SNS COLLEGE OF ENGINEERINGKurumbapalayam(Po), Coimbatore – 641 107

Accredited by NAAC-UGC with ‘A’ GradeApproved by AICTE & Affiliated to Anna University, Chennai

INTERNAL ASSESMENT EXAMINATIONS – IIIAnswer key- PH6251 – Engineering Phiscs - II

Part-A1.Dielectric loss

If a dielectric is subjected to an electric field, the electrical energy is absorbed by the dielectric

and certain quantity of electrical energy is dissipated in the form of heat energy. This is known as

dielectric loss.

2.Four application of ferro-electrics.

Ferro-electric materials are used to produce ultrasonics

They are used in the production of piezo-electric materials and in turn to make microphones.

Ferro-electrics are also used in SONAR, strain gauges, etc.

Ferro-electric semiconductors are used to make positors, which in turn are used to measure

and control the temperature.

3.Uses of Dielectric materials

Caopacitor and Transformer

4.Given , Polarizability = 2.18 x 10- 40 Fm2. N= 2.69 X 1025/ m2.

Ans ; 1

5. Due to pyroelectric effect.

6.Rapid Cooling

7.Four methods employed to produce nano phase materials.

Plasma – arching

Chemical vapour deposition

Sol – gel technique

Electro – deposition

8.NLO materials:

The change in optical properties due to electric and magnetic field associated with

light is called non linear effects and those materials which posses these effect are called non-linear

materials.

Examples:

i. Ammonium-dihydrophosphate (APO)

ii. Potassium-dyhydrophosphate (KDP)

9. Single walled CNT & Multi Walled CNT

10.Birefringence:

When light passes through a material the incident ray splits into two rays viz, one of

same wavelength and other of different wavelength. This phenomenon is called as double

refraction (or) Birefringence.

Kerr effect:

When electric field is applied along the direction of propagation of light, then the light will undergo

double refraction, this is called Kerr Effect.

Part-B

11.a.VARIOUS POLARIZATION MECHANISMS IN DIELECTRICSDielectric polarization is the displacement of charged particles under the action of the electric

field.

Electronic polarization

Ionic polarization

Orientation polarization

Space-charge polarization.

ELECTRONIC POLARIZATION

Electronic polarization occurs due to the displacement of positively charged nucleus and

negatively charged electrons in opposite directions, when an external electric field is applied and

thereby creates a dipole moment in the dielectric.

The induced dipole moment is given by

µ=αeE

Where, αe is the electronic polarizability.

Monoatomic gases exhibit this kind of polarization. Electronic polarizability is proportional to

the volume of the atoms and is independent of temperature.

Calculation of electronic polarizability

Without field

Let us consider a classical model of an atom. Assume the charge of nucleus of that atom is

Ze. The nucleus is surrounded by an electron cloud of charge –Ze, which is distributed in a sphere of

radius R as shown in the fig

The charge density of the charged sphere =−Ze4 π R3

3

(Or) charge density =−3Ze4 π R3 …(1)

With field

When the dielectric is placed in a d.c. electric field E, two phenomenon occur

i. Lorentz force due to the electric field tends to separate the nucleus and the electron

cloud from their equilibrium position.

ii. After separation, an attractive coulomb force arises between the nucleus and the elec-

tron cloud which tries to maintain the original equilibrium position.

Let x be the displacement made by the electron cloud from the positive core, as shown

Since the core is heavy, it will not move when compared to the movement of the electron

cloud. Here x <<R, where R is the radius of the atom.

Since Lorentz and Coulomb forces are equal and opposite in nature, equilibrium is reached.

At Equilibrium,

Lorentz force = Coulomb force

Lorentz force = Charge × Field

= -ZeE … (2)

The negative sign indicates the repulsive force.

Coulomb force = Charge × Field

= +Ze ×Q

4 π∈ox2

The positive sign indicates the attractive force.

Coulomb force = Charge×Total negativecharges(Q)enclosed∈the sphereof radius x

4 π∈o x2 ….(3)

The total number of negative charges (Q) enclosed in the sphere of radius ‘x’

= Charge density of electrons × volume of the sphere

Substitute the charge density from eqn (1), we get

The total number of negative charges (Q) enclosed in the sphere of radius x is

= −3Ze4 π R3 ×

43π x3

∴Q=−Ze x3

R3 …..(4)

Substitute eqn (4) in (3)

Coulomb force ¿Ze

4 π∈ox2 .

−Ze x3

R3

.¿ −Z2e2 x4 π∈oR

3 ..… (5)

At equilibrium position, eqn (2)=eqn (5)

∴−ZeE= −Z2 e2 x4 π∈oR

3

(Or) x=4 π∈oR

3EZe

.....(6)

Therefore, the displacement of electron cloud (x) is proportional to the applied electric field E.

Dipole moment

Now the two electric charges +Ze and –Ze are displaced by a distance x under the influence of

the field and form an induced dipole moment which is given by

Induced dipole moment (µe) = Magnitude of charge × displacement

= Zex

Substituting the value of x from eqn (6), we get

µe=Ze 4π∈o R

3EZe

µe = 4π∈oR3E

µe α E

µe = αeE

Where, αe = 4π∈oR3 (Farad-m3) is called electronic polarization which is proportional to the

volume of the atom.

Relation between αe and Dielectric Constants

We know, the induced electronic dipole moment is proportional to the applied field. This dipole

moment per unit volume is called electronic polarization. This is independent of temperature.

Electronic polarization Pe=N µe

Where, N is the number of atoms

Pe=N αeE …….(8)

SincePeE

= ∈o (∈r-1), we can write

α e=∈o (∈r−1)

N…….(9)

IONIC POLARIZATION

Ionic polarization arises due to the displacement of cations (+ve ions) and anions (- ve ions)

from its original position, in opposite directions in the presence of electric field as shown in figure.

Explanation

Let us assume that there are one cation and one anion present in each unit cell of the ionic

crystal NaCl. When the electric field is applied, let x1 and x2 be the distances to which positive and

negative ions move from their equilibrium positions. The resultant dipole moment per unit cell, due to

ionic displacement is given by

Induced dipole moment = magnitude of charge × displacement

µi = e(x1 + x2) ……… (1)

Where, x1 is the shift of +ve ion and x2 is the shift of –ve ion, from their equilibrium positions.

When the field is applied, the restoring force produced is proportional to the displacements.

For +ve ion,

Restoring force F α x1 or F = β1 x1 ……….(2)

For –ve ion,

Restoring force F α x2 or F = β2 x2 ……….(3)

Here, β1 and β2 are restoring force constants, which depend on the masses of the ions and angular

frequency of the molecule in which the ions are present.

If ‘m’ is the mass of +ve ion and ‘M’ be the mass of the –ve ion and ωois the angular frequency, then

β1 =m ωo2 ….….(4)

β2 =M ωo2 …….(5)

Substituting for β1 in eqn (2), the restoring force for +ve ion can be written as

F = mωo2 x1 …….(6)

We know, F = eE …….(7)

Equating eqn (6) and (7), we get

eE = mωo2 x1

x1=eEmωo

2 ……..(8)

Similarly for –ve ion we can write

x2=eEMωo

2 ……..(9)

Adding eqn (8) and (9) we get

x1+ x2=eEωo

2 ( 1m

+ 1M ) ..…..(10)

Substituting eqn (10) in (1), we get

µi=e2Eωo

2 ( 1m

+ 1M )

Or µi= αiE

Where, αiis the ionic polarization given by

α i=e2

ωo2 ( 1m

+ 1M )

so, the ionic polarizability αiis inversely proportional to the square of the natural frequency of

the ionic molecule and directly proportional to its reduced mass which is given by ( 1m

+ 1M )

ORIENTATION POLARIZATION

Polar molecules are the molecules which have permanent dipole moments even in the absence

of an electric field as shown in figure.

The orientation polarization arises due to the presence of polar molecule in the dielectric

medium. When a dielectric which consists of polar molecules is kept in an electric field, the

molecules align themselves along the field direction. So there is a resultant dipole moment along the

field direction.

Explanation

In the case of a CH3Cl molecule, the +ve and –ve charges do not coincide. The Cl- has more

electronegativity than hydrogen. Therefore the Cl atoms pull the bonded electrons towards it more

strongly than hydrogen atoms. Therefore, even in the absence of field, there exists a net dipole

moment.

Now, when the field is applied, positive portion align themselves along the direction of the

electric field and negative portion align in the opposite direction of the field. This kind of polarization

is called as orientation polarization.

This depends on temperature. When the temperature is increased, the thermal energy tends to

randomize the alignment.

From Langevin’s theory of paramagnetism, net intensity of magnetization

¿ N μ2B

3K BT

Since, the same principle can be applied to the application of electric field we can write,

Orientation polarization

Po=N μ2 E3K BT

Where N is the number of atoms

(Or)po= Nαo E

Where αo is orientation polarizability

α o=μ2

3KBT

Therefore orientational polarizability is inversely proportional to the temperature of the material.

SPACE – CHARGE POLARIZATION

The space-charge polarization occurs due to diffusion of ions, along the field direction and giving rise

to redistribution of charges in the dielectrics.

Explanation

In ferrites and semiconductors and will be very small and considered to be zero.

TOTAL ELECTRIC POLARIZATION

The total electric polarization is the sum of electronic polarization, ionic polarization,

orientationpolarization and space charge polarization. Since space charge polarization is very small

when compared to other kinds of polarization it can be neglected.

Therefore the total polarizability is given by

α= αe + αi + αo

= 4π∈oR3 +e2

ωo2 ( 1m

+ 1M ) + μ2

3K BT

We know total polarization

P= NE α

P = NE [4 π∈oR3+ e

2

ωo2 ( 1m

+ 1M )+ μ2

3KBT ]This equation is called as Langevin – Debye equation.

OR

b.(i). FREQUENCY AND TEMPERATURE DEPENDENCE OF ALL THE POLARIZATION

MECHANISMS

When field is applied, the polarization occurs as a function of time. The polarization P(t) as a

function of time t is given by

P(t)=P

Where, P is the maximum polarization which occurs at a static field applied for a long time

and tr is the relaxation time. i.e., the time taken for polarization. It is a measure of the time scale of a

polarization process.Relaxation time is the time taken for the polarization process to reach 0.63 of the

maximum value of polarization.

The relaxation times are different for different kinds of polarization mechanisms.

a. FREQUENCY DEPENDENCE

1. Electronic Polarization is very very rapid and will complete at the instant the voltage is applied

the reason is that the electrons are very very light elementary particles than ions. Therefore even

for very high frequency applied voltage i.e., in the optical range (1015 Hz) as shown in figure.

This kind of polarization occurs during every cycle of the applied voltage.

2. Ionic Polarization is slightly slower than the electronic polarization. Because ions are heavier

than the electron cloud. Also the frequency of the applied electric field with which the ions will be

displaced is equal to the frequency of the lattice vibrations (~ 10 13 Hz). At optical frequencies,

there is no ionic polarization. If the frequency of the applied voltage is less than 10 13 Hz i.e.,

infrared range as shown. The ions have enough time to respond during each cycle of the applied

field.

3. Orientation polarization is even slower than ionic polarization. The relaxation time for this case

varies with respect to the dielectric materials (i.e., solids or liquids) used.Here polar molecules in

a liquid easily reorient themselves compared to solids. This type of polarization occurs at audio

and radio frequency ranges (~ 106 Hz) as shown in figure.

4. Space charge polarization is the slowest process, because in this case the ions have to diffuse

over several interatomic distances. Also this process occurs at very low frequency in the order 102

Hz as shown in fig.

Therefore from the fig we can observe that, at lower frequencies all the four types of

polarizations occur and the total polarization is maximum. And the total polarization value

decreases with the increase in frequency and becomes minimum at optical frequency range.

b. Temperature Dependence

The electronic and ionic polarizations are independent of temperature, whereas the orientation and

space charge polarizationsare temperature dependent.

The orientation polarization decreases with increase in temperature because the randomizing

action of thermal energy decreases the tendency of the permanent dipoles to align the field

direction.Hence in this case the ∈r decreases.

But in space charge polarization, when the temperature is increased, the ions can easily overcome

the activation barrier and hence they diffused through inter atomic distances. Thus it gives rise to

polarization. So in this case the ∈r will increase in temperature.

(ii).FERRO-ELECTRICITY AND APPLICATIONS

Ferro-Electricity

When a dielectric material exhibits electric polarization even in the absence of external field,

it is known as ferro-electricity and these materials are termed as ferro-electrics.

Ferro-electrics

Ferro-electrics are anisotropic crystals which exhibit spontaneous polarization i.e., they

exhibit polarization even in the absence of external electric field.

Examples:

Rochelle salt

potassium niobate

Lithium tantalate

Barium titanate

Lithium niobateetc

PROPERTIES

The dielectric constant of this ferro-electric material is above 2000 and it will not vary with

respect to temperature.

The dielectric constant reaches maximum value only at a particular temperature called Curie

temperature.

The polarization does not vary linearly with respect to electric field and hence these materials

are also called as non-linear dielectrics.

Ferro-electrics exhibits electric polarization very easily, even in the absence of external

electric field.

They exhibit domain structure similar to that of a ferro-magnetic material.

Ferro-electric materials also exhibit hysteresis, similar to that of ferro-magnetic materials.

HYSTERESIS

When a ferro-electric material is subjected to external electric field (E) the polarization (P)

increases with respect to the field applied and it reaches the maximum value represented by `oa` as

shown in figure.

Now when the external electric field is switched off, then too the polarization in the material

will not become zero (curve ab).This shows that even in the absence of external electric field, the

ferro-electric material posses polarization, so called spontaneous (or) residual polarization.Now to

remove this residual polarization, an electric field has to be applied in the opposite direction (-

E),represented by the curve `oc`, so called co-ercive field. By further increasing the field from E to

Emax, the curve `defa is obtained which results in a complete polarization hysteresis loop.This

process shows that in a ferro-electric material the polarization does not vary linearly with respect to

the applied electric field.

APPLICATIONS

Ferro-electric materials are used to produce ultrasonics

They are used in the production of piezo-electric materials and in turn to make microphones.

Ferro-electrics are also used in SONAR, strain gauges, etc.

Ferro-electric semiconductors are used to make positors, which in turn are used to measure

and control the temperature.

They are also used as frequency stabilizers and crystal controlled oscillations.

Electrets are a type of ferro-electric materials, used in the production of capacitor,

microphones, gas filters etc.

Electrets are also used to bind the fractured bones in the human body.

Pyro-electric materials are used to produce high sensitive infra-red detectors.

12. a.INTERNAL FIELD OR LOCAL FIELD AND DEDUCTION OF CLAUSIUS MOSOTTI EQUATION

When a dielectric material is kept in an external field it exerts a dipole moment in it. Therefore

two fields are exerted, viz.,

I. Due to external field

II. Due to dipole moment.

This long range of coulomb forces which is created due to the dipoles is called as internal field or

local field. This field is responsible for polarizing the individual atoms or molecules.

Lorentz Method for Finding Internal Field

Let us assume a dielectric material kept in an external electric field. Consider an imaginary

sphere in the solid dielectric of radius 'r'.

Here the radius of the sphere is greater than the radius of the atoms. i.e., there are many atomic

dipoles within the sphere.

A small elemental ring is cut with thickness ds. Let y be the radius of the small ring as shown in

figure.

The electric field at the centre of the sphere is called internal field, which arises due to the

following four factors.

Eint = E1 + E2 + E3 +E4 ……..(1)

Where,

E1- Field due to the charge on the plates.(externally applied)

E2- Field due to p[olarization charges on the plane surface of the dielectric.

E3- Field due to polarized charges induced at the spherical surface.

E4- Field due to atomic dipoles inside the sphere considered.

Macroscopically, we can take E= E1+E2 (i.e.). The field externally applied (E1) and the field induced

on the plane surface of the dielectric (E2)as a single field (E).

If the dielectric is highly symmetric then the dipoles will cancel with each other therefore we

can take E4=0

Equation (1) becomes

Eint=E+E3 ……..(2)

To find E3

In the elemental ring, let "q" be the charge on the area ds. Polarization is defined sa the

surface charges per unit area.

If PN is the component of polarization perpendicular

to the area as shown in figure.

Here PN=Pcosθ =-q'/ds

(or) q'=P cosθ ds

Electric field intensity at 'C' due to charge q' is given by

E= q '

4 π ɛo r2

¿ P cosθ4 π ɛo r

2 …….(3)

The above intensity is along the radius 'r'. Resolving

the intensity into two components as shown in figure.

Component Parallel to the field direction Ex=E cosθ

∴Ex=P cos2θds

4 π ɛo r2

Component Perpendicular to the field direction Ey=E sin θ

E x=Pcosθ sin θds

4 π ɛo r2

The perpendicular components are in the opposite directions and hence cancel each other.So

the parallel components are alone taken into consideration.

If the total surface area of the ring is considered as dA then

Ex = E =P cos2θ dA

4π ɛo r2 …….(4)

Where, dA = circumference x thickness

dA=2πy × dS

Since y= r sin θ and dS = r dθ, we can write

dA=2π r sin θ× r dθ

Or dA = 2π r2 sin θ dθ..….(5)

Substitute eqn (5) in (4) we get

Electric field intensity due to the elemental ring

=P cos2θ sin 2θd θ

2ɛo……(6)

∴ Electrical field intensitydue to the whole sphere can be derived by integrating eqn (6) within the

limits 0 to π.

E3=∫0

π P cos2θ sin2θdθ2 ɛo

E3=23.( P2 ɛo )∵∫

0

π

cos2θ sin2θdθ=¿ 23¿

E3=( P3 ɛo )……..(7)

Substituting eqn (7) in (2) we get

∴E∫¿=E+ P

3 ɛo¿………(8)

Where,E∫ ¿¿ is called internal field or Lorentz field.

Clausius – Mosotti Relation

We know D=ɛ E=ɛo E+P

Or E ( ɛ−ɛo )=P

E= Pɛ−ɛo

………(9)

Substituting eqn (9) in eqn (8), we get

E∫ ¿= P

ɛ−ɛo+ P

3 ɛo¿

Rearranging we getE∫ ¿=

P(2ɛo+ɛ )3 ɛo (ɛ−ɛ o)

¿……..(10)

We know polarization P=NαEi

∴E∫¿= P

Nα¿ …….(11)

Comparing eqn (10) & (11) we get

PN α

=P(2 ɛo+ɛ )3 ɛo(ɛ−ɛo)

N α3 ɛo

=ɛ−ɛo

2 ɛo+ɛ

N α3 ɛo

=ɛo (

ɛɛo

−1)

ɛ o(ɛɛo

+2)

N α3 ɛo

=ɛr−1ɛ r+2

..….(12)

The above equation is called Clausius – Mossotti Relation.

OR

b. DIELECTRIC LOSS

If a dielectric is subjected to an electric field, the electrical energy is absorbed by the

dielectric and certain quantity of electrical energy is dissipated in the form of heat energy. This is

known as dielectric loss.

The dielectric loss can occur both in direct and alternating voltages. The dielectric loss

is less in direct voltage than that of alternating voltages.

Loss in Purified gas

If an alternating voltage is applied across the capacitor having vaccum (or) purified gas then

the resulting current leads the applied voltage by 90 degree as shown in fig

If I lead V exactly by 90 degree we can say no electrical energy is lost.

Explanation

We know power loss PL = VI cos θ

When θ=90˚ ; PL=0

Loss in commercial dielectric

Now, when a practical dielectric is present the current leads the voltage by (90- δ ), then it

shows that there is some loss in electrical energy, and is called loss angle as shown

Explanation

In this case the power loss PL = VI cos θ

Since θ=90-δ, we have PL = VI cos(90-δ)

∴PL=VI sin δ ………..(1)

We know V=IR, therefore I=VR

If the capacitive reactance is Xc then we can write,

I= VX c

……….(2)

Substituting eqn (2) in (1) we get

Power lossPL=V2δ /Xc………(3)

We know frequency

f= 12πRC

¿ 12π X cC

∴ Xc=1

2 π f C………(4)

Substituting eqn (4) in (3) we getPL=2 π f CV 2 sin δ

If δ is very small, thensin δ=tan δ

∴Power loss PL=2 π fC V 2 tan δ

Here tan δ is called the power factor of the dielectric. If f, C, V are constants then

PL∝ tan δ

Naturally the power loss varies with frequency. The power loss at various frequency ranges is

shown in figure.

In the electrical frequency regions the power loss is high,due to diffusion of ions from one

equilibrium position to another.

In the optical region the power loss is less because here the dielectric loss is associated

withthe electrons.

13.a.(i). DIELECTRIC BREAKDOWN

When a dielectric is placed in an electric field and if the electric field is increased, when the

field exceeds the critical field, the dielectric loses its insulating property and becomes conducting i.e.,

large amount of current flows through it. This phenomenon is called dielectric breakdown.

The electric field strength at which the dielectric breakdown occurs is known as dielectric

strength.

The dielectric strength =Dielectric voltage/Thickness of dielectric

(ii). There are different mechanisms by which the dielectric break down takes place.Some types of

dielectric breakdowns are

Intrinsic (or) avalanche breakdown

Thermal breakdown

Chemical and electrochemical breakdown

Discharge breakdown

Defect breakdown

Intrinsic Breakdown

When a dielectric is subjected to electric field then the electrons in the valence band acquire

sufficient energy and go to conduction band by crossing the energy gap and hence become conducting

electrons. Therefore large current flows and is called intrinsic breakdown (or) Zener breakdown.

Impurities in the dielectric material create additional energy levels in the energy gap and so

they help the intrinsic breakdown to occur at low applied voltages.

Avalanche Breakdown

This conduction electron on further application of field, collide with the valence electrons in

the co-valent bond and remove more electrons hence transferring them as conduction electrons.

These Secondary conduction electrons again dislodge some other bound electrons in the

valence band and this process continues as a chain reaction. Therefore very large current flows

through the dielectrics and hence called as avalanche breakdown.

Characteristics

It can occur even at lower temperatures.

It requires relatively large electric fields.

This kind of breakdown occurs in thin sample.

It does not depend on the configuration of electrodes and shape of the material.

It occurs within a short span of time (milli seconds)

Thermal Breakdown

In general, when a dielectric is subjected to an electric field, heat is generated. This generated

heat is dissipated by the dielectric.

In some cases the heat generated will be very high compared to the heat dissipated. Under

such conditions the temperature inside the dielectric increases and heat may produce breakdown. This

type of breakdown is known as thermal breakdown.

Characteristics

It occurs at higher temperature.

It requires moderate electric fields.

It depends on the size and shape of the dielectric material.

Since, the dielectric loss is proportional to frequency, the breakdown occurs at relatively

lower field strength for a.c. fields than that of d.c. fields.It occurs in the order of milliseconds.

Chemical and Electrochemical Breakdown

This type of breakdown is almost similar to the thermal breakdown. If the temperature is

increased mobility of the ions will increase and hence the electrochemical reaction may be induced to

take place.

Therefore when mobility of ions are increased, insulation resistance decreases and hence

dielectrics become conducting. This type of breakdown is called as chemical and electro chemical

breakdown.

Characteristics

It occurs only at low temperatures.

It occurs even in the absence of electric field. In rubber, due to oxides produced in air, they

gradually lose their dielectric property.

It depends on concentration of ions, magnitude of leakage current.

Discharge Breakdown

In some dielectric occluded gas bubbles may be present. When these type of dielectrics are

subjected to electric field, the gas present in the material will easily ionize and hence produce large

ionization current and is known as discharge breakdown.

Characteristics

It occurs at low voltages.

It occurs due to the presence of occluded gas bubbles.

It depends upon the frequency of the applied voltage.

Defect Breakdown

Some dielectrics have defects such as cracks, pores, blow holes etc. These vacant position

may have moisture (or) impurities which leads to breakdown called as defect breakdown.

REMEDIES FOR BREAKDOWN MECHANISMS

To avoid breakdown, the dielectric material should have the following properties.

It should have high resistivity.

It must posses high dielectric strength.

It should have sufficient mechanical strength.

Dielectric loss should be low.

Thermal expansion should be small.

It should be fire proof.

It should be resistive to oils, liquids and gases etc.

It must have less density.

There should not be any defects.

It must be in pure form.

OR

b.NON LINEAR OPTICS - DEFINITION

Nonlinear optics is the study of the interaction of intense electromagnetic field with materials

to ace modified, which is different from the input field, both in amplitude and phase.

In non linear optics the modification of the optical properties of a material system is made by

the light.

That too only the laser light is sufficiently intense to modify the optical properties of a

material system.

Reason

We know that the light is a part of electromagnetic spectrum. According to the electro optic

effects, when the light is pass through a material it changes the properties of the medium, but it

depends on the strength of the electromagnetic wave.

For example, if ordinary light passes through the material, it cannot change the properties of

the material (the non linear activity) is absent. Instead if the high intensity light (laser) passes through

the material it changes the properties of the material that means the nonlinear activity is present.

Consequently, the intensity of the light generated at the second harmonic frequency tends to increase

as the square of the intensity of the applied laser light.

Birefringence

When light passes through a material the incident ray splits into two rays viz, one of same

wavelength and other of different wavelength. This phenomenon is called as double refraction (or)

Birefringence. This effect is observed on NLO materials.

Examples:

i. Second harmonic generation

ii. Optical mixing

iii. Self focusing effects

iv. Raman and Rayleigh scattering, etc.

NLO MATERIALS - DEFINITION

The change in optical properties due to electric and magnetic field associated with light is

called non linear effects and those materials which posses these effect are called non-linear materials.

Examples:

iii. Ammonium-dihydrophosphate (APO)

iv. Potassium-dyhydrophosphate (KDP)

v. Lithium iodate (LiO3)

In ordinary light the electric and magnetic field associated with it is so weak and hence we

could not identify non-linear effects in it. But in LASER beam we can identify non-linear effects,

because of the strong electric and magnetic field associated with it.

Faraday Effect

When magnetic field applied along the axis of propagation of light beam to a glass medium,

the plane of polarisation of light is rotated. This is called Faraday Effect.

Kerr effect

Similarly, when electric field is applied along the direction of propagation of light, then the

light will undergo double refraction, this is called Kerr Effect.

Faraday and Kerr effect confirmed that both electrical and magnetic field will change the

optical properties of a medium.

PASSIVE AND ACTIVE MATERIALS

Passive Materials

The materials which are simply used as catalysts without imposing their characteristic internal

resonance frequencies onto the incident beam of light are known as passive materials and this effect is

known as passive optical effect.

Examples:

i. The harmonic generation

ii. Frequency mixing

iii. Optical reflection etc.

Active Materials

The materials which impose their resonance frequencies onto an incident beam of light are

known active materials and this is known as active optical effect.

Examples:

i. Two photon absorption

ii. Stimulated Raman scattering

iii. Rayleigh scattering etc.

Second harmonic generation

Definition

Second harmonic generation represents the generation of new frequencies with the help of the

crystal such as quartz, potassium-dyhydrophophate, etc.

Explanation

Let us consider a material media in which the light is passed through it. We know that light

consists of both electric and magnetic field associated with it. These electric field associated with the

light will distort the atoms and molecules in the material to form oscillating dipoles.

The induced electric dipole is due to the displacement of electron with respect to the centre of

the positive nucleus of an atom. This phenomenon is called electric polarization (P).

Relation between P and E for ordinary light (linear medium)

When light of low intensity (ordinary light) is passed through dielectric medium (glass), the electric

field has smaller amplitude and the oscillation of dipole can follow the field exactly.

Hence the relation between the electric field E and polarization P can be written as,

P=ε0χ0E

Where, χ0 – electric field susceptibility

ε0 – permittivity of the medium

Relation between P and E for laser light (Non – linear medium)

When light of ligher intensity is passed through dielectric medium, the electric field has larger

amplitude and the oscillations of dipoles are distorted. Therefore, some nonlinearity is observed

between P and E and hence second generation is observed.

Thus, the polarization vector can be written as,

P = ε0 (χ0E +χ1E2 + χ2E3 + …….) … (1)

Where, χ0 – Linear susceptibility

χ1,χ2– nonlinear susceptibilities

The higher order non linear susceptibilities are very small when compared to linear

susceptibilities. But the higher order susceptibilities produce so many new optical phenomena.

We know the oscillating electric field on a medium is,

E = E0cosωt … (2)

Substituting eqn (2) in eqn (2), we get

P = ε0χ0E0cosωt +ε0χ1E02cos2ωt +ε0 χ2E0

3cos3ωt + …….

We know cos2ωt = 1+cos2ωt

2 , cos3ωt = cos3ωt+3 cosωt

4

∴ P = ε0χ0E0cosωt +ε0χ1E02 1+cos2ωt

2 +ε0 χ2E03 cos3ωt+3cosωt

4 + …….

P = ε0χ0E0cosωt + ε0χ1E02 12 +ε0χ1E0

2 cos2ωt2 +ε0 χ2E0

3 cos3ωt4 + ε0 χ2E0

3 3 cosωt4

Rearranging we get,

P = 12ε0χ1E0

2 +ε0E0cosωt (χ0 + 34 χ2E0

2) + 12ε0χ1E0

2 + 14 ε0 χ2E0

3cos3ωt

I II III IVReferring equation (3), the first term represents the DC field across the medium which has

less importance. The second term represents the external polarization which is called as first

fundamental harmonic susceptibility, the third term represents oscillating dipoles, which oscillates at a

frequency 2ω and hence called second harmonic of polarization. The fourth term has a cos 3ωt is

called third harmonic of polarization etc.

When the first and third term is added we get the term optical rectification.

Experimental evidence

The observation of second harmonic generation is illustrated by quartz slab

A high power ruby laser is passed through the filter, which filters the red light and allows the

ultraviolet light to the quartz slab. The emerging light from the quartz slab is passed through the UV

transmission filter, which filters the unwanted light and allow the UV light alone to pass through a

photo cell. In this experiment, due to second harmonic generation the wavelength of the incident beam

is made half and hence the wavelength if the emerging beam is recorded as 3471A.

PROPERTIES OF NONLINEAR MATERIALS

Important non linear optical materials are,

1. Lithium niobate

2. Lithium tantalite

3. Barium sodium niobate

Properties

It is a synthetic ferroelectric materials.

It has highest curie temperature.

At high temperature it becomes electrically conductive.

It has multi domain structures.

Polarization is inversely proportional to the temperature.

Applications of nonlinear materials:

Optical grating

Optical amplifier

Optical modulation and switching

Optical frequency doublers

Frequency filters

Delay lines and memories

14.a.METALLIC GLASSES (MET GLASSES)

Metallic glasses are new type of materials which share the properties of both metals and

glasses. In general, they are strong, ductile, malleable, opaque and brittle. They also have good

magnetic properties and corrosion resistance. They are also called as amorphous metals.

Properties of metals + Properties of glasses = Properties of metallic glasses

FORMATION OF METALLIC GLASSES

Metals are made into glassy state by increasing their rate of cooling to a very high level.At

that state the atoms are unable to arrange in a proper manner and thus form an new amorphous state.

These new type of materials which are formed by the rapid cooling technique are called metallic

glasses.

Glass Transition Temperature

The temperature at which the metals in the molten form transforms into glasses (i.e. from

liquid to solid) is known as glass transition temperature. It was found thatthe glass transition

temperature for metallic alloys varies from 200 C to 3000 C.

TECHNIQUES FOR PREPARATION

There are several techniques available for the production of metallic glasses.

1. Melt spinning system

Molten alloy is made to impinge on a fast rotating roller to form metallic glasses.

2. Twin roller system

Molten alloy is made to pass through the two rollers rotating in opposite directions to form

metallic glasses.

3. Metal extracting system

Fast moving roller sweeps off molten droplet into a strip to form metallic glasses.

4. Sputtering

The sputtering gas is ionized and the atoms are made to fly towards the substrate to form

metallic glasses.

PREPARATION OF METALLIC GLASSES

Principle

Quenching is a technique used to form metallic glasses. Quenching means rapid cooling

Atoms move freely in the liquid state. When the liquid is quenched (rapidly cooled) it results in an

irregular pattern, which results in the formation of metallic glasses.

Technique

The process involved in the formation of metallic glasses is melt spinning technique.

MELT SPINNING TECHNIQUE

Experimental setup

The setup consists of a refractory tube with fine nozzle at the bottom. The refractory tube is placed

over the rotating roller made up of copper. An induction heater is wounded over the refractory tube in

order to heat the alloy inside the refractory tube.

Preparation

The alloy is put into the refractory tube and the induction heater is switched ON. This heats

the alloy and hence the molten alloy is ejected through the nozzle of the refractory tubeonto the

rotating roller and is made to cool suddenly. The ejection rate may be increased by increasing the gas

pressure inside the refractory tube. Thus due to rapid quenching a glassy alloy ribbon called metallic

glass is formed over the rotating roller. Hence this technique is used to develop materials that require

extremely high cooling rates in order to form metallic glasses. The cooling rates achievable by melt-

spinning method are in the order of 104–107 Kelvin per second.

TYPES OF METALLIC GLASSES

1. Metal - metal metallic glasses

They are formed by combination of metals.

Example:

(i) Ni - Nb (Nickel & Niobium)

2.Metal - metalloid metallic glasses

They are formed by combination of metals and metalloids.

Example:

Metals like Fe, Co, Ni and metalloid such as B, Si, C, P.

PROPERTIES OF METALLIC GLASSES

(i) Structural properties

They have tetrahedral closely packed structure rather than hexagonal closely packed structure

They do not have any crystal defects

(ii) Mechanical properties

They are strong in nature

They have high corrosion resistance

They posses malleability and ductility

(iii) Magnetic properties

They can be easily magnetized and demagnetized

They have narrow hysteresis loop

(iv) Electrical properties

High electrical resistance

Electrical resistance will not vary with temperature

Low eddy current losses

APPLICATIONS OF METALLIC GLASSES

They are used in cores of high power transformers

Metallic glasses are malleable and ductile and hence they are used in filament winding to re -

inforce pressure vessels

They are used to make different kinds of springs as they are very strong in nature.

They have corrosion resistance and hence they can be used in surgical clips and marine ves -

sels

They are highly resistance and hence they are used to make computer memories

They behave as superconductors and hence they are used in production of high magnetic

fields

They are not affected by magnetic radiation and they are used in nuclear reactors.

OR

b.Biomaterials

Any materials that are brought into the fluids, cell and tissues of living body is called

biomaterials. In recent days, polymers and ceramics are referred to as biomaterials. Biomaterials are

used for both soft and hard tissues replacement, in organ replacement, coatings and adhesives, dental

implants, etc.

Classification of Biomaterials and its applications

Biomaterials are classified into

1. Metal and alloys Biomaterials

2. Polymer Biomaterials

3. Ceramics Biomaterials

4. Bio polymers

Here are some of the examples for the above materials and their applications.

Metals and alloys Biomaterials

1. Stainless steel (wrought bar)

It used to make bone screw and stems of implanted prosthesis.

2. Ti – 6 Al – 4V ELI alloy

It is used in implant devices.

3. Cobalt based alloy (with Ti and stainless steel)

It is used in implant devices.

4. Cast alloy Co – Cr – Mo

It used to make stem and head of implanted hip endoprosthesis.

Polymer Biomaterials

1. Ultra high molecular weight polyethylene with or without

It used as a bearing for joint replacement prosthesis.

2. Acrylic resins and methyl methacrylate acrylic copolymer

It is used as bone cements.

3. Porous polysulfone with Co – Cr – Mo

It is used in orthopaedic implants.

4. Porous high density polyethylene

It is used in dental cortical implants.

Ceramics Biomaterials

1. Al2O3 with some SiO2 and alkali metal oxide

It is used to make femoral head.

2. Apatite ceramics

It is readily allows bone ingrowth.

3. Synthetic hydroxy apatite

It is used in dental and orthopaedie purposes.

4. Porous ceramics

It is used in mirtal valve prosthesis.

Biopolymers

Biopolymers are the protein, nucleic acids and polysaccharides formed in nature during the

growth of all organisms. Biopolymers finds a lot of applications in medical field such as

opthamology, dental etc. as biomaterials.

15.a.(i).NANO PHASE MATERIALS

Nanophase materials are materials with a grain size in the 1 to 100 nm range and these atoms

will not move away from each other.

Ex: ZnO, Cu- Fe alloys

Nanophase materials exhibit greatly altered mechanical properties compared to their normal,

large-grained counterparts with the same chemical composition. For example, nanophase metals are

up to five times harder than the normal materials. While nanophase metals generally become harder

and more brittle, nanophase ceramics become more ductile. In a typical nanophase material, 10 to

50% of the atoms are in grain boundary regions. These new materials are called nano materials and

the developed technology is called nano technology.

SYNTHESIS OF NANO PHASE MATERIALS

Nanophase materials can be synthesised in any of the two ways viz.,

Top down approachin which bulk materials are broken into nanosized materials.

Bottom up approachin which nano materials are made by building atom by atom.

VARIOUS TECHNIQUES

Plasma – arching

Chemical vapour deposition

Sol – gel technique

Electro – deposition

Ball milling

Laser synthesis

Inert gas condensation etc.,

Using the above techniques it is possible to produce nano phase materials in the form of nano –

particles, nano – powders, nano – crystals, nano – films, nano – wires, nano – tubes, nano – dots etc.,

CHEMICAL VAPOUR DEPOSITION

This method is used to prepare nano – powder. In this method, the material is heated

to form a gas and is allowed to deposit on a solid surface under vacuum condition, which forms nano

– powders on the surface of the solid. This method can also be used to grow surfaces, i e., suppose if

an object has to be coated with nano – powders, then the object has to be introduced inside the

chemical vapour deposition area so that the nano – powders can be deposited all over the object.

Examples: (i) Nano – powders of oxides and carbides

(ii) Pure metal nano – powders

Chemical Vapor Synthesis of Nanocrystalline Powders

Chemical Vapor Deposition (CVD) method is used to form nanoparticles.

In CVD, precursors are metalorganics, carbonyls, hydrides, chlorides and other volatile compounds in

gaseous, liquid or solid state are used. The major limitation of the CVD process is the availability of

appropriate precursor materials. The energy for the conversion of the reactants into nanoparticles is

supplied in hot wall (external furnace), flame (reaction enthalpy), plasma (microwave or radio

frequency) and laser (photolysis or pyrolysis) reactors.

The most important process parameters determining the quality of the nanopowders are the

total pressure (typical range from 100 to 100000 Pa), the precursor material (decomposition kinetics

and ligands determining the impurity level), the partial pressure of the precursor (determining the

production rate and particle size), the temperature or power of the energy source, the carrier gas (mass

flow determining the residence time) and the reactor geometry.

The nanoparticles are extracted from the aerosol by means of filters, thermophoretic

collectors, electrostatic precipitators or scrubbing in a liquid. A typical laboratory reactor (shown

schematically in the figure below) consists of a precursor delivery system, a reaction zone, a particle

collector and a pumping system. Modifications of the precursor delivery system and the reaction zone

allow the synthesis of pure oxides, doped oxides, coated nanoparticles, functionalized nanoparticles

and granular films. 

PULSED LASER DEPOSITION

Pulsed laser deposition is the latest technique adopted for the preparation of carbon nano

tubes.

Principle

The technique of laser heat treatment is used in the preparation of carbon nano tubes. Ruby

laser, Nd – YAG laser and CO2 laser are used for this purpose.

Instrumentation

The Instrumentation for the fabrication of carbon nano tubes consists of a quartz tube

containing a graphite target kept in argon gas region. The tube is surrounded by an electric furnace in

order to heat the target. A colder copper collector rod is used to collect the nano carbons emitted by

the graphite. Along with this it also consists of a pulsed laser source to produce laser beam, shutter to

control the intensity of the laser beam and an assembly of lenses to effectively focus the laser onto the

graphite.

Synthesis

Initially the graphite is heated upto 1200oC with the help of the electric furnace. An intense

laser beam can be used to evaporate carbon from the graphite and thus now the laser source is

switched ON. The light reflected by the plane mirror is made to pass through the shutter and hence the

intensity is controlled. Then the beam is made to fall on the focussinglens assembly. This lens

assembly focuses the light effectively onto the window and is made to incident on the graphite.

Due to laser heating the graphite gets heated and evaporates carbon atoms. The argon gas

present inside the quartz tube is used to sweep the carbon atoms towards the colder copper collector

rod. Thus, due to the movement of carbon atoms from a higher temperature to a lower temperature

region it gets condensed and hence carbon nano tubes are formed over the collector rod. The cobalt

and nickel present in the graphite act as catalytic nucleation sites for the formation of carbon nano

tubes.

(ii). PROPERTIES OF NANO MATERIALS

(i) Physical Properties

a) Interparticle spacing is very less in nano materials

b) They have high strength and super hardness because it does not have any dislocation

in it.

c) The melting point of nano materials will be very less.

(ii) Electronic Properties

a) Energy bands in these materials will be very narrow.

b) The ionization potential is very high for nano materials.

c) They have more localized molecular bonds.

(iii) Magnetic Properties

a) The atoms will have less co-ordination number and hence possess local magnetic mo-

ment within themselves.

b) They exhibit spontaneous magnetisation.

c) Ferro – magnetic and anti - ferro magnetic multi layernano materials has GMR (Giant

Magneto Resistance) effect.

d) The nano materials shows variation in their magnetic property, when they change

from bulk state to cluster state.

(iv) Mechanical Properties

a) The hardness of nano phase materials varies from material to material. This may be

due to the phase transformation, stress relief, density and grain boundaries.

b) They exhibit super plastic behaviour.

APPLICATIONS OF NANO MATERIALS

They have applications almost in all Engineering fields as follows.

(i) Mechanical Engineering

a) Since they are stronger, lighter etc., they are used to make hard metals.

b) Smart magnetic fluids are used in vacuum seals, magnetic separators, etc.,

c) They are also used in GMR spin valves.

d) Nano – MEMS are used in ICs, optical switches, pressure sensors, mass sensors

etc.,

(ii) Electrical, Electronics and Communication Engineering

a) Orderly assembled nano materials are used as quantum electronic devices and

photonic crystals.

b) They are also used as sensing elements.

c) They are also used in energy storage devices such as hydrogen storage devices,

magnetic refrigeration and in ionic batteries.

d) Dispersed nano materials are used in magnetic recording devices, rocket propel-

lant, solar cells, fuel cells, etc.,

e) Recently nano robots were designed, which are used to remove the damaged can-

cer cells and also to modify the neuron network in human body.

(iii) Computer Science Engineering and IT

a) They are used to make CD’s and semiconductor laser.

b) They are also used to store the information in smaller chips.

c) They are used in mobiles and lap – tops.

d) They are used in chemical/optical computers.

e) Nano – dimensional photonic crystals and quantum electronic devices plays a vi-

tal role in the recently developed computers.

(iv) Bio – medical and Chemical Engineering

a) Consolidated state nano – particles are used as catalyst, electrodes in solar and

fuel cells.

b) They are also used in the production of DNA – chips and bio – sensors.

c) Nano – structured ceramic materials are used in synthetic bones.

d) Few nano materials are also used in adsorbents, self cleaning glass, fuel additives,

drugs, ferrofluids, paints etc.,

e) Nano – metallic colloids are used as film precursors.

OR

15.b.(i). SHAPE MEMORY ALLOYS

Shape Memory Alloys (SMAs) are the alloy which changes its shape from its original shape

to new shape and while heating/cooling it will return to its original shape. Example: Nitinol

Transformation temperature

The temperature at which the SMA switches from new shape to its original shape is called

transformation temperature or memory transfer temperature.

PHASES OF SMA

(i)Austenite

Austeniteis the solid solution of carbon and other alloying elements in γ - iron

It crystallizes into cubic crystal structure

It is a high temperature phase and it is hard in this phase

(ii) Martensite

Martensite is an interstitial super solution of carbon in α – iron.

It crystallizes into twinned structure

It is a low temperature phase and it is soft in this phase

5.11 PROCESSING OF SMA

Shape memory effect

At lower temperature the SMA will be in martensite structure and when it is heated it will

change its shape to Austenite structure and while cooling it will again return to martensite form. This

effect is called Shape memory effect.

Characteristic temperatures

Mf=Martensitic Finish

Ms=Martensitic Start

As=Austenitic Start

Af=Austenitic Finish

Microscopic Diagram of the Shape Memory Effect

The shape memory effect is observed when the temperature of a piece of shape memory alloy

is cooled to below the temperature Mf. At this stage the alloy is completely composed of Martensite

which can be easily deformed. After distorting the SMA the original shape can be recovered simply

by heating the wire above the temperature Af. The heat transferred to the wire is the power driving the

molecular rearrangement of the alloy, similar to heat melting ice into water, but the alloy remains

solid. The deformed Martensite is now transformed to the cubic Austenite phase, which is configured

in the original shape of the wire.

Microscopic and Macroscopic Views of the Two Phases of Shape Memory Alloys

Martensite, is the relatively soft and easily deformed phase of shape memory alloys, which

exists at lower temperatures. The molecular structure in this phase is twinned in which the

configuration is as shown in the middle of Figure. Upon deformation this phase takes on the second

form shown in Figure, on the right. Austenite, the stronger phase of shape memory alloys, occurs at

higher temperatures. The shape of the Austenite structure is cubic, the structure shown on the left side

of Figure. The un-deformed Martensite phase is the same size and shape as the cubic Austenite phase

on a macroscopic scale, so that no change in size or shape is visible in shape memory alloys until the

Martensite is deformed.

CHARACTERISTICS OF SMA

(i) Transformation occurs not only at a single temperature rather they occur over a range of

temperatures.

(ii) Pseudo elasticity

Pseudo elasticity occurs in some type of SMA in which the change in its shape will occur

even without change in its temperature.

Pseudo-elasticity occurs in shape memory alloys when the alloy is completely composed of

Austenite. Unlike the shape memory effect, pseudo-elasticity occurs without a change in temperature.

The load on the shape memory alloy is increased until the Austenite becomes transformed into

Martensite simply due to the loading. The loading is absorbed by the softer Martensite, but as soon as

the loading is decreased the Martensite begins to transform back to Austenite.

(iii)Superelasticity

The shape memory alloys which have change in its shape at constant temperature are called

super elastic SMAs and that effect is known as superelasticity.

(iv) Hysteresis

The transformation process exhibits the form of Hysteresis curve as shown in figure.

(v) Crystallographicallythermo – elastic martensities are reversible.

TYPES OF SMA

(i) One – way SMA

The SMA remains in the same phase even though there is some change in its temperature, and

hence this type of material is called one way shape memory alloy.

(ii)Two – way SMA

The type of materials which produces spontaneous and reversible deformation just upon

heating and cooling even without load are called two way shape memory alloys.

PROPERTIES OF NI-TI ALLOY

Ni-Ti alloy has high shape memory strain

Density of Ni-Ti alloy is 6.45 gm/cm3

Ni-Ti alloy is more flexible

It has high melting point

It has high thermal stability

It has high corrosion resistance

It has very high yield strength

(ii). APPLICATIONS OF SMA

It is used in eye glass frames, Blood – clot filter

It is used in making toys

It is used in helicopter blades

It is used in fire safety valves

It is used in coffee makers

It is used for cryofit hydraulic couplings

It is used in circuit edge connector and in prevention of cracks

(iii). ADVANTAGES AND DISADVANTAGES OF SMA

Advantages

SMA is very compact in nature

It is safe and smart

They are flexible

They are non – corrosive

Disadvantages

Cost is high

Efficiency is low

Transformation occurs over a range of temperatures

Structural arrangements may sometime get deformed