18MEC108T Materials

Technology – Unit I
Contents
• Crystal Structures
• Imperfection in solids
• Point, line, interfacial and volume defects

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Properties of materials - Factors
• Nature of bonding
• Atomic structure

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Nature of bonding
• An understanding of many of the physical properties of materials is
enhanced by a knowledge of the interatomic forces that bind the
atoms together

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Bonding in solids
• Interatomic forces that bind the atoms together – Bonds
• Primary bonding
• Involves the transfer or sharing of electrons and produces a relatively strong
joining of adjacent atoms.
• Secondary bonding
• involves a relatively weak attraction between atoms in which no electron
transfer or sharing occurs

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Bonding in solids - Types
• Primary bond (Chemical bonds)
• Ionic Bond
• Covalent bond
• Metallic bond
• Secondary bonding
• Van der Waals bonds

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Ionic Bond
• Electron transfer from one atom to another.
• Found in compounds that are composed of both metallic and
nonmetallic elements
• attractive bonding forces are coulombic
• Non-directional
• Predominant bonding in ceramic materials is ionic Ref: James F.
Shackelford
• Ionic materials are characteristically hard and brittle, electrically and
thermally insulative

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Covalent Bond
• Cooperative sharing of valence electrons between two adjacent
atoms
• Highly directional
• Non-metallic elemental molecules - H2
and molecules containing dissimilar atoms
• Polymers and some ceramics

19-01-2021 Dept. of Mechanical Engg. Ref: William D 8

Callister
Metallic Bonding
• Found in metals and their alloys
• Nondirectional
• Valence electrons are not bound to any particular atom
• Valence electrons belong to the metal as a whole forming a
“sea of electrons” or an “electron cloud.”
• Consequence of free electrons - Ductility, permanent
deformation, good conductors of electricity and heat

Ref: William D
Callister

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Bonds – Characteristics - Summary
Hardness Electrical
Bond Melting point Examples
(Ductility) Conductivity
Diamond,
Covalent High Hard (poor) Usually Low
Graphite, Ge, Si
Ionic High Hard (poor) Low NaCl, ZnS, CsCl

Metallic Varies Varies High Fe, Cu, Ag

Van der Waals Low Soft (poor) Low Ne, Ar, Kr

Hydrogen Low Soft (poor) Usually Low Ice

Ref: Materials Science & Engineering - Anand Subramaniam

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Bonds – Characteristics - Summary

Ref: Flake C. Campbell

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Crystalline material
• Atoms are situated in a repeating or periodic array over large atomic
distances;
• All metals, many ceramic materials, and certain polymers form
crystalline structures under normal solidification conditions

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Crystalline Structure
• A crystalline structure consists of atoms, or molecules, arranged in a
pattern that is repetitive in three dimensions.
• The arrangement of the atoms or molecules in the interior of a
crystal is called its crystalline structure.

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Why crystal structures are important?
• Ductility
• Densely packed structures more slip planes plastic deformation
without fracturing

Formability Fracture toughness

Vital for engineering applications

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Crystal structure and Crystal system
• Crystal structure
• Geometry and atomic arrangements within the unit cell

• Crystal system
• Unit cell geometry alone

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 Crystal system vs Crystal structure
Crystal system Crystal structure

Ref: Flake C. Campbell

Ref: William D
Callister
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Unit Cell
• The unit cell of a crystal structure is the smallest group of atoms
possessing the symmetry of the crystal which, when repeated in all
directions, will develop the crystal lattice

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Lattice
• Three dimensional array of points coinciding with atom positions
(or sphere centers).

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Crystal structures of most common metals
• Face-centered cubic (FCC)
• Body-centered cubic (BCC)
• Hexagonal close-packed (HCP)

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Face-centered cubic (FCC)
• Atoms located at each of the corners and the centers of
all the cube faces.
• Some metals with FCC - copper, aluminum, silver, and
gold
• Number of atoms per unit cell:4
• Coordination number : 12
• Atomic Packing Factor: 0.74
Ref: William D
Callister
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Body-centered cubic (BCC)
• Atoms located at all eight corners and a single atom at the cube
center
• Metals with BCC - Chromium, iron, tungsten
• Number of atoms per unit cell:2
• Coordination number:8
• Atomic Packing Factor:0.68
Ref: William D
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Dept. of Mechanical Engg. Callister
Hexagonal close-packed (HCP)
• Unit cell is hexagonal
• The top and bottom faces six atoms that form regular hexagons and
surround a single atom in the center.
• Plane that provides three additional atoms to the unit cell is situated
between the top and bottom planes
• Metals with HCP - cadmium, magnesium, titanium, and zinc
• Number of atoms per unit cell:6
• Coordination number:12
• Atomic Packing Factor:0.74
Ref: William D
Callister
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Crystallographic Directions
• A crystallographic direction is defined as a line directed between
two points, or a vector.
• Typical representation of an unknown/general direction → [uvw].
• Corresponding family of directions → <uvw>.

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Crystallographic Directions - Steps
• A vector of convenient length is positioned such that it passes through the origin
of the coordinate system.
• The length of the vector projection on each of the three axes is determined; these
are measured in terms of the unit cell dimensions a, b, and c.
• These three numbers are multiplied or divided by a common factor to reduce
them to the smallest integer values.
• The three indices, not separated by commas, are enclosed in square brackets,
thus: [uvw].

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Crystallographic Directions - Example
• In cubic crystals, all the
directions represented by the
following indices are
equivalent:

As a convenience, equivalent directions are grouped

together into a family, which is enclosed in angle brackets,
thus: <100>

Ref: William D
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Dept. of Mechanical Engg.
Callister
Crystallographic Plane
• Miller indices (hkl) are used to specify crystallographic planes.
• Unknown/general plane → (hkl).
• Corresponding family of planes → {hkl}.

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Crystallographic planes - Procedure
• If the plane passes through the selected origin, either another parallel plane must be constructed
within the unit cell by an appropriate translation, or a new origin must be established at the
corner of another unit cell.
• At this point the crystallographic plane either intersects or parallels each of the three axes; the
length of the planar intercept for each axis is determined in terms of the lattice parameters a, b,
and c.
• The reciprocals of these numbers are taken. A plane that parallels an axis may be considered to
have an infinite intercept and therefore a zero index.
• If necessary, these three numbers are changed to the set of smallest integers by multiplication or
division by a common factor.
• Finally, the integer indices, not separated by commas, are enclosed within parentheses, thus:
(hkl).
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 Crystallographic planes - Example

Ref: Flake C. Campbell

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Crystallographic planes – contd…
a) b)

c) d) All of these planes consist of the same three numbers,

namely 1,0,0. Crystallographic equivalent planes are
known as family planes and denoted by putting the
integers in braces. In this case, the notation {100}
represents all side faces of the cube collectively as a
family plane.
Ref: Flake C. Campbell

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Why study imperfections in solids?
• Properties of some materials are profoundly influenced by the
presence of imperfections
• Addition of impurity atoms to pure metal experience significant
alterations in properties Eg) brass and copper

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Imperfection in solids
• Perfect crystal
• Orderly repetition of the lattice in every direction in space
• Real crystal
• Not perfect, they always contain a considerable number of imperfections, or
defects, that affect their physical, chemical, mechanical, and electronic
properties.
• Imperfection - any deviation from an orderly array of lattice points

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Crystalline defect
• A crystalline defect refers to a lattice irregularity having one or
more of its dimensions on the order of an atomic diameter

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Crystalline imperfections - Classification
• According to the geometry or dimensionality of the defect
• Point defects
• Line defects
• Planar defects
• Volume defects

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 Point Defects
• Irregularity in the lattice
• Missing atom - Vacancy
No of vacancies
• Extra atom - Interstitial Density, electrical
• Impurity atom - substitutional conductivity
N is the total number of atomic sites
decreases
Qy is the energy required for the
formation of a vacancy,
T is the absolute temperature1 in K

Number of vacancies increases

exponentially with temperature

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Line defects
• Dislocation
• It is a linear or one-dimensional defect around which some of the atoms are
misaligned
• Provides themechanism that allows mechanical deformation
• A crystalline metal without dislocations
• although extremely strong, would also be extremely brittle and practically useless as
an engineering material
• All mechanical properties of metals are, to a significant extent, controlled
by the behavior of line imperfections
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Dislocation
• Edge dislocation • Screw dislocation
• insertion of an extra half-plane • formed by a shear stress that is
of applied to produce the distortion
atoms above (or below) the
dislocation
line.

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Ref: William D 36
Dept. of Mechanical Engg. Callister
 Burgers vector
• The magnitude and direction of the lattice distortion associated with
a dislocation are expressed in terms of a Burgers vector, denoted
by b. Burger vector is parallel to the dislocation line

Burger vector is perpendicular to the dislocation line

19-01-2021 Ref: William D 37
Dept. of Mechanical Engg.
Callister
Planar (Interfacial/Surface) defect
• Boundaries having two dimensions and normally separate regions
of the materials that have different crystal structures and/or
crystallographic orientations
• External surfaces, grain boundaries, phase boundaries, twin boundaries, and
stacking faults.

Ref: Flake C. Campbell

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Volume (Bulk/Engineering) defects
• Normally introduced during processing and fabrication steps
• These defects include pores, cracks, foreign inclusions, and other
phases
• Shrinkage during solidification can result in microporosity
• Volume defects, such as porosity and microcracks, almost always
reduce strength and fracture resistance

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References
• Fundamentals of Materials Science and Engineering, 4th ed. William D
Callister, JR. David G. Rethwisch
• Elements of Metallurgy and Engineering Alloys, ASM International
2008, Flake C. Campbell
• Introduction to Materials Science for Engineers, 8th ed. James F.
Shackelford.
• Materials Science & Engineering An Introductory E-Book, Anandh
Subramaniam & Kantesh Balani – IIT Kanpur
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Contents
• Solidification
• Nucleation and Growth
• Dendritic growth
• Segregation
• Homogenization

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Solidification
• Process of phase transformation of metals and alloys from the liquid
to the solid state.
• Solidification process controls the properties of metals and alloys.

Ref: Flake C. Campbell

Freezing sequence of alloy casting
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Supercooling(undercooling)

Ref: Flake C. Campbell

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 Mechanism of phase transformation - solidification
• Nucleation
• Homogeneous nucleation
• Heterogeneous nucleation
• Crystal growth

Ref: Flake C. Campbell

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Nucleation
• Formation of numerous small particles of the new phase(s), which
increase in size until the transformation has reached completion.

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Types of nucleation
• According to the site at which nucleating events occur
• Homogeneous nucleation
• Heterogeneous nucleation

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Homogeneous nucleation
• Occurs spontaneously & randomly without preferential nucleation
site.
• Formation of nuclei within its own melt without the aid of impurity
or foreign particles.

In practice homogeneous nucleation rarely occurs

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Gibbs free energy (G)
• G is a function of
• Internal energy of the system (enthalpy, H)
• Measurement of the randomness or disorder of the atoms or molecules
(entropy S)

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•

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Homogeneous nucleation - Solidification of pure
metal
•

Ref: William D. Callister

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•

Ref: William D. Callister

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Embryo and Nucleus
•

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•

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 •

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Heterogenous nucleation
• Nuclei form preferentially at structural inhomogeneities, such as
container surfaces, insoluble impurities, grain boundaries,
dislocations, and so on.

Ref: William D. Callister

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 Segregation of alloying elements
Dendritic growth reduces the temperature below
melting point resulting in effective
undercooling

• Under conditions of constitutional supercooling and higher

velocities of interface (growth rate of cells), cells grow into rapidly
advancing projections, sometimes of complex geometry.
• Their treelike forms have given them the name dendrites, after the
Greek word “dendros” for tree

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Dendritic formation

Ref: Flake C. Campbell

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Dendritic growth – contd…
• The secondary arms of dendrites develop perpendicular to the primary
arms
• As the primary arm solidifies and gives off its latent heat of reaction, the
temperature immediately adjacent to the primary arm increases.
• This creates another temperature inversion in the liquid between the
primary arms, so secondary arms shoot out in that direction.

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Dendritic growth – contd…
• The spacing of the secondary arms is proportional to the rate at
which heat is removed from the casting during solidification.
• Faster cooling rates producing smaller dendrite arm spacings.
• Dendrites start as long, thin crystals that grow into the liquid and
thicken.

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 Segregation
• Solidification of a liquid alloy is characterized by a phenomenon called segregation.
• Segregation may be defined as any departure from a uniform distribution of the chemical
elements in the alloy.
• Separation of impurities and alloying elements in different regions of solidified alloy.
• Caused by the rejection of the solutes from a solidified alloy into the liquid phase.
• This rejection is a result of different solubility of impurities in liquid and solid phases at the
equilibrium temperature.
• Alloys can exhibit several types of segregation based on the way in which alloys partition on
freezing.

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Macro-segregation
• It is the result of rejection of the alloy solute at an advancing interface
because it is more soluble in the liquid than the solid.
• As freezing progresses, there is a buildup of the solute in the liquid that
freezes last, such as at the center of the casting.
• Such long-range variations in composition are called macro-segregation.

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Gravity segregation
• Type of macro-segregation
• Occurs due to the differences in density in the liquid melt
• Denser constituents tend to sink toward the bottom, while lighter
ones float toward the top.

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Micro-segregation
• Micro-segregation results from freezing of solute-enriched liquid in
the inter-dendritic spaces
• Homogenization process eliminates majority of micro-segregation.

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Homogenization
• Homogenization is necessary to even out concentration gradients
(segregation) that occur during casting. This helps to prevent ingot
cracking during initial hot working operations.
• During solidification of an ingot during casting, micro-segregation
occurs, resulting in local compositional variations that are often
removed by thermal aging at high temperatures.

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Homogenization – contd…
• As-cast ingots are often reheated to temperatures just below the
melting point and soaked for long times to create more uniform
structures prior to hot working or heat treating
• Homogenization consists of heating to a high temperature, but
below the eutectic temperature, and then soaking for times long
enough to allow diffusion to eliminate a majority of the
micro-segregation.

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References
• Fundamentals of Materials Science and Engineering, 4th ed. William
D Callister, JR. David G. Rethwisch
• Elements of Metallurgy and Engineering Alloys, ASM International
2008, Flake C. Campbell
• Materials Science & Engineering An Introductory E-Book, Anandh
Subramaniam & Kantesh Balani – IIT Kanpur

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 Unit I

Solid Solution
 Alloy

It is a metal composed of two or more elements, at least

one of which is metallic

▪ Solid solutions
▪ Intermediate phases

Impurity atoms have been added intentionally to

impart specific characteristics to the material. Ordinarily
alloying is used in metals to improve mechanical
strength and corrosion resistance.
 Alloy contd…
• Very difficult to refine metals to a purity in
excess of 99.9999% even with relatively
sophisticated techniques.
• At this level, on the order of 1022 to 1023
impurity atoms will be present in one cubic
meter of material.
 Alloy - Example
• Sterling silver is a 92.5% silver–7.5% copper
alloy.
• In normal ambient environments, pure silver is
highly corrosion resistant, but also very soft.
• Alloying with copper enhances the mechanical
strength significantly
 Solid Solution

– The addition of impurity atoms to a metal will

result in the formation of a solid solution and/or
a new second phase, depending on

• the kinds of impurity,

• their concentrations,
• the temperature of the alloy.

– It is an alloy in which one element is dissolved in

another to form a single-phase structure.
 Contd…
– A solid solution forms when, as the solute atoms
are added to the host material, the crystal
structure is maintained, and no new structures
are formed.

– A solid solution is also compositionally

homogeneous; the impurity atoms are randomly
and uniformly dispersed within the solid
 Contd…
– Impurity point defects are found in solid solutions,
of which there are two types
• Susbstitutional solid solution
– Random
– Ordered
• Interstitial solid solution
 Substitutional solid solution
– For substitutional, solute or impurity atoms
replace or substitute for the host atoms

An example of a substitutional solid solution - copper and nickel.

These two elements are completely soluble in one another at all
proportions

Ref: William D Callister

Flake C. Campbell
Substitutional Solid Solution

Random : Cu-Ni Ordered : Cu-Au

Ref: NPTEL
 Rules to be satisfied for substitution
(Hume-Rothery rules)
1. Atomic size factor.
– The atomic radii of the solute and solvent atoms must
differ by no more than 15%

2. Crystal structure.
– The crystal structures of solute and solvent must match.

3. Electronegativity.
• The solute and solvent should have similar
electronegativity. If the electronegativity difference is too
great, the metals will tend to form intermetallic compounds
instead of solid solutions.
 Contd…
4. Valences.

• Complete solubility occurs when the solvent and

solute have the same valency. A metal will dissolve
a metal of higher valency to a greater extent than
one of lower valency.
 Substitution - Example
• Copper and Nickel
– These two elements are completely soluble in one
another at all proportions.

– The atomic radii for copper and nickel are 0.128 and
0.125 nm
– Both have the FCC crystal structure
– Their electro negativities are 1.9 and 1.8
– Valences +1 for copper (although it sometimes can
be + 2) and + 2 for nickel.
 Interstitial Solid Solution
• Atoms of dissolving element fit into the vacant spaces
between base metal atoms in the lattice structure.

• For interstitial solid solutions, impurity atoms fill the voids

or interstices among the host atoms

Ref: Flake C. Campbell

 Contd…
• For metallic materials that have relatively high
atomic packing factors, these interstitial positions
are relatively small.
• Consequently, the atomic diameter of an
interstitial impurity must be substantially smaller
than that of the host atoms.
 Interstitial - Example
• Carbon forms an interstitial solid solution when added to
iron; the maximum concentration of carbon is about 2%.

• The atomic radius of the carbon atom is much less than

that for iron: 0.071 nm versus 0.124 nm.
 Intermediate Phases
• These are phases whose chemical
compositions are intermediate between the
two pure metals, and whose crystalline
structures are different from those of the pure
metals.
• The difference in crystalline structure
distinguishes intermediate phases from
primary solid solutions, which are based on
pure metals.
 Contd…
• Some intermediate phases can accurately be
called intermetallic compounds, when, like
Mg2Pb, they have a fixed simple ratio of the
two kinds of atoms.
• However, many intermediate phases that exist
over a range of compositions are considered
to be intermediate or secondary solid
solutions.
 Important Terms
Phase
Homogeneous portion of a system that has uniform physical
and chemical characteristics.

• Solvent
– Element or compound that is present in the greatest amount; on
occasion, solvent atoms are also called host atoms

• Solute
– Denote an element or compound present in a minor
concentration.
 Important Terms
• Atomic Radius

– Measure of the size of atoms. Distance from the

nucleus to the boundary of surrounding cloud of
electrons.

• Electronegativity

– Chemical property that describes the tendency of an

atom or a functional group to attract electrons towards
itself
 Important Terms

Intermediate Phase

• When the amount of dissolving element in the alloy

exceeds the solid solubility limit of the base metal, a
second phase forms in the alloy.
 Important Terms
• Alloy
– Composed of 2 or more elements one of which is
metal
• Solid Solution
– Two or more elements are completely soluble in each
other
• Substitutional Solid Solution
– Solute or impurity atoms replace or substitute for the
host atoms
• Interstitial Solid Solution
– Atoms of dissolving element fit into the vacant spaces
between base metal atoms in the lattice structure.
 References
• William D Callister, Material Science and
Engineering, John Wiley and Sons, Singapore,
2007
• Elements of Metallurgy and Engineering
Alloys, ASM International 2008, Flake C.
Campbell
• http://nptel.ac.in
 Unit I

Phase Diagrams
 Contents
• Phase diagrams • Cooling curves
– Phase diagram ? • Gibb’s phase rule
– Why study about
phase diagram?
– Binary phase diagram
• Isomorphous phase
diagram
– Information from
phase diagram
 Phase Diagram
• Graphical means of representing the phases of a
metal alloy system as a function of composition and
temperature.
• Indicates the structural changes due to variation of
temperature and composition
• Best method to record the data related to phase
changes in many alloy systems.
• It is also known as equilibrium or constitutional
diagram
 Equilibrium
• State of minimum energy
• Condition at which there will be no change with time
• Equilibrium conditions may be approached by slow
heating and cooling
 Why Phase Diagram?
• Strong correlation between microstructure and
mechanical properties, and the development of
microstructure of an alloy is related to the
characteristics of its phase diagram.

• Provide valuable information about melting, casting,

crystallization, and other phenomena.
 Information from Phase Diagrams
• To show phases present at different compositions and
temperatures under slow cooling (equilibrium) conditions.

• To indicate equilibrium solid solubility of one

element/compound in another.

• To indicate temperature at which an alloy starts to

solidify and the range of solidification.
 Contd…

- To indicate the temperature at which different

phases start to melt.

- Amount of each phase in a two-phase mixture can

be obtained.
Binary Isomorphous : Cu-Ni

Ref: NPTEL
 Contd…
• Liquidus Line
– The line above which the alloy is liquid is called
the liquidus line
– Onset of solidification

• Solidus Line
– The line below which solidification completes is
called solidus line
– Completion of solidification
• Phase
– Homogeneous portion of a system that has uniform physical
and chemical characteristics.
– Physically distinct, chemically homogeneous and mechanically
separable regions of a system

• Component
– pure metals and/or compounds of which an alloy is composed.
For example, in a copper–zinc brass, the components are Cu
and Zn.
• System
– Combination of phases of one or more components
– E.g) iron-carbon, water sugar
– A system contains 2 or more components

• Variable
– A particular phase exists under various conditions of
temperature, pressure and concentration. These physical
parameters are called variables
Sugar Water Phase Diagram

Ref: William D Callister

Solubility Limit
• For many alloy systems and at some specific temperature,
there is a maximum concentration of solute atoms that
may dissolve in the solvent to form a solid solution; this is
called a solubility limit.

• The addition of solute in excess of this solubility limit

results in the formation of another solid solution or
compound that has a distinctly different composition.
Unary Phase Diagram
 Binary Phase Diagram

• A binary alloy is one that contains two components.

• Isomorphous
– Two metals are soluble in each other in the entire
range of compositions in both liquid and solid state
Cooling Curve of Pure Metal
 Cooling curve of pure metal (Cu)
• The liquid metal initially cools at a rate
called as the cooling rate until we
reach the beginning of the thermal
arrest.
• During thermal arrest the phase
change occurs and the metal liberates
its latent heat of fusion while keeping
the temperature constant to reach to
the end of the thermal arrest.
• This point is referred to as the freezing
point of the metal.
• On further cooling the metal tends to
reach the room temperature.
• The Slopes before and after thermal
arrest ,by value , depend upon the
specific heats of the liquid and solid
metals , respectively.
Cooling curves of isomorphous binary system

Ref: NPTEL
Construction of phase diagrams

Ref: NPTEL
 Gibb’s phase rule

P+F=C+2

P – No. of phases in equilibrium

F – No. of degrees of freedom
C – No. of components
2 – No. of external factors (pressure and temperature)
For metallurgical system, pressure has no appreciable effect
P+F=C+1
 Degrees of Freedom
• No. of variables (temperature, pressure or composition)
that could be changed independently without changing
the no. of phases existing in the system
Cooling curve of pure metal
Cooling curve of Binary Solid Solution
Application of Phase Rule to Phase
diagram

Ref: James F. Shackelford

Application of Phase Rule to Phase
diagram

Ref: James F. Shackelford

 Interpretation of Phase Diagram
• Three kinds of information available for a binary
system of known composition and temperature at
equilibrium

– Phases that are present

– Determination of phase composition
– Determination of phase amounts
Determination of phases present

Ref: William D Callister

 Contd…

• An alloy of composition 60 wt% Ni–40 wt% Cu at 1100C

would be located at point A – only single phase is
present

• 35 wt% Ni–65 wt% Cu alloy at 1250C (point B) will

consist of both alpha and liquid phases at equilibrium
Determination of Phase Composition

Ref: William D Callister

 Procedure
A tie line is constructed across the two-phase region at
the temperature of the alloy.

The intersections of the tie line and the phase

boundaries on either side are noted.

Perpendiculars are dropped from these intersections to

the horizontal composition axis, from which the
composition of each of the respective phases is read.
 Contd…
• For example, consider again the 35 wt% Ni–65 wt%
Cu alloy at 1250C located at point B

• The perpendicular from the intersection of the tie line

with the liquidus boundary meets the composition
axis at 31.5 wt% Ni–68.5 wt% Cu, which is the
composition of the liquid phase

• Solid solution phase, of 42.5 wt% Ni–57.5 wt% Cu.

 Determination of phase amounts
(Lever rule or inverse lever rule)

Fraction of phase 1 = (C2 - C) / (C2 - C1)

Fraction of phase 2 = (C - C1) / (C2 - C1).

Determination of Phase Amounts

C(L) – 31.5
C (alpha) – 42.5
C (o) - 35

Ref: William D Callister

Weight Fraction of Liquid Phase

Ref: William D Callister

Weight Fraction of Solid Phase

Ref: William D Callister

Ref: Flake C. Campbell
Ref: Flake C. Campbell
 References
• William D Callister, Material Science and
Engineering, John Wiley and Sons, Singapore,
2007
• Elements of Metallurgy and Engineering
Alloys, ASM International 2008, Flake C.
Campbell
• http://nptel.ac.in
Phase Diagrams - Types
 Components completely soluble in the
liquid state
• Completely soluble in the solid state

Ref: William D Callister

 Components completely soluble in the liquid state
and completely insoluble in solid state

Ref: Sidney H Avner

 Components completely soluble in the liquid
state and partly soluble in solid state

Ref: Sidney H Avner

 Binary Eutectic System – (Cu-Ag)

Ref: William D Callister

 • Point ‘E’ invariant point (Eutectic Point)
• Eutectic – easily melted
• Eutectic Reaction

Ref: William D Callister

 • Three single-phase regions
– phase is a solid solution rich in copper;
– p phase solid solution also has an FCC structure,
but copper is the solute.
– Liquid phase
• Three two-phase regions

Ref: William D Callister

 • Terminal solid solution

Ref: William D Callister

 A

D
C

Ref: William D Callister

• Region AB
P+F=C+1
1+F=2+1
F = 2 (Bivariant system)
• Region BC
P+F=C+1
2+F=2+1
F = 1 (Univariant)
• Region CD
P+F=C+1
3+F=2+1
F = 0 (Invariant system)
• Region DE
P+F=C+1
2+F=2+1
F = 1 (Univariant)
 Components completely soluble in the liquid
state and partly soluble in solid state

Ref: William D Callister

Peritectic phase diagram

Eg. Pt - Ag

Ref: NPTEL
 Monotectic Reaction

Eg. Cu - Pb

Ref: NPTEL
 References
• William D Callister, Material Science and
Engineering, John Wiley and Sons, Singapore,
2007
• Sidney H Avner, Introduction to Physical
Metallurgy, McGRAW-HILL
• http://nptel.ac.in
Iron-Carbide Diagram
Cooling curve of pure iron
 Iron-Carbide Diagram
• Iron is allotropic metal, which means that it exists in
more than one type of lattice structure (BCC/FCC)
depending upon the temperature

• At temperature above 1540 C, iron is in liquid form

• Liquid iron starts solidifying at 1540 C. The temperature

remains constant till solidification is completed

• When solidification is completed, the iron is in δ form,

with a BCC structure
• When the temperature drops down to 1395 C, allotropic
modification of iron takes place from δ-iron to γ-iron with
FCC structure
• Temp. 1395 C to 910 C no change
• At 910 C, γ-iron changes to α–iron with BCC structure
• α–iron at 910 C is non-magnetic and remains so till 768 C
• At 768 C termed as curie temperature, non-magnetic to
magnetic α–iron
 Iron Carbide Diagram
• Most important binary alloy – Iron Carbon
system
– Steels constitute greatest amount of metallic
materials used by man
– Basis for understanding the properties and heat
treatment of steel and the effect of alloying elements
in alloy steel
– Solid state transformations that occur in steels are
varied and interesting.
Ref: William D Callister
• The part of iron-carbon phase diagram plotted for
concentrations (weight percent) up to 6.67% carbon is of
commercial significance

• This part between pure iron and iron carbide (Fe3C) is

called as iron-iron carbide diagram
 Classification of Ferrous alloys.
• Classification of Ferrous alloys based on
carbon content
– Iron : contains less than 0.008 wt% Carbon
– Steels: carbon content between 0.008 and 2.14
wt% . Steels normally contains less than 1 wt% C
– Cast Iron: carbon content between 2.14 and 6.7
wt%. Commercial cast irons contain less than 4.5
wt%
 Individual Phases in Iron-Carbide
1. α–ferrite (BCC) Fe-C solid solution
2. γ-austenite (FCC) Fe-C solid solution
3. δ-ferrite (BCC) Fe-C solid solution
4. Fe3C (iron carbide) or cementite - an inter-metallic
compound
5. liquid Fe-C solution
 α–ferrite

• In the BCC ferrite, only small

concentrations of carbon are
soluble; the maximum solubility is
0.022 wt% at 727 C.
• The limited solubility is explained
by the shape and size of the BCC
interstitial positions, which make it
difficult to accommodate the
carbon atoms.
• Relatively soft, density 7.88 g/cubic
cm
• It is ferromagnetic upto 768 C and
paramagnetic at 768 C during
heating

Ref: William D Callister

 γ-austenite
• Interstitial solid solution of carbon in γ-iron

• Solid solubility of carbon in austenite is maximum of

2.08% at 1147 C

• It is soft, ductile, malleable and non-magnetic

Ref: William D Callister

 δ-ferrite
• Interstitial solid solution
of carbon in BCC δ-iron

• Maximum solid solubility

of carbon is 0.1% C at
1492 C

Ref: William D Callister

 Pearlite
• The eutectoid mixture
of fine plate-like
lamellar mixture of
ferrite and cementite.
• Formed from austenite
that contains 0.80 wt.%
carbon during slow
cooling at 727 C.

Ref: William D Callister

 Ledeburite
• The eutectic mixture of austenite and
cementite.
• Formed from liquid that contains 4.30 wt.%
carbon during slow cooling at 1130 C.
• Not stable below 727 C, where austenite of
ledeburite transformed into pearlite.
• The structure is then called “transformed
ledeburite.”
 Cementite (Fe3C) or iron carbide
• An interstitial intermetallic compound of iron carbide
with an orthorhombic structure.
• Contains 6.67 wt % carbon
• The hardest and brittle structure that appears on the iron
– iron carbide diagram.
• Low tensile strength and high compressive strength
 Phase Reactions
• Peritectic, at 1493 deg.C, with low wt% C
alloys (almost no engineering importance).
• Eutectic, at 1147 deg.C, with 4.3wt% C, alloys
called cast irons.
• Eutectoid, at 727 deg.C with eutectoid
composition of 0.8wt% C, two-phase mixture
(ferrite & cementite). They are steels.
 Contd…
The diagram shows three horizontal lines which indicate
isothermal reactions (on cooling / heating):
•First horizontal line is at 1493°C, where peritectic reaction
takes place:
Liquid + δ ↔ austenite
•Second horizontal line is at 1147°C, where eutectic reaction
takes place:
liquid ↔ austenite + cementite
•Third horizontal line is at 727°C, where eutectoid reaction
takes place:
austenite ↔ pearlite (mixture of ferrite &
cementite)
 Eutectoid Transformation

Pearlite
• The eutectoid mixture of fine plate-like lamellar
mixture of ferrite and cementite.
• Formed from austenite that contains 0.80 wt.%
carbon during slow cooling at 727 C.
Phase transformations – Peritectic
Transformation
Reactions
Microstructure of Eutectoid composition

Ref: William D Callister

 Microstructure of Hypoeutectoid

Ref: William D Callister

 Microstructure of 0.38 wt.% steel

Ref: William D Callister

 Microstructure of Hypereutectoid

Ref: William D Callister

 1.4 wt% steel @1000x

Ref: William D Callister

The crystal structure of austenite is [GATE 2011]
(A) Body centered Cubic
(B) Face centered Cubic
(C) Hexagonal closed packed
(D) Body centered tetragonal
If a particular Fe-C alloy contains less than 0.83
% carbon, it is called [GATE 2006]
(A) High speed steel
(B) Hypoeutectoid steel
(C) Hypereutectoid steel
(D) Cast iron
When the temperature of a solid metal
increases. [GATE 2005]
(A) Strength of the metal decreases but ductility increases.
(B) Both strength and the ductility of the metal decreases.
(C) Both strength and the ductility of the metal increases.
(D) Strength of the metal increases but ductility decreases.
The percentage of carbon in grey cast iron is in
the range of [GATE 2004]
(A) 0.25 to 0.75 percent
(B) 1.25 to 1.75 percent
(C) 3 to 4 percent
(D) 8 to 10 percent
 References
• William D Callister, Material Science and
Engineering, John Wiley and Sons, Singapore,
2007
• Sidney H Avner, Introduction to Physical
Metallurgy, McGRAW-HILL
• http://nptel.ac.in
 S9 - Microstructural aspects and
invariant reactions in Fe-C diagram

08-02-2021 Dept. of Mechanical Engg., 1

 Development of Microstructure in
Iron-Carbon alloys/Fe-C Diagrams

• Various microstructures that may be produced in steel alloys

and their relationships to the iron–iron carbon phase diagram.
• An alloy of eutectoid composition (0.76 wt% C) as it is cooled
from a temperature within the phase region, say, 800˚C—that
is, beginning at point a in Figure, moving down the vertical
line xx.
• The alloy is composed entirely of the austenite phase having
a composition of 0.76 wt% C and corresponding
microstructure.
• The microstructure for this eutectoid steel that is slowly
cooled through the eutectoid temperature consists of
alternating layers or lamellae of the two phases ( and Fe3C)
that form simultaneously during the transformation.
08-02-2021 Dept. of Mechanical Engg., 2
 Microstructure of Eutectoid composition
Schematic representations of the
microstructures for an iron–carbon alloy of
eutectoid composition (0.76 wt% C) above and
below the eutectoid temperature.

Ref: William D Callister

08-02-2021 Dept. of Mechanical Engg., 3

 Microstructure of Hypoeutectoid

Ref: William D Callister

08-02-2021 Dept. of Mechanical Engg., 4

 Microstructure of 0.38 wt.% steel

Ref: William D Callister

08-02-2021 Dept. of Mechanical Engg., 5
 Microstructure of Hypereutectoid

Ref: William D Callister

08-02-2021 Dept. of Mechanical Engg., 6

 1.4 wt% steel @1000x

Ref: William D Callister

08-02-2021 Dept. of Mechanical Engg., 7

08-02-2021 Dept. of Mechanical Engg., 8
08-02-2021 Dept. of Mechanical Engg., 9
The crystal structure of austenite is [GATE 2011]
(A) Body centered Cubic
(B) Face centered Cubic
(C) Hexagonal closed packed
(D) Body centered tetragonal

08-02-2021 Dept. of Mechanical Engg., 10

If a particular Fe-C alloy contains less than 0.83
% carbon, it is called [GATE 2006]
(A) High speed steel
(B) Hypoeutectoid steel
(C) Hypereutectoid steel
(D) Cast iron

08-02-2021 Dept. of Mechanical Engg., 11

When the temperature of a solid metal
increases. [GATE 2005]
(A) Strength of the metal decreases but ductility increases.
(B) Both strength and the ductility of the metal decreases.
(C) Both strength and the ductility of the metal increases.
(D) Strength of the metal increases but ductility decreases.

08-02-2021 Dept. of Mechanical Engg., 12

The percentage of carbon in grey cast iron is in
the range of [GATE 2004]
(A) 0.25 to 0.75 percent
(B) 1.25 to 1.75 percent
(C) 3 to 4 percent
(D) 8 to 10 percent

08-02-2021 Dept. of Mechanical Engg., 13

 References
• William D Callister, Material Science and
Engineering, John Wiley and Sons, Singapore,
2007
• Sidney H Avner, Introduction to Physical
Metallurgy, McGRAW-HILL
• http://nptel.ac.in

08-02-2021 Dept. of Mechanical Engg., 14