SOLID STATE ELECTROCHEMISTRY: LATTICE ENERGY

Crystal lattice contains of cations and anions. The interactions between them are much more complex than the interaction between two ions. This interaction is described in Figure 3, which describes the interactions inside the crystal lattice.

Figure 3. The crystal lattice of NaCl (expanded)
(Effendi, 2008)

interaction between Na+ ion in the centre of cubic di Figure 3. are:

1) Its interaction with 6 Cl- ions with distance of square root of 1.

2) Its interaction with 12 Na+ ions with distance of square root of 2

3) Its interaction with Cl- ions with distance of square root of 3

4) its interaction with 6 Na+ ions with distance of square root of 4.

The total interaction between ions inside a crystal lattice is stated by MADELUNG CONSTANT , A. In NaCl crystal, the Madelung constant of the first four stribes are:

The interaction between ions inside crystal lattice is called as geometric interaction. Due to this geometric interaction, the coulomb's electrostatic energy is become,

The electrostatic energy of 1 mol crystal which contains of N cations and N anions is,

N is the Avogadro's number

The repulsive force between electron clouds of the ions could be ignored only if the distance between ions is far. However, the repulsive force will become stronger as the distance is become smaller. In this state, the repulsion force between electron clouds of ions must be considered. Born stated that the repulsion energy, Erep is described by equation:

B is a constant and n is Born exponent.

The repulsion energy of 1 mol crystal which contains of N cations and N anions is:

The total energy of 1 mol crystal which contains of N cations and N anions is:

The value of Born exponent, n, is depend on ion type. Larger size of ions will have higher electron density than smaller ions. The Born exponent value will be higher as the ionic size become larger.

When the repulsion force is equal to the attraction force, then the lattice energy is minimum. The condition at equilibrium condition might be stated as below,

at equilibrium condition, the lattice energy is stated as Uo and the distance between anion and cation as ro. Substitution of B into U produce the equation below,

This equation is called as Born-Lande equation. This equation can be used to calculate the lattice energy of ionic crystal if the crystal structure and the distance of anion-cation have been known already. The crystal structure is required to calculate the Madelung constant, A. This crystal structure and also the distance of anion-cation are could be founded from crystallographic data (XRD data).

Kapustinski stated that for the ionic compounds of unknown structure, the lattice energy could be estimated from the equation below,

v is the number of ions inside a molecule of ionic compound and ro is the sum of cationic and anionic radius in pm unit. The ionic radius is calculated based on the coordination number.