Dielectrics. Basic concepts. Polarization

1. Dielectrics
Dielectrics

2. Dielectrics are the materials having electric dipole moment permantly.
Dielectrics are the materials having electric dipole moment permantly.
Dipole:
Dipole: A dipole is an entity in which equal positive and negative
A dipole is an entity in which equal positive and negative
charges are separated by a small distance..
charges are separated by a small distance..
DIPOLE moment (µele ):The product of magnitude of either of the
charges and separation distance b/w them is called Dipole moment.
µe = q . x  coul – m
All dielectrics are electrical insulators and they are mainly used to store
All dielectrics are electrical insulators and they are mainly used to store
electrical energy.
electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…
Ex: Mica, glass, plastic, water & polar molecules…
X
q -q
Introduction

3. +
Electric field
Dielectric atom
+
+
+
+
+
+
+
+
_
_
_
_
_
_
_
_
_
dipole

4. There are no free charge
There are no free charge
carriers in dielectrics, but
carriers in dielectrics, but
there are bound charged
there are bound charged
parts in the composition of
parts in the composition of
atoms and molecules.
atoms and molecules.
Therefore, under the action
Therefore, under the action
of an electric field, a
of an electric field, a
complete distribution of
complete distribution of
charges occurs.
charges occurs.
Dielectrics in electric field

5. Dielectric Constant
Dielectric Constant
Dielectric Constant is the ratio between the
Dielectric Constant is the ratio between the
permittivity of the medium to the permittivity of
permittivity of the medium to the permittivity of
free space.
free space.
The characteristics of a dielectric material are
The characteristics of a dielectric material are
determined by the dielectric constant and it has no
determined by the dielectric constant and it has no
units.
units.
0


 
r

6. +
-
+
-
+
-
E
E
Dielectrics in electric field
The shift of positive and negative
bound charges of the dielectric in
opposite directions is called
polarization.

7. Electric Polarization
Electric Polarization
The process of producing electric dipoles by an electric field is
The process of producing electric dipoles by an electric field is
called polarization in dielectrics.
called polarization in dielectrics.
Polarizability:
Polarizability:
The induced dipole moment per unit electric field is called
The induced dipole moment per unit electric field is called
Polarizability.
Polarizability.
The induced dipole moment is proportional to the intensity of the
The induced dipole moment is proportional to the intensity of the
electric field.
electric field.
Is a Polarizability constant
Is a Polarizability constant
constant
lity
polarizabi







E
E

8. Polar Non-polar
Dielectric Polarization
Dielectrics, in whose
Dielectrics, in whose
molecules the centers of
molecules the centers of
distribution of positive and
distribution of positive and
negative charges do not
negative charges do not
coincide, are called
coincide, are called polar
polar.
.
Dielectrics, in whose molecules
Dielectrics, in whose molecules
the centers of distribution of
the centers of distribution of
positive and negative charges
positive and negative charges
coincide, are called
coincide, are called non-polar.
non-polar.

9. Polarization vector:
Polarization vector:
The dipole moment per unit volume of the dielectric
The dipole moment per unit volume of the dielectric
material is called polarization vector.
material is called polarization vector.
V
x
q
P
n
i
i
i


 1

10. Electric flux Density (D):
Electric flux density is defined as charge per unit area and it has
same units of dielectric polarization.
Electric flux density D at a point in a free space or air in terms of
Electric field strength is
At the same point in a medium is given by
As the polarization measures the additional flux density arising
from the presence of material as compared to free space
(1)
-
-
E
D 0
0 

(3)
-
-
P
E
D
i.e, 0 


(2)
-
-
E
D 


11. P
.
)
1
(
P
E
)
-
.
(
(or)
P
E
)
-
(
P
E
E
0
0
0
r
0
0






E
r 








Using equations 2 & 3 we get

12. Electric susceptibility:
Electric susceptibility:
The polarization vector P is proportional to the
The polarization vector P is proportional to the
total electric flux density and direction of electric
total electric flux density and direction of electric
field.
field.
Therefore the polarization vector can be written
Therefore the polarization vector can be written
1
)
1
(
0
0
0
0






r
e
r
e
e
E
E
E
P
E
P










13. Various polarization processes:
Various polarization processes:
When the specimen is placed inside a d.c.
When the specimen is placed inside a d.c.
electric field, polarization is due to four types
electric field, polarization is due to four types
of processes….
of processes….
1.Electronic polarization
1.Electronic polarization
2.Ionic polarization
2.Ionic polarization
3.Orientation polarization
3.Orientation polarization
4.Space charge polarization
4.Space charge polarization

14. Electronic Polarization
When an EF is applied to an atom, +vely charged
nucleus displaces in the direction of field and ẽ could in
opposite direction. This kind of displacement will produce an
electric dipole with in the atom.
i.e, dipole moment is proportional to the magnitude of field
strength and is given by
E
E
e
e
e
or





where ‘αe’ is called electronic Polarizability constant

15. It increases with increase of volume of the atom.
This kind of polarization is mostly exhibited in Monatomic
gases.
10
____ 2
-40
m
F
e 



He
He Ne
Ne Ar
Ar Kr
Kr Xe
Xe
0.18
0.18 0.35
0.35 1.46
1.46 2.18
2.18 3.54
3.54
It occurs only at optical frequencies (1015
Hz)
It is independent of temperature.

16. Expression for Electronic Polarization
Consider a atom in an EF of intensity ‘E’ since the nucleus
(+Ze) and electron cloud (-ze) of the atom have opposite
charges and acted upon by Lorentz force (FL).
Subsequently nucleus moves in the direction of field and
electron cloud in opposite direction.
When electron cloud and nucleus get shifted from their normal
positions, an attractive force b/w them is created and the
seperation continuous until columbic force FC is balanced with
Lorentz force FL, Finally a new equilibriums state is
established.

17. fig(2) represents displacement of nucleus and electron
cloud and we assume that the –ve charge in the cloud
uniformly distributed over a sphere of radius R and the
spherical shape does not change for convenience.
+Ze
R
No field fig(1)
x
R
In the presence of field fig (2)
E

18. Let σ be the charge density of the sphere
sphere.
in the
charge
total
the
represents
Ze
-
3
4 3
R
Ze




 
(1)
-
-
-
-
-
.
.
.
.
3
4
.
q
is
x'
'
radius
of
sphere
in the
charge
ve
-
the
Thus
3
3
3
3
4
3
3
4
3
e
x
R
ze
x
R
ze
x









  (2)
-
-
-
-
-
4
.
4
1
.
.
4
1
F
Now 3
0
2
2
3
3
2
0
2
0
c
R
x
e
z
ze
R
x
ze
x
x
q
q p
e












 



19. Force experienced by displaced nucleus in EF of Strength E
is FL = Eq = ZeE -----(3)
e
e
c
L
zex
R
zex
E
R
zex
R
x
e
z
F
F





moment
dipole
E
4
4
(4)
-
-
-
-
-
ZeE
4
3
0
3
0
3
0
2
2










3
0
4 R
e 
 

Hence electronic Polaris ability is directly proportional to cube of the
radius of the atom.

20. Ionic polarization
Ionic polarization

The ionic polarization occurs, when atoms form
The ionic polarization occurs, when atoms form
molecules and it is mainly due to a relative displacement
molecules and it is mainly due to a relative displacement
of the atomic components of the molecule in the
of the atomic components of the molecule in the
presence of an electric field.
presence of an electric field.

When a EF is applied to the molecule, the positive ions
When a EF is applied to the molecule, the positive ions
displaced by X
displaced by X1
1 to the negative side electric field and
to the negative side electric field and
negative ions displaced by X
negative ions displaced by X2
2 to the positive side of field.
to the positive side of field.
 The resultant dipole moment
The resultant dipole moment µ = q ( X
µ = q ( X1
1 + X
+ X2
2)..
)..

21. Electric field
+
+
+
+
+
+
+
+
_
_
_
_
_
_
_
_
1
x 2
x
anion
cat ion

22. Restoring force constant depend upon the mass of the ion and
natural frequency and is given by
 
M
m
w
eE
x
x
w
m
eE
x
x
w
m
eE
F
1
1
2
0
2
1
2
0
2
0
.
or
.








23. Where ‘M’ mass of anion and ‘m’ is mass of cat ion
 
 
M
m
ionic
ionic
M
m
ionic
w
e
E
w
E
e
x
x
1
1
2
0
2
1
1
2
0
2
2
1
or
)
e(











This polarization occurs at frequency 1013
Hz (IR).
It is a slower process compared to electronic polarization.
It is independent of temperature.

24. Orientational Polarization
It is also called dipolar or molecular polarization. The
molecules such as H2 , N2,O2,Cl2 ,CH4,CCl4 etc., does not carry
any dipole because centre of positive charge and centre of
negative charge coincides. On the other hand molecules like
CH3Cl, H2O,HCl, ethyl acetate ( polar molecules) carries
dipoles even in the absence of electric field.
How ever the net dipole moment is negligibly small since all
the molecular dipoles are oriented randomly when there is no
EF. In the presence of the electric field these all dipoles orient
them selves in the direction of field as a result the net dipole
moment becomes enormous.

25.  It occurs at a frequency 106
Hz to 1010
Hz.
 It is slow process compare to ionic
polarization.
 It greatly depends on temperature.

26.   kT
w
e
R
kT
E
N
kT
E
N
N
P
ori
m
M
o
ori
ionic
elec
orie
o
o
orie
orie
o
3
4
3
.
.
3
.
.
.
2
1
1
2
0
2
3
2
2
























Expression for orientation polarization
This is called Langevin – Debye equation for total Polaris ability in
dielectrics.

27. Internal fields or local fields
Internal fields or local fields
Local field or internal field in a dielectric is the
Local field or internal field in a dielectric is the
space and time average of the electric field
space and time average of the electric field
intensity acting on a particular molecule in the
intensity acting on a particular molecule in the
dielectric material.
dielectric material.

28. Evaluation of internal field
Evaluation of internal field
Consider a dielectric be placed between the
Consider a dielectric be placed between the
plates of a parallel plate capacitor and let there
plates of a parallel plate capacitor and let there
be an imaginary spherical cavity around the
be an imaginary spherical cavity around the
atom A inside the dielectric.
atom A inside the dielectric.
The internal field at the atom site ‘A’ can be
The internal field at the atom site ‘A’ can be
made up of four components E
made up of four components E1
1 ,E
,E2
2, E
, E3
3 & E
& E4
4.
.

29. + +
+ +
+ + + + + +
+
_ _ _ _ _ _ _ _
_
E
Dielectric
material
Spherical
Cavity
A
_
_
_
_
_ _
_
_
+ + + + + +
+
+
+ +
+
+ +
+
+
_
_
_
_
_
_
_
_

30. Field E
Field E1
1:
:
E
E1
1 is the field intensity at A due to the charge density on
is the field intensity at A due to the charge density on
the plates
the plates
)
1
(
..........
0
1
0
0
1
0
0
1





P
E
E
P
E
E
P
E
D
D
E








31. Field E
Field E2
2:
:
E
E2
2 is the field intensity at A due to the charge density
is the field intensity at A due to the charge density
induced on the two sides of the dielectric.
induced on the two sides of the dielectric.
)
2
.(
..........
0
2

P
E


Field E
Field E3
3:
:
E
E3
3 is the field intensity at A due to the atoms
is the field intensity at A due to the atoms
contained in the cavity, we are assuming a cubic
contained in the cavity, we are assuming a cubic
structure, so E
structure, so E3
3 = 0.
= 0.

32. + +
E
 
d r
p q
R
dA
r
A
+
+
+
+ +
+
+
+
+
+
_
_
_
_
_
_
_
_ _
_
_
_

33. Field E
Field E4
4:
:
1.This is due to polarized charges on the surface of
1.This is due to polarized charges on the surface of
the spherical cavity.
the spherical cavity.
Where dA is Surface area between
Where dA is Surface area between θ
θ &
& θ
θ+d
+dθ
θ…
…







d
r
dA
rd
r
dA
qR
pq
dA
sin
.
2
.
sin
.
2
.
.
2
2




34. 2.The total charge present on the surface area dA is…
2.The total charge present on the surface area dA is…
dq = ( normal component of polarization ) X ( surface
dq = ( normal component of polarization ) X ( surface
area )
area )





d
p
r
dq
dA
p
dq
.
sin
.
cos
2
cos
2




35. 3.The field due to this charge at A, denoted by dE
3.The field due to this charge at A, denoted by dE4
4 is given by
is given by
2
0
4
4
1
r
dq
dE


The field in
The field in θ
θ = 0
= 0 direction
direction 2
0
4
cos
4
1
r
dq
dE













d
P
dE
d
p
r
r
dE
.
sin
.
cos
2
cos
)
.
sin
.
cos
2
(
4
1
2
0
4
2
2
0
4



36. 4.Thus the total field E
4.Thus the total field E4
4
due to the charges on the
due to the charges on the
surface of the entire
surface of the entire
cavity is
cavity is
0
4
0
1
1
3
0
1
1
2
0
0
2
0
0
2
0
0
4
4
3
)
3
1
1
(
2
)
3
(
2
.
2
sin
cos
..
.
sin
.
cos
2
.
sin
.
cos
2


















P
E
P
x
P
dx
x
P
d
dx
x
let
d
P
d
P
dE
E






















37. The internal field or Lorentz field can be written as
The internal field or Lorentz field can be written as
o
i
o
o
o
i
i
p
E
E
p
p
p
E
E
E
E
E
E
E




3
3
0
)
(
4
3
2
1












38. Classius – Mosotti relation:
Classius – Mosotti relation:
Consider a dielectric material having cubic
Consider a dielectric material having cubic
structure , and assume ionic Polarizability &
structure , and assume ionic Polarizability &
Orientational polarizability are zero..
Orientational polarizability are zero..
0
0
3
.,
.,
......
..
0







P
E
E
where
E
where
E
N
P
N
P
on
polarizati
i
i
e
i
e
i








39. )
1
.........(
..........
)
3
1
(
)
3
1
(
3
3
)
3
(
0
0
0
0
0















e
e
e
e
e
e
e
e
e
i
e
N
E
N
P
E
N
N
P
E
N
P
N
P
P
N
E
N
P
P
E
N
P
E
N
P












40. relation
Mosotti
Classius
......
2
1
3
)
1
3
1
(
1
3
)
1
3
1
(
3
1
)
1
(
3
1
)
1
(
3
1
)
1
(
3
1
)
1
(
)
3
1
(
)
2
(
&
)
1
(
eq
from
)
2
...(
).........
1
(
on vector
polarizati
the
known that
We
0
0
0
0
0
0
0
0
0
0
0
n
0
























r
r
e
r
e
r
e
r
e
e
r
e
e
r
e
e
r
e
e
r
N
N
N
N
N
E
E
N
N
E
E
N
N
E
N
E
N
s
E
P

































41. Ferro electric materials or Ferro electricity
Ferro electric materials or Ferro electricity

Ferro electric crystals exhibit spontaneous
Ferro electric crystals exhibit spontaneous
polarization I.e. electric polarization with out
polarization I.e. electric polarization with out
electric field.
electric field.

Ferro electric crystals possess high dielectric
Ferro electric crystals possess high dielectric
constant.
constant.

each unit cell of a Ferro electric crystal carries
each unit cell of a Ferro electric crystal carries
a reversible electric dipole moment.
a reversible electric dipole moment.
Examples: Barium Titanate (BaTiO
Examples: Barium Titanate (BaTiO3
3) , Sodium
) , Sodium
nitrate (NaNO
nitrate (NaNO3
3) ,Rochelle salt etc..
) ,Rochelle salt etc..

42. Piezo- electricity
Piezo- electricity
The process of creating electric polarization by mechanical
The process of creating electric polarization by mechanical
stress is called as piezo electric effect.
stress is called as piezo electric effect.
This process is used in conversion of mechanical energy into
This process is used in conversion of mechanical energy into
electrical energy and also electrical energy into mechanical
electrical energy and also electrical energy into mechanical
energy.
energy.
According to inverse piezo electric effect, when an electric
According to inverse piezo electric effect, when an electric
stress is applied, the material becomes strained. This strain is
stress is applied, the material becomes strained. This strain is
directly proportional to the applied field.
directly proportional to the applied field.
Examples: quartz crystal , Rochelle salt etc.,
Examples: quartz crystal , Rochelle salt etc.,
Piezo electric materials or peizo electric semiconductors such
Piezo electric materials or peizo electric semiconductors such
as Gas, Zno and CdS are finding applications in ultrasonic
as Gas, Zno and CdS are finding applications in ultrasonic
amplifiers.
amplifiers.