1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423 603
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Mechanical Engineering
Dr.S.R.Thorat
Assistant Professor
Sanjivani College of Engineering, Kopargaon
E-mail : thoratsandipmech@sanjivani.org.in
Subject :-Material science & Metallurgy
S.Y. B.Tech. Mechanical
Unit III : Iron-iron Carbide Equilibrium Diagarm

2. Introduction
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• One of the most important objective of engineering metallurgy is to determine
properties of material.
• The properties of material is a function of the microstructure which depend on
the overall composition and variable such as pressure and temperature.
• Hence to determine the phase present in the material system , an equilibrium
or phase diagram is plotted.
• Equilibrium diagram or phase diagram is a graphical representation of
various phase present in material system at various temperature and
composition point.
• All the phase diagrams have temperature as the ordinate(Y-axis) and
percentage composition by weight as the abscissa(X-axis)

3. Uses of equilibrium or phase diagram:
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The equilibrium diagram is used to obtain following information:
1. It shows the various phases present at different composition and
temperature.
2. It indicate solid solubility of one element in other.
3. It shows the temperature range over which solidification or liquification of
material system occurs.
4. It indicate the temperature at which different phase start to melt.

4. Basic Terms:
1. System: A part portion of the universe under the study is called as system.
2. Phase: It is a physically and chemically composition of a substance(system),
separated from the other portion by a surface and an interface. Each portion
have different composition and properties.
In a equilibrium diagram, liquid is one phase and solid solution is another phase.
3. Variables: A particular phase exists under various condition of pressure and
temperature and composition. These parameters are known as the variables of
the phase.

5. 4. Component: These are the substances, element or chemical compound
whose presence is necessary and sufficient to make a system. A pure metal
is one component system whereas and alloy of metals is a two component
(binary) system etc. Eg.Cu-Al System
5. Alloy: It is a mixture of two or more elements having metallic properties.
In the mixture, metal is in the large proportion (Solvent) and the other can
be metal and non-metals (Solute).

6. Solid solution and Compound
• The element present in the alloy in the largest portion is referred as base
metal or parent metal or solvent and the other elements are referred as
alloying element or solute.
• Solid solution is a type of alloy in which the atoms of alloying element are
distributed in the base metal and both have similar crystal structure.
• The composition of alloying element may vary but the structure should be
similar to base metal.

7. Thorat S.R. Department Of Mechanical Engineering, Sanjivani COE, Kopargaon

8. 1) Substitutional solid solution
In substitutional solid solution, atoms of
alloying element occupy the atomic size of base
metal.
• They are further classified as:
(a) Regular or ordered substitutional solid
solution:
In this type, the substitution of atoms of
alloying element is in definite order in the base
metal matrix.
Examples: Ni-Al solid solution below 400 C.

9. (b) Random or disordered substitutional solid
solution:
• In this type, substitution of alloying elements is in
any random order in the base metal matrix.
Example: Alpha brass

10. • In Interstitial solid solution, the atoms of alloying
elements occupy the interstitial sites of base
metal.
• This type of solution is formed when atomic size
of alloying element is much smaller compared to
that of the base metal.
Example: Fe-C
(2) Interstitial solid solution:

11. Hume - Rothery’s Rules for Solid Solubility
• Solid solution is an alloy of two or more element where in the atomic crystal
structure of alloying element (solute) is same as that of the base metal
matrix (solvent).
• The solubility limit of the solute in the solvent ( of the alloying element in
base metal matrix) is governed by certain factors.
• These governing factors are known as Hume- Rothery’s rules for solid
solubility.
• These governing factor are as follows.

12. Hume - Rothery’s Rules for Solid Solubility
1. Atomic size:
• Alloying elements having similar atomic size as that of the base metal matrix
have better solid solubility.
• For a favorable solid solution formation, the difference of atomic size of
solute and solvent should be less than 15 %.
2. Chemical affinity:
• Element having lower chemical affinity have greater solid solubility.
• Element having higher chemical affinity have the tendency of formation of
compound and hence restrict formation of solid solution.
• In general, the alloy elements located closer in the periodic table have
higher solid solubility.

13. Hume - Rothery’s Rules for Solid Solubility
3. Relative valency:
• Metals having lower valency have more solubility for metals having higher
valency.
• Hence, for better solubility, the base metal selected should be one that has
lower valency as compared to that of alloying elements.
4. Crystal structure:
• As mentioned earlier, solid solution is an alloy of element having similar
crystal structure.
• Difference in crystal structure limits the solid solubility of elements.

14. GIBB’S PHASE RULE
• Gibbs phase rule establishes the relationship between the number of
variable (F), the number of element (C), and the number of phases(P).
• It is expressed mathematically as follows:
P + F = C + 2 ……….(I)
Where, P = Number of phases in system
F = Number of variables that can be change independently
without effecting number of phases
C = Number of elements
2 = It represent any two variables amongst temperature, pressure
and composition

15. • In general all equilibrium diagram studied at constant pressure, hence Gibb’s
phase rule is modified to”
P + F = C + 1 ……….(II)
• Phase rule helps to determine maximum number of phase present in an
alloy system under equilibrium conditions at any point in phase diagram.
• The phase rule can also be used to determine the degree of freedom that
can be changed
GIBB’S PHASE RULE

16. Solidification of Pure Metals and Alloys
Solidification of Pure Metal:
Solidification is process of forming
Grains (Nucleation) and its growth in the
melt.
• In the first step, nuclei of a solid
phase (crystallite) form from the
liquid.
• In the second step these solid
crystallites begins to grow as an
atoms until complete liquid
solidifies.

17. Solidification of Pure Metals and Alloys
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• Hence solidification is the process of forming grains (nucleation) and its
growth in the melt. The metal exists in liquid form above the melting point.
• When the metal is cooled below its melting point, nuclei begin to form in
different parts of the melt at the same time.
• The rate of formation of nuclei depends upon the degree of undercooling or
supercooling and on the presence of impurities which mainly facilitate
nucleation.
• At any temperature below the melting point, a nucleus has to be of a certain
minimum size so that it will grow. This size is called as critical size of nucleus.
• The critical size is maximum near the melting point, but there are less chances
of forming such a large nucleus.

18. Solidification

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Solidification of Pure Metals and Alloys
Solidification of Metals
• Molten metal possesses high energy and it will lost when metal cools
to form crystals.
• As the heat loss is more rapid near mould walls than its centre, the
formation of nuclei (crystallites) starts here.
• The molten metal finds difficulty in starting nucleation process if there
is no nuclei in the form of impurities are present to start the
crystallisation.
• In such cases, undercooling is done to accelerate nucleation and
thus nuclei or crystals are formed.

20. Solidification of Metals

21. 62
Solidification of Pure Metals and Alloys
Solidification of Metals
a) Shape of Crystals:
• The growth of the crystal varies in different crystallographic
directions.
• Slow cooling rate gives growth of crystals uniformly in all the
directions of growth. Also, it gives equiaxed crystals (the crystals with
equal dimensions in all the directions).
• Similarly, rapid cooling rate gives crystals like tree which are called as
dendrites.
• The exact shape of the crystals depend on the conditions that exist
during solidification.

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Solidification of Pure Metals and Alloys
b) Dendritic Growth:
• A dendrite is a crystal with a tree-like branching structure. In the
current context, we are interested in metallic dendrites formed
when a metal or an alloy of multiple metals, in liquid form freezes
is called dendritic growth.
• This temperature exceeds the freezing temperature of a metal
hence further growth of the crystal in this direction will be stopped.
• The liquid region will have a lower temperature in a perpendicular
direction, because there is no crystallisation and no heat
generation.

23. Solidification of Pure Metals and Alloys
b) Dendritic Growth:
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• This sequence of growth of crystals leads
finally to the structure characteristics of dendrites.
• This type of structures are commonly observed in cast
components.

24. Solidification of Pure Metals
• Due to chilling action of the
mould wall, a thin skin of
solid metal is initially
formed at the interface.
• This thickness of skin
increases to form a shell
around the molten metal as
the solidification
progresses towards the
centre of the cavity.
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25. Solidification of Alloys
• Most of the alloys freeze
over a temperature range
rather than at a single
temperature.
• The exact range depends
on the alloy system
and the particular
composition.
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