# TYPES OF POLARIZATION

Polarization is due to the four types of processes.

1.  Electronic polarization
2.  Ionic polarization
3.  Orientation polarization
4.  Space charge polarization

### ELECTRONIC POLARIZATION

• By applying an electric field, positively charged nucleus and the electrons displaced in opposite directions results in electronic polarization. By applying field the electron cloud shifts toward the positive end. As the nucleus and center of electrons are separated by a certain distance, the dipole moment is created. The shift is proportional to the field strength and the dipole moment is proportional to the field strength.
• A nucleus of charge +Ze is surrounded by the electron cloud of charge – Ze distributed in the sphere of radius R.
• The charge density $\dpi{150}&space;\rho&space;=\frac{-Ze}{(\frac{4}{3})\pi&space;R^3}=\frac{-3}{4}\left&space;(&space;\frac{Ze}{\pi&space;R^3}&space;\right&space;)$
• When electric field E is applied, the nucleus and electrons experience Lorentz forces of magnitude ZeE in opposite directions. Hence the electrons and nucleus pulled apart. When they are separated a column force develops between them. When these two forces are equal and opposite then the equilibrium is reached. Let x be the displacement at equilibrium.
• Lorentz force = -ZeE
• columb force =$\dpi{150}&space;Ze\times&space;\left&space;[&space;\frac{charge&space;enclosed&space;in&space;the&space;sphere&space;of&space;radius&space;x}{4\pi&space;\alpha&space;\epsilon&space;_0x^2}&space;\right&space;]$

Charge enclosed = $\dpi{150}&space;\frac{4}{3}\pi&space;x^3\rho$

$\dpi{150}&space;=\frac{4}{3}\pi&space;x^3\left&space;[&space;\frac{-3}{4}&space;\left&space;(&space;\frac{Ze}{\pi&space;R^3}&space;\right&space;)\right&space;]$

$\dpi{150}&space;=-\frac{Zex^3}{R^3}$

Columb force$\dpi{150}&space;=\frac{Ze}{4\pi&space;\epsilon&space;_0x^2}\left&space;[&space;\frac{-Zex^3}{R^3}&space;\right&space;]=\frac{Z^2e^2x}{4\pi&space;\epsilon&space;_0R^3}$

In equilibrium position -ZeE = $\dpi{150}&space;\frac{-Z^2e^2x}{4\pi&space;\epsilon&space;_0R^3}$

$\dpi{150}&space;E=\frac{Zex}{4\pi&space;\epsilon&space;_0R^3}$ or $\dpi{150}&space;x=\frac{4\pi&space;\epsilon&space;_0R^3E}{Ze}$

The charge +Ze and -Ze are separated by a distance x. Induce electric dipole moment $\dpi{150}&space;\mu&space;_e=Zex=\frac{Ze4\pi&space;\epsilon&space;_0R^3E}{Ze}=4\pi&space;\epsilon&space;_0R^3E$

• i.e., $\dpi{150}&space;\mu&space;_e=\alpha&space;_eE$   where $\dpi{150}&space;\alpha&space;_e=4\pi&space;\epsilon&space;_0R^3$ is called electronic polarizability.  The dipole moment per unit volume is called electronic polarization. It is independent of temperature.

$\dpi{150}&space;P_e=N\mu&space;_e=N\alpha&space;_eE$

$\dpi{150}&space;P_e=\epsilon&space;_0E(\epsilon&space;_r-1)=N\alpha&space;_eE$

$\dpi{150}&space;(\epsilon&space;_r-1)=\frac{N\alpha&space;_e}{\epsilon&space;_0}$

$\dpi{150}&space;hence=\alpha&space;_e=\frac{\epsilon&space;_0(\epsilon&space;_r-1)}{N}$

### IONIC POLARIZATION

• The ionic polarization is due to the displacement of cations and anions in the opposite direction and occurs in an ionic solid. When the field is applied in +x direction, positive ions move to the right by x₁ and negative ions move to the left by x₂.
• Dipole moment per unit cell is $\dpi{150}&space;\mu&space;=e(x_1+x_2)$
• If $\dpi{150}&space;\beta&space;_1&space;,&space;\beta&space;_2$ are restoring force constants of cations and anions.

$\dpi{150}&space;F=\beta&space;_1x_1=\beta&space;_2x_2$

• $\dpi{150}&space;x_1=\frac{F}{\beta&space;_1}$. Restoring force depends on mass, angular frequency.

$\dpi{150}&space;x_1=\frac{eE}{mw_0^2};x_2=\frac{eE}{Mw_o^2}$

• where m is the mass of +ve ions and M is the mass of -ve ions.

$\dpi{150}&space;\therefore&space;x_1+x_2=\frac{eE}{w_0^2}\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)$

$\dpi{150}&space;\mu&space;=e\left&space;(&space;x_1+x_2&space;\right&space;)=\frac{e^2E}{w_0^2}\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)$

$\dpi{150}&space;\alpha&space;_i=\frac{\mu&space;}{E}=\frac{e^2}{w_0^2}\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)$

• The ionic polarization is inversely proportional to square of angular frequency  $\dpi{150}&space;\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)^-^1$

### ORIENTATION POLARIZATION

• In some of the molecules, the positive and negative charges coincide. Then no permanent dipole moment in some molecules positive and negative charges does not coincide. Then it is having permanent dipole moment when an electric field is applied to such molecules, which possess permanent dipole moment, they tend to align themselves in the direction of the field. Such alignment is called orientational polarization.

$\dpi{150}&space;P_0=N\mu&space;^2\frac{E}{3KT}$

$\dpi{150}&space;=N\alpha&space;_0E$

• Orientational polarizability $\dpi{150}&space;\alpha&space;_0=\frac{P_0}{NE}=\frac{\mu&space;^2}{3KT}$
• $\dpi{150}&space;\alpha&space;_0$ is the inveresely proportional to absolute temperature.

### SPACE CHARGE POLARIZATION

• Space charge polarization occurs due to the accumulation of charges at the interfaces in a multiphase material. The ions diffuse over appreciable distance, then it gives redistribution of charges in dielectric medium.
• Total polarization$\dpi{150}&space;P_t_o_t_a_l=P_e+P_i+P_0+P_3$

$\dpi{150}&space;P=N\alpha&space;E$

$\dpi{150}&space;\alpha&space;=\alpha&space;_e+\alpha&space;_i+\alpha&space;_0$

$\dpi{150}&space;=4\pi&space;\epsilon&space;_0R^3+\frac{e^2}{w_0^2}\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)+\frac{\mu&space;^2}{3KT}$

$\dpi{150}&space;P=N\alpha&space;E=NE\left&space;\{&space;4\pi&space;\epsilon&space;_0R^3+\frac{e^2}{w_0^2}\left&space;(&space;\frac{1}{M}+\frac{1}{m}&space;\right&space;)+\frac{\mu&space;^2}{3KT}&space;\right&space;\}$

• This equation is known as Langevin Debye equation