Dielectric Polarization | Types of Polarization in Dielectrics

In this lecture, we are going to learn about Dielectric Polarization, the types of polarization in dielectrics, and various polarization methods. So let’s start with the definition of polarization.

Polarization

In the dielectric material, most of the electrons are bound to the nuclear. When an external electric field is applied then the bound electrons of an atom are displaced such that the centroid of the electronic cloud is separated from the centroid of the nucleus. hence, an electric dipole is created and the atom is said to be polarized. This phenomenon is known as polarization.

When a dielectric material is placed in an electric field, the induced dipoles produce a secondary electric field such that the resultant field and the polarization vector satisfy

\boxed{\vec P = \epsilon_o\chi_e\vec E}

Where, \chi_e is a dimensionless parameter, known as the electric susceptibility. it measures the ability of the material to become polarized and differs from one dielectric to another.

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Also Read: Engineering Materials | Classification Of Engineering Materials

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Types of Polarization in Dielectrics

There are four basic types of polarization mechanisms:

• Electronics or induced polarization
• Ionic polarization
• Oriental polarization
• Interfacial or space charge polarization

1. Electronic Polarization

• Electronic polarization is defined as an electric strain produced in an atom due to the application of an external electric field to the bulk material. It is the result of the displacement of the positively charged nucleus and the negative electrons of an atom in the opposite direction.

• Consider an atom having atomic number Z and e^– is the charge of an electron.

• Atomic dipole moment is given by, P_{ind}=Ze.x.

• Let us say that q represents the charge contained in the sphere of radius x then,

q=\frac{-Ze}{\frac{4}{3}\pi R^3} \times \frac{4}{3} \times \pi x^3

q=\frac{-Ze}{R^3} .x^3

• The magnitude of Coulomb attraction between this charge treated concentrated at a point, and the nucleus will be,

F=-\frac{(Ze)^2x}{4\pi \epsilon_0R^3}

• The total force on the nucleus must be zero in equilibrium, so we obtain,

ZeE=\frac{(Ze)^2x}{4\pi \epsilon_0R^3}

or, x= \left (\frac{4\pi \epsilon_0R^3}{Ze}\right )E

• The dipole moment induced by the filed will be given by,

\boxed{P_{ind}=Zex=4\pi \epsilon_oR^3E=\alpha_eE}

• The dipole is induced by the field and never existed in the absence of the field. The induced dipole moment is proportional to the field strength and the proportionality factor \alpha_e is called the electronics polarizability. Note that \alpha_e is proportional to R3, i.e., to the volume of the electron cloud.

• If gas has N such atoms per m³, subjected to a homogenous field E, then electronics polarization is given by,

P_e=N \alpha_eE

• For rare gases,

\boxed{\epsilon_r=1+4\pi NR^3}

• Electronics polarizability depends only upon the electronics radius ad it is independent of temperature variations.

2. Ionic Polarization

• Ionic polarization is due to the displacement of cations and anions of an ionic solid subjected to the externally applied field.

• Ionic polarization exists only for those types of materials that have a net positive charge and a net negative charge, even in the absence of an applied field. HCL molecules have a permanent dipole moment “e.d”, where d is the distance of separation of ions. In an electrical field, the resultant torque lines up the dipoles parallel to the field at absolute zero temperature, as indicated below figure.

• The field produces forces on the two charges \pm e, as well as a torque on the dipole. The distance between ions increases from d to d + x. The field has induced an additional dipole moment, P_{ind}=e.x in the molecules.

• The induced dipole moment is proportional to the applied electric field, and the proportionality constant is ionic polarizability.

\boxed{P_{ind}=\alpha_i E}

where \alpha_i is the ionic polarizability.

• The simultaneous occurrence of electronic and ionic polarization (P_e and P_i, respectively) results in a volume polarization P, which is the sum of the individual effects such that,

\boxed{P=P_e+P_i=N(\alpha_e + \alpha_i) E}

• Both ionic and electronic polarizabilities are independent of temperature.

3. Orientational Polarization

• Orientational polarization is observed in the materials having a covalent bond of ionic character and molecules having a partial ionic bond.

• The existence of a permanent moment is purely a matter of molecular geometry. Two hypothetical cases are shown in the figure below. The molecules are of the form ABA. B atom i is negatively charged, whereas A’s are positively charged. The arrangements of the figure give a net-zero dipole moment in the absence of the field, whereas the molecular geometry of the figure gives a resultant dipole moment in the absence of the field. CO₂ is an example of the first case and NO₂, and H₂O are examples of the second case.

• The permanent dipole moment has been denoted as P_p, and the presence of an electric field will tend to align P_p along its own direction since E exerts a torque on P_p. The contribution of this process of the orientation of the permanent dipoles in the direction the field contributed additionally to total polarization and is called the orientational polarisation denoted as P₀.

• For moderate fields and all but very low temperatures, the orientational polarization P₀ may be given by,

\boxed{P_0=\frac{N{p_p}^2E}{3kT}}

• For the above expression orientational polarizability \alpha_0 is defined as,

\boxed{\alpha_0=\frac{{p_p}^2}{3kT}}

here N, P_p, and E are defined previously, k is Boltzmann’s constant, and T is temp[erature is kelvin.

• Orientational polarizability is a function of temperature and it decreases as temperature increases.

4. Space Charge Polarization

Space charge polarization is also known as interfacial polarization. It is observed in multiphase materials. materials with defects are known as multiphase materials.

Space charge polarization arises due to the accumulation of charge in lattice vacancies of material. these charges will induce image charges and thus generate +ve and -ve charge centers separated by a small distance which results in a dipole moment. These dipole moments give rise to a polarization known as space charge or interfacial polarization.

The total polarization of a multiphase material containing permanent dipoles is given by,

\boxed{P=P_e+P_i+P_0+P_s}

For a single-phase dielectric containing permanent dipoles,

\boxed{P=P_e+P_i+P_0}

=N(\alpha_e+\alpha_i)E+\frac{N{p_p}^2 E}{3kT}

Note:

• At a visible range of frequencies, only electronic polarization is effective. I.e. at f\geq 5 \times 10^{14} Hz \;;P=P_e

• Ionic polarization is effective upto infrared range of frequencies i.e. at f < 10^{14} Hz \;;P=P_e+P_i

• Orientational polarization is effective up to radio frequency range i.e. at f <10^{10} Hz \;;P=P_e+P_i+P_0

• Space charge polarization is effective upto audio frequency range i.e. at f < 10^{3} Hz \;;P=P_e+P_i+P_0+P_s

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Also Read: Superconductivity | Properties of superconductivity |Types of superconductors | Application of superconductivity

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Frequently Asked Questions on Dielectric Polarization

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Also Read: CRYSTAL SYSTEMS AND BRAVAIS LATTICES

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