Types of polarization mechanisms

Polarization is the alignment or creation of electric dipoles in a dielectric by an applied field; $P$ is the net dipole moment per unit volume, $P = \varepsilon_0(\varepsilon_r - 1)E$. There are four main mechanisms, and the total polarization is their sum: $P = P_e + P_i + P_d + P_{if}$.

1. Electronic polarization

• The field shifts the electron cloud of each atom relative to its nucleus, creating an induced dipole.
• Present in all materials (atoms, molecules, ions).
• $p_e = \alpha_e E_{loc}$, with $\alpha_e = Ze^2/(m_e\omega_0^2)$; for a hydrogen-like atom $\alpha_e = 4\pi\varepsilon_0 R^3$.
• Very fast (follows up to about $10^{15}$ Hz, UV); independent of temperature.
• Example: Si, Ge, diamond, inert gases.

 E=0:  ( (+) )        E -->:  ( (+))
       cloud centred          cloud shifted left

2. Ionic (atomic) polarization

• In ionic crystals (NaCl, KCl), the field displaces positive ions along $E$ and negative ions opposite, changing the inter-ionic spacing and creating a net dipole per ion pair.
• $p_i = \alpha_i E_{loc}$, $\alpha_i = e^2/\beta$ where $\beta$ is the bond "spring" constant.
• Ions are heavy, so it follows the field only up to the infrared (about $10^{12}$–$10^{13}$ Hz); nearly independent of temperature.

 E -->    Na+ ->  <- Cl-  ->Na+  <- Cl-

3. Orientational (dipolar) polarization

• Occurs in polar molecules with a permanent dipole $p_0$ (H₂O, HCl, nitrobenzene).
• Without a field dipoles point randomly ($P = 0$); a field tends to rotate them into line, while thermal motion opposes this.
• Average dipole along field $= \dfrac{p_0^2}{3kT}E$, so $\alpha_d = \dfrac{p_0^2}{3kT}$, which decreases with temperature.
• Slow (rotation of molecules): follows up to about $10^{6}$–$10^{10}$ Hz; large losses near the relaxation frequency.

4. Interfacial (space-charge) polarization

• Charges (ions, electrons) drift and pile up at interfaces, grain boundaries, defects or electrodes in non-homogeneous dielectrics.
• The accumulated charge acts like a large dipole.
• Slowest: important only at low frequency (below about $10^{3}$ Hz); it gives very large apparent $\varepsilon_r$ at DC and low frequencies.

Comparison

As frequency rises, mechanisms drop out one after another, so $\varepsilon_r'$ falls in steps (from interfacial at low frequency down to electronic only at optical frequency).