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MEC281
MATERIALS SCIENCES
This course covers some fundamentals of materials science, which are
necessary for the understanding of materials properties for their
appropriate applications. The major families of materials such as
metals, ceramics, polymers and composite are discussed for their
structures, properties and applications.
Course Description
• CO1 :Explain basic concepts of structure, mechanical and physical
properties of engineering materials. [PO1, LO1].
• CO2 ;Apply the basics concepts to identify the relationships
between properties and structure of materials. [PO3, LO3, SS1].
• CO3 :Choose the suitable material for appropriate engineering
applications. [PO3, LO3, SS1].
Course Outcome
• Course Work : 40%
Test 1 : 15%
Test 2 : 15%
Quiz (x4) : 10% (i-Learn)
• Final Examination : 60%
• Total : 100%
ASSESSMENT
Syllabus content
CHAPTER CONTENT/SUB-CHAPTER
1
STRUCTURE
(10 HOURS)
1. Atomic Structure.
2. Interatomic Bonding Amorphous and Crystalline Solid.
3. Crystal Structures.
4. Efficiency of Atomic Packing, Density Computation, Miller Indices.
5. Relationship between Atomic Structure, Crystal Structures and
Properties of Material.
2
METALLIC MATERIALS
(14 HOURS)
1. Solidification Of Pure Metal And Alloys
2. Phase Diagram: Microstructure Development, Microconstituent of
Phases.
3. Fe-Fe3C System: Microstructure Development, Microconstituent of
Phases.
4. Ferrous and Non-Ferrous Metals
3
THERMAL
TREATMENT OF
METALLIC MATERIALS
(8 HOURS)
1. Heat Treatment of Ferrous Metals
2. Hardenability
3. Isothermal Transformation Diagram (TTT Diagram)
4
ENGINEERING
MATERIALS
(10 HOURS)
1. Classification of Engineering Materials
2. Plastics And Elastomer: Molecular Structures, Properties and
Applications
3. Ceramic: Structure, Properties, and Applications
4. Composite Materials: Types, Properties and Applications.
REFERENCES
 William D. Callister, Jr., Materials Science and
Engineering and Engineering, An Introduction, John
Wiley & Sins, Inc., 2011.
 William F. Smith, Foundations of Materials Science and
Engineering, Second Edition. McGraw-Hill, 2000.
 William F. Smith, Structure and Properties of
Engineering Alloys, Second Edition, McGraw-Hill, 1993.
 K.R. Tretheway and J. Chamberlain, Corrosion,
Longman Scientific Technical, 1998.
Teaching Plan (June – October 2014)
Week Date Syllybus Activity(s)
1* 9/6/14 – 15/6/14
CHAPTER 12* 16/6/14 – 22/6/14 Tutorial 1
3 23/6/14 – 29/6/14 Tutorial 2
4 30/6/14 – 6/7/14
CHAPTER 2
Tutorial 3
5 7/7/14 – 13/7/14 Tutorial 4 & QUIZ 1’
6 14/7/14 – 20/7/14 Tutorial 5
7 21/7/14 – 25/7/14
26/7/14 – 3/8/14 Mid Term Break
8 4/8/14 – 10/8/14 TEST 1 (8/8/14)
9 11/8/14 – 17/8/14
CHAPTER 3
Tutorial 6 & QUIZ 2’
10 18/8/14 – 24/8/14 Tutorial 7
11 25/8/14 – 31/8/14 Tutorial 8 & QUIZ 3’
12 1/9/14 – 7/9/14
CHAPTER 4
Tutorial 9
13** 8/9/14 – 14/9/14 TEST 2 (12/9/14)
14** 15/9/14 – 21/9/14 Tutorial 10 & QUIZ 4’
2 days 22/9/14 – 23/9/14 Revision
3 weeks 24/9/14 – 17/10/14 Examination
Remarks: (online –iLearn )
*Entrance Survey
**Exit Survey
Quiz’
SuFO (18 Ogos – 3 September 2014)
Lecture Notes, Tutorial, etc. - FOLDER (June – October 2014)
Tutorial
Tutorial Topic
1 Atomic structure
2 Interatomic bonding, Crystal Structures
3 APF, Density Computation, Miller Indices.
4 Phase diagram
5 Iron-Iron Carbide Phase Diagram
6 Ferrous and Non-Ferrous Metal
7 TTT- Diagram
8 Heat Treatment of Ferrous Metal
9 Plastic and Elastomer
10 Ceramic and Composite materials
CHAPTER 1 : STRUCTURE
(10 hours)
SUBCONTENT :
1.1 ATOMIC STRUCTURE.
1.2 INTERATOMIC BONDING AMORPHOUS AND CRYSTALLINE SOLID.
1.3  CRYSTAL STRUCTURES.
1.4 EFFICIENCY OF ATOMIC PACKING, DENSITY COMPUTATION, 
MILLER INDICES. 
1.5 RELATIONSHIP BETWEEN ATOMIC STRUCTURE, CRYSTAL STRUCTURES
AND PROPERTIES OF MATERIAL.
You should be able:
Describe an atomic structure
Configure electron configuration
Differentiate between each atomic bonding
Briefly describe ionic, covalent, metallic, hydrogen 
and Van der Waals bonds
Relate the atomic bonding with material 
properties
LEARNING OBJECTIVE
4
1.1 ATOMIC STRUCTURE
All matter is made up of tiny particles called atoms.
What are ATOMS?
Since the atom is too small to be seen even with the most powerful
microscopes, scientists rely upon on models to help us to understand the
atom.
Even with the world’s best
microscopes we cannot clearly
see the structure or behavior
of the atom.
5
Even though we do not know what an
atom looks like, scientific models
must be based on evidence. Many of
the atom models that you have seen
may look like the one below which
shows the parts and structure of the
atom.
Is this really an  ATOM?
This model represents the 
most modern version of the 
atom.
Bohr Theory
Wave Mechanical Atomic Model
6
Protons and neutrons join together 
to form the nucleus – the central 
part of the atom
+
+ ‐‐
Electrons 
move 
around the 
nucleus
Neutron
Proton
Electron
Nucleon or 
Nucleus
Fig. : A simplified diagram of atom
Shell @ Orbital @ Energy level
•Atoms are made of a nucleus that contains protons, neutrons and electrons that 
orbit around the nucleus at different levels, known as shells.
What does an ATOM look like?
7
•These particles have the following properties:
Particle Charge Location Mass (amu) Symbol
Proton Positive (+ve) Nucleus 1.0073
Neutron Neutral Nucleus 1.0087
Electron Negative (-ve) Orbital 0.000549
‐
To describe the mass of atom, a unit of mass called the atomic mass unit (amu) is used.
•The number of protons, neutrons and electrons in an atom completely determine 
its properties and identity. This is what makes one atom different from another. 
+
8
Most atoms are electrically neutral, meaning that they have an equal number of
protons and electrons. The positive and negative charges cancel each other out.
Therefore, the atom is said to be electrically neutral.
Why are all ATOMS are ELECTRICALLY
NEUTRAL?
+
‐
Neutron
Proton
Electron
++
+‐
‐
+ ‐
Fig. : Beryllium atom 
Proton    = 4
Electron = 4
NEUTRAL
CHARGE
9
cation ‐ ion with a positive charge
‐ If a neutral atom loses one or more electrons, it becomes a cation.
anion ‐ ion with a negative charge 
‐ If a neutral atom gains one or more electrons, it becomes an anion.
Na
11 protons
11 electrons Na+ 11 protons
10 electrons
Cl
17 protons
17 electrons
Cl‐
17 protons
18 electrons
Cations are smaller than their “parent atom” because 
there is less e‐e repulsion
Anions are larger than their “parent atom” because there is 
more e‐‐ e repulsion
If an atom gains or loses electrons, the atom is no longer neutral and
it become electrically charged . The atom is then called an ION.
10
periodic: a repeating pattern
table: an organized collection of information
Periodic Table (P.T.)
An arrangement of elements in
order of atomic number;
elements with similar
properties are in the same
group.
Basics of the PERIODIC TABLE
11
The periodic table below is a simplified representation which
usually gives the :
1) period: horizontal row on the P.T.
•Designate electron energy levels
2) group or family: vertical column on the P.T.
Two main classifications in P.T.
12
ATOMIC NUMBER and ATOMIC MASS
1) ATOMIC NUMBER 2) ATOMIC MASS
Atom can be described using :
The element helium has the atomic number 2, is represented by
the symbol He, its atomic mass is 4 and its name is helium.
ATOMIC MASS , A =
no. of protons (Z) + number of neutrons (N)
SYMBOL
ATOMIC NUMBER, Z = no. of protons
PERIODIC TABLE 
14
ATOMIC NUMBER tells how many PROTONS (Z) are in its atoms which determine the 
atom’s identity. 
The list of elements (ranked according to an increasing no. of protons) can be looked up 
on the Periodic Table. So, if an atom has 2 protons (atomic no. = 2), it must be helium(He). 
ATOMIC MASS tells the sum of the masses of  PROTONS (Z) and NEUTRONS (N) within the 
nucleus  E.g :
Lithium:
Atomic number = 3
3 protons, Z
4 neutrons, N
Atomic mass, A = 3 + 4 = 7
BUT...  although each element has a defined number of protons, the number of neutrons 
is not fixed   isotopes
15
•Atoms which have the same 
number of protons but different 
numbers of neutrons.
•Atoms which have the same
atomic number but different atomic 
mass .
•Eg : Hydrogen has 3 isotopes. 
Natural
Isotope
Proton Neutron Atomic
Mass
Hydrogen 1
(hydrogen)
1 0 1
Hydrogen 2
(deuterium)
1 1 2
Hydrogen 3
(tritium)
1 2 3
H1
1 H (D)2
1 H (T)3
1
Same atomic no. @ no. of protons
Different mass number
ISOTOPES
Exercise of isotopes :
Element Name
Number of
Proton
Nucleon 
Number
Number of 
Neutron
Hydrogen
Hydrogen
Deuterium
Tritium
Oxygen
Oxygen‐16
Oxygen‐17
Oxygen‐18
Carbon
Carbon‐12
Carbon‐13
Carbon‐14
Chlorine
Chlorine‐35
Chlorine‐37
Sodium
Sodium‐23
Sodium‐24
17
Naturally occurring carbon consists of three isotopes, 
12C, 13C, and 14C.  State the number of protons, 
neutrons, and electrons in each of these carbon atoms. 
12C 13C 14C
6 6                        6
#p   _______         _______                _______     
#n   _______         _______             _______     
#e   _______         _______            _______     
EXERCISE
18
The electron cloud that surrounded the nucleus is divided into 7 shells (a.k.a energy level)
 K (1st shell, closest to nucleus) followed by L, M, N, O, P, Q.
Each of the shell, hold a limited no. of electrons. 
 E.g : K (2 electrons), L (8 electrons), M (18 electrons), N (32 electrons).
3rd shell
4th shell
2nd shell
1st shell
K (2 electrons)
L (8 electrons)
M (18 electrons)
N (32 electrons)
ELECTRON SHELLS
• Within each shell, the electrons occupy sub shell (energy sublevels)
– s, p, d, f, g, h, i. Each sub shell holds a different types of orbital.
• Each orbital holds a max. of 2 electrons.
• Each orbital has a characteristic energy state and characteristic shape.
• s - orbital
–Spherical shape
–Located closest to nucleus (first energy level)
–Max 2 electrons
• p - orbital
- There is 3 distinct p - orbitals (px, py, pz)
- Dumbbell shape
- Second energy level
- 6 electrons
ORBITAL
20
d- orbital
- There is 5 distinct d – orbitals
- Max 10 electrons
- Third energy level
Table : The number of available electron states in some of the electrons
shells and subshells.
The max. no. of electrons that can occupy a specific shell can be found
using the following formula:
Electron Capacity = 2n2
• The following representation is used :
• Example: it means that there are two electrons in the ‘s’ orbital of the
first energy level. The element is helium.
ELECTRON CONFIGURATIONS
Electron configuration – the ways in which electrons are arranged
around the nucleus of atoms. The following representation is used :
1s2
Energy level @
Principal
quantum no.
Orbital
No. of electrons
in the orbital
Based on the Aufbau principle, which assumes that electrons
enter orbital of lowest energy first.
The electrons in their orbital are represented as follows :
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f146d107p6
The sequence of addition of the
electrons as the atomic number
increases is as follows with the
first being the shell number the
s, p, d or f being the type of
subshell, the last number being
the number of electrons in the
subshell.
24
e-e- e-
2nd shell
(energy
level)
Lithium (3 electrons)
How to Write the  Electron Configuration of the Element?
e-e- e- e-
e-
e-
e-
e-
e-
3rd shell
(energy
level)
Magnesium (12 electrons)
e-
e-
e-
25
Exercise: Electron Configurations
Atom Symbol Atomic Number Electron configuration
Hydrogen H
Helium He
Lithium Li
Beryllium Be
Chlorine Cl
Argon Ar
Potasium K
Calcium Ca
TRANSITION ELEMENT 
Cr [Z = 24] 1s2 2s2 2p6 3s2 3p6 4s1 3d5 (correct) halfly filled
Mo [Z = 42] … 5s1 4d5 (correct) halfly filled
Cu [Z = 29] 1s2 2s2 2p6 3s2 3p6 4s1 3d10 (correct) completely filled
Ag [Z = 47] … 5s1 4d10 (correct) completely filled
Au [Z = 79] …6s1 5d10 (correct) completely filled
Exercise
Write the electron configuration for below element.
a) K
b) K1+
c) Fe
d) Fe3+
1s2 2s2    2p6    3s2    3p6    4s2    3d10   4p6 5s2    4d10    5p6    6s2   
4f14     5d10 6p6     7s2    5f14    6d10 7p6
Answer: TEST 1 [July 2011]
1a] With the aid of sketches, describe the Bohr Model of the 
sodium [Na] and its ion in terms of valence electron , number of 
electron and shell.
[4 marks]
1.2 INTERATOMIC BONDING AMORPHOUS
AND CRYSTALLINE SOLID
2) Secondary Atomic Bonding
Van der Waals
1) Primary Interatomic Bonding
Metallic, ionic and covalent
• The forces of attraction that hold atoms together are called chemical bonds which can 
be divided into 2 categories :
• Chemical reactions between elements involve either the releasing/receiving or sharing of 
electrons .
How is ionic bonding formed??
30
1) IONIC BONDING
PRIMARY INTERATOMIC BONDING
•Often found in compounds composed of electropositive 
elements (metals) and electronegative elements (non metals)
•Electron are transferred to form a bond
•Large difference in electronegativity required 
• Example: NaCl
• Properties :
 Solid at room temperature (made of ions)
 High melting and boiling points
 Hard and brittle
 Poor conductors of electricity in solid state
 Good conductor in solution or when molten
IONIC BONDING
• Predominant bonding in Ceramics
Give up electrons Acquire electrons
He
-
Ne
-
Ar
-
Kr
-
Xe
-
Rn
-
F
4.0
Cl
3.0
Br
2.8
I
2.5
At
2.2
Li
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Fr
0.7
H
2.1
Be
1.5
Mg
1.2
Ca
1.0
Sr
1.0
Ba
0.9
Ra
0.9
Ti
1.5
Cr
1.6
Fe
1.8
Ni
1.8
Zn
1.8
As
2.0
CsCl
MgO
CaF2
NaCl
O
3.5
EXAMPLE : IONIC BONDING
Exercise : Final Exam [April 2008]
1c] With the aid of sketches, describe how Sodium and Chlorine 
atoms are joined.
[3 marks]
EXERCISE
Draw the following ionic bonding?
IONIC BONDING :
Group 1 metal + Group 7 non metal, eg : NaCl
Group 2 metal + Group 7 non metal, eg : MgF₂, BeF₂, MgBr₂, CaCl₂ or CaI₂
Group 2 metal + Group 6 non metal, eg : CaO, MgO, MgS, or CaS
• Electrons are  shared to form a bond. 
• Most frequently occurs between atoms with similar electronegativities. 
• Often found in:
2) COVALENT BONDING
How is covalent bonding formed??
• Molecules with nonmetals
• Molecules with metals and nonmetals
(Aluminum phosphide (AlP)
• Elemental solids (diamond, silicon, germanium)
• Compound solids (about column IVA)
(gallium arsenide - GaAs, indium antimonide - InSb
and silicone carbide - SiC)
• Nonmetallic elemental molecules (H₂, Cl₂, F₂, etc)
Properties
• Gases, liquids, or solids (made of molecules)
• Poor electrical conductors in all phases
• Variable ( hard , strong, melting temperature, boiling point)
2) COVALENT BONDING
• Molecules with nonmetals
• Molecules with metals and nonmetals
• Elemental solids
• Compound solids (about column IVA)
He
-
Ne
-
Ar
-
Kr
-
Xe
-
Rn
-
F
4.0
Cl
3.0
Br
2.8
I
2.5
At
2.2
Li
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Fr
0.7
H
2.1
Be
1.5
Mg
1.2
Ca
1.0
Sr
1.0
Ba
0.9
Ra
0.9
Ti
1.5
Cr
1.6
Fe
1.8
Ni
1.8
Zn
1.8
As
2.0
SiC
C(diamond)
H2O
C
2.5
H2
Cl2
F2
Si
1.8
Ga
1.6
GaAs
Ge
1.8
O
2.0
columnIVA
Sn
1.8
Pb
1.8
EXAMPLE : COVALENT BONDING
Draw the following covalent bonding?
SINGLE BOND :
Hydrogen
Fluorine
Water
DOUBLE BOND :
Oxygen
TRIPLE BOND :
Nitrogen
EXERCISE
• Occur when some electrons in the valence shell separate
from their atoms and exist in a cloud surrounding all the
positively charged atoms.
• The valence electron form a ‘sea of electron’.
• Found for group IA and IIA elements.
• Found for all elemental metals and its alloy.
3) METALLIC BONDING
How is metallic bonding formed??
3) METALLIC BONDING
42
Properties:
 Good electrical conductivity
 Good heat conductivity
 Ductile
 Opaque
3) METALLIC BONDING
Explain why are metals ductile and can conduct 
electricity?
• Arise from atomic or molecular dipoles
VAN DER WAALS
SECONDARY INTERATOMIC BONDING
• Three bonding mechanism 
– Fluctuating Induced Dipole Bonds
• Eg: Inert gases, symmetric molecules (H2, Cl2)
– Polar molecule‐Induced Dipole Bonds
• Asymmetrical molecules such as HCl, HF
– Permanent Dipole Bonds
• Hydrogen bonding
• Between molecules  
• H‐F, H‐O, H‐N
• Molecule is considered the smallest particle of a pure 
chemical substance that still retains its composition 
and chemical properties.
• Most common molecules are bound together by 
strong covalent bonds.
• E.g. : F2, O2, H2.
• The smallest molecule : Hydrogen molecule .
MOLECULE
48
Summary of BONDING
* Directional bonding       – Strength of bond is not equal in all directions
* Nondirectional bonding – Strength of bond is equal in all directions
Type Bond energy Melting point Hardness Conductivity Comments
Ionic
bonding
Large
(150-370kcal/mol)
Very high Hard and
brittle
Poor
-required
moving ion
Nondirectional
(ceramic)
Covalent
bonding
Variable
(75-300 kcal/mol)
Large -Diamond
Small – Bismuth
Variable
Highest –
diamond
(>3550)
Mercury (-39)
Very hard
(diamond)
Poor Directional
(Semiconductors,
ceramic, polymer
chains)
Metallic
bonding
Variable
(25-200 kcal/mol)
Large- Tungsten
Small- Mercury
Low to high Soft to hard Excellent Nondirectional
(metal)
Secondary
bonding
Smallest Low to
moderate
Fairly soft Poor Directional
inter-chain
(polymer)
inter-molecular
Ceramics
(Ionic & covalent bonding):
Metals
(Metallic bonding):
Polymers
(Covalent & Secondary):
secondary bonding
Large bond energy
large Tm
large E
small 
Variable bond energy
moderate Tm
moderate E
moderate 
Directional Properties
Secondary bonding dominates
small T
small E
large 
SUMMARY : PRIMARY BONDING
Exercise : Final Exam [March 2002]
1a] Briefly describe differences between metallic bond and covalent bond.
Support your answer with an example and simple sketch.
(7 Marks)
1.3 CRYSTAL STRUCTURE
1.3 CRYSTAL STRUCTURE
Crystal
structure
Crystalline
Material
Single Crystal polycrystal
Noncrsytalline
material
(Amorphous)
* comprised of many single
crystal or grain
• atoms pack in periodic, 3D arrays
• typical of:
Crystalline materials...
-metals
-many ceramics
-some polymers
• atoms have no periodic packing
• occurs for:
Noncrystalline materials...
-complex structures
-rapid cooling
Si Oxygen
crystalline SiO2
noncrystalline SiO2
"Amorphous" = Noncrystalline
•No recognizable long-
range order
•Completely ordered
•In segments
•Entire solid is made up
of atoms in an orderly
array
Amorphous
Polycrystalline
Crystal
•Atoms are disordered
•No lattice
•All atoms arranged on
a common lattice
•Different lattice
orientation for each
grain
Structure of SOLID
• Some engineering applications require single crystals:
--turbine blades
The single crystal turbine blades
are able to operate at a higher
working temperature than
crystalline turbine blade and thus
are able to increase the thermal
efficiency of the gas turbine cycle.
• Most engineering materials are polycrystals.
grain
1a] With the aid of sketches, explain the following terms :
i. Crystalline materials
ii. Amorphous materials
iii. Single crystalline
iv. Polycrystalline
[8 marks]
QUESTION : FINAL EXAM [OCT 2012]
59
Lattice (lines network in 3D) + Motif (atoms are arranged in a repeated pattern)
= CRYSTAL STRUCTURE
Most metals exhibit a crystal structure which show a unique arrangement of atoms
in a crystal.
A lattice and motif help to illustrate the crystal structure.
CRYSTAL STRUCTURE
lattice motif crystal structure
=+
Lattice - The three
dimensional array
formed by the unit cells
of a crystal is called
lattice.
Unit Cell - When a solid
has a crystalline
structure, the atoms are
arranged in repeating
structures called unit
cells. The unit cell is the
smallest unit
that demonstrate the full
symmetry of a crystal.
A crystal is a three-
dimensional repeating
array.
+
=
61
Fig. : The crystal structure (a) Part of the space lattice for natrium chloride (b)Unit cell for natrium
chloride crystal
Unit cell - a tiny box that
describe the crystal structure.
•Crystal structure may be present with any of the
four types of atomic bonding.
•The atoms in a crystal structure are arranged
along crystallographic planes which are designated
by the Miller indices numbering system.
•The crystallographic planes and Miller indices are
identified by X-ray diffraction.
Fig. : The wavelength of the X-ray is
similar to the atomic spacing in crystals.
62
BRAVAIS LATTICE - describe the geometric arrangement of the lattice points and
the translational symmetry of the crystal.
CRYSTAL SYSTEM AND CRYSTALLOGRAPHY
cubic, hexagonal,
tetragonal,
rhombodhedral,
orthorhombic, monoclinic,
triclinic.
•7 crystal systems :
•By adding additional
lattice point to 7 basic
crystal systems –
form 14 Bravais
lattice.
Crystal Structure of Metals
• Simple Cubic (SC) ‐ Manganese
• Body‐centered cubic (BCC) ‐ alpha iron, chromium, molybdenum, tantalum, 
tungsten, and vanadium.
• Face‐centered cubic (FCC) ‐ gamma iron, aluminum, copper, nickel, lead, silver, 
gold and platinum.
Common crystal structures for metals:
FCCSC BCC
64
SIMPLE CUBIC (SC)
• The atoms lie on a grid: layers of rows and 
columns.
• Sit at the corners of stacked cubic
No. of atom at corner
= 8 x 1/8 = 1 atom
Total No. of atom in
one unit cell
= 1 atom
Example : Manganese
Body‐centered Cubic Crystal 
Structure
The body-centered cubic (bcc) crystal structure:
(a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
66
BODY CENTERED CUBIC STRUCTURE (BCC)
• Cubic unit cell with 8 atoms located at the corner & single atom at cube
center
Example : Chromium, Tungsten,Molybdenum,Tantalum, Vanadium
No. of atom at corner = 8 x 1/8 = 1 atom
No. of atom at center = 1 atom
Total No. of atom in one unit cell = 2 atoms
Face‐centered Cubic Crystal 
Structure
The face-centered cubic (fcc) crystal structure:
(a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
68
FACE CENTERED CUBIC STRUCTURE (FCC)
Atoms are located at each of the corners and the centers of all the
cube faces. Each corner atom is shared among 8 unit cells,face
centered atom belong to 2.
Example : Cu,Al,Ag,Au, Ni, PtNo. of atom at corner
= 8 x 1/8 = 1 atom
No. of atom at face
= 6 x 12 = 3 atoms
Total No. of atom in
one unit cell
= 4 atoms
69
1.4 EFFICIENCY OF ATOMIC
PACKING,DENSITY COMPUTATION
AND MILLER INDEX
70
APF = no. of atom, n x volume of atoms in the unit cell, (Vs)
volume of the unit cell, (Vc)
ATOMIC PACKING FACTOR
•Atomic packing factor (APF) is defined as the efficiency of atomic arrangement
in a unit cell.
•It is used to determine the most dense arrangement of atoms. It is because how
the atoms are arranged determines the properties of the particular crystal.
•In APF, atoms are assumed closely packed and are treated as hard spheres.
•It is represented mathematically by :
71
close-packed directions
a
R=0.5a
contains 8 x 1/8 =
1 atom/unit cell
EXAMPLE
Calculate the APF for Simple Cubic (SC)?
72
EXERCISE
a) BCC b) FCC
Calculate the APF for BCC and FCC ?
73
a (lattice constant) and
R (atom radius)
Atoms/unit
cell
Packing
Density
(APF)
Examples
Simple
cubic a = 2R
1 52% CsCl
BCC
a = 4R/√3
2 68% Many metals:
α-Fe, Cr, Mo, W
FCC
a = 4R/√2
4 74% Many metals : Ag,
Au, Cu, Pt
Table : APF for simple cubic, BCC, FCC and HCP
74
1a] Give the definition of a unit cell. Briefly describe lattice constant in the unit cell.
[ 4 marks]
1b] Give the definition of APF for a unit cell and calculate the APF for FCC.
[4 marks]
QUESTION : FINAL EXAM [Oct 2010]
75
DENSITY COMPUTATIONS
• A knowledge of the crystal structure of a metallic 
solid permits computation of its density through the 
relationship :
Where
ρ = n A
Vc NA
n = number of atoms associated with each unit cell
A = atomic weight
Vc = volume of the unit cell
NA = Avogadro’s number (6.023 x 1023 atoms/mol)
76
Calculate the density for nickel (simple cubic structure).
Note that the unit cell edge length (a) for nickel is 0.3524 nm.
EXAMPLE
77
Copper has an atomic radius of 0.128 nm, FCC crystal structure and an atomic
weight of 63.5 g/mol. Compute its density and compare the answer with its
measured density.
EXERCISE
Element Symbol Atomic
weight
(amu)
Density of
solid, 20oC
(g/cm3)
Crystal
Structure,
20oC
Atomic
radius
(nm)
Copper Cu 63.55 8.94 FCC 0.128
78
1b] Platinum has a FCC structure, a lattice parameter of 0.393 nm and an atomic weight
of 195.09 g/mol. Determine :
i. Atomic radius [in cm]
ii. Density of platinum
[ 6marks]
QUESTION : TEST 1 [August 2012]
79
Miller indices is used to label the planes and directions of atoms in a crystal.
Why Miller indices is important?
To determine the shapes of single crystals, the interpretation of X-ray
diffraction patterns and the movement of a dislocation , which may determine
the mechanical properties of the material.
MILLER INDICES
Miller indices
• (h k l) : a specific crystal plane or face
• {h k l} : a family of equivalent planes
• [h k l] : a specific crystal direction
• <h k l> : a family of equivalent directions
Figure : Planes of the form {110} in cubic systems
80
POINT COORDINATES
- The position of any point located within a unit cell may be
specified in terms of its coordinates (x,y,z)
z
y
x
Example : BCC structure
Point
Number x axis y-axis z-axis
Point
Coordinated
1
2
3
4
5
6
7
8
9
81
MILLER INDICES OF A DIRECTION
How to determine crystal direction indices?
i) Determine the length of the vector
projection on each of the three axes,
based on .
ii) These three numbers are expressed as the
smallest integers and negative quantities
are indicated with an overbar.
iii) Label the direction [hkl]. Figure : Examples of direction
Axis X Y Z
Head (H) x2 y2 z2
Tail (T) x1 y1 z1
Head (H) –Tail (T) x2-x1 y2-y1 z2-z1
Reduction (if necessary)
Enclosed [h k l]
* No reciprocal involved.
82
EXAMPLE : CRYSTAL DIRECTION INDICES
0,0,0
1,1,01
1
1,0,0
0,1,0
83
EXERCISE : CRYSTAL DIRECTION INDICES
0½
1
1
0
1
1
1
1
84
EXERCISE : CRYSTAL DIRECTION INDICES
0
½
0
¾
½
½
½
Determine the direction indices of the cubic
direction between the position coordinates
TAIL (3/4, 0, 1/4) and HEAD (1/4, 1/2, 1/2)?
Draw the following Miller Indices
direction.
a) [ 1 0 0 ]
b) [ 1 1 1 ]
c) [ 1 1 0 ]
d) [ 1 1 0 ]
87
i) Determine the points at which a given crystal plane
intersects the three axes, say at (a,0,0),(0,b,0), and (0,0,c). If
the plane is parallel an axis, it is given an intersection ∞.
ii) Take the reciprocals of the three integers found in step (i).
iii) Label the plane (hkl). These three numbers are expressed
as the smallest integers and negative quantities are indicated
with an overbar,e.g : a.
MILLER INDICES OF A PLANE
How to determine crystal plane indices?
Figure : Planes with different Miller
indices in cubic crystals
Axis X Y Z
Interceptions
Reciprocals
Reduction (if necessary)
Enclosed (h k l )
+x
+y
+z
_
z
_
y
_
x
(1 , 0 , 0)
(0 , 1 , 0)
(0 , 0 , 1)
_
(0 , 0 , 1)
_
(0 , 1 , 0)
_
(1 , 0 , 0)
89
EXERCISE. : CRYSTAL PLANE INDICES
EXERCISE. : CRYSTAL PLANE INDICES
0
EXERCISE. : CRYSTAL PLANE INDICES
½
Determine the Miller Indices plane for the
following figure below?
Draw the following Miller Indices
plane.
a) ( 1 0 0 )
b) ( 0 0 1 )
c) ( 1 0 1 )
d) ( 1 1 0 )
94
NOTE (for plane and direction):
• PLANE
Make sure you enclosed your final answer in brackets (…) with no
separating commas → (hkl)
• DIRECTION
Make sure you enclosed your final answer in brackets (…) with no
separating commas → [hkl]
• FOR BOTH PLANE AND DIRECTION
Negative number should be written as follows :
-1 (WRONG)
1 (CORRECT)
Final answer for labeling the plane and direction should not have fraction
number do a reduction.
95
1.5 RELATIONSHIP BETWEEN
ATOMIC STRUCTURE, CRYSTAL
STRUCTURES AND PROPERTIES OF
MATERIALS
96
PHYSICAL PROPERTIES OF METALS
•Solid at room temperature (mercury is an exception)
•Opaque
•Conducts heat and electricity
•Reflects light when polished
•Expands when heated, contracts when cooled
•It usually has a crystalline structure
Physical properties are the characteristic responses of materials to
forms of energy such as heat, light, electricity and magnetism.
The physical properties of metals can be easily explained as follows :
Mechanical Properties
 Terminology for Mechanical Properties
 The Tensile Test: Stress‐Strain Diagram
 Properties Obtained from a Tensile Test
 Hardness of Materials
98
MECHANICAL PROPERTIES OF METALS
Mechanical properties are the characteristic dimensional changes in response to
applied external or internal mechanical forces such as shear strength, toughness,
stiffness etc.
The mechanical properties of metals can be easily explained as follows :
99
Tensile Test
specimen
machine
100
Tensile Test
Terminology
 Load ‐ The force applied to a material during testing.
 Strain gage or Extensometer ‐ A device used for 
measuring change in length (strain).
 Engineering stress ‐ The applied load, or force, 
divided by the original cross‐sectional area of the 
material.
 Engineering strain ‐ The amount that a material 
deforms per unit length in a tensile test.
Stress-Strain Diagram
Strain ( ) (L/Lo)
4
1
2
3
5
Elastic
Region
Plastic
Region
Strain
Hardening Fracture
ultimate
tensile
strength
Elastic region
slope =Young’s (elastic) modulus
yield strength
Plastic region
ultimate tensile strength
strain hardening
fracture
necking
yield
strength
UTS
y
εEσ 
ε
σ
E 

12
y
εε
σ
E


Stress-Strain Diagram (cont)
• Elastic Region (Point 1 –2)
- The material will return to its original shape
after the material is unloaded( like a rubber band).
- The stress is linearly proportional to the strain in
this region.
εEσ 
: Stress(psi)
E : Elastic modulus (Young’s Modulus) (psi)
: Strain (in/in)
σ
ε
- Point 2 : Yield Strength : a point where permanent
deformation occurs. ( If it is passed, the material will
no longer return to its original length.)
ε
σ
E or
• Strain Hardening
- If the material is loaded again from Point 4, the
curve will follow back to Point 3 with the same
Elastic Modulus (slope).
- The material now has a higher yield strength of
Point 4.
- Raising the yield strength by permanently straining
the material is called Strain Hardening.
Stress-Strain Diagram (cont)
• Tensile Strength (Point 3)
- The largest value of stress on the diagram is called
Tensile Strength(TS) or Ultimate Tensile Strength
(UTS)
- It is the maximum stress which the material can
support without breaking.
• Fracture (Point 5)
- If the material is stretched beyond Point 3, the stress
decreases as necking and non-uniform deformation
occur.
- Fracture will finally occur at Point 5.
Stress-Strain Diagram (cont)
Figure : Stress strain diagram
Typical regions that can
be observed in a stress-
strain curve are:
• Elastic region
• Yielding
• Strain Hardening
• Necking and Failure
• This diagram is used to determine how material will react under a certain load.
107
108
Important Mechanical Properties
from a Tensile Test 
• Young's Modulus: This is the slope of the linear portion 
of the stress‐strain curve, it is usually specific to each 
material; a constant, known value. 
• Yield Strength: This is the value of stress at the yield 
point, calculated by plotting young's modulus at a 
specified percent of offset (usually offset = 0.2%). 
• Ultimate Tensile Strength: This is the highest value of 
stress on the stress‐strain curve. 
• Percent Elongation: This is the change in gauge length 
divided by the original gauge length. 
The stress-strain curve for an aluminum alloy.
1100.2
8
0.6
1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
Graphite
Si crystal
Glass-soda
Concrete
Si nitride
Al oxide
PC
Wood( grain)
AFRE( fibers)*
CFRE*
GFRE*
Glass fibers only
Carbon fibers only
Aramid fibers only
Epoxy only
0.4
0.8
2
4
6
10
20
40
60
80
100
200
600
800
1000
1200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PS
PET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers
Composites
/fibers
E(GPa)
Eceramics
> Emetals
>> Epolymers
109 Pa Composite data based on
reinforced epoxy with 60 vol%
of aligned carbon (CFRE),
aramid (AFRE), or glass (GFRE)
fibers.
Young’s Moduli: Comparison
111
T
E
N
S
I
L
E
P
R
O
P
E
R
T
I
E
S
112
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yieldstrength,y(MPa)
PVC
Hardtomeasure,
sinceintension,fractureusuallyoccursbeforeyield.
Nylon 6,6
LDPE
70
20
40
60
50
100
10
30
200
300
400
500
600
700
1000
2000
Tin (pure)
Al (6061)a
Al (6061)ag
Cu (71500)hr
Ta (pure)
Ti (pure)a
Steel (1020)hr
Steel (1020)cd
Steel (4140)a
Steel (4140)qt
Ti (5Al-2.5Sn)a
W (pure)
Mo (pure)
Cu (71500)cw
Hardtomeasure,
inceramicmatrixandepoxymatrixcomposites,since
intension,fractureusuallyoccursbeforeyield.
HDPE
PP
humid
dry
PC
PET
¨
Room T values
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength: Comparison
113
tensile stress, 
engineering strain, 
y
p = 0.002
Yield Strength, y
tensile stress, 
engineering strain, 
Elastic
initially
Elastic+Plastic
at larger stress
permanent (plastic)
after load is removed
p
plastic strain
114
F

bonds
stretch
return to
initial
1. Initial 2. Small load 3. Unload
F

Linear-
elastic
Non-Linear-
elastic
Elastic Deformation
• Atomic bonds are stretched but not
broken.
• Once the forces are no longer
applied, the object returns to its
original shape.
• Elastic means reversible.
115
Typical stress-strain
behavior for a metal
showing elastic and
plastic deformations,
the proportional limit P
and the yield strength
σy, as determined
using the 0.002 strain
offset method (where there
is noticeable plastic deformation).
P is the gradual elastic
to plastic transition.
116
1. Initial 2. Small load 3. Unload
.
F

linear
elastic
linear
elastic
plastic
planes
still
sheared
F
elastic + plastic
bonds
stretch
& planes
shear
plastic
Plastic Deformation (Metals)
• Atomic bonds are broken and new
bonds are created.
• Plastic means permanent.
117
Permanent Deformation
• Permanent deformation for metals is
accomplished by means of a process called
slip, which involves the motion of
dislocations.
• Most structures are designed to ensure that
only elastic deformation results when stress
is applied.
• A structure that has plastically deformed, or
experienced a permanent change in shape,
may not be capable of functioning as
intended.
118
• After yielding, the stress necessary to 
continue plastic deformation in metals 
increases to a maximum point (M) and 
then decreases to the eventual fracture 
point (F).
• All deformation up to the maximum 
stress is uniform throughout the tensile 
sample. 
• However, at max stress, a small 
constriction or neck begins to form.
• Subsequent deformation will be confined 
to this neck area.
• Fracture strength corresponds to the 
stress at fracture. 
Region between M and F:
• Metals: occurs when noticeable necking starts.
•  Ceramics: occurs when crack propagation starts.
•  Polymers: occurs when polymer backbones are aligned and about to break.
Tensile Strength, TS
119
In an undeformed
thermoplastic polymer 
tensile sample, 
(a) the polymer chains are 
randomly oriented. 
(b) When a stress is 
applied, a neck 
develops as chains 
become aligned locally.  
The neck continues to 
grow until the chains 
in the entire gage 
length have aligned. 
(c) The strength of the 
polymer is increased
120
Room T values
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensilestrength,TS(MPa)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure)a
Steel (1020)
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Cu (71500) cw
LDPE
PP
PC PET
20
30
40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride
HDPE
wood ( fiber)
wood(|| fiber)
1
GFRE(|| fiber)
GFRE( fiber)
CFRE(|| fiber)
CFRE( fiber)
AFRE(|| fiber)
AFRE( fiber)
E-glass fib
C fibers
Aramid fib
Based on data in Table B4, Callister 6e.
a     = annealed
hr   = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt   = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber‐reinforced epoxy
composites, with 60 vol%
fibers.
Tensile Strength: Comparison
121
• Tensile stress, : • Shear stress, :
Area, A
Ft
Ft
 
Ft
Ao
original area
before loading
Area, A
Ft
Ft
Fs
F
F
Fs
 
Fs
Ao
Stress has units: N/m2 or lb/in2
Engineering Stress
122
VMSE
http://www.wiley.com/college/callister/0470125373/vmse/strstr.htm
http://www.wiley.com/college/callister/0470125373/vmse/index.htm
123
Engineering tensile strain, 
Engineering
tensile
stress, 
smaller %EL
(brittle if %EL<5%)
larger %EL
(ductile if
%EL>5%)
• Another ductility measure: 100% x
A
AA
AR
o
fo 

•  Ductility may be expressed as either percent elongation (% plastic strain at fracture) 
or percent reduction in area.
• %AR > %EL is possible if internal voids form in neck. 
Lo Lf
Ao
Af
100% x
l
ll
EL
o
of 

Ductility, %EL
Ductility is a measure of the plastic 
deformation that has been sustained at 
fracture:
A material that 
suffers very 
little plastic 
deformation is 
brittle.
124
Toughness
Lower toughness: ceramics
Higher toughness: metals
Toughness is
the ability to
absorb
energy up to
fracture (energy
per unit volume of
material).
A “tough”
material has
strength and
ductility.
Approximated
by the area
under the
stress-strain
curve.
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve.
21
smaller toughness-
unreinforced
polymers
Engineering tensile strain, 
Engineering
tensile
stress, 
smaller toughness (ceramics)
larger toughness
(metals, PMCs)
Toughness
126
Linear Elastic Properties
Modulus of Elasticity, E:
(Young's modulus)
• Hooke's Law:  = E 
• Poisson's ratio:
metals:  ~ 0.33
ceramics:  ~0.25
polymers:  ~0.40

Linear-
elastic
1
E

Units:
E: [GPa] or [psi]
: dimensionless
F
F
simple
tension
test
xy
127
Engineering Strain
Strain is dimensionless.
128
Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in 
response to an imposed tensile stress. 
True Stress and True Strain
 True stress The load divided by the actual cross-sectional
area of the specimen at that load.
 True strain The strain calculated using actual and not
original dimensions, given by εt ln(l/l0).
•The relation between the true stress‐true 
strain diagram and engineering stress‐
engineering strain diagram.  
•The curves are identical to the yield point.
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
The stress-strain behavior of brittle materials compared with
that of more ductile materials
131
‐‐brittle response (aligned chain, cross linked & networked case)
‐‐plastic response (semi‐crystalline case) 
Stress-Strain Behavior: Elastomers
3 different responses:
A – brittle failure
B – plastic failure
C ‐ highly elastic (elastomer)
initial: amorphous chains are
kinked, heavily cross-linked.
final: chains
are straight,
still
cross-linked
0
20
40
60
0 2 4 6
(MPa)
 8
x
x
x
elastomer
plastic failure
brittle failure
Deformation
is reversible!
132
Stress-Strain Results for Steel
Sample
133
Metals can fail by brittle or ductile fracture.
FRACTURE MECHANISM OF METALS
Ductile fracture is better than brittle fracture because :
Ductile fracture occurs over a period of time, where as brittle fracture is fast
and can occur (with flaws) at lower stress levels than a ductile fracture.
Figure : Stress strain curve for brittle and ductile material
Ductile Vs Brittle Fracture
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
• Localized deformation of a ductile material during a tensile test produces a
necked region.
• The image shows necked region in a fractured sample
Ductile Fracture
136
1c] Ductility is one of the important mechanical properties.
i] Define the ductility of a metal.
ii] With the aid of schematic diagrams, describe elastic and plastic deformations.
[6 marks]
QUESTION : FINAL EXAM [April 2011]
Ductile fracture Brittle fracture
What are the differences between
ductile fracture & brittle fracture?
Hardness of Materials
 Hardness test - Measures the resistance of a material to
penetration by a sharp object.
 Macrohardness - Overall bulk hardness of materials
measured using loads >2 N.
 Microhardness Hardness of materials typically measured
using loads less than 2 N using such test as Knoop
(HK).
 Nano-hardness - Hardness of materials measured at 1–
10 nm length scale using extremely small (~100 µN)
forces.
139
Hardness
• Hardness is a measure of a material’s resistance
to localized plastic deformation (a small dent or
scratch).
• Quantitative hardness techniques have been
developed where a small indenter is forced into
the surface of a material.
• The depth or size of the indentation is measured,
and corresponds to a hardness number.
• The softer the material, the larger and deeper the
indentation (and lower hardness number).
140
•  Resistance to permanently indenting the surface.
•  Large hardness means:
‐‐resistance to plastic deformation or cracking in
compression.
‐‐better wear properties.
e.g.,
10mm sphere
apply known force
(1 to 1000g)
measure size
of indent after
removing load
dD
Smaller indents
mean larger
hardness.
increasing hardness
most
plastics
brasses
Al alloys
easy to machine
steels file hard
cutting
tools
nitrided
steels diamond
Hardness
141
Hardness Testers
Hardness Testers
Indentation Geometry for Brinnel 
Testing
Figure Indentation geometry in
Brinell hardness testing: (a)
annealed metal; (b) work-
hardened metal; (c) deformation
of mild steel under a spherical
indenter. Note that the depth of
the permanently deformed zone
is about one order of magnitude
larger that the depth of
indentation. For a hardness test
to be valid, this zone should be
developed fully in the material.
Hardness 
Scale 
Conversions
Figure Chart for converting
various hardness scales. Note
the limited range of most scales.
Because of the many factors
involved, these conversions are
approximate.
146
Conversion of 
Hardness Scales
Also see: ASTM E140 - 07
Volume 03.01
Standard Hardness Conversion
Tables for Metals Relationship
Among Brinell Hardness, Vickers
Hardness, Rockwell Hardness,
Superficial Hardness, Knoop
Hardness, and Scleroscope
Hardness
147
Correlation 
between 
Hardness and 
Tensile 
Strength
• Both hardness and tensile
strength are indicators of
a metal’s resistance to
plastic deformation.
• For cast iron, steel and
brass, the two are roughly
proportional.
• Tensile strength (psi) =
500*BHR
148
1c] Hardness is one of the important mechanical properties
in engineering. Describe FOUR [4] types of hardness
measurement method in terms of name and types of
indenter.
[ 4 marks]
QUESTION : FINAL EXAM [Oct 2012]
149
•  Stress and strain:  These are size‐independent
measures of load and displacement, respectively.
•  Elastic behavior:  This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
•  Plastic behavior:  This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches y.
•  Toughness:  The energy needed to break a unit
volume of material.
•  Ductility:  The plastic strain at failure.
Summary
CHAPTER 2
METALLIC MATERIALS
(14 hours) 
1
CONTENTS
2.1 Solidification of Pure Metal and Alloys
2.2 Phase diagram: Microstructure development, 
Microconstituent of phases.
2.3 Fe‐Fe3C system: Microstructure development, 
Microconstituent of phases.
2.4 Ferrous and Non‐Ferrous Metals
2
2.1 Solidification of Pure Metal 
and Alloys
3
2.1 Solidification of Pure Metal and Alloys
• Terminology
• Solution
– Metal Solid Solution
– Type of Solid Solution
• Substitutional Solid Solution
• Interstitial Solid Solution
– The Solubility Limit
• Solidification
4
• Cooling Curve
– Cooling Curve of Pure Metal
– Cooling Curve of Alloys
– Development  of Phase 
Diagram
– Cooling Curve for Binary 
Isomorphous
LEARNING OBJECTIVE
Students should be able to :
• Understand the phase transformation during 
solidification process.
• Differentiate between cooling curve for pure 
metal and alloys.
5
6
Solvent
In an alloy, the element or compound present in greater amount.
Solute
In an alloy, the element or compound present in lesser amount.
Solution
When two components combine to form a single phase.
Solubility
Degree to which the two components mix.
Solubility limit
The max. concentration of solute that may be added without forming
a new phase.
TERMINOLOGY
Components:
The elements or compounds which are mixed initially
(e.g., Al and Cu)
Phases:
The physically and chemically distinct material regions
that result (e.g.,  and ).
Example :
Liquid
L (liquid) + α (alpha-solid)
Aluminum-Copper Alloy
(darker
phase)
 (lighter
phase)
TERMINOLOGY
* Note that solid, gas and liquid is a phase. 7
SOLUTION
• When 2 components combined they can 
either remain separate or combine to form 
a single phase which is referred to as a 
solution.
• i.e.
– Alcohol and water – completely soluble
– Hot choc – powder mix soluble in water but 
limited extent
– Oil and vinegar – insoluble liquids can be 
temporarily mixed
8
9
• Most metals are combined to form alloy in order to impart 
specific characteristic.
• An alloy is a combination of two or more elements (added 
impurity atoms), at least one of which is a metal.
• The addition of impurity atoms to a metal will result in the 
formation of a solid solution.
• A solid solution is a solid‐state solution of one or more 
solutes in a solvent. 
• E.g : Steel/Cast Iron (Iron base alloys), 
Bronze/Brass (Copper base alloys), 
Al alloys, Ni base alloys, Mg base alloys, Ti alloys.
METALLIC SOLID SOLUTION
10
Characteristic of solid solution:
• Form when solute atoms are added to the host material.
• Crystal structure is maintained.
• No new structure formed.
• Compositionally homogeneous.
Solute
Used to denote an 
element/compound present in a 
minor concentration
Solvent
Element / compound that is 
present in the greatest amount 
(host atoms)
METALLIC SOLID SOLUTION
11
TYPES OF SOLID SOLUTION
i. Substitutional solid solution
ii. Interstitial solid solution
Known as point defects
(where an atom is missing or
is in an irregular place in the
lattice structure).
Substitutional Solid Solution
Hume -Rothery Rules
Substitutional solid solution with complete solubility exists when :
RULE     PROPERTIES CONDITIONS
1 Atomic radius Less than about ± 15% difference in   atomic radii
2 Crystal structure Same crystal structure (e.g : BCC, FCC or HCP).
3 Electronegativity Similar electronegativity/ smaller diff.
4 Valence electron Similar valance electron 
12
Note:
Not all alloys
systems that fit these rules
will form appreciable solid
solutions
Host atoms are replaced/substitute with solute/ impurity atoms.
13
EXAMPLE 1 : Cu-Ni system
• Both metals are completely soluble in each other
because all the requirement of Hume Rothery Rules
have been satisfactorily fulfilled.
• The solid phase is a substitutional solid solution.
System RULE 1
Atomic radius, R (nm)
RULE 2
Crystal structure
RULE 3
E/negativity
RULE 4
Valences
Cu
Ni
0.128
0.125
FCC
FCC
1.90
1.80
+2
+2
Substitutional Solid Solution
14
EXAMPLE 2: Cu-Ag system
• Both metals are partially soluble in each other because
one of the requirement of Hume Rothery Rules have not
been satisfactorily fulfilled.
• The solid phase is a substitutional solid solution.
System RULE 1
Atomic radius, R (nm)
RULE 2
Crystal structure
RULE 3
E/negativity
RULE 4
Valences
Cu
Ag
0.128
0.144
FCC
FCC
1.90
1.80
+2
+1
Substitutional Solid Solution
15
The atoms of the parent or
solvent metal are bigger
than the atoms of the
alloying or solute metal. In
this case, the smaller atoms
fit into spaces between the
larger atoms.
Interstitial Solid Solution exists when :
• Impurity atoms fill the voids in the solvent atom lattice.
• It interstices among the host atoms.
• Atomic diameter of an interstitial impurity must be smaller
than host atoms.
• Normal max. allowable concentration of interstitial
impurity atom is low (<10%).
Interstitial Solid Solution
• Solubility Limit: Max concentration for which only a solution
occurs.
• Question : What is the solubility limit at 20oC?
Answer :
If Co < 65wt% sugar:
If Co > 65wt% sugar:
• Solubility limit increases with T:
Ex: Phase Diagram:
Water-Sugar System
Pure
Sugar
Temperature(°C)
0 20 40 60 80 100
Co=Composition (wt% sugar)
L
(liquid solution
i.e., syrup)
Solubility
Limit L
(liquid)
+
S
(solid
sugar)
65
20
40
60
80
100
Pure
Water
THE SOLUBILITY LIMIT
16
SOLIDIFICATION OF PURE METAL
& ALLOYS
COOLING CURVE
PHASE DIAGRAM
17
SOLIDIFICATION
• Solidification is the most important phase transformation
because most of metals/alloys undergo this transformation
before becoming useful objects.
• Solidification involve liquid-solid phase transformation,
e.g : casting process.
• The solidification process differs depending on whether
the metal is a pure element or an alloy.
18
19
Liquid
Nucleus
Liquid
Grain
Grain boundaries
(means region between crystals)
Crystals growing
(irregular grain)
(a) (b) (c)
Nucleation 
of Crystals
Crystal 
Growth
Crystals Grow 
Together and Form 
Grain Boundaries
Solution
(Liquid State)
SOLIDIFICATION
Solidification of Pure Metal and Alloys
1. The formation of stable nuclei in the melt (nucleation)
2. The growth of nuclei into crystal
3. The formation of a grain structure
SOLIDIFICATION OF PURE METAL
& ALLOYS
COOLING CURVE
PHASE DIAGRAM
20
• Used to determine phase transition temperature.
• Temperature and time data of cooling molten metal is 
recorded and plotted.
• Produce a graph known as PHASE DIAGRAM which 
shows the relationship among temperature, 
composition and phases present in alloy
COOLING CURVE
21
22
A pure metal solidifies at a constant temperature
equal to its freezing point, which is the same as its
melting point.
Figure : Cooling curve for a pure metal during casting
Cooling Curve of Pure Metal
23
Most alloys freeze over a temperature range rather than at
a single temperature.
Figure : a) Phase diagram for a copper-nickel alloy system and
b) Associated cooling curve for a 50%Ni-50%Cu composition during casting
Cooling Curve of Alloys
• Series of cooling curves at different metal composition are
first constructed.
• Points of change of slope of cooling curves (thermal arrests)
are noted and phase diagram is constructed.
• More the number of cooling curves, more accurate is the
phase diagram.
Development  of Phase Diagram
24
25
• For pure metal, the cooling 
curves show horizontal 
thermal arrest at their 
freezes points, as seen for 
pure A and pure B (at AB 
and CD).
• Different composition will 
give different cooling 
curves.
• The slope changes at L1‐L9 
are correspond to the 
liquidus point.
• The slope changes at S1‐S9 
are correspond to the 
solidus points.
Freezing
zone
Cooling Curve For
Binary Isomorphous
L1
S1
A B
D
C
L9
S9
1
26
L1
S1
By removing the time axis and
replacing it with composition
get straight lines
Connection of points on a phase
diagram representing the temp. at
which each alloy in the system begins
to solidify --- obtain liquidus line
Join all the points where the liquid has
solidified is complete --- obtain solidus
line
Red regions – material is liquid
Green regions – solid and liquid
phases are in equilibrium.
Blue regions – material is solid
2
3
SOLIDIFICATION OF PURE METAL
& ALLOYS
COOLING CURVE
PHASE DIAGRAM
27
2.2 Phase diagram
Microstructure development, 
Microconstituent of phases.
28
2.2 Phase diagram: Microstructure development, 
Microconstituent of phases.
• Phase Diagram
• The Lever Rule
• Binary Phase Diagram
– Binary Isomorphous Phase Diagram
(COMPLETE SOLID SOLUTION)
– Binary Eutectic Phase Diagram
(NO SOLID SOLUTION)
– Binary Eutectic Phase Diagram
(LIMITED SOLID SOLUTION)
29
• Invariant Equilibrium
• Terminology
Learning objective:
Students should be able to:
• Schematically sketch and label the various phase 
regions for simple binary phase diagrams.
• Determine the phase(s) present, composition(s)
and relative amount of phase(s).
• Discuss the development of the microstructures, 
upon cooling, for several situations. 
• Locate the invariant point and write reaction for 
all the transformations for either heating or 
cooling.
30
31
What is PHASE DIAGRAM?
A graphical representations of what phases are present in a 
materials system at various temperature (T), pressure (P) and 
composition (C).
Why do I need to know about PHASE DIAGRAM?
1. Because there is a strong correlation between microstructure 
and mechanical properties.
2. Besides, development of alloy microstructure is related to the 
characteristics of its phase diagram.
Applications of PHASE DIAGRAM?
1. Casting
2. Soldering
PHASE DIAGRAM
32
Types of PHASE DIAGRAM?
1. Unary – Consists of One components in an alloy
2. Binary – Consists of two components in an alloy
3. Ternary‐ Consists of three components in an alloy
Example: Unary Phase Diagram
PHASE DIAGRAM
33
What do I need to know about BINARY PHASE DIAGRAM?
Definition : Consists two components in an alloy. 
Types :
1. Complete solid solution (e.g. Cu and Ni are completely soluble)
2. No solid solution (e.g. Pb insoluble in copper)
3. Limited solid solution (e.g. Sn has limited solubility in Pb)
PHASE DIAGRAM
34
There are three(3) types of binary phase diagram :
1) Complete solid
solution
2) No solid solution 2) Limited solid
solution
Alcohol and water Oil and water Pepper powder and water
−Complete solubility in
liquid and solid
- Result in single phase
- Result in multi phase −Often soluble up to limit
- Result in multi phase
Cu and Ni Pb and Copper Zinc and Copper,
Sn and Pb
BINARY PHASE DIAGRAM
35
BINARY
ISOMORPHOUS
PHASE DIAGRAM
(COMPLETE SOLID SOLUTION)
36
Isomorphous
• Complete liquid & solid solubility
• Only one solid phase forms
• Same crystal structure
Example : Cu-Ni system
• 2 phases: L (liquid), α (FCC solid solution)
• 3 different phase fields/regions
1) Liquid phase(L)
 homogeneous liquid solution (Cu + Ni)
2) Two phases
 α (FCC solid solution) + liquid (L)
3) α phase (FCC solid solution)
 substitutional solid solution (consists both Cu-Ni)
Figure : Cu-Ni system
Note that :
• Liquidus is line above which all of alloy is liquid
• Solidus is line below which all of alloy is solid
BINARY ISOMORPHOUS
PHASE DIAGRAM
37
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
wt% Ni20 40 60 80 1000
100 0
110 0
120 0
130 0
140 0
150 0
160 0
T(°C)
L (liquid)

(FCC solid
solution)
L + 
liquidus
solidus
A(1100,60)
B(1250,35)
Cu-Ni system
Some common features of
phase diagrams
 “α”,“β” and “γ” and etc. are used
to indicate solid solution
phases.
 “L” represents a liquid.
BINARY ISOMORPHOUS PHASE DIAGRAM:
# and types of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase (weight percent, wt%).
wt% Ni
20
1200
1300
T(°C)
L (liquid)

(solid)L + 
liquidus
solidus
30 40 50
TA
A
D
TD
TB
B
tie line
L + 
433532
CoCL C
Cu-Ni system
Determination of phase compositions
1. Locate the temperature.
2. If one phase present, the composition
= overall composition (Co) of alloy.
3. If two phase present, use tie line.
BINARY ISOMORPHOUS PHASE DIAGRAM:
composition of phases
38
• Sum of weight fractions:
• Conservation of mass (Ni):
• Combine above equations:
WL  W  1
Co  WLCL  WC
 R
R  S
W 
Co  CL
C  CL
 S
R  S
WL
 C  Co
C  CL
• A geometric interpretation:
Co
R S
WWL
CL C
moment equilibrium:
1 W
solving gives Lever Rule
WLR  WS
THE LEVER RULE
Let WL = fraction of liquid and Wα = fraction of solid (unknown)
39
Ask yourself ?
Larger distanceSmaller
distance
Higher mass
smaller mass
40
THE LEVER RULE
• Rule 3: If we know T and Co, then we know:
--the amount of each phase [e.g: Single phase (1.0 or 100%)].
Cu-Ni system
SR
Note
•Within single phase alloy, the alloy is completely
(100%) that phase.
•If two phase alloy exists, use Lever Rule
41
BINARY ISOMORPHOUS PHASE DIAGRAM:
weight fractions of phases
wt% Ni
20
1200
1300
T(°C)
L (liquid)

(solid)
L + 
liquidus
solidus
30 40 50
TA
A
D
TD
TB
B
tie line
L + 
433532
CoCL C
R S
42
EXAMPLE : Calculate the amounts of α and L at 1250°C in the
Cu-35% Ni alloy?
THE LEVER RULE
43
EXERCISE : Determine the relative amount on each phase in the Cu 40% Ni alloy
shown in Figure below at 1300°C, 1270°C, 1250°C and 1200°C ?
THE LEVER RULE
44
Consider Co = 35wt% Ni
Figure : Cooling of Cu-Ni alloy
Microstructure
A
B
C
D
E
BINARY ISOMORPHOUS PHASE DIAGRAM:
Microstructure
wt% Ni
20
1200
1300
30 40 50
1100
L (liquid)

(solid)
L + 
L + 
T(°C)
A
D
B
35
Co
L: 35wt%Ni
: 46wt%Ni
C
E
L: 35wt%Ni
46
43
32
24
35
36
: 43wt%Ni
L: 32wt%Ni
L: 24wt%Ni
: 36wt%Ni
45
BINARY EUTECTIC
PHASE DIAGRAM
(NO SOLID SOLUTION)
46
•Region above line ced = liquid solution
•Line ce and ed = liquidus
•Line cfegd = solidus
•Region below line feg = mixture of solid A & B
•Point e = eutectic point 
(the lowest temp. at which a liquid solution can exist)
BINARY EUTECTIC PHASE DIAGRAM
(NO SOLID SOLUTION)
Eutectic: the composition of
a mixture that has the lowest
melting point where the
phases simultaneously
crystallize from molten solution
at this temperature.
From the Greek 'eutektos',
meaning ‘easily melted’.
No solid solution where the
components are completely
soluble in the liquid state
but complete insoluble in
the solid state.
Example : Pb-Cu system
47
Determination of phase and phase composition:
Same as in binary isomorphous system.
Determination of weight fraction
Weight fraction of liquid,
WL= R/(R+Q)
Weight fraction of solid A,
WA = Q/(R+Q)
BINARY EUTECTIC PHASE DIAGRAM
(NO SOLID SOLUTION)
HYPOEUTECTIC HYPEREUTECTIC
Three phases in equilibrium at
eutectic point compositions and
temperature
Eutectic reaction
L A+ B
48
EUTECTIC
HYPOEUTECTIC
HYPEREUTECTIC
The eutectic microstructure forms in the alternating layers which
is known as lamellar:
→ atomic diffusion of lead and tin only occur over relatively short distances
in solid state.
Eutectic α Eutectic β
Figure : Lamellar eutectic structure
BINARY EUTECTIC PHASE DIAGRAM
(NO SOLID SOLUTION)
49
50
Liquid
Hypoeutectic alloy Hypereutectic alloy
When the composition of an
alloy, places it to the left of the
eutectic point
When the composition of an
alloy, places it to the right of
the eutectic point
First solid to form : Primary α
(a.k.a. proeutectic α)
First solid to form : Primary β
(a.k.a. proeutectic β)
β
BINARY EUTECTIC PHASE DIAGRAM
(NO SOLID SOLUTION)
51
1. Cooling curve at eutectic alloy
Same as single component (pure metal) because solidification 
takes place at a single temperature.
A Solid
Liquid
Figure : Cooling curve at eutectic alloy
BINARY EUTECTIC PHASE DIAGRAM
(NO SOLID SOLUTION)
52
2.  Cooling curve at hypo/hypereutectic alloy
Once the liquid reach TE, it will have the eutectic composition and 
will freeze at that temperature to form solid eutectic mixture of 
two phases.   
TL = temperature of liquid
TE = temperature at eutectic point
Figure : Cooling curve at hypo/hyper
eutectic alloy
Liquid + Solid
Liquid
Solid
BINARY EUTECTIC PHASE DIAGRAM
(No SOLID SOLUTION)
TE
HYPOEUTECTIC HYPOEUTECTIC
53
BINARY EUTECTIC
PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
54
Limited solid solution where the components are completely 
soluble in the liquid state but limited solubility in the solid state. 
E.g : Sn‐Pb system, Cu‐Ag system
α, β = solid solution
ae, be = liquidus
ac, cd, bd = solidus
cf, dg = solvus
• 3 single phase region = α, β, L
• Solvus cf denotes the solubility
limit of B in A
• Solvus dg shows the solubility
limit of A in B
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
CE
Eutectic temp.
(TE) : below TE
form 2 different
solid phases.
Eutectic point
a.k.a. triple point.
Eutectic composition (CE)Figure : Copper-silver phase diagram
Solvus
Liquidus
Solidus
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
TM Ag
TM Cu
55
56
Determination of phase and phase composition:
Same as in binary isomorphous system
Determination of weight fraction
Weight fraction of liquid,
WL= Q/(R+Q)
Weight fraction of β,
Wβ = R/(R+Q)
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
• 3 single phase regions
(L, )
• Limited solubility:
: mostly Cu
: mostly Ni
• TE: No liquid below TE
• CE: Min. melting T
composition
Ex.: Cu-Ag system
L (liquid)
 L +  L+

Co, wt% Ag
20 40 60 80 1000
200
1200
T(°C)
400
600
800
1000
CE
TE 8.0 71.9 91.2
779°C
Cu-Ag system
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
Eutectic reaction
L α + β
(Liq.) (s.s) (s.s)
57
EXERCISE:
1) Label each phase region
(i), (ii) and (iii).
2) Determine Tm for pure
Sn and Bi.
3) Determine the eutectic
temperature and
eutectic composition.
Sn-Bi phase diagram
β
α + L
(i)
(ii)
(iii)
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
58
EXAMPLE:  Pb‐Sn EUTECTIC SYSTEM
For a 40wt%Sn-60wt%Pb alloy at
150oC, find...
--the phases present:
--the compositions of
the phases:
--the relative amounts
of each phase:
Pb-Sn system
L + 
L+

200
T(°C)
18.3
Co, wt% Sn
20 40 60 80 1000
Co
300
100

L (liquid)
 183°C
61.9 97.8
150
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
59
EXERCISE:
a) What is the TE and CE?
b) Consider an alloy contains 20wt% 
Cu, what are the compositions of 
the  phase in equilibrium at just 
above and  below TE?
c) Consider Ag‐Cu alloy contains  
40 wt% Ag, at temperature just 
below TE, find the relative amounts 
of each phase. 60
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION) : MICROSTRUCTURES
1. Consider Co < 2wt% Sn
Liquid
Pb-Sn system
Liquid +  grains of solid                    
polycrystal of  grains
phase solid)
61
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION) : MICROSTRUCTURES
: Cowt%Sn
L + 
200
T(°C)
Co, wt% Sn
10
18.3
200
Co
300
100
L

30
L: Cowt%Sn
 + 
400
(sol. limit at TE)
TE
2
(sol. limit at Troom)
L



2. Consider 2wt%Sn < Co < 18.3wt%Sn
 polycrystal + fine  crystals
phase solid)
Pb-Sn system
Liquid
Liquid +  grains of solid                    
polycrystal of  grains
phase solid)
62
L + 
200
T(°C)
Co, wt% Sn
20 400
300
100
L

60
L: Cowt%Sn
 + 
TE
: 18.3wt%Sn

0
80 100
L + 
CE18.3 97.8
61.9
183°C
: 97.8wt%Sn
3. Consider Co = CE = 61.9 wt% Sn
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION) : MICROSTRUCTURES
Eutectic reaction
L α + β
(Liq.) (s.s) (s.s)
Pb-Sn system
EUTECTIC
Cooling Curve
63
L + 
200
T(°C)
Co, wt% Sn
20 400
300
100
L

60
L: Cowt%Sn
 + 
TE

0
80 100
L + 
Co18.3 61.9
L

L
primary 
97.8
S
S
R
R
eutectic 
eutectic 
4.  Consider 18.3wt%Sn < Co < 61.9wt%Sn
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION) : MICROSTRUCTURES
HYPOEUTECTIC
64
5.  Consider 61.9wt%Sn < Co < 97.8wt%Sn
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION) : MICROSTRUCTURES
HYPEREUTECTIC
Pb‐Sn system
65
HYPOEUTECTIC & HYPEREUTECTIC
BINARY EUTECTIC PHASE DIAGRAM
(LIMITED SOLID SOLUTION)
Eutectic
mixture

Proeutectic β
or Primary β
Proeutectic 
or Primary 
Eutectic
mixture

: Co=85wt%Sn
Eutectic reaction
L α + β
(Liq.) (s.s) (s.s)
66
67
Different systems have different types of alloy transformation.
Invariant equilibrium involve :
– 3 phases co‐exist in. 
– Exist only at one temperature / fixed temp.
– Composition for 3 phases co‐exist is fixed at the point.
– Zero degree of freedom.
Below are the example of alloy transformation at invariant 
equilibrium :
1.Eutectic 
2.Eutectoid
3.Peritectic
4.Peritectoid
INVARIANT EQUILIBRIUM
5. Metatectic
6. Monotectic
7. Synthectic
INVARIANT EQUILIBRIUM
Invariant Point Reaction Example System
Eutectic l α + β Ag‐Cu, 
Pb‐Sn
Eutectoid γ α + β Fe‐C, 
Al‐C
Peritectic l + α β Cu‐Zn
Peritectoid β + α γ Al‐Ni, 
Cu‐Zn
Metatectic α l + β U‐Mn
Monotectic l1 α + l2 Cu‐Pb
Syntectic l1 +  l2 α K‐Zn, 
Na‐Zn
L
α β
L + α L + β
α + β
γ
α βγ + α γ + β
α + β
α
β
L
β + α
L + α
L + β
α β
γγ + α
α + β
γ + β
α
β L
β + α L + α
L + β
L1
α L2
L1 + α L1 + L2
L2 + α
L1
α
L2L1 + α
L1 + L2
L2 + α
68
69
EXAMPLE: Find the eutectoid and peritectic reactions in the
Cu-Zn system?
INVARIANT EQUILIBRIUM
70
INVARIANT EQUILIBRIUM
Exercise: Refer to zinc‐copper phase diagram. Specify temperature‐composition points at 
which all eutectics, eutectoids and peritectics phases’ transformation occurs. Also for each, 
write the reaction upon cooling. 
71
• Liquidus : Line above which all of alloy is liquid.
• Solidus : Line below which all of alloy is solid.
• Solvus : Boundaries between solid phase regions.
• Invariant point : It is a point at which three phases are in
equilibrium.
• Eutectic structure : The resulting microstructure consists of
alternating layers, called lamellae, of α and β that form during
eutectic reaction.
• Proeutectic : Form before (higher temperature) eutectic.
• Terminal solid solutions : Phases containing the pure components
which situated at the end of the phase diagram.
• Hypoeutectic : Having a composition less than eutectic.
• Hypereutectic : Having a composition greater than eutectic.
TERMINOLOGY
2.3  Fe‐Fe3C system
Microstructure development,             
Microconstituent of phases.
72
2.3  Fe‐Fe3C system: Microstructure development, 
Microconstituent of phases.
• Fe‐Fe3C Phase Diagram
− Allotropy  Transformation
− Solid Phases
− Phase Transformation Reactions
− Microstructural Changes
Eutectoid
Hypoeutectoid Steel
Hypereutectoid Steel
73
LEARNING OBJECTIVE
74
Students should be able to :
• Sketch and label in the iron‐iron carbide phase 
diagram up to eutectic isotherm. 
• Specify whether the alloy is hypoeutectoid or 
hypereutectoid.
• Identify the proeutectoid phase.
• Explain the development of the microstructure
at a temperature just below the eutectoid.
• Compute the relative amount of pearlite and 
proeutectoid phase.
The effect of 
adding C into Fe 
will introduce 
various types of 
steel and cast iron 
which are 
represented by 
the iron‐iron 
carbide phase 
diagram.
75
Fe-Fe3C PHASE DIAGRAM
Fe-Fe3C PHASE DIAGRAM
76
ALLOTROPIC TRANSFORMATION
• A material that can exist in more than one lattice structure 
(depending on temperature‐heating@cooling)                allotropic.
• An allotropic material is able to exist in two or more forms having 
various properties without change in chemical composition.
• E.g : Upon heating, pure iron experiences two changes in crystal 
structure:
– At room temperature, it exists as ferrite,or α iron (BCC).
– When we heat it to 912°C, it experiences an allotropic 
transformation to austenite,or γ iron (FCC).
– At 1394°C, austenite reverts back to a BCC phase called δ ferrite.
77
912°C
1538°C
768°C
ALLOTROPIC TRANSFORMATION
Allotropy of iron(Fe) 
Delta iron Austenite  Alfa iron
(BCC)                      (FCC)                 (BCC)
High Temp
Low Temp
Moderate 
Temp
78
Phases present in Fe-Fe3C system :
1) δ Ferrite
2) γ (Austenite)
3) α Ferrite
4) Fe3C (Cementite)
5) α + Fe3C (Pearlite)
79
SOLID PHASES
80
1) δ Ferrite
• This is a solid solution of carbon in iron and has a BCC crystal 
structure (same structure as α‐ferrite).
• It is a phase which exists at extreme temperature (>1400°C) 
and stable only at high temperature, above 1394 °C.
• It melts at 1538 °C.
• The maximum solubility of C in Fe is 0.09% at 1495°C. This has 
no real practical significance in engineering. 
SOLID PHASES
Figure : δ Ferrite crystal structure
81
2) Austenite (γ Iron)   
• It is also known as (γ) gamma‐iron, which is an interstitial solid 
solution of carbon dissolved in iron with a face centered cubic 
crystal (FCC) structure. 
• Transforms to BCC δ‐ferrite at 1394°C.
• The maximum solubility of carbon in austenite, 2.14%.
• Austenite is normally unstable below eutectoid temperature 
unless cooled rapidly.
• It is a non magnetic material.
Figure :Austenite (γ iron) crystal structure
SOLID PHASES
82
3. α Ferrite
• It is also known as alpha(α) iron, which is an interstitial solid 
solution of a small amount of carbon dissolved in iron with a Body 
Centered Cubic (BCC) crystal structure.  
• It is the softest structure on the iron‐iron carbide diagram.  
• Stable form of iron at room temperature.
• The maximum solubility of C is 0.022 wt%. 
• Ferrite dissolves considerably less carbon than austenite. 
• Transforms to FCC γ‐austenite at 912°C.
• α ‐ferrite is magnetic (below 768°C).
Figure : Ferrite (α iron) crystal structure
SOLID PHASES
83
3) Cementite (Fe3C)
• Cementite is also known as iron carbide which has a chemical formula,
Fe3C.
• Fe3C is an intermetallic compound. It is because a fixed amount of C
and a fixed amount of Fe are needed to form cementite (Fe3C).
• It is a hard and brittle material, low tensile strength and high
compressive strength.
• It contains 6.70 wt% C and 93.3 wt% Fe.
• This intermetallic compound is metastable,
it remains as a compound indefinitely at room
temperature, but decomposes (very slowly,
within several years) into α-Fe and C
(graphite) at 650 - 700°C.
SOLID PHASES
84
5) α + Fe3C (Pearlite)
• It is resulted from transformation of austenite of eutectoid 
composition on very   slow cooling. 
• Pearlite is a laminated structure (lamellar structure) formed of 
alternate layers of ferrite (white matrix‐ferritic background) and
cementite (thin plate). 
• In most steels, the microstructure consists of both α+Fe3C 
(pearlite) phases.
• It has intermediate mechanical properties between α and Fe3C. 
Cementite
(hard)
Ferrite
(soft)
Figure : Pearlite microstructure
(Light background is the ferrite matrix,
dark lines are the cementite network)
SOLID PHASES
85
PhaseTransformation Reactions
C
3 Invariant points:
The iron-carbon diagram exhibits three phase transformation reactions :
86
PhaseTransformation Reactions
%
Carbon
HYPOHYPO HYPER HYPER
EUTECTOID EUTECTIC
Peritectic
PhaseTransformation Reactions
87
MICROSTRUCTURAL CHANGES
• Microstructure that exists in those reactions depends on :
− Composition(carbon content) 
− Heat treatment 
• Three significant regions can be made relative to the steel portion of the 
diagram which known as:
1) Eutectoid
− Carbon content 0.76% and temperature 727°C.
− It entirely consists of pearlite (α + Fe3C).
2) Hypoeutectoid
− Carbon content from 0.022 to 0.76%.
− It consist of pearlite and primary (proeutectoid) ferrite.
3) Hypereutectoid
− Carbon content from 0.76 to 2.14%.
− It consist of pearlite and primary (proeutectoid) cementite.
88
89
EUTECTOID STEEL
γ α +    Fe3C
austenite                 pearlite
αFe3C
Pearlite
Figure : Photomicrograph of a
eutectoid steel showing the pearlite
microstructure consisting of
alternating layers of α ferrite
(thick layers, light phase) and
Fe3C (thin layers most of which
appear dark).
Note :
• Many cementite layers are so thin 
that adjacent phase boundaries are 
indistinguishable (appear dark).
• Alternating layers  of α and Fe3C 
form pearlite.
90
The layers of alternating phases in 
pearlite are formed for the same 
reason as layered structure of eutectic 
structures:
Redistribution C atoms
between ferrite (0.022 wt%) 
and cementite (6.7wt%) by 
atomic diffusion.
The pearlite exist as grains, 
often termed as colonies.
EUTECTOID STEEL
91
HYPOEUTECTOID STEEL
Figure : Microstructures for Fe-Fe3C system of
hypoeutectoid composition Co
α’        +       α +    Fe3C 
(proeutectoid ferrite)    +      (pearlite)
Note :
Eutectoid α = Ferrite that is present in the
pearlite.
Proeutectoid (meaning pre- or before
eutectoid) = Formed above eutectoid
temperature.
α’               +             γ
(proeutectoid ferrite)   +      (Austenite)
γ
(Austenite)
92
HYPOEUTECTOID STEEL
93
EXERCISE
Consider an Fe – C alloy containing 0.25 wt% C, at a
temperature just below the eutectoid temperature.
Determine
a) the mass fractions of proeutectoid ferrite and pearlite
HYPOEUTECTOID STEEL
b) the mass fractions of total ferrite, eutectoid ferrite
and cementite.
94
HYPEREUTECTOID STEEL
Note :
Eutectoid Fe3C= Cementite that is present in
the pearlite
Figure : Microstructures for Fe-Fe3C system of
hypereutectoid composition
Fe3C’           +        γ
(proeutectoid cementite)  +  (Austenite)
γ
(Austenite)
Fe3C’      +     α +    Fe3C 
(proeutectoid cementite)  +         (pearlite)
95
HYPEREUTECTOID STEEL
96
EXERCISE
Consider an Fe – C alloy containing 1.25 wt% C, at a
temperature just below the eutectoid temperature. Determine
a) the mass fractions of proeutectoid cementite and pearlite
HYPEREUTECTOID STEEL
b) the mass fractions of total ferrite, cementite and
eutectoid cemmentite.
97
Figure : Photomicrograph of a 1.4wt% C steel
having a microstructure consisting of a white
proeutectoid cementite network surrounding
the pearlite colonies.
Hypereutectoid steel
+Fe3C (pearlite)
+
proeutectoid cementite(Fe3C)
Hypoutectoid steel
+Fe3C (pearlite)
+
proeutectoid ferrite(α)
Figure : Photomicrograph of a 0.38wt% C
steel having a microstructure consisting of
pearlite and proeutectoid ferrite.
HYPO vs HYPER EUTECTOID STEEL
2.4Ferrous and 
Non‐Ferrous Metals
98
2.4 Ferrous and Non‐Ferrous Metals
• Introduction
• Classification of Metal Alloys
• Classification of Ferrous Alloys
– Steel
• Plain Carbon Steel
• Low Carbon Steel
• Medium Carbon Steel
• High Carbon Steel
• Stainless Steel
• Tool Steel
– Cast Iron
• Gray Cast Irons
• Nodular (Ductile) Cast Irons
• White Cast Irons
• Malleable Cast Irons
99
• Non‐Ferrous Alloys
– Aluminium and its alloys
– Copper and its alloys
– Magnesium and its alloys
– Titanium and its alloys
– The Noble  Metal
– The Refractory Metals
LEARNING OBJECTIVE
Students should be able to :
• Differentiate the differences between ferrous 
and nonferrous metals.
• Describe the characteristics of white, gray, 
ductile and malleable cast irons.
• Understand the properties and applications of 
metals and its alloys.
100
INTRODUCTION
1. Ferrous
• Metal alloys that 
contain iron as a prime 
constituent.
• E.g : steels, cast iron.
• Tend to have a higher 
chance of corrosion. 
2) Nonferrous 
• Metal alloy contain less 
@ no iron. 
• E.g : Cu, Al, Mg, Ti and 
its alloys
• Have a much higher 
resistance to corrosion.
Metal alloys can be divided into two categories :
Note :
The word ferrous is derived from the Latin term "Ferrum" which means
"containing iron".
101
INTRODUCTION
Advantages of Ferrous 
alloys  over Non‐Ferrous 
alloys:
Advantages of Non‐Ferrous 
alloys  over ferrous alloys:
– Generally greater strength.
– Generally greater stiffness.
– Better for welding
– Good resistance to corrosion.
– Casting and cold working 
processes and are often 
easier.
– High ductility.
– Higher thermal and electrical 
conductivities.
– Colors.
102
CLASSIFICATION OF METAL ALLOYS
103
Al Cu Mg Ti
Noble 
Metal
Refractory 
metal
CLASSIFICATION OF FERROUS ALLOY
 Definition : Those of which iron is the prime constituent.
 Advantages :
1. Iron ores exist in abundant quantities within  the earth’s 
crust.
2. Produced from economical process : Extraction, refining, 
alloying and fabrication techniques are available. 
3. Versatile material : Wide range of mechanical and physical 
properties. 
 Disadvantages :
1. Tends to corrode.
2. High density.
3. Low electrical conductivity. 
104
CLASSIFICATION OF FERROUS ALLOY
• The ferrous alloys are classified based on the 
percentage of carbon present in the ferrous. 
(steel <2.14 %C, cast iron 2.14 ‐ 4.3%C)
• Carbon is the most important commercial 
steel alloy (↑C, ↑hardness, ↑ strength, 
↑bri leness, ↓ weldability)
105
106
CLASSIFICATION OF FERROUS ALLOY
Low Alloy High Alloy
low carbon
<0.25wt%C
med carbon
0.25-0.6wt%C
high carbon
0.6-1.4wt%C
Uses auto
struc.
sheet
bridges
towers
press.
vessels
crank
shafts
bolts
hammers
blades
pistons
gears
wear
applic.
wear
applic.
drills
saws
dies
high T
applic.
turbines
furnaces
V. corros.
resistant
Example 1010 4310 1040 4340 1095 4190 304
Additions none
Cr,V
Ni, Mo
none
Cr, Ni
Mo
none
Cr, V,
Mo, W
Cr, Ni, Mo
plain HSLA plain
heat
treatable
plain tool
austentitic
stainless
Name
Hardenability 0 + + ++ ++ +++ 0
TS - 0 + ++ + ++ 0
EL + + 0 - - -- ++
increasing strength, cost, decreasing ductility
Steels
107
Steels
• Are iron carbon alloys that may contain carbon 
less than 2.14%.
• Classification by carbon content
– Low, medium and high carbon type
• Subclasses by concentration of other alloying 
elements :
– Plain carbon steel
– Alloy steel
• The microstructures of steel are normally ferrite 
and relatively soft and weak but good ductility 
and toughness.
108
First digit indicates the family to which the steel belongs (a.k.a. the major alloying elements) : 
Second digit indicate % of major alloying elements (1 means 1%). 
Last two digits(3rd and 4th number) indicate amount of carbon in steel (10 means 0.10% C). 
Example
• SAE 5130 means alloy chromium steel, containing 1% of chromium and 0.30% of Carbon.
• AISI 1020 which means 10 indicates plain carbon steel with 0.2% amount of Carbon.
*SAE : Society of Automotive Engineers             *AISI : American Iron and Steel Institute 109
Steels
Plain Carbon Steels
• Iron with less than 1% carbon alloy contains a 
small amount of manganese, phosphorous, sulfur 
and silicon.
• Disadvantages of plain carbon steel:
– Hardenability is low
– Loss of strength and embrittleness
– Subjected to corrosion in most environments
• 3 groups:
– Low carbon steels
– Medium carbon steels
– High carbon steels
110
Low Carbon Steels (< 0.25%C )
Plain carbon steels
• unresponsive to heat treatments 
intended to form martensite.
• Microstructures consist of ferrite 
and pearlite
• Properties:
– Relatively soft and weak, but 
possess high ductility and toughness
– Good formability, Good weldability
– Low cost
– Rated at 55‐60% machinability
• Application: Auto‐body 
components, structural shapes, 
sheets for pipelines, building, 
bridges, tin cans, nail, low 
temperature pressure vessel.
High‐strength low alloy (HSLA) 
steels
• Low Carbon Steel combine with 10 
wt% of alloying elements, such as 
Mn, Cr, Cu, V, Ni, Mo
• Properties:
– higher strength than plain low 
carbon steels.
– ductile, formable and machinable
– More resistance to corrosion
• Strengthening by heat treatment.
• Application : bridges, towers, 
support columns in high rise 
building, pressure vessels.
111
Medium Carbon Steel
• Composition: 0.25 ‐ 0.6% C
• Advantages:
– Machinability is 60‐70%. 
Both hot and cold rolled 
steels machine better 
when annealed. 
– Good toughness and 
ductility
– Fair formability
– Responds to heat 
treatment but often used 
in natural condition.
• Plain medium carbon steel 
−Low hardenability
− Heat treatment:   
quenching and tempering
• Heat treatable steel  
−Containing Cr, Ni and Mo
−Heat treated alloy stronger   
than Low Carbon Steel, lower 
ductility and toughness than 
Low Carbon Steel 
Applications : Couplings, forgings, gears, crankshafts other high‐strength 
structural components. 
: Steels in the 0.40 to 0.60% C range are also used for rails, 
railway wheels and rail axles. 112
High Carbon Steels
• Composition:  0.6% ‐ 1.4% C
• Properties: 
– hardest
– strongest
– least ductile of the carbon 
steels
• Application: 
– Used for withstanding wear.
– A holder for  a sharp cutting 
edge. 
E.g : drills, woodworking tools, 
axes, turning and planning tools, 
milling cutters, knives.
– Used for spring materials, 
high‐strength wires, cutting 
tools, and etc.
• Advantages:
– Hardness is high
– Wear resistance is high
– Fair formability
• Disadvantages:
– Low toughness, formability
– Not recommended for 
welding
– Usually joined by brazing with 
low temperature silver alloy 
making it possible to repair or 
fabricate tool steel parts without 
affecting their heat treated 
condition.
113
Stainless Steels
• Primary alloying element  is chromium (>11%) 
• Others element : Nickel, Manganese, Molybdenum.
• Called stainless because in the presence of oxygen, they develop a 
thin, hard, adherent film of chromium oxide (Cr2O3) that protect the 
metal from corrosion.
• Highly resistance to corrosion.
• 3 basic types of stainless are
– Martensite
– Ferritic
– Austenitic
• Applications
− Decorative trim, nozzles.
− Springs, pump rings, aircraft fittings.
− Cookware, chemical and food processing equipment.
− Turbine blades, steam boilers, parts in heating furnaces.
− Temporary implant devices such as fractures plates, screw and hip nails.
− The best choice for the walls of a steam boiler because it is corrosion resistant 
to the steam and condensate.
114
Tool Steels
• High carbon steel alloys (containing Cr, V,  W and Mo)
that have been designed to prevent wear resistance 
and toughness combined with high strength.
• Have excess carbides (carbon alloys) which make 
them hard and wear resistant.
• Most tool steels are used in a heat treated state 
generally hardened and tempered.
• Applications: 
– gauges, shear knives, punches, chisels, cams, mould for 
die casting.
– Best choice for a drill bit because it is very hard and wear 
resistant and thus will retain a sharp cutting edge.
115
Cast Irons
• Carbon contents :  Greater than 2.14wt% C.
• Si content  : 0.5‐3wt%Si 
(used to control kinetics of carbide formation)
• Commercial range : 3.0‐4.5 wt% C + other alloying elements.
• The differences between cast irons and steels :
– Carbon content.
– Silicon content.
– Carbon microstructure (stable form and unstable form).
• Properties : 
– Low melting points (1150‐1300°C).
– Some cast iron are brittle.
• Microstructure:  
– Most commonly graphite (C) & ferrite.
116
Cast Irons
• Properties of cast iron is controlled by three main factors:
– The chemical composition of the iron
– The rate of cooling of the casting in the mould
– The type of graphite formed
• Advantages:
– Low tooling and production cost
– Ready availability
– Good machinability without burring
– Readily cast into complex shapes
– High inherent damping
– Excellent wear resistance and high hardness
• Types of cast irons :
• Gray Cast Irons
• Nodular (Ductile) Cast Irons
• White Cast Irons
• Malleable Cast Irons
117
Gray Cast Irons
• Composition : Carbon content : 2.5 ‐ 4.0 wt% C and
Silicon content  : 1.0 ‐ 3.0wt% Si.
• Microstructure : Graphite flakes surrounded by  α‐ferrite or 
pearlite matrix. 
• The formation of graphite occurs because of the cooling rate is 
too slow where austenite in unstable position and brake down 
to give graphite microstructure. 
• Properties:
– Less hard and brittle (easy to machine)
– Very weak in tension due to the pointed and sharp end of graphite flake
– Good during compression (high compressive strength)
– Low shrinkage in mould due to formation of graphite flakes
– High damping capacity
– Low melting temperature (1140‐1200oC).
• Applications: Base choice for milling machine base because it 
effectively absorbs vibration (good vibration damping).
118
THE MICROSTRUCTURE OF
GRAY CAST IRONS
Graphite flakes
* Graphite flakes shows fracture surface (gray appearance).
Figure : Dark graphite flakes in a‐Fe matrix.
119
Ductile (Nodular) Cast Irons
• Composition: Mg or Ce is added to the gray iron composition 
before casting occurs (to prevent the formation of 
graphite flakes during the slow cooling of the iron)
• Microstructure  :  Nodular or spherical‐like graphite structure in 
pearlite or ferritic matrix.
• Properties : 
– Significant increase in material ductility.
– Tensile strength > gray cast iron.
– Others mechanical properties ≈ steel.
• Applications  : Valves, pump bodies, gear and other automotive 
and machine components.
• A HT can be applied to pearlite nodular iron to give 
microstructure of graphite nodules in ferrite (ferrite structure is 
more ductile and weldable but less tensile strength)
120
THE MICROSTRUCTURE OF
DUCTILE (or NODULAR) CAST IRONS
Figure : Dark graphite nodules in α‐Fe matrix.
Graphite nodules (a.k.a. spherical‐like)
* Note that the carbon is in the shape of small sphere, not flakes.
121
White Cast Iron
• Composition: 2.5 < C < 4.0%C and Si<1%
• Microstructure : Pearlite and cementite
(due to rapid cooling).
• An intermediate metal for the production of malleable cast 
iron.
• Properties:
– Relatively very hard, brittle and not weldable compare 
to gray cast iron
– When it is annealed, it become malleable cast iron
– Not easily to machine
– Fracture surface: white appearance
122
THE MICROSTRUCTURE OF
WHITE CAST IRONS
Figure : Light Fe3C regions surrounded by pearlite.
Pearlite
Fe3C
(Light regions)
123
Malleable Cast Irons
• Is produced by the HT of white cast irons
− Heating temperature: 800oC – 900oC 
− Duration : 2 or 3 days (50 hours)
− Heating environment: Neutral atmosphere
• Microstructure : A clumps (rossette) of graphite 
(due to decomposition of cemmentite) surrounded by a  
ferrite or pearlite matrix
• Properties:
− Similar to nodular cast iron and give higher strength 
− More ductile and malleability
• Applications : Pipe fittings, valve parts for railroad, marine 
and other heavy duty.
124
THE MICROSTRUCTURE OF
MALLEABLE CAST IRONS
Figure : Dark graphite rosettes in α‐Fe matrix.
Graphite rosettes
125
Non‐Ferrous Alloys
• Definition: Used for alloys which do not have iron as 
the base element.
• Examples: Al alloys, Cu alloys, Mg alloys, Ti alloys, 
Noble metals, Refractory metals, etc.
• Advantages of Ferrous alloys over Non‐Ferrous alloys:
– Generally greater strength
– Generally greater stiffness ( ↑E)
– Better for welding
• The advantages of Non‐Ferrous alloys over ferrous 
alloys:
– Good resistance to corrosion
– Much lower density
– Casting is often easies ( ↓ mel ng points)
– Cold working processes are often easier (ductility)
– Higher thermal and electrical conductivities
– colors 126
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