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Properties of Materials
Dr. Anurag Srivastava
Web address: http://tiiciiitm.com/profanurag
Email: [email protected]
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
htt
p:/
/ww
w.r
epai
rfaq
.org
/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
