding intermolecular interactions. In Fig 16.3, the total interaction is shown as a sum of the attractive (Coulombic) and repulsive interactions.

 
       
 
Figure 16.3 Interaction energy between a positive ion and a negative ion as a function of interionic distance r.
 

The repulsive term is dominated by exchange interactions(see lecture 10). The above form is for a pair of ions. When ion pairs are stable at a distance r0, why are lattices fromedat all? To see why, consider a one dimensional chain of sodium and chloride ions as shown in fig 16.4.

 
            
 
Figure 16.4 A one dimensional sodium chloride lattice.
 
Let the central sodium ion be at r = 0. The other sodium ions, will be at 2r0, 4r0, 6r0, and so on and the chlorides at r0, 3 r0, 5 r0 and so on. The total Coulombic interaction for this central ion is
 
U ionic = -2e2/r0 [ (1-1/2) + (1/3 - 1/4) +(1/5 -1/6)+...] (16.1)