Dielectric
Dielectrics are insulator: They are non metallic materials of high specific resistance and have negative
temperature coefficient of resistance. The examples of dielectrics are air, mica, glass porcelain,
asbestos, plastic, paper etc.
Electric dipole: A system of consisting two equal and opposite charges
separated by a distance is called electric dipole.
Dipole moment: Product of charge and distance between the charges is called dipole moment is
denoted by μ . Then μ = q.d coulomb meter
Capacitor: It is a two terminal device of electrical conductor separated by dielectric
material.
Capacitance: It is the ability of storing charge of conductor or system of conductors. It is denoted by C
and C= charge /Voltage.
And also 𝐶 =
𝜖𝐴
𝑑
where 𝜖 is the permittivity of the medium, A is the area of the plate and d is the
distance between the two plates.
The unit of capacitance is farad.
Electric field: It is the ratio of potential difference between the plates and the separation between the
plates. Electric field is denoted by E and unit is volt per meter.
Then E =V/d volt /meter
And also 𝐸 =
𝑞
4𝜋𝜖𝑟 2
where q is the + charge, r is the radius of spherical surface.
Polarization: The process of producing dipoles by the influence of an electric field is called electric
polarization. For example, when an electric field is applied to a crystal or a glass containing positive and
negative charges, the positive charges are displaced in the direction of the field while negative charges
are displaced in the opposite direction. The displacement of charges produce local dipole throughout
the solid. This process is called polarization.
Polarization are of four types
1.
2.
3.
4.
Electronic polarization
Ionic polarization
Orientation polarization
Space charge polarization
⃗ ): It is defined as the average dipole moment present per unit volume of a
Polarization vector( ⃗𝑷
dielectric. If N is the no of atoms present per unit volume and 𝜇̅ is the average dipole moment then 𝑃⃗ =
𝑁𝜇̅ . The unit is coulomb/meter2
Dielectric constant: The dielectric characteristic can be determined by the dielectric constant or relative
permittivity єr of the material. It is the ratio between the permittivity of the medium and the permittivity
of free space.
𝜖𝑟 =
𝜖
𝐶
𝐸0 𝑉0
=
=
=
𝜖0 𝐶0
𝐸
𝑉
It has no unit.
It is a measure of polarization of dielectric material.
Electric flux density:
The no of electric lines of force received per unit area is called flux density. It is denoted by D and the
unit is coulomb/m2. It is expressed as =
𝑞
4𝜋𝑟 2
,
The electric flux density at any point in a material is given by 𝐷 = 𝜀𝐸 = 𝜀0 𝜀𝑟 𝐸
E is the applied electric field.
Permittivity: permittivity of a medium is the ratio between the electric induction ‘D’ and electric field
intensity ‘E’. It determines the easily polarizable nature of the medium. It is denoted by 𝜀 and unit is
Farad per meter. It represent dielectric property of the medium. The permittivity of free space is 8.854 x
10-12 F/m.
Relationship between D, E and P
Consider a parallel plate capacitor connected with a voltage source V without a dielectric as shown in
the figure. Then the electric field at the
Gaussian surface is
𝑞
∫ 𝐸. 𝑑𝐴 = 𝜀 where E is the electric field at
0
Gaussian surface, A is the area of the plate q is
the amount charge present on the plate of the
capacitor and 𝜀0 is the permittivity of free space.
Then integrating 𝐸0 =
𝑞
𝐴𝜀0
When a dielectric slab is inserted in between the parallel plate of the capacitor, then the electric field at
the Gaussian surface is
∫ 𝐸. 𝑑𝐴 =
𝑞−𝑞′
𝜀0
where q’ represent induced charges on the surface on the dielectric.
𝑞′
𝑞
Integrating 𝐸 = 𝐴𝜀 − 𝐴𝜀
0
0
𝐸𝜀0 =
𝑞 𝑞′
−
𝐴 𝐴
𝑞
We know that 𝐷 = 𝐴 and
𝑃=
𝑞′
𝐴
Therefore 𝐸𝜀0 = 𝐷 − 𝑃
𝐷 = 𝐸𝜀0 + 𝑃
Similarly
𝐸𝜀 = 𝐸𝜀0 + 𝑃
𝐸𝜀𝑟 𝜀0 = 𝐸𝜀0 + 𝑃
𝜀0 (𝜀𝑟 − 1) =
𝑃
𝐸
Electronic susceptibility:
The polarization vector ‘P’ is proportional to the total electric field intensity E and is in the same
direction of E. Therefore the polarization vector can be written as
𝜒𝑒 =
𝑃
= (𝜀𝑟 − 1)
𝜀0 𝐸
Polarizability: It is found that the average dipole moment 𝜇̅ of a system is proportional to the electric
field (E) applied.
Then 𝜇̅ ∝ 𝐸
𝜇̅ = 𝛼𝐸
Where 𝛼 is the polarizability. Hence it can be defined as it is the ratio of a average dipole moment to the
electric field applied. i.e.
̅
𝜇
𝐸
𝛼 = farad/meter2
Dielectric strength: Dielectric strength of a dielectric can be defined as the minimum voltage required to
produce dielectric breakdown. Dielectric strength decreases with the increase of temperature, humidity,
age of the material and electric field. The unit of dielectric strength is volt/meter.
Types of polarization:
Polarization occurs due to several atomic mechanism. When the specimen is placed inside a dc electric
field, polarization occur due to four types of process.
1) Electronic 2) Ionic 3) Orientational 4) Space charge
Electronic polarization:
The displacement of +ve charged nucleus and electrons of an atom in opposite directions on application
of an electric field, result in electronic polarization. On applying a field, the electron cloud around the
nucleus readily shifts towards the + ve end of the field. As the nucleus and the centre of electron cloud
are separated by a certain distance, dipole moment is created
within each atom. The extent of this shift is proportional to the
field strength. Then
𝜇∝𝐸
𝜇 ∝ 𝛼𝑒 𝐸
Where 𝛼𝑒 is the electronic polarizability and is independent of temperature. Polarization is very rapid.
Expression of electronic polarizability:
Consider an atom of radius R, when no E field is applied, the centre of charges coincides at point ‘o’.
Therefore net dipole moment is zero.
Let the atomic no. of atom is ‘Z’. Then total –ve charge present in the atom is ‘Ze’ and are distributed in
the space.
Then the charge density
𝜌=
−𝑍𝑒
𝜌=4
𝜋𝑅3
---------------
𝑇𝑜𝑡𝑎𝑙 𝑐ℎ𝑎𝑟𝑔𝑒
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝ℎ𝑒𝑟𝑒
(1)
3
When external field is of intensity E is applied, the nucleus and electrons experience Lorentz forces of
magnitude ZeE in opposite directions. Hence the nucleus and electron clouds are pulled apart. When
they are separated, a coulomb force is developed which tends to oppose the displacement. When these
forces namely Lorentz and coulomb forces are opposite and equal, equilibrium is reached and let ‘x’ be
the displacement under this condition.
Then Lorentz force = -ZeE
Coulomb force =
−𝑍𝑒×[𝐶ℎ𝑎𝑟𝑔𝑒 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑠𝑝ℎ𝑒𝑟𝑒 𝑜𝑓 𝑟𝑎𝑑𝑖𝑢𝑠 ′𝑥′]
4𝜋𝜀0 𝑥 2
The charge enclosed = Volume x charge density
--------------(2)
4
=3 𝜋𝑥 3 𝜌3 -----------------------(3)
Substitute (3) in (1)
4
−𝑍𝑒
𝑐ℎ𝑎𝑟𝑔𝑒 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 = 𝜋𝑥 3
4
3
3
3 𝜋𝑅
𝑐ℎ𝑎𝑟𝑔𝑒 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 =
−𝑍𝑒𝑥 3
𝑅3
--------------(4)
Substitute (4) in (2)
Hence coulomb force is
−𝑍𝑒𝑥3
]
𝑅3
–𝑍𝑒×[
4𝜋𝜀0
𝑥2
=
−𝑍2 𝑒 2 𝑥
4𝜋𝜀0 𝑅3
At equilibrium
Lorentz force = Coulomb force
−𝑍𝑒𝐸 =
𝐸=
𝑥=
−𝑍 2 𝑒 2 𝑥
4𝜋𝜀0 𝑅3
−𝑍𝑒𝑥
4𝜋𝜀0 𝑅3
4𝜋𝜀0 𝑅3 𝐸
𝑍𝑒
The displacement of electron cloud is proportional to applied electric field. Thus two charges +Ze and
–Ze are separated by x distance under the applied force.
Then the induced dipole moment
𝜇𝑒 = 𝑍𝑒𝑥 = 𝑍𝑒
4𝜋𝜀0 𝑅 3 𝐸
= 4𝜋𝜀0 𝑅 3 𝐸
𝑍𝑒
But
𝜇 ∝ 𝛼𝑒 𝐸
Then
𝛼𝑒 = 4𝜋𝜀0 𝑅3
Then electronic polarization
𝑃𝑒 = 𝑁𝜇𝑒 = 𝑁𝛼𝑒 𝐸 where N represent no of atom per unit volume
𝑃𝑒 = 𝜀0 𝐸(𝜀𝑟 − 1) = 𝑁𝛼𝑒 𝐸
(𝜀𝑟 − 1) =
𝛼𝑒 =
𝑁𝛼𝑒
𝜀0
𝜀0 (𝜀𝑟 − 1)
𝑁
Ionic polarization
The ionic polarization occurs due to the displacement of cations and
anions in direction and occurs in ionic solid with the application of
electric field.
It is also independent of temperature. It does not occur in material atoms which are bonded with
covalent bond (like diamond)
When electric field is applied on the ions the displacement of ions takes place. Therefore, dipole
moment.
𝜇 = 𝑒(𝑥1 + 𝑥2 ) Where x1 and x2 are the displacement of ions
from their initial position.
Force acting on the ions
𝐹 = 𝛽1 𝑥1 = 𝛽2 𝑥2
𝑥1 =
𝐹
𝛽1
=
𝑒𝐸
𝑚𝜔02
where 𝛽1 is a constant and equal to 𝑚𝜔02 and 𝜔0 is the angular velocity and m is the
mass of the +ve ion.
𝐹
𝑒𝐸
𝑥2 = 𝛽 = 𝑀𝜔2 where M is the mass of –ve ion
2
0
Then 𝑥1 + 𝑥2 =
𝑒𝐸 1
[
𝜔02 𝑀
1
+ 𝑛]
The dipole moment
𝜇 = 𝑒(𝑥1 + 𝑥2 ) =
𝑒 2𝐸 1 1
[ + ]
𝜔02 𝑀 𝑛
Ionic polarizability is
𝜇
𝛼𝑖 = 𝐸 = 𝑒(𝑥1 + 𝑥2 ) =
𝑒2𝐸 1
[
𝜔02 𝑀
1
+ 𝑛] is independent of temperature
Orientational polarization
There are certain dielectric material (CH3Cl) which contain polar molecule (dipole) even in the absence
of electric field. They are oriented randomly such that net dipole moment is zero.
When electric field is applied they tried to align themselves along the direction of the field and due to
this there is a resultant dipole moment. This kind of polarization is called orientational polarization.
Average dipole moment
𝜇̅ =
𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑝𝑜𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡
𝑡𝑜𝑡𝑎𝑙 𝑛𝑜 𝑜𝑓 𝑑𝑖𝑝𝑜𝑙𝑒
𝜇2
𝜇̅ = [
]𝐸
3𝐾𝑇
𝜇2
𝑃0 = 𝑁𝜇̅ = 𝑁 [
]𝐸
3𝐾𝑇
𝑃0
𝑁𝐸
=
𝜇2
3𝐾𝑇
= 𝛼0 where 𝛼0 is the orientation polarizibility and is strongly dependent of temperature.
Space charge polarization
This occurs due to the accumulation of charges at the electrodes at the interfaces in a multiphase
material. The ions diffuse over appreciable distances in response to the applied field giving rise to
redistribution of charges in the dielectric medium is called space charge polarization. The magnitude of
space charge polarization is very less and independent of temperature is denoted by Ps. The space
charge polarization process is very slow.
Total polarization
The total polarization is denoted by P
Then 𝑃 = 𝑃𝑒 + +𝑃𝑖 + 𝑃𝑜 + 𝑃𝑠 since 𝑃𝑠 is very small therefore neglected.
𝑃 = 𝑃𝑒 + +𝑃𝑖 + 𝑃𝑜 then the polarizability
𝛼 = 𝛼𝑒 + 𝛼𝑖 + 𝛼0
𝛼 =
𝜀0 (𝜀𝑟 − 1) 𝑒 2 𝐸 1 1
𝜇2
+ 2 [ + ]+
𝑁
3𝐾𝑇
𝜔0 𝑀 𝑛
Then 𝑃 = 𝑁𝛼𝐸
𝜀0 (𝜀𝑟 − 1) 𝑒 2 𝐸 1 1
𝜇2
𝑃 = 𝑁𝐸 [
+ 2 [ + ]+
]
𝑁
3𝐾𝑇
𝜔0 𝑀 𝑛
The above equation is known as langevin-debye equation.
Local field
Consider a parallel plate
capacitor filled with dielectric
material of dielectric constant
𝜀𝑟 .
Let there be an imaginary
spherical cavity around atom A
inside the dielectric. It is
assumed that radius of the
cavity is large compared to the
radius of the atom. The internal field at the atom inside A can be considered to be made up of the
following four components. They are E1, E2, E3 and E4.
Field E1 : E1 is the field intensity at A due to the charge density on the plates
𝐷
Then 𝐸1 = 𝜀
0
𝐷 = 𝜀0 𝐸1
Where 𝜀0 is the permittivity of the free space
And also
𝐷 = 𝜀0 𝐸 +P
𝜀0 𝐸1 = 𝜀0 𝐸 + 𝑃
𝐸1 =
𝜀0 𝐸+𝑃
𝜀0
Field E2: E2 is the field intensity at A due to the
charge density induced on the two sides of the
dielectric. Therefore
𝐸2 =
−𝑃
𝜀0
Field E3 : E3 is the field intensity at due to other atoms contained in the cavity. We are assuming a cubic
stricter, so E3 = 0.
Field E4 : E4 is the field intensity at A due to induced charges on the surface of
the cavity. Consider the above figure. Let dA is the surface area of the sphere
of radius r lying between θ and dθ and θ is the direction with reference to the
direction of the applied force.
Then 𝑑𝐴 = 2𝜋(𝑃𝑄)(𝑄𝑅)
But 𝑆𝑖𝑛𝜃 =
𝑃𝑄
𝑟
𝑃𝑄 = 𝑟𝑆𝑖𝑛𝜃
𝑑𝜃 =
𝑄𝑅
𝑟
𝑄𝑅 = 𝑟𝑑𝜃
Hence 𝑑𝐴 = 2𝜋(𝑟𝑆𝑖𝑛𝜃)(𝑟𝑑𝜃)
𝑑𝐴 = 2𝜋𝑟 2 𝑆𝑖𝑛𝜃 𝑑𝜃
The charge dq on the surface dA is equal to the normal component of the polarization multiplied by the
surface area.
Therefore
𝑑𝑞 = 𝑃𝐶𝑜𝑠𝜃𝑑𝐴
Where 𝑃𝐶𝑜𝑠𝜃 is the normal component of polarization
The field due to the charge dq is denoted by dE4 at ‘A’ in
the direction θ = 00, Therefore
𝑑𝐸4 =
𝑑𝑞𝐶𝑜𝑠𝜃
4𝜋𝜀0 𝑟 2
But 𝑑𝑞 = 𝑃(2𝜋𝑟 2 𝑆𝑖𝑛𝜃 𝐶𝑜𝑠𝜃)𝑑𝜃
Then
𝑃𝐶𝑜𝑠𝜃(2𝜋𝑟 2 𝑆𝑖𝑛𝜃 𝐶𝑜𝑠𝜃)𝑑𝜃
𝑑𝐸4 =
4𝜋𝜀0 𝑟 2
𝑑𝐸4 =
𝑃𝐶𝑜𝑠𝜃(2𝜋𝑟 2 𝑆𝑖𝑛𝜃 𝐶𝑜𝑠𝜃)𝑑𝜃
4𝜋𝜀0 𝑟 2
𝑑𝐸4 =
𝑃𝐶𝑜𝑠 2 𝜃𝑆𝑖𝑛𝜃𝑑𝜃
2𝜀0
Integrating the equation we get
𝐸4 =
𝑃 𝜋
∫ 𝐶𝑜𝑠 2 𝜃𝑆𝑖𝑛𝜃𝑑𝜃
2𝜀0 0
Let Cosθ = x ; -Sinθ dθ = dx when θ = 0 ; x = 1 and θ = π; x = -1
Then
𝐸4 =
−𝑃 −1 2
∫ 𝑥 𝑑𝑥
2𝜀0 1
−1
−𝑃 𝑥 3
𝐸4 =
[ ]
2𝜀0 3 1
𝐸4 =
𝑃 2
2𝜀0 3
𝐸4 =
𝑃
3𝜀0
Then the local field EL at point A on the atom
EL = 𝐸1 + 𝐸2 + 𝐸4
Substituting the value of 𝐸1 , 𝐸2 𝑎𝑛𝑑𝐸4 , we get
𝐸𝐿 =
𝜀0 𝐸 + 𝑃 −𝑃
𝑃
+
+
𝜀0
𝜀0 3𝜀0
𝐸𝐿 = 𝐸 +
𝑃
3𝜀0
Clausius and Mosotti relation
Consider a dielectric material. Since, there are no permanent dipoles, ionic polarization and
orientational polarization is zero i.e. 𝛼𝑖 = 0; 𝛼0 = 0
The local field
𝐸𝐿 = 𝐸 +
𝑃
3𝜀0
The dipole moment is proportional to electric field EL where EL the local field
Then polarization 𝑃 = 𝑁𝛼𝑒 𝐸𝐿 where 𝛼𝑒 is the electronic polarizability
𝑃 = 𝑁𝛼𝑒 (𝐸 +
𝑃 = 𝑁𝛼𝑒 𝐸 +
𝑃−
𝑃 [1 −
𝑁𝛼𝑒
]
3𝜀0
= 𝑁𝛼𝑒 𝐸
𝑃
)
3𝜀0
𝑁𝛼𝑒 𝑃
3𝜀0
𝑁𝛼𝑒 𝑃
= 𝑁𝛼𝑒 𝐸
3𝜀0
𝑃=
𝑁𝛼𝑒 𝐸
[1−
𝑁𝛼𝑒
]
3𝜀0
-----------------------(A)
We also know that
𝐷 = 𝐸𝜀0 + 𝑃
And
𝑃 = 𝐸𝜀0 (𝜀𝑟 − 1)---------------------(B)
Equating equation (A) and (B)
𝐸𝜀0 (𝜀𝑟 − 1) =
𝑁𝛼𝑒 𝐸
𝑁𝛼
[1 − 3𝜀 𝑒 ]
0
1−
𝑁𝛼𝑒
𝑁𝛼𝑒
=
[ 𝜀0 (𝜀𝑟 − 1)]
3𝜀0
1=
𝑁𝛼𝑒
𝑁𝛼𝑒
+
3𝜀0 [ 𝜀0 (𝜀𝑟 − 1)]
1=
𝑁𝛼𝑒 1
1
( +
)
[(𝜀
𝜀0 3
𝑟 − 1)]
1=
𝑁𝛼𝑒 𝜀𝑟 + 2
(
)
3𝜀0 𝜀𝑟 − 1
3𝜀0
𝜀𝑟 + 2
=(
)
𝑁𝛼𝑒
𝜀𝑟 − 1
The above equation gives the relationship between polarizability and relative permittivity. This equation
also known as clausius and mosotti relation.
Frequency dependence of dielectric constant
The polarization and consequently the dielectric constant depend on the frequency of the applied field.
This phenomenon is called dielectric dispersion.
Electronic polarization is the extremely rapid. It can occur at a very high frequency is optical frequency
range(1015Hz). It occurs during every cycle of the applied voltage.
Ionic polarization is due to displacement of ions over a small distance due to the applied field. Since,
ions are heavier than electron cloud. The time taken for displacement is longer. It occurs at lower
frequency 1013Hz. At higher frequency it will not respond.
Orientational polarization is even slower than the ionic polarization. Orientational polarization occurs at
audio frequency of the applied voltage of frequency up to 106 to 1010Hz.
Space charge polarization is even slower than Orientational polarization. The typical value is 50Hz to
70Hz.
Dielelectric breakdown:
When a dielectric material losses its resistivity and permits very large current to flow through it, then
the phenomenon is called the dielectric breakdown.
There are many causes of breakdown.
1. Intrinsic Breakdown:
The dielectric strength is defined as the breakdown voltage per unit thickness of the material. When the
applied electric field is large, some of the electrons in the valence band cross over to the conduction
band across the large forbidden energy gap giving rise to large conduction currents. The liberation or
movement of electrons from valence band is called field emission of electron and the breakdown is
called the intrinsic breakdown or zener breakdown.
When the electric field is sufficiently high 106 V/cm the electrons are accelerated to very high velocity,
colliding with the other atoms and molecules, thereby releasing more electrons and hole breaking
covalent bond between them. The number of bonds broken and hence number of charge carriers
released increases enormously with time and finally dielectric breakdown occurs. This type of
breakdown is called avalanche breakdown.
This requires relatively large electric fields and hence this breakdown occurs in thin samples.
2. Thermal breakdown
Thermal breakdown occurs in a dielectric when the rate of heat generation is greater than the rate
of dissipation. Energy due to the dielectric loss appears as heat. If the rate of generation of heat is
larger than the heat dissipated to the surrounding the temperature of the dielectric increases which
eventually results in local melting. Once melting starts, that particular region becomes highly
conductive, enormous current flows through the material and dielectric breakdown occurs.
3. Electro chemical breakdown
Chemical and electrochemical type of breakdowns is very much related to thermal breakdown.
Temperature rise in an insulating material accelerates the chemical deterioration takes place. When
ionic mobility increases leakage current also increases and this may lead to dielectric breakdown.
Field induced chemical reaction gradually decreases the insulation resistance and finally results in
breakdown.
4. Defect breakdown
If the surface of the dielectric material has defects such as cracks and porosity, then impurities such
as dust or moisture collect at these discontinuities leading to breakdown.
Required qualities of good insulating material
1. Electrical property
a) Should have high electrical resistivity and high dielectric strength to withstand high voltage
b) The dielectric loss must be minimum
2. Mechanical property
a) Should have sufficient mechanical strength to withstand mechanical vibration
3. Thermal property
a) Should have good heat conducting property
b) Should have small thermal expansion and it should be non ignitable
4. Chemical property
a) Should be resistant to oils, acids and alkalies
b) Should be water proof
Relaxation Time
On application of an electric field a polarization process occurs as a function of time. The polarization
P(t) as a function of time t is given by
𝑃(𝑡) = 𝑃 [1 − 𝑒
(
−𝑡
)
𝑡𝑟 ]
Where P is the maximum polarization attained on prolonged application of a static field and t r is the
relaxation time for the particular polarization process.
Ferro electric material
Ferro electricity
The dielectric materials which are having spontaneous polarization in the absence of electric field are
called ferroelectric materials.
The phenomenon of possessing spontaneous polarization in the absence of electric field is called Ferro
electricity.
The examples are Rochelle salt, KH2PO4, BaTiO3, LiNbO3 and KNbO3
Properties :
1. All Ferro electric materials posses spontaneous polarization
below a certain temperature.
2. As the temperature increases the spontaneous polarization
decreases and at a particular temperature spontaneous
polarization vanishes called curie temperature
3. Curie temperature can be defined as the temperature at which ferroelectric material converts into
Para electric material.
4. Below Curie temperature, the dielectric constant is function
of electric field. Above curie temperature dielectric constant
varies with temperature. According to curie-wiss law
𝑐
𝜖𝑟 = 𝑇−𝑇
𝑐
where T > Tc
5. When a sufficiently strong electric field is applied on a Ferro
electric material then it converts into electorate.
6. All ferroelectric materials exhibit the property of piezoelectricity and pyro-electricity.
7. The phenomenon of producing electric emf by the application of thermal stress is know as pyroelectricity.
Hysteresis:
When electric field is applied on a Ferro-electric material then polarization takes place. This
polarization always lags behind the applied electric field. This phenomenon is known as hysteresis of
a Ferro electric material.
1. When electric field is applied on a Ferro electric
material, the polarization increases rapidly with the
applied field to a value and remains constant. This
polarization is known as saturation polarization (Ps).
2. Subsequently, if electric field on the material is
reduced back to zero, polarization will not travel in
the initial path, creates a new path and reaches to
remanent polarization (Pr).
3. To reduce remanent polarization to zero, negative
field has to be applied. At a particular –ve field
applied, the remanent polarization becomes zero
and the field is known as –ve coercive field (-Ec).
Further field increased –ve
polarization and
polarization reaches to the negative saturation and constant
with further application of field.
4. If the –ve field is decreased back to zero, the –ve saturation
polarization (-Ps) will bot travel in the initial path creates a
new path and reaches to –ve remanent polarization (-Pr).
5. To decrease the –ve remanent polarization to zero some
positive fields has to be applied. The amount of electric field
required to bring remanent polarization to zero is known as
coercive field (Ec).
6. Further, the increase of positive electric field the polarization reaches to positive saturation again
and it is a cyclic process.
7. It should be observed that the polarization vector which is started from origin does not reach back
to that point. Hence it is an irreversible process and the polarization always lags behind the electric
field applied.
8. The shape of the hysteresis loop changes with temperature. The height and width of the hysteresis
decreases with increase of temperature. At a certain temperature known as Ferro electric curie
temperature, the loop merges into a straight line as shown in the figure and the ferro electric
behavior disappears.
9. The hysteresis loop area represents the dielectric loss that occurs in dielectric materials.
10. The spontaneous polarization of the ferro electric material depends upon
a) Shape of the hysteresis loop
b) Dimensions of the specimen
c) Temperature
d) The thermal and electrical properties of the crystal
BaTiO3
The cube unit cell of barium titanate crystal is
shown in the figure. Barium ions are at the
corners and the oxygen ions are at the face
centers, the titanium ion is in the octahedral
void at the body centre. Above 1200C barium
titanet is a cubic crystal. In this state, the
centers of the negative and the positive charges
coincide. There is no spontaneous dipole
moment. If the crystal is cooled to below 1200 C
the titanium ions shift to one side of the body centre. Neighboring oxygen ions are also getting shifted.
The crystal changes from a cubic to tetragonal structure. The centre of positive and negative charges no
longer coincides. i.e. local dipoles are created. The dipoles of neighboring unit cell aligned
systematically.
Application
a)
b)
c)
d)
Used as dielectric amplifiers
Magnetrictive transducer
Capacitor
Electromechanical filters.
Piezo electricity
The phenomenon of becoming electrically polarized with mechanical stress is applied is known as piezo
electricity.
The material which exhibits the piezo electricity is called piezo electric material.
Or
Materials which are polarized when subjected to mechanical deformation are called piezo electric
materials.
All ferro electric crystals exhibit the piezo electricity but all piezo electric crystal need not exhibit ferro
electricity.
When piezo electric crystals are subjected to compression or tension, opposite kinds of charges are
developed at the opposite faces perpendicular to the direction of the applied forces. The charges
produced are proportional to the applied force. This property is utilized in conversion of mechanical
energy to electrical energy and vice versa.
The quartz crystal is a very good example of one such transducer material.
Example : SiO2
SiO2
The arrangement of atoms in quartz is shown in the figure. Quartz crystal consists of three axes, x-axis is
known electrical axis, y-axis is known as mechanical axis and
z axis is known as optical axis. This optical axis is
perpendicular to the electrical and mechanical axes.
In the absence of the external stress. All the charges are
balanced, net polarization is zero. But when external stress
is applied to the crystal the balance is disturbed and the
crystal is polarized. As a result, electrical charge is
developed on the faces. The charge developed per unit
force is called the charge sensitivity.
Application
a) Used in piezo electro oscillators
b) Used as crystal microphones
c) Generation and detection of ultrasonic waves
Pyro electricity
Pyro electricity, development of opposite electrical charges on different parts of a crystal that is
subjected to temperature change. First observed (1824) in quartz, pyroelectricity is exhibited only in
crystallized nonconducting substances having at least one axis of symmetry that is polar (that is, having
no centre of symmetry, the different crystal faces occurring on opposite ends). Portions of the crystal
with the same symmetry will develop charges of like sign. Opposite temperature changes produce
opposite charges at the same point; i.e., if a crystal develops a positive charge on one face during
heating, it will develop a negative charge there during cooling. The charges gradually dissipate if the
crystal is kept at a constant temperature.
Application : pyroelectric thermometer
Some important insulating material
Transformer oil
1.
2.
3.
4.
It is a special mineral oil used for insulation and cooling of transformers
It is having high dielectric strength and thermal stability.
It should be away form moisture as it reduces the dielectric s strength.
To remove moisture content from oil, it should be dehydrated periodically
Glass
1.
2.
3.
4.
It is an inorganic insulating material, which is composition of complex system of oxides.
Silicon dioxide plays vital role is making glasses
It is used for insulation in electronic valves, memory switches, x-ray tubes etc.
It is also used in capacitors as dielectrics
Ceramics
1.
2.
3.
4.
These are non metallic inorganic compounds like silicates, aluminates etc.
These are widely used in making electric switches, plugs, cathode heaters, etc.
These are also used in capacitor as dielectrics
These are brittle in nature, hence delicate to handle.
Important question
1.
2.
3.
4.
5.
6.
7.
8.
9.
What is internal field in a dielectric material?
Derive an expression for calculation of internal field for a cubic dielectric crystal
Write notes on dielectric theory of ferro electricity?
What is meant by polarization mechanism in dielectric? Discuss the different polarization
mechanisms in dielectrics
Distinguish between ferro-electricity and piezo electricity
Find the electric susceptibility of a dielectric gas having dielectric constant of 1.000041
Derive an expression between electronic polarization and electric susceptibility of the dielectric
medium
Describe Lorentz method to calculate the internal field of a cubic structure
What is pyro electricity? Write the applications of pyro electric materials
10. What is electronic polarization? Derive an expression for electronic polarizability in terms of the
radius of the atom
11. What is piezo electricity? Write the applications of piezo electric materials
12. The electronic polarizability of a dielectric material having no ions and permanent dipoles, is
1.5x10 -40 farad-meter2. The density of the material is 2.5x1028 atoms per m3. Calculate the
dielectric constant of the material.
13. Explain in detail, the terms a) dielectric constant b) susceptibility c) displacement vector
14. Distinguish between Ferro electricity and piezo electricity.
15. The radius of a gaseous atom is 0.062nm. Calculate the polarizability of the gas and its relative
permittivity. Given that the number of atoms of the gas is 2.7 x 1025 per m3.