DIELECTRIC PROPERTIES OF MATERIALS

Dielectrics are insulators, they do not have free electrons, and

they do not conduct electricity. They affect the electric field in which
they are placed.
A pair of equal and opposite point charges separated by a small
distance is called electric dipole. The product of the magnitude of one
of the charges and the distance between them is called the dipole
moment.

𝜇 = 𝑞. 𝑙
Polarization: When an electric field is applied to dielectric material,
there is displacement of charged particles leading to formation of
dipoles and hence dipole moment which is called polarization of
dielectric.
Dielectrics are of two types: 1) Polar dielectrics 2) Non polar
dielectrics
1) In a polar dielectric molecule the centers of positive and negative
charge distributions are separated by a small distance. They act
like tiny poles and posses permanent electric dipole moment.
In the absence of external field, the dipoles are oriented
randomly, it results in a net zero dipole moment for the material.
2) In non polar dielectric molecule the centers of positive and
negative charge distribution coincide. It has no permanent dipole
moment. In the presence of an external field the charge
distribution are separated by a small distance and acquire dipole
moment. It is the induced dipole moment.
The relation between electric intensity E and the flux density D
for an isotropic material is given by
D=𝜖𝑜𝜖𝑟E
Where 𝜖0=8.854x10−12F/m dielectric
constant of air or vacuum.
𝜖𝑟 is the relative permittivity of the materials.
Electric Polarization and Dielectric susceptibility χ

Consider a dielectric material of area A subjected to an external

electric field E.‘t’ is the thickness of the slab +q & -q be the induced
charges.

The total dipole moment of the material = (charge) x (distance of

separation)

=q x t

The dipole moment per unit volume is called the polarization P.

𝑞
i.e., P=
𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑝𝑜𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
=
𝑞𝑡 = 𝑐𝑚−2
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑡𝐴 𝐴

Thus magnitude of polarization is equal to the induced charge

density. But polarization P is directly proportional to the applied field
E.

i.e., P  E

P=𝜖𝑜 χ E

where  is called dielectric susceptibility.

Relation between polarization P and Dielectric constant 𝜖𝑟 :

Consider a dielectric slab placed between the two plates and

subjected to external electric field𝐸0. σ be the charge per unit area of
𝜎
the plates. By Gauss theorem 𝐸𝑜 = --------------------(1)
𝜖0

Because of polarization of the slab, a field 𝐸′is established within the

slab. This field is opposite to that of 𝐸𝑜.
The resultant field 𝐸 = 𝐸𝑜 − 𝐸′ --------------- (2)
If 𝜎𝑝 is the charge/unit area on the slab surface, then similar to eqn.
(1)
𝜎𝑝
𝐸′ = ----------------------------(3)
𝜖0
From equations (1), (2) & (3)
 p
E= −
0 0
𝜖𝑜𝐸 = 𝜎 − 𝜎𝑝--------------------(4)
i.e., 𝜖𝑜𝐸 = 𝐷 − 𝑃 [∵P = charge/unit area; P = σP ; D = σ
By Gauss law]
𝐷 = 𝜖𝑜𝐸 + 𝑃 -------------------(5)
But D=𝜖𝑜𝜖𝑟E
∴ 𝜖𝑜 𝜖𝑟 E = 𝜖0 E+P

P =  0 ( r −1) E
P = 𝜖𝑜 χ E
where χ = (𝜖𝑟 − 1) is dielectric susceptibility of the material.

Polarizability ( )
The dipole moment µ acquired by the dielectric atom or
molecule is proportional to the applied electric field E
i.e., µ  E
i.e., µ =  E
where  is the polarizability of the atom. Its unit is Fm2.
TYPES OF POLARIZATION: There are four different types of
polarization. They are,
1) Electronic Polarization,
2) Ionic Polarization
3) Oriental polarization and
4) Space charge polarization.
1) Electronic polarization : There is displacement of positive and
negative charges due to applied external electric field. This leads
to development of dipole moment. Thus material gets polarized.
 ( − 1 )
The electronic polarization  e = 0 r
N
Where N is the number of atoms per unit volume.
2) Ionic Polarization : There is displacement of adjacent opposite
ions due to applied external electric field. Depending on the
location of ions there is increase or decrease in displacement of
ions. This leads to development of dipole moment of the
material.

3) Orientation polarization : In the absence of the external field, the

dipoles are oriented randomly, the net dipole moment is zero. In
the presence of the external field each of the dipoles undergo
rotation so as to reorient in the direction of the field. Thus
material develops electrical polarization. It is the temperature
dependant and decreases with increase of temperature.
Electric field
+e

-e

2
It is given by 0
3KT
µ-permanent dipole moment,
k-Boltzmann constant, T- Temperature.
 4) Space charge polarization: It occurs in multiphase dielectric
materials where there is change of resistivity between different
phases. At high temperatures when the material is subjected to
electric field charges are settled at the interface due to sudden
drop of conductivity across the boundary. Opposite nature of
charges are settled at opposite parts in the low resistivity phase.
Thus the material acquires dipole moment in the low resistivity
phase. Space charge polarization is negligible in most
dielectrics.

Temperature dependence of polarization mechanism

The distribution of electrons in the constituent molecules is

affected by the increase in the temperature. Thus there is no
influence on the electronic and ionic polarization mechanisms. But
the increase in temperature changes the dipole orientation
established by the applied field. This changes the orientation
polarization. The orientation polarization is inversely proportional to
the temperature. The thermal energy support in movement by
diffusion which intern aids the molecules to align in the field
direction. Thus increase in temperature supports space charge
polarization and orientation polarization.

Expression for the internal field in the case of liquids and solids:
(One dimensional)

Internal or local field is the resultant of the applied field and

field due to all the surrounding dipoles on an atom of a solid or a
liquid dielectric material.

REFER PPT FILES IN MOODLE FOR DERIVATON

CLAUSIUS – MOSSOTTI RELATION:

Consider a dielectric material of dielectric constant r.
The dipole moment / unit volume= N
Where N is the number of atoms per unit volume,  is the dipole
moment of each atom. If Ei is the internal field and e is the electronic
polarizability of atoms, then = eEi
The dipole moment / unit volume = N eEi

i.e., polarization p= N eEi

𝑝
𝐸𝑖 = 𝑁𝛼𝑒
(1)

But 𝑝 = 𝜖0 (𝜖𝑟 − 1)𝐸 where E is the applied field

𝑝
∴𝐸= (2)
𝜖0 (𝜖𝑟−1)
We have
𝐸𝑖 = 𝐸 +  𝑝
(3)
𝜖0
where  is the internal field constant
From Equations (1), (2) and (3)
𝑝 𝑝 𝑝
= +𝛾
𝑁𝛼𝑒 𝜖0 (𝜖𝑟 − 1) 𝜖0
1 1 1
= [ + 𝛾]
𝑁𝛼𝑒 𝜖0 (𝜖𝑟 − 1) 1
Taking internal field in the material to be Lorentz field 𝛾=
3
 1 1 1 1 1 3 + 𝜖𝑟 − 1
= [ + ]= [ ]
𝑁𝛼𝑒 𝜖0 (𝜖𝑟 − 1) 3 𝜖0 (𝜖𝑟 − 1)3

𝜖0 = [
𝜖𝑟 + 2
𝑁𝛼𝑒 ]
(𝜖𝑟 − 1)3
(𝜖𝑟 − 1) 𝑁𝛼𝑒
= [ ]
(𝜖𝑟 + 2) 3𝜖0
This is Clausius- Mossotti equation.

Dielectric loses:- It is the loss of energy in the form of heat due to

internal friction that is developed as a consequence of switching
action of dipoles under certain a.c. conditions.

Dipolar relaxation:- It is the time required for the dipole to reach the
equilibrium orientation from the disturbed position in an alternating
field condition. The reciprocal of relaxation time is the relaxation
frequency.
Frequency dependence of Dielectric constant.

The dielectric constant r of a dielectric material changes with the

frequency of the applied voltage. If the frequency is low the
polarization is following the variation of the field without any lag. As
the frequency increases the heavy positive and negative ions cannot
follow the field variations. r becomes a complex quantity. It is
denoted as r* given by
 * =   − j   , where   and   are real and imaginary parts of  * .
r r r r r r
All the four different polarization mechanisms respond differently at
different frequencies under alternating field conditions, because
relaxation frequencies of different polarization processes are
different.

 e  i   0
As the frequency of the applied a.c. is increased, different polarization
mechanisms disappears in the order, orientation, ionic and
electronic.

The peaks in the variation of  r over frequency regions corresponding

to the decrements in  r indicates the losses that the material suffer
 
over those frequencies. It can be shown that tan  = r
; where  is
 r
phase angle. Large value of tan  refers to higher dielectric loss. It
is called tangent loss.
Ferro-electric materials

Dielectric materials which possess electric polarization in the

absence of electric field are called Ferroelectric materials. They
exhibit electrical hysteresis similar to ferromagnetic materials exhibit
magnetic hysteresis, hence the name ferroelectrics. Ferroelectric
materials possess electrical properties similar to magnetic properties
such as hysteresis, spontaneous magnetization, high susceptibility
etc., Ex: - Barium titanate (BaTiO3), potassium dihydrogen
phosphate (KH2PO4) and Rochelle salt (NaKC4H4O64H2O).
Properties of Ferroelectric materials-

1. Ferroelectric Hysteresis:- Consider a

ferroelectric specimen consisting of
large number of domains. In the
absence of the external field, these
domains are oriented randomly. It is
represented at O in the graph of E
versus P.
When the external electric field is
increased domains whose polarization
components parallel to external field
expand in size and the components
which are opposite direction undergo shrinkage. The curve
OAB is obtained in the graph E versus P. For a particular
applied field the specimen behaves as a single domain. The
saturation point C is obtained. CD produced meets the
polarization axis at Ps the saturation polarization point Ps. As
the field is reduced to E=0, the curve DF is obtained. OF=Pr is
called remanent polarization. As the field is reverted and
increased to E=Ec polarization become zero. The curve FG is
traced. OG=Ec is called coercive field. Further increase in field,
shows that specimen reaches the saturation at H. The curve
GH is traced. As the field is decreased to zero and increased in
opposite direction, the curve HIJ is traced which completes the
hysteresis cycle. The area within the curve represents the loss
of electrical energy/ cycle.
2. Temperature dependence of dielectric constant
The temperature at which ferroelectric material loses its
ferroelectric property is called critical temperature or curie
temperature Tc. The material loses spontaneous polarization
property above Tc. The dipoles orient randomly. The static
dielectric constant r and temperature T are related as
𝑐
𝜖𝑟 = 𝑇−𝜃 for T>Tc
c is a constant,  is close to Tc. It is called curie-wiess law. r
is constant as T is constant above Tc.
The graph shown variation of r versus T for T>Tc. Below Tc the
dielectric constant changes with the strength of the applied field
dp
following hysteresis. It is given by 𝜖0 (𝜖𝑟 − 1) = 𝜒 where  =
dE
is the dielectric susceptibility.
Applications of dielectric materials

Dielectric materials are used in capacitors to increase charge storage

capacity. Quartz, Lead Zirconate titanate, Rochelle salt, Barium
titanate and poly vinylidene fluoride are piezoelectric materials.
Quartz is piezoelectric but not ferroelectric. It is in the form of SiO2.
Piezoelectric crystals used in Electronics industry in frequency
control of oscillators. A properly cut piezoelectric crystal is placed in
between the plates of a capacitor of a circuit whose frequency is same
as the natural frequency of mechanical vibration of the crystal. The
circuit acts as a tuned circuit of very high Q-value and possesses
excellent frequency stability. They are also used as electro-acoustic
transducers (to convert electrical energy into mechanical and vice
versa). Transducers are used in ultrasonic’s for Sound Navigation
and Ranging (SONAR), in ultrasound imaging of human body, non-
destructive testing of materials, measurement of velocity of
ultrasound in solids and liquids.

Lead Zirconate titanate (Pb Ti1-x Zrx O3) or (PZT) are used in
accelerometers, earphones etc., PZT piezoelectric crystals are used in
gas lighters, car ignition.

Rochelle salt (Na KC4 H4O6 4H2O) is both piezoelectric and

ferroelectric, it is hygroscopic and could be used in the range of
temperature of 180 to 240c. It is highly sensitive.

Barium titanate ( Ba Ti O3) is less sensitive than Rochelle salt. It has

an advantage of serving over a wide range of temperature. It can
withstand atmospheric corrosion. It is used in accelerometers.
Polyvinylidene fluoride (PVDF) is inexpensive.