PHYSICS
05/03/23Prepared By Soham Kansodaria
Dielectrics are the materials having electric dipole moment permnantly.
Dipole: A dipole is an entity in which equal positive and negative 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 electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…
Xq -q
Introduction
05/03/23Prepared By Soham Kansodaria
+
Electric field
Dielectric atom
++
+
++
+++
-
Dipole----
----
05/03/23Prepared By Soham Kansodaria
0 r
Dielectric Constant Dielectric Constant • Dielectric Constant is the ratio between the permittivity of the Dielectric Constant is the ratio between the permittivity of the
medium to themedium to thepermittivity of free space.permittivity of free space.
• The characteristics of a dielectric material are determined by the The characteristics of a dielectric material are determined by the dielectric constant and it has no units.dielectric constant and it has no units.
05/03/23Prepared By Soham Kansodaria
Electric PolarizationThe process of producing electric dipoles by an electric field is called polarization in dielectrics.
Polarizability:
The induced dipole moment per unit electric field is called Polarizability.The induced dipole moment is proportional to the intensity of the electric field .
constant lity polarizabi
EE
05/03/23Prepared By Soham Kansodaria
Polarization vector:
The dipole moment per unit volume of the dielectric material is called polarization vector.
V
xqP
n
iii
1
05/03/23Prepared By Soham Kansodaria
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 00 (3) -- P E D i.e, 0
(2) --E D
05/03/23Prepared By Soham Kansodaria
Using equations 2 & 3 we get
P.)1( P E ) - .( (or)
P E ) - (P E E
0
00r
0
0
Er
05/03/23Prepared By Soham Kansodaria
Electric susceptibility:The polarization vector P is proportional to the total electric flux density and direction of electric field.Therefore the polarization vector can be written
1
)1(
0
0
0
0
re
r
e
e
EE
EP
EP
05/03/23Prepared By Soham Kansodaria
Various polarization processes:
When the specimen is placed inside a d.c. electric field, polarization is due to four types of processes….
1.Electronic polarization2.Ionic polarization
3.Orientation polarization4.Space charge polarization
05/03/23Prepared By Soham Kansodaria
Electronic PolarizationWhen an EF is applied to an atom, +ve 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
where ‘αe’ is called electronic Polarizability constant
E
E
e
e
e
or
05/03/23Prepared By Soham Kansodaria
It increases with increase of volume of the atom. This kind of polarization is mostly exhibited in Monatomic gases.
10 ____ 2-40 mFe
HeHe NeNe ArAr KrKr XeXe
0.180.18 0.350.35 1.461.46 2.182.18 3.543.54
It occurs only at optical frequencies (1015Hz) It is independent of temperature.
05/03/23Prepared By Soham Kansodaria
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. 05/03/23Prepared By Soham Kansodaria
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
05/03/23Prepared By Soham Kansodaria
Let σ be the charge density of the sphere
sphere. in the charge total therepresents Ze-
34 3R
Ze
(1)-----
...
.34.q
is x'' radius of sphere in the charge ve- theThus
33
334
334
3e
xRze
xRze
x
(2)----- 4
.4
1..
41F Now 3
0
22
3
3
20
20
c Rxezze
Rxze
xxqq pe
05/03/23Prepared By Soham Kansodaria
Force experienced by displaced nucleus in EF of Strength E is FL = Eq = ZeE -----(3)
ee
cL
zexRzex
ERzexRxez
FF
moment dipole E 4
4
(4)----- ZeE 4
30
30
30
22
304 Re
Hence electronic Polaris ability is directly proportional to cube of the radius of the atom.
05/03/23Prepared By Soham Kansodaria
Ionic polarization
The ionic polarization occurs, when atoms form molecules and it is mainly due to a relative displacement of the atomic components of the molecule in the presence of an electric field.
When a EF is applied to the molecule, the positive ions displaced by X1 to the negative side electric field and negative ions displaced by X2 to the positive side of field.
The resultant dipole moment µ = q ( X1 + X2)..05/03/23Prepared By Soham Kansodaria
Electric field++++
1x 2x
anioncat ion
++++
----
----
05/03/23Prepared By Soham Kansodaria
Restoring force constant depend upon the mass of the ion and natural frequency and is given by
MmweExx
wmeEx
xwmeEF
1120
21
20
20
.
or .
05/03/23Prepared By Soham Kansodaria
Where ‘M’ mass of anion and ‘m’ is mass of cat ion
Mmionic
ionic
Mmionic
we
E
wEexx
1120
2
1120
2
21
or
)e(
This polarization occurs at frequency 1013 Hz (IR).It is a slower process compared to electronic
polarization.It is independent of temperature. 05/03/23Prepared By Soham Kansodaria
Orientational PolarizationIt 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.
05/03/23Prepared By Soham Kansodaria
It occurs at a frequency 106 Hz to 1010Hz. It is slow process compare to ionic polarization. It greatly depends on temperature.
05/03/23Prepared By Soham Kansodaria
kTw
eR
kT
ENkT
ENNP
orimMooriionicelec
orieo
oorie
orieo
34
3
..3
...
211
20
23
2
2
Expression for orientation polarization
This is called Langevin–Debye equation for total Polaris ability in dielectrics.
05/03/23Prepared By Soham Kansodaria
Internal fields or local fields
Local field or internal field in a dielectric is the space and time Local field or internal field in a dielectric is the space and time average of the electric field intensity acting on a particular average of the electric field intensity acting on a particular molecule in the dielectric material.molecule in the dielectric material.
05/03/23Prepared By Soham Kansodaria
Evaluation of internal field
Consider a dielectric be placed between the plates of a parallel plate capacitor and let there be an imaginary spherical cavity around the atom A inside the dielectric.
The internal field at the atom site ‘A’ can be made up of four components E1 ,E2, E3 & E4.
05/03/23Prepared By Soham Kansodaria
+ ++ ++ + + + + ++
_ _ _ _ _ _ _ __
E
Dielectricmaterial
Spherical Cavity
A
__
_
__ ___
+ + + + + ++
+
+ ++
+ ++
+
_
_
___
___
05/03/23Prepared By Soham Kansodaria
Field E1:E1 is the field intensity at A due to the charge density on the plates
)1(..........0
1
0
01
0
01
PEE
PEE
PED
DE
05/03/23Prepared By Soham Kansodaria
Field EField E22::EE22 is the field intensity at A due to the charge is the field intensity at A due to the charge density induced on the two sides of the density induced on the two sides of the dielectric.dielectric.
)2.(..........0
2 PE
Field EField E33::
EE33 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 Estructure, so E33 = 0. = 0. 05/03/23Prepared By Soham Kansodaria
+ +
E
d r
p q
R
dA
r
A
+
++
+ +++
+++
_
__
___
__ _
__
_05/03/23Prepared By Soham Kansodaria
Field E4:1.This is due to polarized charges on the surface of the spherical cavity.
Where dA is Surface area between θ & θ+dθ…
drdA
rdrdAqRpqdA
sin.2
.sin.2..2
2
05/03/23Prepared By Soham Kansodaria
2.The total charge present on the surface area dA is…
dq = ( normal component of polarization ) X ( surface area )
dprdq
dApdq
.sin.cos2
cos2
05/03/23Prepared By Soham Kansodaria
3.The field due to this charge at A, denoted by dE4 is given by
20
4 41
rdqdE
20
4cos
41
rdqdE
dPdE
dprr
dE
.sin.cos2
cos).sin.cos2(4
1
2
04
22
04
05/03/23Prepared By Soham Kansodaria
4.Thus the total field E4 due to the charges on the surface of the entire cavity is
04
0
11
3
0
1
1
2
0
0
2
0
0
2
0
044
3
)3
11(2
)3
(2
.2
sincos..
.sin.cos2
.sin.cos2
PE
PxP
dxxP
ddxxlet
dP
dP
dEE
05/03/23Prepared By Soham Kansodaria
The internal field or Lorentz field can be written as
oi
oooi
i
pEE
pppEE
EEEEE
3
30)(
4321
05/03/23Prepared By Soham Kansodaria
Classius – Mosotti relation:Consider a dielectric material having cubic structure , and assume ionic Polarizability & Orientational polarizability are zero..
0
0
3.,
.,........
0
PEEwhere
EwhereENPNPonpolarizati
i
ieie
i
05/03/23Prepared By Soham Kansodaria
)1.........(..........)
31(
)3
1(
3
3
)3
(
0
0
0
0
0
e
e
ee
ee
ee
e
ie
NENP
ENNP
ENPNP
PNENP
PENP
ENP
05/03/23Prepared By Soham Kansodaria
relation Mosotti Classius......21
3
)1
31(
13
)1
31(3
1
)1(31
)1(31
)1(31
)1()
31(
)2(&)1(eq from
)2...().........1(on vector polarizati theknown that We
0
0
0
00
00
00
0
0
n
0
r
re
r
e
r
e
r
ee
r
ee
r
ee
re
e
r
N
N
N
NNE
ENNE
ENN
ENENs
EP
05/03/23Prepared By Soham Kansodaria
Ferro electric materials or Ferro electricity Ferro electric crystals exhibit spontaneous polarization I.e. electric
polarization with out electric field. Ferro electric crystals possess high dielectric constant. each unit cell of a Ferro electric crystal carries
a reversible electric dipole moment.
Examples: Barium Titanate (BaTiO3) , Sodium nitrate (NaNO3) ,Rochelle salt etc..
05/03/23Prepared By Soham Kansodaria
Piezo- electricity
The process of creating electric polarization by mechanical stress is called as piezo electric effect.
This process is used in conversion of mechanical energy into electrical energy and also electrical energy into mechanical energy.
According to inverse piezo electric effect, when an electric stress is applied, the material becomes strained. This strain is directly proportional to the applied field.
Examples: quartz crystal , Rochelle salt etc.,Piezo electric materials or peizo electric semiconductors such as Gas, Zno and CdS are finding applications in ultrasonic amplifiers.05/03/23Prepared By Soham Kansodaria
THANK YOUTHANK YOU05/03/23Prepared By Soham Kansodaria