Chapter 4

4.0 IMPERFECTIONS IN SOLIDS AND
PHASE DIAGRAM

4.1 IMPURITIES IN SOLIDS

• impurities are chemical substances inside a confined amount of liquid, gas, or
solid, which differ from the chemical composition of the material or compound.

• Any irregularity in the pattern of crystal arrangement in a solid lattice is
called imperfection in solids (also called impurities). The occurrence of defects
takes place when crystallization (the process of formation of crystals) occurs at a
very fast or at an intermediate rate.

• There is no such thing as a perfect crystal. Crystalline imperfections (or defects) are
always present. In addition, impurity atoms are always present. Many of the
properties of materials are sensitive to the presence of imperfections, and not
necessarily in an adverse way

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4.1 IMPURITIES IN SOLIDS

• Point defects exist by definition as a point (0 – dimensional) and include
vacancies, interstitial atoms, and substitutional impurity atoms.

• These point defects are shown in the two figures below:

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4.1 IMPURITIES IN SOLIDS

4.1 (a) Term And Formation Of Solid Solutions

• Solid solution is a solid-state solution of one or more solutes
in a solvent.

• Solvent: Solvent is a substance with dissolving capability, thus
can dissolve another substance.

• Solute: Solute is a substance that dissolves in a solvent in
order to form a solution.

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4.1 IMPURITIES IN SOLIDS

4.1 (a) Term And Formation Of Solid Solution

Add to

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

There are two type of solid solution:

a. Substitution solid solution
b. Interstitial solid solution

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

a. Substitutional Solid Solution
- atoms of the solvent metal and solute element - similar sizes
(not more than 15% difference)
- part of the solvent atoms are substituted by atoms of the

alloying element

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

a. Substitutional Solid Solution
• Two types of substitutional solid solution:

– Disordered/Randomly Arrange: Atomic particles (solute) take place of
the main atoms (solvent) at random and haphazard arrangement

– Ordered/Properly Arrange: Atomic particles take place of the main
atoms (solvent) and their arrangements are in order.

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

a. Substitutional Solid Solution

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

b. Interstitial Solid Solution
• Atoms of the alloying elements are smaller than the

atoms of the matrix metal
• Atomic of small particles (solute) fill the spaces

between the main atoms (solvent) in the lattice.

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4.1 IMPURITIES IN SOLIDS

4.1(b) Types Of Solid Solution

b. Interstitial Solid Solution

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4.2 PHASE
DIAGRAM

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4.2 PHASE DIAGRAM

• Phase diagram is a graphical representation of the physical states of
a substance under different conditions of temperature and
pressure.

• A typical phase diagram has pressure on the y-axis and temperature
on the x-axis. As we cross the lines or curves on the phase diagram,
a phase change occurs. In addition, two states of the substance
coexist in equilibrium on the lines or curves.

• Phase diagrams are useful to metallurgists for selection of alloys
with a specific composition and design and control of heat
treatment procedures that will produce specific properties. They
are also used to troubleshoot quality problems.

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4.2 PHASE DIAGRAM

4.2(a) Solubility limits
What is solubility?
• A substance is soluble in another if the solute atoms dissolve in the solvent to form

a solution.

• The behaviour of sugar in water can be plotted on a graph of composition against

temperature. There is a solubility limit, shown by the line on the graph.

• At all temperatures and compositions to the left of this line, there is one phase - a

solution of sugar in water. To the right of this line, there are two phases present,

the solution and solid sugar (that settles at the bottom of the cup). 17

4.2 PHASE DIAGRAM

4.2(a) Solubility limits
• Solubility Limit of a component in a phase is the

maximum amount of the component that can be
dissolved in
• The same concepts apply to solid phases:
**Cu and Ni are mutually soluble in any amount
(unlimited solid solubility), while C has a limited solubility
in Fe.

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4.2 PHASE DIAGRAM

1. Equilibrium a state of balance of stability.

2. Equilibrium is graphical representations of what
Phase Diagram phases are present in a materials
system at various temperatures,
pressures and compositions.

3. Phase is a portion of a system that has
uniform physical and chemical
characteristics.

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4.2 PHASE DIAGRAM

4. Homogeneous a single-phase system.

5. Heterogeneous systems with two or more phases
systems.

6. Compositions percentage of certain materials
contains purposely or not added to
another material.

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Phase Equilibrium

• Phase diagrams are essential tools for phase equilibrium
engineering as they provide valuable hints to understand the
process and to assess the feasible and optimum operating
regions.

• A system is at equilibrium if at constant temperature,pressure
and composition the system is stable, not changing with time.

• For one component systems, the equilibrium state of the
system is defined by two independent parameters (P and T),
(T and V), or (P and V).

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4.2(b) BINARY ISOMORPHOUS SYSTEM

• Isomorphous system - complete solid
solubility of the two components (both in the
liquid and solid phases).

• Example of isomorphous system: Cu-Ni (the
complete solubility occurs because both Cu
and Ni have the same crystal structure, FCC,
similar radii and electronegativity).

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CHAPTER 4.0 SOLID SOLUTION AND EQUILIBRIUM PHASE DIAGRAM DJJ3213 MATERIAL SCIENCE

4.2(b) BINARY ISOMORPHOUS SYSTEM

the temperature above
which the substance is
stable in a liquid state

Solidus line

Liquidus line the temperature below
which the substance is
the substance consists stable in the solid state
of a mixture of crystals
and liquid. Solidus,

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Figure 4.2 (b) Cu-Ni Phase Diagram

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4.2 (c) Interpretation of phase diagram

• Figure 4.2 (b) contains the copper-nickel phase diagram. Its system
is termed as being isomorphous.

• This diagram has three different phase regions, the alpha region,
the liquid region, and the alpha + liquid region, which are defined
by specific compositions and temperatures as illustrated in figure.

• Both points A and B are located in the alpha and the alpha + liquid
regions respectively.

• The phase boundaries are separated by two lines. The line
separating the liquid and the alpha + liquid regions is the liquidous
line. The line separating the alpha and the alpha + liquid regions is
the solidus line. The intersection of these two lines signify the
melting temperatures of the two constituents individually.

• The Cu-Ni system is especially noted for its complete liquid and
solid solubility of its constituents, and is thusly identified as an
isomorphous system.

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Metal solidification process

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4.3 (d) Development of microstructure in isomorphous alloys

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4.3 (d) Development of
microstructure in isomorphous alloys

• Figure 4.3(d) represents the development of microstructure
during the equilibrium solidification of a 35 wt% Ni - 65
wt% Cu alloy.

• Solidification in the solid + liquid phase occurs gradually
upon cooling from the liquidus line.

• The composition of the solid and the liquid change
gradually during cooling.

• Nuclei of the solid phase form and they grow to consume
all the liquid at the solidus line.

• Diffusion in the solid state is very slow.
• The new layers that solidify on top of the existing grains

have the equilibrium composition at that temperature but
once they are solid their composition does not change.

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IRON-CARBON
PHASE DIAGRAM

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4.3 IRON – CARBON Phase Diagram

STEEL CAST IRON

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4.3 IRON – CARBON Phase Diagram

❖In their simplest form, steels are alloys of Iron
(Fe) and Carbon (C). The Fe-C phase diagram is
a fairly complex, but we will only consider the
steel part of the diagram, up to around 7%
Carbon.

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• C is an interstitial impurity in Fe. It forms a solid
solution with α, γ, δ phases of iron.

• Maximum solubility in BCC α-ferrite is limited
(max. 0.022 wt% at 727 °C) - BCC has relatively
small interstitial positions

• Maximum solubility in FCC austenite is 2.14 wt%
at 1147 °C - FCC has larger interstitial positions.

• Mechanical properties: Cementite is very hard
and brittle - can strengthen steels. Mechanical
properties also depend on the microstructure,
that is, how ferrite and cementite are mixed.

• Magnetic properties: α -ferrite is magnetic below
768 °C, austenite is non-magnetic

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CHAPTER 4.0 SOLID SOLUTION AND EQUILIBRIUM PHASE DIAGRAM DJJ3213 MATERIAL SCIENCE

4.3 IRON – CARBON EQUILIBRIUM PHASE
DIAGRAM

Phases Description
α-ferrite • Solid solution of carbon in iron.
• Soft and ductile structure
• BCC crystal structure
• The maximum carbon solubility of carbon in iron is 0.022%

at 723oC.
• Stable form of iron at room temperature

γ-austenite • solid solution of carbon in γ iron
• FCC crystal structure
• high solubility for carbon compared with α ferrite.
• maximum solubility 2.14% at 1147oC.
• Is not stable below the eutectic temperature (727 °C)

unless cooled rapidly

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CHAPTER 4.0 SOLID SOLUTION AND EQUILIBRIUM PHASE DIAGRAM DJJ3213 MATERIAL SCIENCE

4.3 IRON – CARBON EQUILIBRIUM PHASE
DIAGRAM

Phases Description
δ - Ferrite • solid solution of carbon in iron
• BCC crystal structure
• The maximum solubility or C in Fe is 0.09% at 1495oC.
• Stable only at high T, above 1394 °C
• Melts at 1538 °C

Fe3C (iron • Cementite is an intermetallic compound which contains
carbide or 6.67% C and 93.3% Fe.
cementite)
• Cementite is a hard and brittle compound.

Pearlite • When alloy of eutectoid composition (0.76 wt % C) is

cooled slowly it forms perlite, a lamellar or layered structure
of two phases: α-ferrite and cementite (Fe3C).
• Mechanically, pearlite has properties intermediate to soft,

ductile ferrite and hard, brittle cementite.

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Development of microstructure in
iron-carbon alloys

Draw, explain & Submit - cidos

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The influence of other alloying
elements

Answer & Submit - cidos

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Ferrite to pearlite transformation

Ferrite Pearlite

0.8% Carbon

CARBON CONTENT RISES

CHAPTER 4.0 SOLID SOLUTION AND EQUILIBRIUM PHASE DIAGRAM DJJ3213 MATERIAL SCIENCE

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