Properties of Materials

Dr. Anurag Srivastava

Web address: http://tiiciiitm.com/profanurag

Email: profanurag@gmail.com

Visit me: Room-110, Block-E, IIITM Campus

Properties of materials

A property of a material is a description of the

characteristics which it has. They are

adjectives which tell us about the material.

Materials have different properties and

characteristics depending on what they are

used for.

Some materials are hard, others are soft.

Some are strong, others are weak.

Fundamentals of Electrical EnginPHYring

2

Properties which describe different materials:

Shiny – It reflects light

Strong – It won’t break easily

Flexible – It can be bent easily without breaking

Light - It doesn’t weigh much

Heavy – It weighs a lot

Coloured – Has colour

Magnetic – It’s attracted to magnets

Bendy - Flexible

Hard – Something which can’t be bent easily

Brittle – It’s hard but will break easily

Malleable – It can be shaped easily

Magnetic – It’s attracted to magnets

Transparent – Something you can see through

Translucent – Something you can partially see through

Opaque – Something you can not see through

Conductor – It allows heat or electricity to pass through

Insulator – It doesn’t allow heat or electricity to pass through. 3

Chemical Properties

how a material interacts with another material

“social” behavior

response to other matter (or lack of response)

reactions

Chemical Properties

Examples: burning

reaction with acid

reaction with water

corrosion/rusting/oxidation

others????

Physical Properties

characteristics it possesses by itself (in and of itself)

“personal” characters

response to energy

Physical Properties color

size

texture

melting point

boiling point

solubility

luster

density

magnetism

odor

viscosity

crystalline structure

Physical Properties

Electrical properties conductor or insulator

Optical properties – response to light index of refraction – bending of light

transparent – light passes through

translucent – some light passes through but no distinct image

opaque – no light passes through

Physical Properties

Thermal properties – response to heat

conductivity

specific heat – how much energy it takes to change temperature

thermal expansion – example: iron wire demo

Mechanical Properties

subgroup of physical

response to force or stress

force – a push or pull

stress – force causing a deformation or distortion (force per unit area)

Mechanical Properties Examples

workability malleability – can be flattened

ductility – can be drawn into wire (stretched), bent, or extruded

Mechanical PropertiesExamples

brittleness breaks instead of deforming when stress is

applied

hardness resistance to denting or scratching

Mechanical PropertiesExamples

elasticity ability to return to original shape after being

deformed by stress

rubber ball or piece of elastic

plasticity retains new shape after being deformed by

stress

wet clay ball or piece of saran wrap

Some of the properties

At your tables you will find some signs with

different physical properties.

Go around between tables and answer the

questions on a separate piece of paper.

Index of RefractionQuestion. What two materials here have a similar index of refraction?

(the three materials are glass, HDPE, and mineral oil)

Electrical conductivityWhat materials here are non-conductive electrically?

(the materials are brass, copper coated steel, wax, glass and carbon fiber)

HardnessWhich material here is the hardest?

(Pine and Melamine)

Mechanical PropertiesExamples

toughness ability to absorb energy resistance to fracture

strength resistance to distortion by stress or force several types: tensile, compressive, torsional,

bending, shear

Tension pulling

examples: tug-of-war, slingshot

Compression pushing together or squeezing

examples: bed springs, can crusher, bench vise

Types of Stresses/Forces

stress

strain

Ceramic orglass

metal

polymer

straight line = elastic regioncurved line = plastic region

General Classes of Materials

Polymers

Ceramics

Composites

Metals and Alloys

Metals and Alloys

Wood and Wood Products

32

ISSUES TO ADDRESS...

• How are electrical conductance and resistance characterized?

• What are the physical phenomena that distinguish conductors, semiconductors, and insulators?

• For metals, how is conductivity affected by imperfections, temperature, and deformation?

• For semiconductors, how is conductivity affected by impurities (doping) and temperature?

Electrical Properties

Ohm’s Law

34

Electrical Conduction

• Ohm's Law:V = I R

voltage drop (volts = J/C)

C = Coulomb

resistance (Ohms)current (amps = C/s)

1

• Conductivity,

• Resistivity, :

-- a material property that is independent of sample size and

geometry

RA

l

surface area

of current flow

current flow

path length

35

Electrical Properties

Which will have the greater resistance?

Analogous to flow of water in a pipe

Resistance depends on sample geometry and

size.

D

2D

R1 2

D

2

2

8

D2

2

R2

2D

2

2

D2

R1

8

36

Definitions

Further definitions

J = <= another way to state Ohm’s law

J current density

electric field potential = V/

flux a like area surface

current

A

I

Electron flux conductivity voltage gradient

J = (V/ )

38

Metals: Influence of Temperature and

Impurities on Resistivity

• Presence of imperfections increases resistivity

-- grain boundaries

-- dislocations

-- impurity atoms

-- vacancies

These act to scatter

electrons so that they

take a less direct path.

• Resistivity

increases with:

=

Adapted from Fig. 18.8, Callister & Rethwisch 8e. (Fig. 18.8

adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A.

Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill

Book Company, New York, 1970.)

T (ºC)-200 -100 0

1

2

3

4

5

6

Resis

tivity,

(10

-8O

hm

-m)

0

d-- %CW

+ deformation

i

-- wt% impurity

+ impurity

t

-- temperature

thermal

39

Estimating Conductivity

Adapted from Fig. 7.16(b), Callister & Rethwisch 8e.

• Question:

-- Estimate the electrical conductivity of a Cu-Ni alloy

that has a yield strength of 125 MPa.

mOhm10 x 30 8

16 )mOhm(10 x 3.31

Yie

ld s

tre

ng

th (

MP

a)

wt% Ni, (Concentration C)0 10 20 30 40 50

60

80

100

120

140

160

180

21 wt% Ni

Adapted from Fig.

18.9, Callister &

Rethwisch 8e.

wt% Ni, (Concentration C)R

esis

tivity,

(10

-8O

hm

-m)

10 20 30 40 500

10

20

30

40

50

0

125

CNi = 21 wt% Ni

From step 1:

30

40

Charge Carriers in Insulators

and Semiconductors

Two types of electronic charge carriers:

Free Electron

– negative charge

– in conduction band

Hole

– positive charge– vacant electron state in

the valence band

Adapted from Fig. 18.6(b),

Callister & Rethwisch 8e.

Move at different speeds - drift velocities

41

Intrinsic Semiconductors Pure material semiconductors: e.g., silicon &

germanium

Group IVA materials

• Compound semiconductors

– III-V compounds

• Ex: GaAs & InSb

– II-VI compounds

• Ex: CdS & ZnTe

– The wider the electronegativity difference between

the elements the wider the energy gap.

42

Intrinsic Semiconduction in Terms of

Electron and Hole Migration

Adapted from Fig. 18.11,

Callister & Rethwisch 8e.

electric field electric field electric field

• Electrical Conductivity given by:

# electrons/m3 electron mobility

# holes/m3

hole mobilityhe epen

• Concept of electrons and holes:

+-

electron holepair creation

+-

no applied applied

valence electron Si atom

applied

electron holepair migration

43

Number of Charge CarriersIntrinsic Conductivity

)s/Vm 45.085.0)(C10x6.1(

m)(10219

16

hei

en

For GaAs ni = 4.8 x 1024 m-3

For Si ni = 1.3 x 1016 m-3

• Ex: GaAs

he epen

• for intrinsic semiconductor n = p = ni

= ni|e|(e + h)

44

Intrinsic Semiconductors:

Conductivity vs T• Data for Pure Silicon:

-- increases with T

-- opposite to metals

Adapted from Fig. 18.16,

Callister & Rethwisch 8e.

material

Si

Ge

GaP

CdS

band gap (eV)

1.11

0.67

2.25

2.40

Selected values from Table 18.3,

Callister & Rethwisch 8e.

ni eEgap /kT

ni e e h

Optical Properties of Materials

Overview The study of the optical properties of materials is a huge

field and we will only be able to touch on some of the

most basic parts

So we will consider the essential properties such as

absorption/reflection/transmission and refraction

Then we will look at other phenomena like luminescence

and fluorescence

Finally we will mention applications, in particular optical

fibres and lasers

Nature of light

Light is an electromagnetic wave:

with a velocity given by c = 1/(00) = 3 x 108 m/s

In view of this, it is not surprising that the electric field

component of the wave should interact with electrons

electrostatically

Many of the electronic properties of materials,

information on the bonding, material

composition etc. was discovered using

spectroscopy, the study of absorbed or

emitted radiation

evidence for energy levels in atoms

evidence for energy bands and band-gaps

photoelectric effect

General description of

absorption

Because of conservation of energy, we can say that I0 = IT + IA + IR Io is the intensity (W/m2) of incident light and subscripts refer to

transmitted, absorbed or reflected

Alternatively T + A + R = 1 where T, A, and R are fractions of the

amount of incident light

T = IT/I0, etc.

So materials are broadly classed as

transparent:relatively little absorption

and reflection

translucent:light scattered within

the material (see right)

opaque:relatively little transmission

If the material is not perfectly transparent, the

intensity decreases exponentially with distance

Consider a small thickness of material, x

The fall of intensity in x is I so I = -a.x.I

where a is the absorption coefficient (dimensions are m-1)

In the limit of x 0, we get

The solution of which is I = I0 exp(–ax)

Taking “ln” of both sides, we have:

which is known as Lambert’s Law (he also has a unit of light

intensity named for him)

dI

dx aI

ax lnI

I0

Thus, if we can plot -ln(I) against x, we

should find a from the gradient

Depending on the material and the

wavelength, light can be absorbed by

nuclei – all materials

electrons – metals and small band-gap materials

ATOMIC ABSORPTION

How the solid absorbs the radiation depends

on what it is!

Solids which bond ionically, show high

absorption because ions of opposite charge

move in opposite directions

in the same electric field

hence we get effectively twice the interaction

between the light and the atoms

Generally, we would expect absorption

mainly in the infrared

because these frequencies match the thermal

If we think of our atom-on-springs model,

there is a single resonance peak:

But things are more complex when the atoms

are connected – phonons

recall transverse and longitudinal optical phonons

f0

f

absorption

Electronic absorption Absorption or emission due to excitation or relaxation

of the electrons in the atoms

Molecular materials

Materials such as organic (carbon containing)

solids or water consist of molecules which are

relatively weakly connected to other molecules

Hence, the absorption spectrum is dominated by

absorptions due to the molecules themselves

e.g. water molecule:

The spectrum of liquid water

Since the bonds have different “spring

constants”, the frequencies of the modes are

different

when the incident illumination is of a wavelength that

excites one of these modes, the illumination is

preferentially absorbed

This technique allows us to measure

concentrations of different gas species in, for

example, the atmosphere

by fitting spectra of known gases to the measured

atmospheric spectra, we can figure out the quantities

of each of the gases

Optical properties of metals

Recall that the energy diagram of a metal looks like:

EF is the energy below which, at 0K, all electron states are full and

above which they are empty

this is the Fermi Energy

For T > 0, EF is the energy at which half of the available

energy states are occupied

Semiconductors also have a Fermi level

for an intrinsic material EF is in the middle of the bandgap

nearer Ec for n-type; nearer Ev for p-type

full

levels

empty

levelsT = 0K

EF

This structure for metals means that almost any

frequency of light can be absorbed

Since there is a very high concentration of electrons,

practically all the light is absorbed within about 0.1µm of

the surface

Metal films thinner than this will transmit light

e.g. gold coatings on space suit helmets

Penetration depths (I/I0 = 1/e) for some materials are:

water: 32 cm

glass: 29 cm

graphite: 0.6 µm

gold: 0.15µm

So what happens to the excited atoms in the

surface layers of metal atoms?

they relax again, emitting a photon

The energy lost by the descending electron is

the same as the one originally incident

So the metal reflects the light very well –

about 95% for most metals

metals are both opaque and reflective

the remaining energy is usually lost as heat

In terms of electrostatics, the field of the

radiation causes the free electrons to move

The metal appears “silvery” since it acts as a

perfect mirror

OK then, why are gold and copper not

silvery?

because the band structure of a real metal is not

always as simple as we have assumed

there can be some empty levels below EF and the

energy re-emitted from these absorptions is not in

the visible spectrum

Metals are more transparent to very high

energy radiation (x- & - rays) when the

inertia of the electrons themselves is the

Reflection spectra for gold and aluminum are:

blue red

gold reflects lots of

red wavelengths

aluminum

spectrum is

relatively flat

http://www.thermo.com/eThermo/CMA/Images/Various/109Image_12275.gif

Electronic absorption in non-metals

Dielectrics and semiconductors behave essentially the

same way, the only difference being in the size of the

bandgap

We know that photons with energies greater than Eg will

be absorbed by giving their energy to electron-hole pairs

which may or may not re-emit light when they relax

EC

EV

EG

hole

Hence, the absorption coefficients of

various semiconductors look like:

Semiconductors can appear “metallic” if visible

photons are all reflected (like Ge) but those with

smaller Eg, such as CdS look coloured

yellow for CdS which absorbs 540nm and above

The above picture is good for pure materials but

impurities can add extra absorption features

EC

EV

phononhf1

hf2

Impurity levels divide up the bandgap to allow transitions

with energies less than Eg

Recombination can be either radiative (photon) or non-

radiative (phonon) depending on the transition

probabilities

Practical p-n diodes usually contain a small amount of

impurity to help recombination because Si has a

relatively low recombination “efficiency”

for the same reason that Si is inefficient at generating light

Refraction in non-metals One of the most important optical properties of non-

metallic materials is refraction

This refers to the bending of a light beam as it passes

from one material into another

e.g. from air to glass

We define the index of refraction to be

n = c/v

where c is the speed of light in a vacuum and v is the speed of

light in the material (which is in general wavelength-dependent)

A familiar example is the prism where the different

amounts of bending separates out the wavelengths

Refraction is also vital for other applications, such as:

optical fibres – keeps the light in

semiconductor laser – keeps the light in the amplifying cavity of

the laser

Given that

where µ and µ0 (= µrµ0) are the permeability of the material and

free space, respectively (a magnetic property)

and and 0 (= r0) are the permittivity of the material and free

space, respectively (an electrostatic property)

We find that n = √(µrr) (≈ √r for many materials)

v 1

and c

1

00

Since light is an electromagnetic wave, the connection

with both the dielectric permittivity () and the magnetic

permeability (µ) is not surprising

The index of refraction is therefore a consequence of

electrical polarization, especially electronic polarization

Hence, the radiation loses energy to the electrons

+–

Since E = hv/, and doesn’t change, the

velocity must be smaller in the material than in

free space

since we lose E to the atoms, v must also decrease

Electronic polarization tends to be easier for

larger atoms so n is higher in those materials

e.g. glass: n ~ 1.5

lead crystal: n ~ 2.1 (which makes glasses and

chandeliers more sparkly!)

n can be anisotropic for crystals which have non-

cubic lattices

Reflection in non-metals Reflection occurs at the interface between two materials

and is therefore related to index of refraction

Reflectivity, R = IR/I0, where the I’s are intensities

Assuming the light is normally incident to the interface:

where n1 and n2 are the indices for the two materials

Optical lenses are frequently coated with antireflection

layers such as MgF2 which work by reducing the overall

reflectivity

some lenses have multiple coatings for different wavelengths

R n2 n1n2 n1

2

n1 n2

Spectra

So we have seen that reflection and absorption are

dependent on wavelength

and transmission is what’s left over!

Thus the three components for a green glass are:

Colours

Small differences in composition can lead to large

differences in appearance

For example, high-purity single-crystal Al2O3 is

colourless

sapphire

If we add only 0.5 - 2.0% of Cr2O3 we find that the

material looks red

ruby

The Cr substitutes for the Al and introduces impurity

levels in the bandgap of the sapphire

These levels give strong absorptions at:

400nm (green) and 600nm (blue)

leaving only red to be transmitted

The spectra for ruby and sapphire look like:

A similar technique is used to colour glasses or pottery

glaze by adding impurities into the molten state:

Cu2+: blue-green, Cr3+: green

Co2+: blue-violet, Mn2+: yellow

http://www.valleydesign.com/images/sapp.jpg

http://home.achilles.net/~jtalbot/glossary/photopumping.gif

Translucency

Even after the light has entered the material, it might yet

be reflected out again due to scattering inside the

material

Even the transmitted light can lose information by being

scattered internally

so a beam of light will spread out or an image will become

blurred

In extreme cases, the material could become opaque

due to excessive internal scattering

Scattering can come from obvious causes:

grain boundaries in poly-crystalline materials

fine pores in ceramics

different phases of materials

In highly pure materials, scattering still occurs

and an important contribution comes from

Rayleigh scattering

This is due to small, random differences in

refractive index from place to place

In amorphous materials such as glass this is

typically due to density or compositional

differences in the random structure

In crystals, lattice defects, thermal motion of

atoms etc. also give rise to Rayleigh scattering

Rayleigh scattering also causes the sky to be

blue. The reason for this is the wavelength-

dependence of Rayleigh scattering

scattering goes as -4

so since red ~ 2blue blue light is scattered ~16

times more than red light

This mechanism is of great technological

importance because it governs losses in

optical fibres for communication

But before we get onto fibres, we will mention

a couple more basic effects

Dispersion

Dispersion is a general name given to things

which vary with wavelength

For example, the wavelength-dependence of the

index of refraction is termed the dispersion of the

index

Another important case arises because the

speed of the wave depends on its wavelength

If a pulse of white light is transmitted through a

material, different wavelengths arrive at the

other end at different times

this is also called dispersion

Luminescence

Luminescence is the general term which describes the

re-emission of previously absorbed radiative energy

Common types are photo- , electro-, and cathodo-

luminescence, depending on whether the original

incident radiation was

light of a different wavelength – e.g. fluorescent light

electric field – e.g. LED

electrons – e.g. electron gun in a cathode ray tube (CRT)

There is also chemo-luminescence due to chemical

reactions which make the glowing rings seen at

fairgrounds!

Luminescence is further divided into

phosphorescence and fluorescence

Fluorescence and phosphorescence are

distinguished by the electron transitions requiring no

change or a change of spin, respectively

hence fluorescence is a faster process because no change of

spin is required, around 10-5 – 10-6s

phosphorescence takes about 10-4 – 101s

Thus the energy diagram might be like:

E2

E1

E3

phosp.

phosp.

fluor.

incident

flip

flip

If the energy levels are actually a range of energies,

then:

So the light emitted by fluorescence is of longer

wavelength than the incident light

since the energy is smaller

and phosphorescent light is typically longer wavelength than

fluorescent light

phonon emission

~10-12s per hop

fluorescence, ~10-5s

In fluorescent lights, the plasma generates UV light,

and a fluorescent coating on the walls of the tube

converts this to visible light

these lights have a visible flicker because (60Hz)-1 > 10-5s

Rather confusingly, materials that do this are

generally called phosphors

To obtain a white light, a mixture of phosphors must

be used, each fluorescing at a different wavelength

TV tubes usually use materials doped with different

elements to give the colours:

ZnS doped with Cu+ gives green

ZnS:Ag gives blue

YVO4:Eu gives red

Optical fibres

Fibre-optic technology has revolutionised

telecommunications owing to the speed of data

transmission:

equivalent to >3 hrs of TV per second

24,000 simultaneous phone calls

0.1kg of fibre carries same information as

30,000kg of copper cable

Owing to attenuation in the cable, transmission is

usually digital and the system requires several

sections:

encoder conversion

to optical

repeater detection decoder

optical optical

http://www.ngflscotland.gov.uk/connected/connected5/images/fibreoptic.jpg

Obviously, the loss in the cable is important because

is determines the maximum uninterrupted length of

the fibre

We know that losses depend on the wavelength of

the light and the purity of the material

recall the penetration depth for glass was ~30cm

In 1970, 1km of fibre attenuated 850nm light by a

factor of 100

By 1979, 1km of fibre attenuated 1.2µm light by a

factor of only 1.2

this light is infrared

Now, over 10km of optical fibre silica glass, the loss

is the same as 25mm of ordinary window glass!

The Rayleigh scattering results from minute local density

variations which are present in the liquid glass due to

Brownian motion and become frozen into the solid

The really clever part about optical fibres is that the light

is guided around bends in the fibre

This is achieved by total internal reflection at the

boundary of the fibre

Thus, the cross section of the fibre is designed as

follows

The light is transmitted in the core and total internal

reflection is made possible by the difference in the

index of refraction between the cladding and the core

A simple approach is the “step-index” design:

The main problem with this design is that different

light rays follow slightly different trajectories

n

So different light rays from an input pulse will take

slightly different paths and will therefore reach the output

at different times

Hence the input pulse is found to broaden during

transmission:

This limits the data rate of digital communication

in out

signal

t t

signal

Such broadening is largely eliminated by using a

“graded-index” design:

This is achieved by doping the silica with B2O3 or GeO2

parabolically as shown above

Now, waves which travel in the outer regions, do so in a

lower refractive index material

and their velocity is higher (v = c/n)

n

Therefore, they travel both further and faster

as a result, they arrive at the output at almost the same time

as the waves with shorter trajectories

Anything that might cause scattering in the core must

be minimised

Cu, Fe, V are all reduced to parts per billion

H2O and OH concentrations also need to be very low

Variations in the diameter of the fibre also cause

scattering

this variation is now <1µm over a length of 1km

To avoid dispersion of different wavelengths, lasers

are used as the light sources

many data channels are possible using wavelength division

multiplexing (WDM)

A convenient fact is that compound semiconductor

lasers can emit IR light close to the 1.55µm wavelength

where the fibre absorbs least

Referring back to the system diagram, it would be

advantageous to integrate the encoder and transmitter

so the circuits and the light emitter can be integrated

This is why there is so much interest in getting light out

of porous silicon or Si compounds

where thin strands of material exhibit quantum-mechanical

effects which adjust the Si band structure to facilitate efficient

light emission

http://porous.silicon.online.fr/images/poreux.jpg

http://ghuth.com/Porous%20silicon.jpg

Lasers

LASER stands for Light

Amplification by the Stimulated

Emission of Radiation

The key word here is “stimulated”

All of the light emission we have mentioned so far is

spontaneous

it happened just due to randomly occurring “natural” effects

Stimulated emission refers to electron transitions that are

“encouraged” by the presence of other photons

Einstein showed that an incident photon with E ≥ Eg was

equally likely to cause stimulated emission of light as to

be absorbedhttp://www.007sdomain.com/gf_laser.jpg

The emitted light has the same energy and phase as

the incident light (= coherent)

Under normal circumstances, there are few excited

electrons and many in the ground-state,

so we get predominantly absorption

If we could arrange for more excited than non-excited

electrons, then we would get mostly stimulated

emission

equally likely

as

Since we get more photons out than we put in, this is

optical amplification

hence lAser

this system was first used to amplify microwaves for

communications (maser)

Such a condition is called a population inversion

This stimulated emission is what gives the laser its

coherent output

which is what makes it useful for holography, for example

Clearly, random spontaneous emission “wastes”

electron transitions by giving incoherent output

so we minimise them by using transitions for which the

spontaneous emissions are of low probability

so-called metastable states

The energy levels of a laser material therefore look

like:

Ruby is a common laser material, which we saw was

Al2O3 (sapphire) with Cr3+ impurities

http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter4a_files/image022.gif

So all we need to make a laser is to achieve

(i) a population inversion

(ii) enough photons to stimulate emission

The first is achieved by filling the metastable states with

electrons generated by light from a xenon flash lamp

The second condition is achieved by confining the

photons to travel back and forth along the rod of ruby

using mirrored ends

next slide

The ruby laser has an output at 694.3 nm

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p:/

/ww

w.r

epai

rfaq

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/sam

/las

ero

p.g

if

In order to keep the coherent emission, we must ensure

that the light which completes the round trip between the

mirrors returns in phase with itself

Hence the distance between the mirrors should obey 2L

= N

where N is an integer, is the laser wavelength and L is the

cavity length

Semiconductor lasers work in just the same way except

that they achieve the population inversion electrically

by using a carefully designed band structure

Some laser characteristics are given in the

following table:

Callister

Summary

We have looked at how the electronic structure of atoms

and their bonding leads to varying optical behaviours in

materials

In particular, properties such as absorption and emission

are closely related to the electrons

Applications of this knowledge include

anti-reflective coatings for lenses

fibre-optic communications

lasers