Ionic Polarisation

IONIC POLARISATION

Ionic polarisation is due to the displacement of cations (positive ions) and anions (negative ions) in opposite directions.

This occurs in ionic dielectrics (e.g. NaCl crystal) by the influence of external electrical field (fig. 1.6 (a)).

When an electrical field (E) is applied on an ionic dielectric, there is a shift of one ion with respect to another from their mean positions.

The positive ions displace in the direction of applied electrical field through the distance x₁. The negative ions displace in opposite direction through the distance x₂ (fig. 1.6 (b)).

We assume that there is one cation and one anion in each unit cell of the ionic crystal.

Hence, the net distance between two ions

x = x₁ + x₂.................. (1)

When the ions are displaced from their mean positions in their respective directions, then the restoring forces appear which tend to move the ions to move back to their mean position. The restoring force produced is proportional to the displacement.

For positive ion

Restoring force F ∝ x₁

or Restoring force acting on the positive ion F = β₁x₁ ... (2)

For negative ion

Restoring force F ∝ x₂

or Restoring force acting on the negative ion F = β₂ X₂....(3)

where β₁, and β₂ are restoring force constants which depend upon the masses of ions and angular frequency of vibrating molecule in which ions are present.

If m is the mass of positive ion, M is the mass of negative ion and ω₀  is the angular frequency, then

β₁ = mω₀²........(4)

β₂ = Mω₀².......(5)

Substituting for β₁, from eqn (4) in eqn (2), the restoring force for positive ion can be rewritten as

F = mω₀² x₁ ..............(6)

We know that force F = eE .......(7)

Equating the eqn (6) and (7), we get

eE = mω₀² x₁

or x₁ =eE / m ω₀² ...(8)

Similarly for the negative ion, we can write

X₂ = eE / Mω₀² .....(9)

Adding the equations (8) and (9), we have

The dipole moment is equal to the product of charge and distance of separation between the charges.

i.e., μ = e × x ...(11)

Substituting x from eqn (10) in eqn (11), we have

But μ α Ε

Or μ = α_i Ε.....(13)

where α_i is ionic polarisability of dielectric material

On comparing the equations (12) and (13), we have

Conclusion

 (i) Ionic polarisability (∝_i) is inversely proportional to the square of angular frequency of the ionic molecule.

(ii)It is directly proportional to its reduced mass given by (1/ m  + 1/M )

(iii) It is independent of temperature.

(iv) It occurs in ionic substance.