Dielectric

All dielectric materials are basically electrical insulators. The distinction between a dielectric material and an insulator lies in the application. The insulating materials are used to resist the flow of current through it when a difference of potential is applied across its ends. On the other hand, dielectric materials are used to store electrical energy. Almost all practical capacitors have one or the other type of dielectric material. The introduction of the dielectric material between the plates of the capacitors increases the capacitance of the capacitor and increase the maximum operating voltage of the capacitor.

Dielectric constant and polarization of dielectric materials

In dielectric materials, electrons are strongly bound to the nucleus. When dielectrics are subjected to an external electric field, positive charges are displaced in the direction of the field while negative charges are moved in the opposite direction. Hence electric dipoles are developed which produces electric field. This process is called electric polarization.

For a dielectric material, flux density or electric displacement vector D is given by,

D = e₀e_rE -------- (1)

where E is the electric field strength, e₀ = 8.854×10^-12 F/m is the dielectric constant (permittivity) of free space and e_r is the relative dielectric constant for the materials. e_r is also called static dielectric constant since its value remains constant when the applied field is static. e_r varies with material to material and also with the frequency of the voltage applied to the plates of the capacitor.

The dipole moment per unit volume is known as polarization P.

For most of the dielectric materials, polarization P is directly proportional to the external field E.

i.e, P µ E

Or, P = e₀(e_r -1) E -------- (3)

Expression for static dielectric constant e_r

A dielectric medium of dielectric constant e_r is filled between the plates of a capacitor as shown in figure 1. When an electric field E₀ is applied across the capacitor, the charge developed on the plates are +Q and –Q respectively.

where A is the area of the plate.

Due to the polarization, charges (+q and –q) will induce at the surface of the dielectric. These induced charges will tend to weaken the applied field and hence the resultant electric field,

But Q/A = D = e₀e_rE [From equation (1)]

And P = q/A [From equation (2)]

Substituting these results,

Polarizability (a )

Let m be the electric dipole moment acquired by an atom. It is found that m µ E

Or, m = a E --------- (5)

where a is called polarizability of the atom. Its unit is Farad-m².

It is important to note that polarizability is not a bulk property of the material but the property of an individual atom or molecule or ion. It is considered as an important microscopic electrical parameter of a dielectric.

Polar and non-polar dielectrics

In the molecules (or atoms) of some dielectric materials, the effective centre of the negative charge distribution coincides with the effective centre of the positive charges, thus neutralizing each other’s effect. Such materials are called non-polar dielectrics with low dielectric constant.

Dielectric materials possessing an intrinsic dipole moment are called polar dielectrics. Dielectric constant of polar dielectrics is high.

Types of polarization

There are 4 types of polarization mechanisms through which electrical polarization can occur in dielectric materials when they are subjected to an external field.

1. Electronic polarization

Electronic polarization occurs due to the displacement of the positively charged nucleus and negatively charged electrons in an atom owing to the application of an external electric field. This results in the creation of electric dipole. If ‘N’ represent number of atoms pet unit volume, then electronic polarization P_e = Na_eE --------- (6)

where a_e is electronic polarizability.

Electronic polarization is temperature independent.

2. Ionic polarization

Ionic polarization occurs in ionic crystals. When an external electric field is applied, adjacent ions of opposite sign undergo displacement, resulting in a net dipole moment.

Ionic polarization is given by, P_i = Na_iE -------- (7)

where a_i is ionic polarizability

Ionic polarization is temperature independent.

3. Orientation polarization

This occurs in polar dielectrics which consist of molecules having permanent dipole moment. In the absence of external electric field, the orientation of dipoles is random resulting in a complete cancellation of each other’s effect. Under the influence of an applied electric field, each of the dipole undergoes rotation so as to reorient in the direction of the field, producing electrical polarization. Since the randomness in orientation is due to thermal agitation, orientation polarization is strongly temperature dependent and decreases with increase of temperature. Orientation polarization is given by, P_o = Na_oE -------- (8)

where a_o = m²/kT is the orientation polarizability.

4. Space charge polarization

Space charge polarization occurs in multiphase dielectric materials in which there is a change in resistivity between two phases. When electric field is applied, charges get accumulated at the interface. This type of polarization is called space charge polarization which is very small and can be neglected.

Space charge polarization is temperature dependent.

We can write an expression for total polarization as,

P_tot = P_e + P_i + P_o

= Na_eE + Na_iE + Na_oE

= N [a_e+ a_i + a_o] E

= N [a_e+ a_i + m²/kT] E

But from equation (3), P = e₀(e_r -1) E

\e₀(e_r -1) = N [a_e+ a_i + m²/kT] -------- (9)

Internal fields in liquids and solids (one dimensional)

When a dielectric material either solid or liquid is subjected to an external electric field, each of the atoms develops a dipole moment, and acts as electric dipole. Hence the resultant field at any given atom will be the sum of applied electric field and the electric field due to the surrounding dipoles. This resultant local field is called internal field.

i.e., internal field E_i = E + E’

where E is the applied electric field and E’ electric field due to the surrounding dipoles.

To find E’, consider a one dimensional solid consisting of a string of equidistant identical atoms, each of polarizability a.

Let ‘2d’ be the length of the electric dipole and ‘a’ the separation between the atoms.

When an electric field ‘E’ is applied in a direction parallel to the string, the dipole moment induced in each atom is m = a E_i where E_i is the internal field.

The field at ‘A’ due to the dipole located at a distance of ‘na’ from it is given by,

Since d <<>2 and d⁴ values can be neglected. Then the above equation reduces to,

But dipole moment m = Ze2d

Taking into account all atoms to the left and to the right of A,

If ‘N’ is the number of atoms per unit volume, N = 1/a³

But mN = P

This is the case of an infinite chain of atoms. General expression can be written as,

where g is a constant called internal field constant.

Lorentz found that for cubic crystals, the internal field constant g = 1/3

This field is called Lorentz field.

Clausius-Mosotti equation

Consider a non-polar elemental solid dielectric which exhibits only electronic polarization. The electronic polarizability,

where N is the number of atoms per unit volume and E_i the local internal field. Substituting the value of E_i from equation (11), for cubic crystals,

But from equation (3), E = P/e₀(e_r -1)

This equation is known as Clausius-Mosotti equation which is valid for non-polar solid dielectrics having cubic crystal symmetry.

Frequency dependence of dielectric constant

The dielectric constant e_r of a material remains unchanged when subjected to a dc voltage. But when it is subjected to an ac voltage, the value of e_r changes depending on the frequency of the applied voltage. In addition, e_r becomes a complex quantity which is given by,

e_r^* = e_r^’ - je_r^”

where e_r^’ is the real part which is responsible for increase of capacitance in a capacitor. e_r^”

is the imaginary part which represent loss. We can rewrite e_r^* as

e_r^* = e_r(1-je_r^’/e_r^”) = e_r(1-j tand)

where tand = e_r^’/e_r^” is called loss factor or tangent loss.

The variation of e_r^’ and e_r^” with frequency is given below.

Dielectric loss

When a dielectric material is subjected to an ac field, a part of the energy is lost each time the field changes its direction. This is due to the fact that each time the field is reversed, the direction of the dipoles has to change. In this process, a loss of energy due to friction occurs. This energy loss appears in the form of heat. This energy loss depends on the frequency of ac field.

Important applications of dielectric materials

1. As insulating materials

2. In capacitors

3. Dielectric ceramic materials are used in high voltage power lines

4. Liquid dielectrics such as petroleum oil are used in transformers for cooling, circuit breakers and in cables.

5. In dielectric heating devices

6. Non linear dielectrics (piezoelectrics and ferroelectrics where e_r depend on the intensity of the applied electric field) are used in many applications.