2. Syllabus:
• Definitions of Terms,
• Rules of Solid Solubility
• Gibb’s Phase Rule
• Solidification of Pure metal
• Plotting Equilibrium Diagrams
• Lever Rule
• Iron-Iron carbide equilibrium
diagram
• Critical temperatures
• Solidification and microstructure
of slowly cooled steels
• Non-equilibrium cooling of steels
• Classification and application of
steels
• Specification of steels
• TTT diagram
• Critical cooling rate
• CCT diagram
3. Definition of Terms
• System: A part of the universe under study
• System: A part of the universe under study
• Phase: A homogeneous, physically distinct and
mechanically separable part of the system under
study
• Phase: A homogeneous, physically distinct and
mechanically separable part of the system under
study
• Component: Elements present in the system.
• Component: Elements present in the system.
• Alloy: Mixture of two or more elements having
metallic properties.
• The element present in the largest proportion is
metal.
• Others can be metals or non-metals.
• Alloy: Mixture of two or more elements having
metallic properties.
• The element present in the largest proportion is
metal.
• Others can be metals or non-metals.
4. Concept of Alloying
• Alloy- A substance that possesses metallic properties and is composed of two or
more elements of which at least one is metal, is called an alloy
• Base Metal- The metal present in the alloy in largest portion
• Alloying Elements- Other elements which are in small proportion
Why Alloying elements are added?
Added intentionally , to get desirable
properties which are not found in the
base metal
• Tensile strength, hardness and
toughness
• Corrosive and oxidation resistance
• Machinability
• Elasticity
• Hardenability
• Creep strength
• Fatigue resistance
Why the properties of an alloy are
different from base metal?
As the structure of the alloy is
changed due to addition of alloying
element.
The type and extent of change of
properties depend on whether the
alloying elements are insoluble in,
dissolved in or form a new base with base
metal
Each constituent of an alloy is called
component
Pure Metal- One component
Alloy- Two component, three
component etc
5. Solution
It is the homogeneous mixture consisting of one phase only
Types of Solution
1. Simple Eutectic Solution
-The two components of an alloy system are soluble in liquid state but
separate out in the solid state, each maintaining its own identity.
-e.g. Cadmium and Bismuth
2. Solid Solution
- The two components of an alloy system are soluble in each other both in
liquid and solid state
- e.g. Copper and Nickel
3. Combination type solution
- on solidifying, the two components of a binary alloy may show limited
solubility
4. Intermetallic Compounds
- These types of compounds may find place in between the solid solution and
chemical compound
- Elements combine to form inter-metallic compounds on solidification,
when their affinity is great
- Intermetallic compound contain definite proportions of each components
- They are hard and brittle
- used as a bearing material
Example- Formation of cementite (Intermetallic compound) when 6.67%
carbon is added to iron
6. Solid Solution
• It is a homogenous mixture of two different kinds of atoms in solid state and have
single crystal structure
• A solid solution is formed when two metals are completely soluble in liquid state as
well as in solid state
• Solute - Minor part of the solution
• Solvent- Major part of the solution
• Examples - Sterling Silver (92.5% Silver + 7.5% Copper), Brass (64% Copper + 36%
Zinc) Solid Solutions
Substitutional
solid solution
Ordered Solid
Solution
Disordered
Solid Solution
Interstitial
solid solution
7. Substitutional Solid Solution
• The atoms of the solute substitute for atoms of the solvent in the lattice structure of the
solvent
• Formation is possible, if the atomic size of the two metals are nearly equal
• Copper atoms substitute for nickel without disturbing the FCC structure of nickel
Substitutional
solid solution
Ordered Solid
Solution
Disordered
Solid Solution
8. ORDERED SUBSTITUTIONAL
SOLID SOLUTION
• Substitution of solute atoms in
solvent atoms is by definite order
• Hard
DIS-ORDERED SUBSTITUTIONAL
SOLID SOLUTION
• No definite order
• Soft
9. Interstitial Solid Solution
• Atoms of solute occupy the interstitial sites of solvent atoms
• Atomic size of solute is very much small as compared to atomic size of
solvent atoms
• Soft, ductile, and malleable
• Examples- Iron with Carbon
10. Interstitial Solid Solution
Vs
Substitutional Solid Solution
Interstitial Solid Solution Substitutional Solid Solution
1. In this solid solution the solute atom
occupies position in between the
interstitial sites or vacant places of
solvent atoms.
1. In this solid solution the solute atom
replaces the position of solvent
atom.
2. The atomic size of solute is smaller
than solvent atom
2. The atomic size of solute and
solvent atoms are almost equal.
3. It is not governed by Hume Rothery
rules.
3. It is governed by Hume Rothery
rules.
4. Formed via interstitial mechanism 4. Formed via atom exchange
mechanism
5. e.g. Steel 5. e.g. Au-Cu solution, bronze (Cu-Sn)
11. Hume Rothery’s Rules for the formation of Substitutional
Solid Solutions
1. Crystal Structure Factor
The two elements should have the same
type of crystal structure
2. Relative Size Factor
For extensive solid solubility the
difference in atomic radii of two
elements should be less than 15 pm
Element Atomic
Radius
Crystal
Structure
Difference
between
Atomic Radii
Solubility
Silver 144 pm FCC 31pm (>15) 1.5%
Lead 175pm FCC 0.1%
Copper 128pm FCC 4pm (<15) Completely
Soluble
Nickel 124pm FCC
3. Chemical Affinity Factor
Solid solubility is favoured when the two
metals have lesser chemical affinity
4. Relative Valence Factor
• A metal of higher valency
can dissolve only a small
amount of a lower valency
metal, while the lower
valency metal may have
good solubility for the
higher valency metal
• Aluminium- Nickel Alloy
system
• Al dissolves in Nickel 5%
• Nickel dissolves in Al only
0.04%
In the formation of solid solutions, the solubility limit of solute in the
solvent is governed by certain factors. These factors are known as Hume
Rothery’s rules of solid solubility
12.
13. Gibb’s Phase Rule
Statement: Under the equilibrium conditions, the following relations must be satisfied
𝑃 + 𝐹 = 𝐶 + 2
Where,
P= No. of phases existing in a system
F = Degree of freedom i.e. the no. of variables such as temp. press. or concentration that can be
changed independently without changing the number of phases existing in the system
C = no. of elements in the system and
2 = represents any two variables out of temp. press. or concentration
Most of the common studies are done at constant pressure i.e. 1 atm and
hence pressure is no more variable . For such cases Gibb’s Phase Rule
becomes
𝐹 = 𝐶 − 𝑃 + 1
14. Significance of Gibb’s Phase Rule
• It enables us to predict and check the processes that can occur in alloys during
heating or cooling
• Using this rule, it is possible to determine whether the solidification process
takes place at a constant temperature or within a certain temperature
interval
• It also indicates the number of phases that can exists simultaneously in a
system
15. Solidification of Pure Metal
Small nuclei act as centres
for crystal growth
Small dendrites begin to
develop from the nuclei
Dendrites continue to
grow
As the dendrites grow,
the spaces between them
fill in
Solidification is complete; little
evidence of the dendrite structure
remains
16. Cooling Curves
• Cooling curve is a graph that represents the change of phase of a system typically from
gas to solid or liquid to solid
• The variable Time is taken on X-axis and Temperature on Y-axis
a cooling curve used in castings
Types of Cooling Curves
1. for pure metal
2. for binary solid solutions
alloys
3. For binary eutectic alloy
4. for off-eutectic binary alloys
17. Cooling Curve for Pure Metals
Application of Phase rule
In region AB
P + F = C +1
1 + F = 1 + 1
Therefore, F = 1 (Univarient system)
The meaning of, F = 1 is that the temperature
can be varied without changing the liquid
phase existing in the system.
In region BC;
P + F =C + 1
2 + F = 1 + 1 Therefore, F = 0 (Non-variant
system)
The meaning of F= 0 is that the temperature
cannot be varied without changing the liquid
and solid phases existing in the system.
Hence pure metals solidify at constant
temperature.
In region CD:
P + F = C + 1
1 + F = 1 + 1
Therefore, F = 1
The meaning of F =1, so temperature can be
changed without changing the solid phase
existing in the system.
18. Cooling Curve for Binary Solid Solution Alloy
Application of Phase rule
In the region AB:
P + F = C + 1
1 + F = 2 + 1
Therefore, F = 2
It means that, in the region AB, both the
temperature and concentration can be varied
independently without changing the liquid phase.
In region BC:
P + F = C + 1
2 + F = 2 + 1
Therefore, F = 1
It means that any one variable out of
temperature and concentration can be changed
independently without changing the solid and
liquid phases existing in the system.
From this it is clear that solid solution alloys
solidify over a range of temperature.
In region CD:
P + F = C + 1
1 + F = 2 + 1
F = 2
19. Cooling Curve for Binary Eutectic Alloy
Application of Phase rule
In the region AB:
P + F = C + 1
1 + F = 2 + 1
Therefore, F = 2
Bivarient system.
In region BC:
P + F = C + 1
3 + F = 2 + 1
Therefore, F = 0
Invariant system
In region CD:
P + F = C + 1
2 + F = 2 + 1
F = 1
Univariant system
20. Cooling Curve for Off-eutectic Binary Alloy
Application of Phase rule
In the region AB:
P + F = C + 1
1 + F = 2 + 1
Therefore, F = 2
Bivarient system.
In region BC:
P + F = C + 1
2 + F = 2 + 1
Therefore, F = 1
Univariant system
In region DE:
P + F = C + 1
2 + F = 2 + 1
F = 1
Univariant system
In region CD:
P + F = C + 1
3 + F = 2 + 1
F = 0
Nonvariant system
21. Equilibrium Diagram
• Indicates the phases existing in the system at any temperature
and composition
• Parameters X-axis (Weight percentage of solute), Y-axis
(Temperature)
• Used to find out the amounts of phases existing in a given alloy
with their compositions at any temperature
• From the amounts of phases at room temperature, in certain
cases, it is possible to estimate the approximate properties of
the alloy.
22. Plotting of Equilibrium or Phase Diagram
(Demonstrated by using Cu-Ni System)
• Plotted by the method of thermal analysis using the data obtained by
cooling curves
• Cu-Ni have 100% solubility in the liquid and solid state
Stapes used to obtain Phase Diagram
• Prepare large number of alloys of varying compositions, say with variations of
10% Ni and mark them as below ; Material no. 1 and 11 are pure metals, and no.
2 to 10 and alloys.
% Cu 100 90 80 70 60 50 40 30 20 10 0
% Ni 0 10 20 30 40 50 60 70 80 90 100
Material No. 1 2 3 4 5 6 7 8 9 10 11
23. Stapes used to obtain Phase Diagram
• Note down the liquidus and solidus temperatures of these
materials.
(Since material 1 and 11 are pure metals, they solidify at constant
temperature)
• Transfer these temperatures to temperature v/s concentration
graph.
• Corresponding to material 1 and 11 (Pure Metals) only one point
is obtained
• Draw the smooth curves through the points L1 to L11 and S1 to S11
which represents liquidus and solidus
27. Steps to Determine the amount of phases in a
binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
28. Steps to Determine the amount of phases in
a binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
Draw a vertical line for the
composition
29. Steps to Determine the amount of phases in
a binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
Draw horizontal line at the
required temperature (T) on
both sides of the composition
till it touches the liquidus and
solidus lines
T
P Q R
Intercepts P and R are called
arms of lever
Line PR is called a Tie line
30. Steps to Determine the amount of phases in
a binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
T
P Q R
Consider the composition Q which
contains
(S) Amount of Solid and
(L) Amount of Liquid
Let,
S + L = 1
Therefore,
L = 1 - S
Now,
Q = S × R + L × P
= S × R + (1 – S) × P
=SR + P – SP
Therefore,
Q – P = S (R – P)
𝐒 =
𝐐 − 𝐏
𝐑 − 𝐏
31. Steps to Determine the amount of phases in a
binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
T
P Q R
𝐒 =
𝐀𝐫𝐦 𝐏𝐐
𝐀𝐫𝐦 𝐏𝐑
Therefore,
The amount of Solid phase,
And
The amount of Liquid phase,
𝐋 = 𝟏 − 𝐒
𝐋 = 𝟏 −
𝐀𝐫𝐦 𝑷𝑸
𝐀𝐫𝐦 𝑷𝑹
𝐋 =
𝐀𝐫𝐦 𝐐𝐑
𝐀𝐫𝐦 𝑷𝑹
32. The tie line PR acts as a lever arm and point Q acts as a Fulcrum point, hence it is
called as Lever Rule
LIQUID SOLID
P Q R
Lever Arm
Fulcrum Point
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐒𝐨𝐥𝐢𝐝 =
𝐀𝐫𝐦 𝐏𝐐
𝐀𝐫𝐦 𝐏𝐑
=
𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐋𝐞𝐧𝐠𝐭𝐡 𝐨𝐟 𝐀𝐫𝐦
𝐓𝐨𝐭𝐚𝐥 𝐋𝐞𝐧𝐠𝐭𝐡 𝐨𝐟 𝐀𝐫𝐦
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐥𝐈𝐐𝐔𝐈𝐃 =
𝐀𝐫𝐦 𝐐𝐑
𝐀𝐫𝐦 𝐏𝐑
=
𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐋𝐞𝐧𝐠𝐭𝐡 𝐨𝐟 𝐀𝐫𝐦
𝐓𝐨𝐭𝐚𝐥 𝐋𝐞𝐧𝐠𝐭𝐡 𝐨𝐟 𝐀𝐫𝐦
33. Types of Phase Diagram
• Isomorphous System
• Eutectic System
• Partial Eutectic System
• Layer System
34. Isomorphous System
Exemples: Cu-Ni, Au-Ag, Au-Cu, Mo-W,
Mo-V, Mo-Ti, W-V, Au-Ni, and Bi-Sb
These diagrams are of a
loop type and are obtained
for two metals having
complete solubility in the
liquid state as well as solid
state
35. Eutectic system
Liquid and two solid phases exist in equilibrium at the eutectic composition and the
eutectic temperature
the melting point of the eutectic alloy is lower
than that of the components
Examples: Pb-As, Bi-Cd, Th-Ti, and Au-Si
36. Partial Eutectic System
These diagrams are obtained for two metals which have complete solubility in the liquid
state and partial solubility in the solid state.
Examples- Ag-Cu, Pb-Sn, Sn-Bi, Pb-Sb, Cd-Zn, and Al-Si
37. Layer Type System
These diagrams are obtained for two metals which have complete insolubility in the
liquid as well as solid state.
Examples- Cu-Mo, Cu-W, Ag-W, Ag-Fe etc.
38.
39. • Consider a binary
system
• Lever rule will be used
to determine the
amount of liquid and
amount of solid
Steps:
• Draw a vertical line
for the composition.
• Horizontal line is
drawn at the required
temperature on both
Steps:
• Draw a vertical line
for the composition.
• Horizontal line is
drawn at the required
temperature on both
sides of the composition line, till it intercepts the transformation lines.
• The intercepts on either side of the composition line are called as
arms of lever and complete line is called tie line
sides of the composition line, till it intercepts the transformation lines.
• The intercepts on either side of the composition line are called as
arms of lever and complete line is called tie line
40. The relation between arms of
lever and amount of phases
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 × 𝐴𝑟𝑚 𝑃𝑄
= 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑 × 𝐴𝑟𝑚 𝑄𝑅
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 =
41. Steps to Determine the amount of phases in a
binary system
Liquid
Liquid + Solid
Solid
Weight % B
0
100
Temperature
0
C
Liquidus
solidus
T
P Q R
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐒𝐨𝐥𝐢𝐝
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐋𝐢𝐪𝐮𝐢𝐝
=
𝐀𝐫𝐦 𝑷𝑸
𝐀𝐫𝐦 𝐏𝐑
𝐀𝐫𝐦 𝐐𝐑
𝐀𝐫𝐦 𝐏𝐑
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐒𝐨𝐥𝐢𝐝
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐋𝐢𝐪𝐮𝐢𝐝
=
𝐀𝐫𝐦 𝑷𝑸
𝐀𝐫𝐦 𝑸𝑹
𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐒𝐨𝐥𝐢𝐝 × 𝐀𝐫𝐦 𝐐𝐑
= 𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐋𝐢𝐪𝐮𝐢𝐝 × 𝐀𝐫𝐦 𝐏𝐐
