Introduction to Software Engineering lecture notes

Basic materials science concepts

Chapter – 1

Complied by:

Dr. Indranil Lahiri

Metallurgical and Materials Engineering and

Center of Nanotechnology

IIT Roorkee

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)

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

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

Chapter 1

PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or

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Elementary Materials

Science Concepts

The shell model of the atom in which electrons are confined to live within certain shells and in subshells within shells

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).

Virial Theorem

Average kinetic energy is related to the average potential energy

KE = −1

2PE

Total Average Energy

E = PE + KE

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

(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

Net Force in Bonding Between Atoms

FN

= FA

+ FR

= 0

At equilibrium

r0

= Bond length

E0

= Bond energy

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.

(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.

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.

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.

The formation of ionic bond between Na and Cl atoms in NaCl. The attraction

Is due to coulombic forces.

(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.

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

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.

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

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]

Induced dipole-induced dipole interaction and the resulting van der Waals force

• 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

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

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

(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.

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

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

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

The gas molecules in the container are in random motion

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

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

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

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

Possible translational and rotational motions of a diatomic molecule. Vibrational

motions are neglected.

(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.

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

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.

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.

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

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.

Solid in equilibrium in air. During collisions between the gas and solid atoms, kinetic

energy is exchanged.

Fluctuations of a mass attached to a spring due to random bombardment of air molecules.

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

Random motion of conduction electrons in a conductor results in electrical noise.

Charging and discharging of a capacitor by a conductor due to the random thermal

motions of the conduction electrons.

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 =

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.

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.

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.

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.

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

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)

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.


Unit cell

Lattice parameters: a, b, c, α, β and γ


The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.

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.


FCC


BCC


HCP


DC


A C G H

D F I J

G

H

I

Jx

Z

Materials Science (Electrical and Electronic Materials)

67

Jx

ZnS


SiO2


Graphite


C60


Fig 1.43Three allotropes of carbon


CNT


NaCl


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.

NaCl or halite crystals are transparent

|SOURCE: Photo by SOK

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.

Fig 1.40


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

-79Materials Science (Electrical and

Electronic Materials)

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}


Fig 1.41

Labeling of crystal planes and typical examples in the cubic lattice


Miller indices of lattice planes


Miller Index


The hexagonal unit cell :

Miller –Bravais indices of planes and directions


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


Coordination number

Number of nearest neighbors of an atom in the crystal lattice


• 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


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.


• 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


• 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


• 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)


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.


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


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.


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


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


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

• 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


• 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].)


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


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)

Generation of a vacancy by the diffusion of atom to the surface and the subsequent diffusion

of the vacancy into the bulk.

Point defects in the crystal structure. The regions around the point defect become distorted;

the lattice becomes strained.

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


Void types


Point defects in ionic crystals

Non stochiometry

Conduction in ionic crystal

ZnO crystal containing extra Zn2+

Crystal is electronically neutral, (i.e. 2+ & 2- )

108

Zn2+

O2-


Stoichiometry and nonstoichiometry and the resulting crystal structure

Dislocation line and b are perpendicular to each other110Materials Science (Electrical and


Movement of edge dislocation


Dislocation line and b are parallel to each other


Cause of slip


Elastic stress field responsible for electron scattering andincrease in electrical resistivity

lattice strain around dislocation


The plane and directions for the dislocation movement

The closest packed plane and the closest packed direction of FCC


By resolving, the contribution

from both types of

dislocations can bedetermined


TEM

-dislocaions


Solidification of a polycrystalline solid from the melt. (a) Nucleation. (b) Growth. (c) The

solidified polycrystalline solid. For simplicity cubes represent atoms.

3. Surface defects


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.

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.

Typically a crystal surface has many types of imperfections such as steps, ledges, kinks,

cervices, holes and dislocations.

Low angle GB


Stacking fault-occurs when there is a

flaw in the stacking

sequence


Interfaces of phasesAl-Cu system

Coherent semi-coherent incoherent


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.


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


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


Types of Phase diagram

1. Unary phase diagram

2. Binary phase diagrams

3. Ternary phase diagram

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3. Ternary phase diagram


Unary phase diagram

Pre

ssu

re

Critical pressure Liquid

phase

Pre

ssu

re

Temperature

Solid Phase gaseous phase


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


Solid solutions can be disordered substitutional, ordered substitutional and interstitial

substitutional

Binary phase diagram- isomorphous system


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.


microstrucures


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

Cooling of a 80%Cu-20%Ni alloy from the melt to the solid state.

Segregation in a grain due to rapid cooling (nonequilibrium cooling)

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

The phase diagram of Si with impurities near the low-concentration region

The principle of zone refining

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).

Binary phase diagram

–2. limited solubility

• A phase diagram for a

binary system

displaying an eutectic

point.


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).

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.

Cu-Ag system


Sn-Bi system


Pb-Sn system

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Pb-Sn system


Pb-Sn system

Mechanism

of growth


Cu- Zn system


Ternary phase diagrams

MgO-Al2O3-SiO2 system at 1 atm. pressure Fe-Ni-Cr ternary alloy system


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


(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.

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.

Left: Silicon crystal ingots grown by the Czochralski crystal drawers in the background


Right: 200 mm and 300 mm Si


Crystalline and amorphous structures illustrated schematically in two dimensions

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.

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.

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.

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

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


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.


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.


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)


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.


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


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

.


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.


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.


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.


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


Design of semiconducting compound materials

Ternary and quaternary compounds

Basic criteriaEg requirements

Application oriented

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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?


D

CC

Q.1: Give the Miller Indices of planes A,B & directions C,D.

4

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.

Q.3: Draw a neat sketch of DC unit cell.Calculate the Packing Factor of DC.

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