Dielectrics. Dielectrics are the materials having electric dipole moment permantly. Dipole: A dipole is an entity in which equal positive and negative.

DielectricsDielectrics

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…

Xq -q

Introduction

Dielectric Constant Dielectric Constant

Dielectric Constant is the ratio between Dielectric Constant is the ratio between the permittivity of the medium to the the permittivity of the medium to the permittivity of free space.permittivity of free space.

The characteristics of a dielectric The characteristics of a dielectric material are determined by the material are determined by the dielectric constant and it has no units.dielectric constant and it has no units.

0 r

Electric PolarizationElectric PolarizationThe 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

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

xqP

n

iii

1

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

P.)1(

P E ) - .( (or)

P E ) - (

P E E

0

00r

0

0

Er

Using equations 2 & 3 we get

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 writtenTherefore the polarization vector can be written

1

)1(

0

0

0

0

re

r

e

e

E

E

E

P

EP

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 polarization1.Electronic polarization

2.Ionic polarization2.Ionic polarization

3.Orientation polarization3.Orientation polarization

4.Space charge polarization 4.Space charge polarization

Electronic Polarization

When an EF is applied to an atom, +vely charged nucleus displaces in the direction of field and ẽ 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

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.

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.

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

Let σ be the charge density of the sphere

sphere. in the charge total therepresents Ze-

34 3R

Ze

(1)-----

...

.3

4.q

is x'' radius of sphere in the charge ve- theThus

33

334

334

3e

xR

ze

xR

ze

x

(2)----- 4

.

4

1..

4

1F Now

30

22

3

3

20

20

c R

xezze

R

xze

xx

qq pe

Force experienced by displaced nucleus in EF of Strength E is FL = Eq = ZeE -----(3)

ee

cL

zex

R

zex

ER

zex

R

xez

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.

Ionic polarizationIonic 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 Xdisplaced by X1 1 to the negative side electric field and to the negative side electric field and

negative ions displaced by Xnegative 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 ( Xµ = q ( X11 + X + X22)..)..

Electric field+

+

+

+

+

+

+

+

_

__

_

_

_

_

_

1x 2x

anioncat ion

Restoring force constant depend upon the mass of the ion and natural frequency and is given by

Mmw

eExx

wm

eEx

xwmeEF

1120

21

20

20

.

or

.

Where ‘M’ mass of anion and ‘m’ is mass of cat ion

Mmionic

ionic

Mmionic

w

e

E

w

Eexx

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.

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.

It occurs at a frequency 106 Hz to 1010Hz. It is slow process compare to ionic

polarization. It greatly depends on temperature.

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.

Internal fields or local fieldsInternal 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.

Evaluation of internal fieldEvaluation 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 Emade up of four components E1 1 ,E,E22, E, E3 3 & E& E44..

+ ++ ++ + + + + ++

_ _ _ _ _ _ _ __

E

Dielectricmaterial

Spherical Cavity

A

__

_

__ ___

+ + + + + ++

+

+ ++

+ ++

+

_

_

___

___

Field EField E11::

EE1 1 is the field intensity at A due to the charge density is the field intensity at A due to the charge density

on the plateson the plates

)1(..........0

1

0

01

0

01

PEE

PEE

PED

DE

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 dielectric.density induced on the two sides of the dielectric.

)2.(..........0

2 P

E

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.

Field EField E44::

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 θθ & & θθ+d+dθθ……

drdA

rdrdA

qRpqdA

sin.2

.sin.2

..2

2

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 )

dprdq

dApdq

.sin.cos2

cos2

3.The field due to this charge at A, denoted by dE3.The field due to this charge at A, denoted by dE4 4 is given by is given by

20

4 4

1

r

dqdE

The field in The field in θθ = 0 = 0 directiondirection 20

4

cos

4

1

r

dqdE

dP

dE

dprr

dE

.sin.cos2

cos).sin.cos2(4

1

2

04

22

04

4.Thus the total field E4.Thus the total field E44 due to the charges on the due to the charges on the surface of the entire surface of the entire cavity is cavity is

04

0

11

3

0

1

1

2

0

0

2

0

0

2

0

0

44

3

)3

11(

2)

3(

2

.2

sincos..

.sin.cos2

.sin.cos2

PE

PxP

dxxP

ddxxlet

dP

dP

dEE

The internal field or Lorentz field can be written asThe internal field or Lorentz field can be written as

oi

oooi

i

pEE

pppEE

EEEEE

3

30)(

4321

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

PEEwhere

EwhereENP

NPonpolarizati

i

ieie

i

)1.........(..........)

31(

)3

1(

3

3

)3

(

0

0

0

0

0

e

e

ee

ee

ee

e

ie

NEN

P

ENN

P

ENP

NP

PNENP

PENP

ENP

relation Mosotti Classius......2

1

3

)1

31(

1

3

)1

31(

31

)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

NN

E

ENN

E

ENN

ENEN

s

EP

Ferro electric materials or Ferro electricityFerro 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 carrieseach unit cell of a Ferro electric crystal carries

a reversible electric dipole moment.a reversible electric dipole moment.

Examples: Barium Titanate (BaTiOExamples: Barium Titanate (BaTiO33) , Sodium ) , Sodium

nitrate (NaNOnitrate (NaNO33) ,Rochelle salt etc..) ,Rochelle salt etc..

Piezo- electricityPiezo- 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.