introduction to software engineering lecture notes
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Introduction to Software Engineering lecture notesTRANSCRIPT
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Basic materials science concepts
Chapter – 1
Complied by:
Dr. Indranil Lahiri
Metallurgical and Materials Engineering and
Center of Nanotechnology
IIT Roorkee
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Types of Materials• Metals:
– Strong, ductile
– High thermal & electrical conductivity
– Opaque, reflective.
• Polymers/plastics: Covalent bonding � sharing of e’s
– Soft, ductile, low strength, low density
– Thermal & electrical insulators
2
– Thermal & electrical insulators
– Optically translucent or transparent.
• Ceramics: ionic bonding (refractory) – compounds of metallic & non-metallic elements (oxides, carbides, nitrides, sulfides)
– Brittle, glassy, elastic
– Non-conducting (insulators)
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1. Pick Application Determine required Properties
Properties: mechanical, electrical, thermal,
magnetic, optical, deteriorative.
2. Properties Identify candidate Material(s)
The Materials Selection Process
3
Processing: changes structure and overall shape
ex: casting, sintering, vapor deposition, doping
forming, joining, annealing.
Material: structure, composition.
3. Material Identify required Processing
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ELECTRICAL• Electrical Resistivity of Copper:
Adapted from Fig. 18.8, Callister &
Rethwisch 8e. (Fig. 18.8 adapted from: J.O. Linde, Ann Physik 5, 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd edition, McGraw-Hill Company, New York, 1970.)
3
4
5
6
Resis
tivity,
ρ
Oh
m-m
)
4
• Adding “impurity” atoms to Cu increases resistivity.
• Deforming Cu increases resistivity.
T (ºC)-200 -100 0
1
2
3
Resis
tivity,
(10
-8O
hm
0
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Chapter 1
PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or
distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators
permitted by McGraw-Hill for their individual course preparation. If you are a student using this PowerPoint slide, you are using it without permission.
Elementary Materials
Science Concepts
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The shell model of the atom in which electrons are confined to live within certain shells and in subshells within shells
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Atoms in Excited State
Ionization Energy:
Smallest energy required to remove a single electron from a
neutral atom and thereby create a positive ion (cation) and an
isolated electron.
Electron Affinity:Electron Affinity:
Energy needed or released, when we add an electron to a neutral
atom to create a negative ion (anion).
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Virial Theorem
Average kinetic energy is related to the average potential energy
KE = −1
2PE
Total Average Energy
E = PE + KE
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The planetary model of the hydrogen atom in which the negatively charged
electron orbits the positively charged nucleus.
Important definitions to remember:Atomic mass
Atomic number
Avogadro’s number
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(a) Force vs. interatomic separation
(b) Energy vs. interatomic separation
FN
= FA
+ FR
FN
= dE/dr
FN
= net force
FA
= attractive force
FR
= repulsive force
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Net Force in Bonding Between Atoms
FN
= FA
+ FR
= 0
At equilibrium
r0
= Bond length
E0
= Bond energy
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Formation of a covalent bond between two hydrogen atoms leads to the H2
molecule. Electrons spend majority of their time between the two nuclei
which results in a net attraction between the electrons and the two nuclei
which is the origin of the covalent bond.
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(a) Covalent bonding in methane, CH4, involves four hydrogen atoms sharing
Bonds with one carbon atom. Each covalent bond has two shared electrons.
The four bonds are identical and repel each other.
(b) Schematic sketch of CH4 in paper.
(c) In three dimensions, due to symmetry, the bonds are directed towards the
Corners of a tetrahedron.
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The diamond crystal is a covalently bonded network of carbon atoms. Each carbon
atom is covalently bonded to four neighbors forming a regular three dimensional
pattern of atoms which constitutes the diamond crystal.
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Specific arrangement of atom in space -
Crystal
In metallic bonding the valence electrons from the metal atoms form a “cloud of
electrons” which fills the space between the metal ions and “glues” the ions together
through the coulombic attraction between the electron gas and the positive metal
ions.
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The formation of ionic bond between Na and Cl atoms in NaCl. The attraction
Is due to coulombic forces.
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(a) (b)
(a) A schematic illustration of a cross section from solid NaCl. NaCl is made of Cl-
and Na+ ions arranged alternatingly so that the oppositely charged ions are closest
to each other and attract each other. There are also repulsive forces between
the like ions. In equilibrium the net force acting on any ion is zero.
(b) Solid NaCl.
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Sketch of the potential energy per ion-pair in solid NaCl. Zero energy
corresponds to neutral Na and Cl atoms infinitely separated.
Important definitions:
Atomic cohesive energy
Coordination number
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Secondary Bonding
(a) A permanently polarized molecule is called an electric dipole moment.
(b) Dipoles can attract or repel each other depending on their relative
orientations.
(c) Suitably oriented dipoles can attract each other to form van der Walls bonds.
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The origin of van der Walls bonding between water molecules.
(a) The H2O molecule is polar and has a net permanent dipole moment
(b) Attractions between the various dipole moments in water gives rise to
van der Walls bonding
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F
dEdx
p A comb, immediately after combing hair
A dipole moment in a nonuniform field experiences a net force F that depends on the dipole moment p and the field gradient dE/dx.When a charged comb (by combing hair) is brought close to a water jet, the field from the comb attracts the polarized water molecules toward higher fields.[See Question 7.7 in Chapter 7]
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Induced dipole-induced dipole interaction and the resulting van der Waals force
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• Bonding:
-- Can be ionic and/or covalent in character.
--% ionic character increases with difference in electronegativity of atoms.
• Degree of ionic character may be large or small:
Mixed Bonding
CaF2: large
24
Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by
Cornell University.)
SiC: small
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Bond HybridizationBond Hybridization is possible when there is significant
covalent bonding
– hybrid electron orbitals form
– For example for SiC
• XSi = 1.8 and XC = 2.5
25
% ionic character = 100 {1- exp[-0.25(XSi − XC)2]} = 11.5%
• ~ 89% covalent bonding
• Both Si and C prefer sp3 hybridization
• Therefore, for SiC, Si tomas occupy tetrahedral sites
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Definition of Elastic Modulus
σ = applied stress (force per unit area), Y = elastic modulus, ε =
elastic strain (fractional increase in the length of the solid)
σ = Yε
Elastic Modulus and BondingElastic Modulus and Bonding
oo rrorr
N
o dr
Ed
rdr
dF
rY
==
≈
≈
2
211
Y = elastic modulus, ro = interatomic equilibrium separation, FN = net
force, r = interatomic separation, E = bonding energy
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(a) Applied forces F stretch the solid elastically from L0 to δL. The force is
divided amongst chains of atoms that make the solid. Each chain carries a
a force δFN.
(b) In equilibrium, the applied force is balanced by the net force δFN between
the atoms as a result of their increased separation.
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Elastic Modulus and Bond Energy
Y = elastic modulus
Y ≈ fEbond
ro
3
f = numerical factor (constant) that depends on the type of
the crystal and the type of the bond
Ebond = bonding energy
ro = interatomic equilibrium separation
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Kinetic Molecular Theory for Gases
PV =1
3Nmv
2
= gas pressureP = gas pressure
= mean square velocity
N = number of gas molecules
m = mass of the gas molecules
2v
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N = number of molecules, R = gas constant, T = temperature,
P = gas pressure, V = volume, NA = Avogadro’s number
PV = (N/NA)RT
Ideal Gas Equation
Change in Momentum of a Molecule
∆p = 2mvx
∆p = change in momentum, m = mass of the molecule, vx = velocity
in the x direction
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The gas molecules in the container are in random motion
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Rate of Change of Momentum
F =∆p
∆t=
2mvx
(2a / vx )=
mvx
2
a
F = force exerted by the molecule, ∆p = change in momentum, ∆t =
change in time, m = mass of the molecule, vx = velocity in the x
direction, a = side length of cubic containerdirection, a = side length of cubic container
Total Pressure Exerted by N Molecules
P =mNvx
2
V
P = total pressure, m = mass of the molecule, = mean square
velocity along x, V = volume of the cubic container
2
xv
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Mean Square Velocity
Mean Velocity for a Molecule
Mean square velocities in the x, y, and z directions are the same
vx
2= vy
2= vz
2
Mean Velocity for a Molecule
v2
= vx
2+ vy
2+ vz
2= 3vx
2
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Gas Pressure in the Kinetic Theory
P = gas pressure, N = number of molecules, m = mass of the gas
molecule, v = velocity, V = volume, ρ = density.
22
3
1 =
3 = v
V
vNmP ρ
molecule, v = velocity, V = volume, ρ = density.
Mean Kinetic Energy per Atom
k = Boltzmann constant, T = temperature
KE = 1
2mv
2 =
3
2kT
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Internal Energy per Mole for a Monatomic Gas
Molar Heat Capacity at Constant Volume
U = total internal energy per mole, NA = Avogadro’s number, m =
mass of the gas molecule, k = Boltzmann constant, T = temperature
U = NA
1
2mv
2
=
3
2NAkT
Molar Heat Capacity at Constant Volume
Cm = dU
dT =
3
2NAk =
3
2R
Cm = heat capacity per mole at constant volume (J K-1 mole-1), U =
total internal energy per mole, R = gas constant
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Possible translational and rotational motions of a diatomic molecule. Vibrational
motions are neglected.
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(a) The ball and spring model of solids in which the springs represent the interatomic
bonds. Each ball (atom) is linked to its nearest neighbors by springs. Atomic
vibrations in a solid involve 3 dimensions.
(b) An atom vibrating about its equilibrium position stretches and compresses its
springs to the neighbors and has both kinetic and potential energy.
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Internal Energy per Mole
U = NA61
2kT
= 3RT
U = total internal energy per mole, NA = Avogadro’s number, R = gas
constant, k = Boltzmann constant, T = temperature
Dulong-Petit Rule
Cm = Heat capacity per mole at constant volume (J K-1 mole-1)
Cm = dU
dT = 3R = 25 J K
-1 mol
-1
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Thermal Expansion
The potential energy PE curve has a minimum when the atoms in the solid attain the
interatomic separation r = r0. Due to thermal energy, the atoms will be vibrating and
will have vibrational kinetic energy. At T = T1, the atoms will be vibrating in such a way
that the bond will be stretched and compressed by an amount corresponding to the KE of the
atoms. A pair of atoms will be vibrating between B and C. This average separation will be at
A and greater than r0.
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Vibrations of atoms in the solid. We consider, for simplicity a pair of atom. Total energy
E = PE + KE and this is constant for a pair of vibrating atoms executing simple harmonic
Motion. At B and C KE is zero (atoms are stationary and about to reverse direction of
oscillation) and PE is maximum.
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Definition of Thermal Expansion Coefficient
λ = thermal coefficient of linear expansion or thermal expansion
coefficient, Lo = original length, L = length at temperature T
T
L
Lo δ
δλ ⋅=
1
coefficient, Lo = original length, L = length at temperature T
Thermal Expansion
L = Lo[1+ λ (T − To )]
L = length at temperature T, Lo = length at temperature To
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Dependence of the linear thermal expansion coefficient λ (K-1) on temperature T (K) on a
log-log plot. HDPE, high density polyethylene; PMMA, Polymethylmethacrylate (acrylic);
PC, polycarbonate; PET, polyethylene terepthalate (polyester); fused silica, SiO2; alumina,
Al2O3.
SOURCE: Data extracted from various sources including G.A. Slack and S.F. Bartram,
J. Appl. Phys., 46, 89, 1975.
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Solid in equilibrium in air. During collisions between the gas and solid atoms, kinetic
energy is exchanged.
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Fluctuations of a mass attached to a spring due to random bombardment of air molecules.
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Root Mean Square Fluctuations of a Body
Attached to a Spring of Stiffness K
∆x( )rms =kT
K
K = spring constant, T = temperature, (∆x)rms = rms value of the
fluctuations of the mass about its equilibrium position.
rmsK
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Random motion of conduction electrons in a conductor results in electrical noise.
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Charging and discharging of a capacitor by a conductor due to the random thermal
motions of the conduction electrons.
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Root Mean Square Noise Voltage Across a
Resistance
kTRBv 4rms =
R = resistance, B = bandwidth of the electrical system in which noise
is being measured, vrms = root mean square noise voltage, k =
Boltzmann constant, T = temperature
kTRBv 4rms =
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Tilting a filing cabinet from state A to its edge in state A* requires an energy EA. After
reaching A*, the cabinet spontaneously drops to the stable position B. PE of state B is lower
than A and therefore state B is more stable than A.
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Diffusion of an interstitial impurity atom in a crystal from one void to a
neighboring void. The impurity atom at position A must posses an energy EA to
push the host atoms away and move into the neighboring void at B.
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Rate for a
Thermally Activated Process
ϑ = Avο exp(−EA/kT)
EA = UA* − UA
ϑ = frequency of jumps, A = a dimensionless constant that has only a
weak temperature dependence, vo = vibrational frequency, EA =
activation energy, k = Boltzmann constant, T = temperature, UA* =
potential energy at the activated state A*, UA = potential energy at
state A.
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An impurity atom has four site choices for diffusion to a neighboring interstitial
interstitial vacancy. After N jumps, the impurity atom would have been displaced
from the original position at O.
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Mean Square Displacement
L = “distance” diffused after time t, a = closest void to void
separation (jump distance), ϑ = frequency of jumps, t = time, D =
diffusion coefficient
L2 = a2ϑt = 2Dt
Diffusion coefficient is thermally activated
−==
kT
EDaD A
o exp2
21 ϑ
D = diffusion coefficient, DO = constant, EA = activation energy, k =
Boltzmann constant, T = temperature
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Crystal Systems
• Most solids are crystalline with their atoms arranged in aregular manner.• Long-range order : the regularity can extend throughout thecrystal.• Short-range order : the regularity does not persist overappreciable distances. eg. amorphous materials such as glassand wax.and wax.• Liquids have short-range order, but lack long-range order.• Gases lack both long-range and short-range order
Ref: http://me.kaist.ac.kr/upload/course/MAE800C/chapter2-1.pdf
55Materials Science (Electrical and Electronic Materials)
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Crystal Structures (Contd…)
• Five regular arrangements of lattice points that can occur in two dimensions.
(a) square; (b) primitive rectangular;
(c) centered rectangular; (d) hexagonal;
(e) oblique.(e) oblique.
56Materials Science (Electrical and Electronic Materials)
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Unit cell
Lattice parameters: a, b, c, α, β and γ
57Materials Science (Electrical and Electronic Materials)
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The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.
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Number of lattice points per cell
Where,
Ni = number of interior points,
Nf = number of points on faces,Nf = number of points on faces,Nc = number of points on corners.
59Materials Science (Electrical and Electronic Materials)
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FCC
60Materials Science (Electrical and Electronic Materials)
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61Materials Science (Electrical and Electronic Materials)
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BCC
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BCC
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HCP
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DC
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A C G H
D F I J
G
H
I
Jx
Z
Materials Science (Electrical and Electronic Materials)
67
Jx
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ZnS
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SiO2
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Graphite
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C60
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Fig 1.43Three allotropes of carbon
Materials Science (Electrical and Electronic Materials)
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CNT
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NaCl
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A possible reduced sphere unit cell for the NaCl (rock salt) crystal. An alternative
Unit cell may have Na+ and Cl- interchanged. Examples: AgCl, CaO, CsF, LiF, LiCl,
NaF, NaCl, KF, KCl, MgO.
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NaCl or halite crystals are transparent
|SOURCE: Photo by SOK
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A possible reduced sphere unit cell for the CsCl crystal. An alternative unit cell may have
Cs+ and Cl- interchanged. Examples: CsCl, CsBr, CsI, TlCl, TlBr, TlI.
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Fig 1.40
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Lattice directions- MI
The direction of any line in a lattice
may be described by first drawing a line through the origin parallel
to the given line and to the given line and then giving the coordinates of any point on the line
through the origin.
-smallest integer value
- Negative directions are shown by bars eg.
0,0,0
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Plane designation by Miller indices
-Miller indices are always cleared of fractions
- If a plane is parallel to a given axis, its fractional intercept on that
axis is taken as infinity, Miller index is zero
- If a plane cuts a negative axis, the corresponding index is negative and is written with a bar over it.and is written with a bar over it.
-Planes whose indices are the negatives of one another are parallel and lie on opposite sides of the origin, e.g., (210) and (2l0).
-- Planes belonging to the same family is denoted by curly bracket , {hkl}
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Fig 1.41
Labeling of crystal planes and typical examples in the cubic lattice
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Miller indices of lattice planes
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Miller Index
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85Materials Science (Electrical and Electronic Materials)
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The hexagonal unit cell :
Miller –Bravais indices of planes and directions
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Zone= zonal planes + zonal axis
-Zone axis and (hkl) the zonal plane
All shaded planes belong to the same zonei.e parallel to an axis called zone axsis
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Coordination number
Number of nearest neighbors of an atom in the crystal lattice
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• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.
• Coordination # = 6(# nearest neighbors)
SIMPLE CUBIC STRUCTURE (SC)SIMPLE CUBIC STRUCTURE (SC)
5(Courtesy P.M. Anderson) 89Materials Science (Electrical and
Electronic Materials)
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APF = Volume of atoms in unit cell*
Volume of unit cell
*assume hard spheres
• APF for a simple cubic structure = 0.52
volume
ATOMIC PACKING FACTORATOMIC PACKING FACTOR
6
APF =
a3
4
3π (0.5a)31
atoms
unit cellatom
volume
unit cell
volumeclose-packed directions
a
R=0.5a
contains 8 x 1/8 = 1 atom/unit cell
Adapted from Fig. 3.19,Callister 6e.
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• Coordination # = 8
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shadeddifferently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE (BCC)BODY CENTERED CUBIC STRUCTURE (BCC)
7
Adapted from Fig. 3.2,Callister 6e.
(Courtesy P.M. Anderson)91Materials Science (Electrical and
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• APF for a body-centered cubic structure = 0.68
Close-packed directions: length = 4R = 3 a
Unit cell contains: 1 + 8 x 1/8
ATOMIC PACKING FACTOR: BCCATOMIC PACKING FACTOR: BCC
aR
8
1 + 8 x 1/8 = 2 atoms/unit cell
Adapted fromFig. 3.2,Callister 6e.
APF =
a3
4
3π ( 3a/4)32
atoms
unit cell atom
volume
unit cell
volume
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• Coordination # = 12Coordination # = 12Coordination # = 12Coordination # = 12
Adapted from Fig. 3.1(a),
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shadeddifferently only for ease of viewing.
FACE CENTERED CUBIC STRUCTURE (FCC)FACE CENTERED CUBIC STRUCTURE (FCC)
9
Callister 6e.
(Courtesy P.M. Anderson)
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Unit cell contains: 6 x 1/2 + 8 x 1/8
• APF for a body-centered cubic structure = 0.74
Close-packed directions: length = 4R = 2 a
ATOMIC PACKING FACTOR: FCCATOMIC PACKING FACTOR: FCC
APF =
a3
4
3π ( 2a/4)34
atoms
unit cell atom
volume
unit cell
volume
6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell
a
10
Adapted fromFig. 3.1(a),Callister 6e.
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ρ = nA
VcNA
# atoms/unit cell Atomic weight (g/mol)
Volume/unit cell
(cm3/unit cell)
Avogadro's number
(6.023 x 1023 atoms/mol)
THEORETICAL DENSITY, THEORETICAL DENSITY, ρρρρρρρρ
14
Example: Copper
Data from Table inside front cover of Callister (see next slide):
• crystal structure = FCC: 4 atoms/unit cell• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)• atomic radius R = 0.128 nm (1 nm = 10 cm)-7
Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10
-23cm3
Compare to actual: ρCu = 8.94 g/cm3
Result: theoretical ρCu = 8.89 g/cm3
95Materials Science (Electrical and Electronic Materials)
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Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon
Symbol Al Ar Ba Be B Br Cd Ca C
At. Weight (amu) 26.98 39.95 137.33 9.012 10.81 79.90 112.41 40.08 12.011
Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071
Density
(g/cm3) 2.71 ------ 3.5 1.85 2.34 ------ 8.65 1.55 2.25
Crystal Structure FCC ------ BCC HCP Rhomb ------ HCP FCC Hex
Adapted fromTable, "Charac-teristics ofSelectedElements",inside front
Characteristics of Selected Elements at 20C
15
Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen
C Cs Cl Cr Co Cu F Ga Ge Au He H
12.011 132.91 35.45 52.00 58.93 63.55 19.00 69.72 72.59 196.97 4.003 1.008
0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------
2.25 1.87 ------ 7.19 8.9 8.94 ------ 5.90 5.32 19.32 ------ ------
Hex BCC ------ BCC HCP FCC ------ Ortho. Dia. cubic FCC ------ ------
cover,Callister 6e.
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ρmetals ρceramics ρpolymers
(g/cm3)
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
20
30Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers
in an epoxy matrix). 10
5
Steels Cu,Ni
Tin, Zinc
Silver, Mo
Tantalum Gold, W Platinum
Zirconia
Metals have...• close-packing(metallic bonding)
• large atomic mass
Ceramics have...• less dense packing
DENSITIES OF MATERIAL CLASSESDENSITIES OF MATERIAL CLASSES
16
ρ (g/cm
1
2
3
4
5
0.3
0.4 0.5
Magnesium
Aluminum
Titanium
Graphite
Silicon
Glass-soda Concrete
Si nitride Diamond Al oxide
HDPE, PS PP, LDPE
PC
PTFE
PET PVC Silicone
Wood
AFRE*
CFRE*
GFRE*
Glass fibers
Carbon fibers
Aramid fibers
• less dense packing(covalent bonding)
• often lighter elements
Polymers have...• poor packing(often amorphous)
• lighter elements (C,H,O)
Composites have...• intermediate values
Data from Table B1, Callister 6e.97Materials Science (Electrical and
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Physical Properties•Acoustical properties
•Atomic properties
Mechanical properties•Compressive strength
•Ductility
•Fatigue limit
•Flexural modulus
•Flexural strength
•Fracture toughness
•Hardness
•Poisson's ratio
•Shear modulus
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98
•Atomic properties
•Chemical properties
•Electrical properties
•Environmental properties
•Magnetic properties
•Optical properties
•Density
•Shear modulus
•Shear strain
•Shear strength
•Softness
•Specific modulus
•Specific weight
•Tensile strength
•Yield strength
•Young's modulus
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• Most engineering materials are polycrystals.
Adapted from Fig. K, color inset pages of Callister 6e.(Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)
1 mm
POLYCRYSTALSPOLYCRYSTALS
18
• Nb-Hf-W plate with an electron beam weld.• Each "grain" is a single crystal.• If crystals are randomly oriented,
overall component properties are not directional.• Crystal sizes typ. range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
1 mm
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• Single Crystals
-Properties vary withdirection: anisotropic.
-Example: the modulusof elasticity (E) in BCC iron:
• Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
Data from Table 3.3, Callister 6e.(Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.)
SINGLE VS POLYCRYSTALSSINGLE VS POLYCRYSTALS
19
• Polycrystals
-Properties may/may notvary with direction.-If grains are randomlyoriented: isotropic.(Epoly iron = 210 GPa)
-If grains are textured,anisotropic.
200 µm Adapted from Fig. 4.12(b), Callister 6e.(Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
100Materials Science (Electrical and Electronic Materials)
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Crystal defects
1.Point defect-Vacancy, Impurity atoms ( substitutional and interstitial)Frankel and Schottky defect ( ionic solids & nonstochiometric)
2. Line defect-
101
Edge dislocation
Screw dislocation, Mixed dislocation
3. Surface defects-Grain boundariesTwin boundary Surfaces, stacking faultsInterphases
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Equilibrium Concentration of Vacancies
nv = vacancy concentration
nv = N exp −Ev
kT
v
N = number of atoms per unit volume
Ev = vacancy formation energy
k = Boltzmann constant
T = temperature (K)
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Generation of a vacancy by the diffusion of atom to the surface and the subsequent diffusion
of the vacancy into the bulk.
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Point defects in the crystal structure. The regions around the point defect become distorted;
the lattice becomes strained.
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Interstitial Sites
X on figure is called an octahedral site
The radius(aoct) of octahedral site is = 0.41421ao
where ao is the radius of the spheres.the spheres.
There are also smaller sites, called tetrahedral sites, labeled T
This is a smaller site since its radius aT= 0.2247ao
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Void types
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Point defects in ionic crystals
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Non stochiometry
Conduction in ionic crystal
ZnO crystal containing extra Zn2+
Crystal is electronically neutral, (i.e. 2+ & 2- )
108
Zn2+
O2-
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Stoichiometry and nonstoichiometry and the resulting crystal structure
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Dislocation line and b are perpendicular to each other110Materials Science (Electrical and
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Movement of edge dislocation
111Materials Science (Electrical and Electronic Materials)
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112Materials Science (Electrical and Electronic Materials)
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Dislocation line and b are parallel to each other
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Cause of slip
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Elastic stress field responsible for electron scattering andincrease in electrical resistivity
lattice strain around dislocation
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116Materials Science (Electrical and Electronic Materials)
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The plane and directions for the dislocation movement
The closest packed plane and the closest packed direction of FCC
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By resolving, the contribution
from both types of
dislocations can bedetermined
118Materials Science (Electrical and Electronic Materials)
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TEM
-dislocaions
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Solidification of a polycrystalline solid from the melt. (a) Nucleation. (b) Growth. (c) The
solidified polycrystalline solid. For simplicity cubes represent atoms.
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3. Surface defects
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The grain boundaries have broken bonds, voids, vacancies, strained bonds and “interstitial”
type atoms. The structure of the grain boundary is disordered and the atoms in the grain
boundaries have higher energies than those within the grains.
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At the surface of a hypothetical two dimensional crystal, the atoms cannot fulfill their
bonding requirements and therefore have broken, or dangling, bonds. Some of the surface
atoms bond with each other; the surface becomes reconstructed. The surface can have
physisorbed and chemisorbed atoms.
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Typically a crystal surface has many types of imperfections such as steps, ledges, kinks,
cervices, holes and dislocations.
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127Materials Science (Electrical and Electronic Materials)
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Low angle GB
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Stacking fault-occurs when there is a
flaw in the stacking
sequence
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Interfaces of phasesAl-Cu system
Coherent semi-coherent incoherent
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Definition of Phase:• A phase is a region of material that is chemically
uniform, physically distinct, and (often)mechanically separable.
• A phase is a physically separable part of thesystem with distinct physical and chemicalproperties.
• System - A system is that part of the universe• System - A system is that part of the universewhich is under consideration.
• In a system consisting of ice and water in aglass jar, the ice cubes are one phase, the wateris a second phase, and the humid air over thewater is a third phase. The glass of the jar isanother separate phase.
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Gibbs' phase rule proposed by Josiah Willard Gibbs
The phase rule is an expression of the number of variablesin equation(s) that can be used to describe a system in equilibrium.
Degrees of freedom, F
F = C − P + 2 F = C − P + 2
Where,Where,
P is the number of phases in thermodynamic equilibrium with each other
C is the number of components
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Phase rule at constant pressure Phase rule at constant pressure
• Condensed systems have no gas phase. When their properties are insensitive to the (small) changes in pressure, which results in the phase rule at constant pressure as,
F = C − P + 1
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Types of Phase diagram
1. Unary phase diagram
2. Binary phase diagrams
3. Ternary phase diagram
135
3. Ternary phase diagram
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Unary phase diagram
Pre
ssu
re
Critical pressure Liquid
phase
Pre
ssu
re
Temperature
Solid Phase gaseous phase
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Binary phase diagrams
1. Binary isomorphous systems (complete solid solubility)
2. Binary eutectic systems (limited solid 2. Binary eutectic systems (limited solid solubility)
3. Binary systems with intermediate phases/compounds
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Solid solutions can be disordered substitutional, ordered substitutional and interstitial
substitutional
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Binary phase diagram- isomorphous system
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The Lever RuleFinding the amounts of phases in a two phase region:1. Locate composition and temperature in diagram2. In two phase region draw the tie line or isotherm3. Fraction of a phase is determined by taking the length of the
tie line to the phase boundary for the other phase, anddividing by the total length of tie line
The lever rule is a mechanical analogy to the mass balancecalculation. The tie line in the two-phase region is analogous tocalculation. The tie line in the two-phase region is analogous toa lever balanced on a fulcrum.
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microstrucures
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Solidification of an isomorphous
alloy such as Cu-Ni.
(a) Typical cooling curves
(b) The phase diagram marking the
regions of existence for the
phases
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Cooling of a 80%Cu-20%Ni alloy from the melt to the solid state.
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Segregation in a grain due to rapid cooling (nonequilibrium cooling)
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Lever Rule
WL =CS − CO
CS − CL
and
LS
LOS
CC
CCW
−
−=
WL = the weight fraction of the liquid phase, WS = the weight fraction
of the solid phase, CS = composition of the solid phase, CL =
composition of the liquid phase, CO = overall composition.
S L
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The phase diagram of Si with impurities near the low-concentration region
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The principle of zone refining
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We can only dissolve so much salt in brine (solution of salt in water).
Eventually we reach the solubility limit at Xs, which depends on the temperature. If
we add more salt, then the excess salt does not dissolve and coexists with the brine. Past
Xs we have two phases, brine (solution) and salt (solid).
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Binary phase diagram
–2. limited solubility
• A phase diagram for a
binary system
displaying an eutectic
point.
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The equilibrium phase diagram of the Pb-Sn alloy. The microstructure on the left show
the observations at various points during the cooling of a 90% Pb-10% Sn from the melt
along the dashed line (the overall alloy composition remains constant at 10% Sn).
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The alloy with the eutectic composition cools like a pure element exhibiting a single
solidification temperature at 183°C. The solid has the special eutectic structure. The alloy with
the composition 60%Pb-40%Sn when solidified is a mixture of primary a and eutectic solid.
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Cu-Ag system
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Sn-Bi system
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Pb-Sn system
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Pb-Sn system
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Pb-Sn system
Mechanism
of growth
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Cu- Zn system
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Ternary phase diagrams
MgO-Al2O3-SiO2 system at 1 atm. pressure Fe-Ni-Cr ternary alloy system
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Single crystal
A single crystal solid is a material in which the crystal lattice of the entire sample is continuous
no grain boundaries- grain boundaries can no grain boundaries- grain boundaries can have significant effects on the physical and electrical properties of a material
single crystals are of interest to electric device applications
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(a) Schematic illustration of the growth of a single-crystal Si ingot by the Czochralski technique.
(b) The crystallographic orientation of the silicon ingot is marked by grounding a flat. The ingot can
be as long as 2m. Wafers are cut using a rotating annula diamond saw. Typical wafer thickness is
0.6-0.7 mm.
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Silicon
A silicon ingot is a single crystal of Si. Within the bulk of the crystal, the atoms are
arranged on a well-defined periodical lattice. The crystal structure is that of
diamond.
|Courtesy of MEMC, Electronic Materials Inc.
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Left: Silicon crystal ingots grown by the Czochralski crystal drawers in the background
|Courtesy of MEMC, Electronic Materials Inc.
Right: 200 mm and 300 mm Si
|Courtesy of MEMC, Electronic Materials Inc.
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Crystalline and amorphous structures illustrated schematically in two dimensions
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Silicon can be grown as a semiconductor crystal or as an amorphous semiconductor film.
Each line represents an electron in a band. A full covalent bond has two lines, and a
broken bond has one line.
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It is possible to rapidly quench a molten metallic alloy,
thereby bypassing crystallization, and forming a glassy
metal commonly called a metallic glass. The process is
called melt spinning.
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Amorphous silicon, a-Si, can be prepared by an electron beam evaporation of
silicon. Silicon has a high melting temperature so that an energetic electron beam is
used to melt the crystal in the crucible locally and thereby vaporize Si atoms. Si
atoms condense on a substrate placed above the crucible to form a film of a-Si.
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Hydrogenated amorphous silicon, a-Si:H, is generally prepared by the decomposition of
silane molecules in a radio frequency (RF) plasma discharge. Si and H atoms condense on a
substrate to form a film of a-Si:H
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Doping
� Minute addition of elements in a controlled way to the matrix is called doping.
� During Bulk crystal growth dopants can be added� An epitaxial layer can be doped during deposition
by adding impurities to the source gas, such as arsine, phosphine or diborane. The concentration
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arsine, phosphine or diborane. The concentration of impurity in the gas phase determines its concentration in the deposited film.
� Doping can be done by diffusion, allowing the dopants to diffuse at elevated temperature.
� Ion implantation- bombarding the dopants at high speed
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Thin films: Epitaxial growth
�Epitaxy, The term epitaxy comes from the Greek roots,epi, meaning "above“ taxis, meaning "in ordered manner“
� Epitaxial growth refers to the method of depositing a
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� Epitaxial growth refers to the method of depositing a monocrystalline film on a monocrystalline substrate.
� The deposited film is denoted as epitaxial film or epitaxial layer.
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Applications
Epitaxy is used in nanotechnology and in semiconductorfabrication.
Semiconductor materials (technologically important) are,silicon-germanium, gallium nitride, gallium arsenide, indiumphosphide and graphene.
Epitaxy is also used to grow layers of pre-doped silicon on thepolished sides of silicon wafers, before they are processed into
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polished sides of silicon wafers, before they are processed intosemiconductor devices. This is typical of power devices, such asthose used in pacemakers, vending machine controllers,automobile computers, etc.
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Methods
1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition.
2. Liquid-phase epitaxy (LPE)
3. Solid-phase epitaxy is used primarily for crystal-damage healing
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4. Molecular-beam epitaxy (MBE)
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1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition
Silicon is most commonly deposited from
silicon tetrachloride in hydrogen at 1200 °C:
SiCl4(g)
+ 2H2(g)
↔ Si(s)
+ 4HCl(g)
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SiCl4(g)
+ 2H2(g)
↔ Si(s)
+ 4HCl(g)
Growth rates above 2µm/minute to produce polycrystalline
silicon.
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Hydrogenated amorphous silicon
� High-quality hydrogenated amorphous silicon films (a-Si:H) have been produced by decomposition of low-pressure silane gas on a very hot surface with deposition on a nearby, typically 210 °C substrate.
� A high-temperature tungsten filament provides the surface for heterogeneous thermal decomposition of the low-pressure silane
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heterogeneous thermal decomposition of the low-pressure silaneand subsequent evaporation of atomic silicon and hydrogen.The silane reaction occurs at 650 °C :
SiH4 → Si + 2H2
� The substrates: flat, oxide-free, single-crystal silicon
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2. Liquid-phase
From the melt containing dissolved semiconductor
on solid substrates.
The thermal expansion coefficient of substrate and grown
layer should be similar
Deposition rates for films range from 0.1 to 1 μm/minute.
Doping can be achieved by the addition of dopants.
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Doping can be achieved by the addition of dopants.
Example :
ternary and quaternary III-V compounds on gallium arsenide
(GaAs) and indium phosphide (InP) substrates
.
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3. Solid-phase
Solid Phase Epitaxy (SPE) is a transition between the
amorphous and crystalline phases of a material.
It is usually done by first depositing a film of amorphous
material on a crystalline substrate.
The substrate is then heated to crystallize the film.
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The substrate is then heated to crystallize the film.
The single crystal substrate serves as a template for crystal
growth.
The annealing step used to recrystallize or heal silicon layers
amorphized during ion implantation is also considered one type
of Solid Phase Epitaxy.
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4. Molecular-beam
In MBE, a source material is heated to produce an evaporated
beam of particles.
These particles travel through a very high vacuum (10-8 Pa;
practically free space) to the substrate, where they condense.
MBE has lower throughput than other forms of epitaxy.
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MBE has lower throughput than other forms of epitaxy.
This technique is widely used for growing III-V semiconductor
crystals.
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Lattice matching- essential condition for the epitaxial growth
� Matching of lattice structures between two different semiconductor
materials, allows a region of band gap change to be formed in a materialwithout introducing a change in crystal structure.
� It allows construction of advanced light-emitting diodes and diode lasers.
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For example, gallium arsenide, aluminium gallium arsenide, and aluminium
arsenide have almost equal lattice constants, making it possible to growalmost arbitrarily thick layers of one on the other one.
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The beginning of the grading layer will have a ratio to match the underlying lattice and the alloy at the end of the layer growth will match the desired final lattice.
For example, Indium gallium phosphide layers with a band-gap above 1.9 eV can be grown on Gallium
Lattice grading
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band-gap above 1.9 eV can be grown on Gallium Arsenide wafers with index grading
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Design of semiconducting compound materials
Ternary and quaternary compounds
Basic criteriaEg requirements
Application oriented
181
1. Design GaxAl(1-x)As for different device applications.
2. How can GaxIn(1-x)AsyP(1-y) compoundis designed for device applications?
3. What is graded semiconducting compound?
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D
CC
Q.1: Give the Miller Indices of planes A,B & directions C,D.
4
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Pb-Sn system
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Draw the microstructure of the alloy at ‘B’. Give the weight fractions of the phase/s and concentration of Pb & Sn elements of each phase.
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Q.3: Draw a neat sketch of DC unit cell.Calculate the Packing Factor of DC.
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