Question

Potassium chloride (KCl), with lattice parameter equal to 0.629 nm, has the same crystal structure as NaCl. The ionic polarizability per ion pair (per K+ -Clion) is 4.58×10-40 Fm² , while the electronic polarizability of K+ is 1.264 ×10-40 Fm² and that of Clis 3.408 ×10-40 Fm² . Calculate the dielectric constant under dc operation and at optical frequencies (experimental values are respectively 4.84 and 2.19).

Answer 1

4 KCl ion pairs per unit cell.

Number of ion per unit volume=4/a^3=4/(0.629*10^(-9))^3=1.607*10^28

using Clausius-Mossotti equation:

under dc condition (low frequency)

(Er-1)/(Er+2)=(1/3*epsilon)*N*(E_k+E_cl+E)

where Er=relative permitivity =dielectric constant

epsilon=8.85*10^(-12)

E_k=1.264*10^(-40)

E_cl=3.408*10^(-40)

E=4.58*10^(-40)

then calcuating for Er, we get Er=4.8182 which is close to 4.82

under high frequency or optical condition:

(Er-1)/(Er+2)=(1/3*epsilon)*N*(E_k+E_cl)

using the values, we get

Er=2.1828 which is close to 2.19