Unit2 - Equilibrium Diagram

Materials Science and
Metallurgy
Chapter 2
Equilibrium Diagrams
By
Prof. A. H. Kamble
M.E. (Mech.- Prod. Engg.) – Govt. College of Engg. Karad
PhD (Pursuing)
Prof. S. K. Khillare
M.Tech (CAD/CAM) – SGGS, Nanded
PhD (Pursuing)
Chapter 2 Equilibrium Diagrams

Contents: Definitions of terms, rules of solid-solubility, Gibb’s phase rule,
solidification of a pure metal, plotting of 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
Questions asked in University Examinations

1. Explain Iron-Iron carbide equilibrium diagram with neat sketch. [MAY 2019,
6M]
2. What is Solid Solution? Differentiate between substitutional and interstitial solid
solution? [AUG 2023, DEC- 2019, 6M]
3. Draw neatly iron carbon-carbon equilibrium diagram and mention the three
variant reactions involved in the phase diagram. [AUG 2023, 6M]
4. Draw Fe-Fe3C equilibrium diagram. Show all temperatures and phases. [DEC-
2019, 6M]
5. Draw Iron-Carbide Equilibrium diagram and define all the phases. [MAR-2023,
6M]
6. Explain Hume-Rothery’s rules of solid solubility. What is Gibb’s phase rule.
[MAR-2023, 6M]
2.1 Introduction
 Equilibrium diagrams are also called phase diagrams.
 Equilibrium diagrams are the diagrams which indicate the phases existing in the
system at any temperature and composition.
 The coordinate system of binary phase diagrams uses temperature as the ordinate Y-
axis) and weight percent of second element (i.e. solute) as abscissa (X-axis).
 These diagrams are 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.
Prof. A. H. Kamble, Prof. S. K. Khillare 2-1

 These diagrams also help in understanding the phenomena that occur during heating
and cooling of the alloys.
Before studying the equilibrium diagrams, the meanings of terms used here are defined
in the next section.
2.2 Definition of Terms

1) System
A part of the universe under study is called system.
2) Phase
Phase is homogeneous, physically distinct and mechanically separable part of the
system under study.
3) Variable
A particular phase exists under various conditions of temperature, pressure and
concentration. These parameters are called as the variables of the phase.
4) Component
Components are pure metals and/or compounds of which an alloy is composed.
For example, in a copper–zinc (brass) alloy, the components are Cu and Zn.
2.3 Concept of Alloying

 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.
 The metal present in the alloy in largest proportion is called the base metal.
 All other elements present in the form of metal or non-metal, are called alloying
elements.
 Alloying elements are added intentionally to get certain desirable properties which
are not found in the base metal. The structure resulting from addition of alloying
elements to a base metal determines the properties of the alloy as a whole.
 The type and extent of change of properties depend on whether the alloying elements
are insoluble in, dissolve in or form a new base with the base metal.
 Each constituent of an alloy is called a component. A pure metal comprises of a one-
component. But alloys may be binary or two components, ternary or three
component etc.

 Alloys are classified as binary alloys, composed of two components; as ternary

alloys, composed of three components; or as multicomponent alloys. Most
commercial alloys are multicomponent.
 The composition of an alloy is described by giving the percentage (either by weight
or by atoms) of each element in it. Metal alloys by virtue of composition, are often
grouped into two classes: ferrous and non-ferrous.
 Ferrous alloys are those in which iron is the major component, include steels and
cast irons.
 The nonferrous alloys are all alloys that are not iron based. Alloys are widely used
in industry because their physical and chemical properties can be easily varied to
suit the exact individual requirement. One can achieve this by preparing alloys of
different metals.
 Most of the times metallic objects are manufactured from alloys instead of pure
metals.
 The alloying elements are added to improve one or more of the following properties:
(a) Tensile strength, hardness and toughness
(b) Corrosive and oxidation resistance,
(c) Machinability,
(d) Elasticity
(e) Hardenability
(f) Creep strength and
(g) Fatigue resistance, etc.
 The improvement in the properties of an alloy system depends upon the following
factors:
(i) The way in which the two or more metals are mixed with each other.
(ii) The percentage of different alloying metals/or elements.
(iii) Temperature at which these are cooled, etc.
2.4 Solution
 Solution is a homogeneous mixture composed of two or more substances.
 When an alloy is in a liquid state the atoms of the constituent are distributed
randomly through the liquid.
 When solidification takes place, there appears number of possibilities.
 A number of different types of solutions may form, which are given below;

2.4.1 Simple Eutectic Solution

 In this case the two components of an alloy system (binary) are soluble in liquid state
but separate out in the solid state, each maintaining its own separate identity. In the
solid state, the two components are said to be insoluble in each other.
 Example- cadmium and bismuth are soluble in each other in liquid state but
insoluble in each other in the solid state.
2.4.2 Solid Solution

 When the two components of a binary alloy remain completely mixed in each other
both in liquid and solid state, the two components are said to be soluble in each other
and a different type of solution may be formed. It is called a solid solution.
 Example-copper and nickel are soluble in each other in the liquid as well as in solid
state. It cannot be distinguished copper from nickel.
2.4.3 Combination type Solution

 On solidifying, the two components of a binary alloy may show limited solubility in
each other. This type of solution combines characteristics of both components.
2.4.4 Intermetallic Compound

 It is observed that the elements may combine to form inter-metallic compounds on
solidification, when their affinity is great.
These types of compounds may find place in between the solid solution and chemical
compound.
 A familiar example is of copper-zinc system. When the solubility, of copper in zinc
is exceeded, a zinc rich β-phase appears with the Cu-rich α-phase. In general, inter-
metallic compounds are hard and brittle and can be used as bearing metals.
2.5 Solid Solution

 When homogeneous mixtures of two or more kinds of atoms of metals occur in the
solid state, they are known as solid solutions.
 A solid solution is formed when two metals are completely soluble in liquid state
and also completely soluble in solid state.
 The solute is the minor part of the solution or the material which is dissolved, while
the solvent constitutes the major portion of the solution.

Examples
 Sterling silver (92.5% silver and the remainder copper) is a solid solution of silver
and copper. In this case silver atoms are solvent atoms whereas copper atoms are
solute atoms.
 Brass is a solid solution of copper (64%) and zinc (36 %). In this case copper atoms
are solvent atoms whereas zinc atoms are solute atoms.
2.5.1 Types of Solid Solution

Solid solutions are of two types. They are;
(1) Substitutional solid solutions.
(2) Interstitial solid solutions.
1 Substitutional Solid Solution

 If the atoms of the solvent or parent metal are replaced in the crystal lattice by atoms
of the solute metal then the solid solution is known as substitutional solid solution.
 For example, copper atoms may substitute for nickel atoms without disturbing the
F.C.C. structure of nickel.
 Substitutional solid solution formation is possible if the atomic sizes of the two
metals are nearly equal.
 Depending upon the distribution of the solute atoms in solvent atoms, substitutional
solid solutions are classified into two types.
a) Regular or ordered substitutional solid solution
b) Random or disordered substitutional solid solution.
 In regular or ordered substitutional solid solutions the substitution of solute atoms in
solvent is by definite order (Fig 2-1). Au-Cu solution up to 400oC is the example of
ordered solid solution.
 In random or disordered substitutional solid solution, there is no definite order or
regularity (Fig 2-2). Au-Cu solution above 400oC is the example of disordered solid
substitutional solid solution.
 Complete regularity throughout is possible only when the two metals are mixed in
some fixed proportion like 1:1, 1:3 etc.
 Ordered solid solutions are harder than disordered solid solution.

Fig 2-1 Ordered substitutional solid solution
Fig 2-2 Disordered substitutional solid solution
2 Interstitial Solid Solution

 In an interstitial solid solution (Fig 2-3), the atoms of solute occupy the interstitial
sites of solvents.
 Formation of this type of solid solution is possible when the atomic size of solute
atom is very much small as compared to atomic size of solvent atoms.
 Examples- Interstitial solid solution with iron are carbon, boron, oxygen.
 In general, interstitial solid solutions are soft, ductile, and malleable and therefore
they can be cold worked.

Fig 2-3 Interstitial solid solution
2.5.2 Difference between Substitutional solid solution and interstitial solid solutions
Interstitial Solid Solution Substitutional Solid Solution
1. In this solid solution the solute atom 1. In this solid solution the solute atom
occupies position in between the replaces the position of solvent atom.
interstitial sites or vacant places of
solvent atoms.
2. The atomic size of solute is smaller 2. The atomic size of solute and solvent
than solvent atom atoms are almost equal.
3. It is not governed by Hume Rothery 3. It is governed by Hume Rothery rules.
rules.
4. It produces more strong and hard 4. It produces less strong and hard
alloys. alloys.
5. e.g. Steel 5. e.g. Au-Cu solution.
2.6 Hume Rothery’s Rules of Solid Solubility

By studying a number of alloy systems, Hume Rothery formulated certain rules which
govern the formation of substitutional solid solutions. These are:
1 Crystal structure factor

For complete solid solubility, the two elements should have the same type of crystal
structure i.e., both elements should have either F.C.C. or B.C.C. or H.C.P. structure.

2 Relative size factor

As the size (atomic radii) difference between two elements increases, the solid solubility
becomes more restricted. For extensive solid solubility the difference in atomic radii of
two elements should be less than about 15%. If the relative size factor is more than 15%,
solid solubility is limited.
For example, both silver and lead have F.C.C. structure and the relative size factor is
about 20%. Therefore the solubility of lead in solid silver is about 1.5% and the
solubility of silver in solid lead is about 0.1%. Copper and nickel are completely soluble
in each other in all proportions. They have the same type of crystal structure (F.C.C.)
and differ in atomic radii by about 2%.
3 Chemical affinity factor

Solid solubility is favoured when the two metals have lesser chemical affinity. If the
chemical affinity of the two metals is greater, greater is the tendency towards compound
formation. Generally, if the two metals are separated in the periodic table widely then
they possess greater chemical affinity and are very likely to form some type of
compound instead of solid solution.
4 Relative valence factor

It is found that a metal of lower valence tends to dissolve more of a metal of higher
valence than vice versa.
For example in aluminium-nickel alloy system, nickel (lower valance) dissolves 5
percent aluminium but aluminium (higher valence) dissolves only 0.04 percent nickel.
2.7 Gibb’s Phase Rule

The Gibb’s phase rule states that under equilibrium conditions, the following relation
must be satisfied.
F CP2
Where,
P = Number of phases existing in a system under consideration.
F = Degree of freedom i.e. the number of variables such as temperature, pressure or
concentration (i.e. composition) that can be changed independently without changing
the number of phases existing in the system.
C = Number of components (Elements) in the system, and

2 = It represents any two variables out of the above three i.e. temperature, pressure and
concentration.
Most of the studies are done at constant pressure i.e. one atmospheric pressure and hence
pressure is no more variable. For such cases, Gibb’s phase rule becomes;
F  C  P 1
In the above rule, 1 represents any one variable out of the remaining two i.e. temperature
and concentration.
Significance of Gibb’s Phase rule in metallurgical system

Gibb’s phase rule enables us to predict and check the processes that 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 exist simultaneously
in a system.
2.8 Solidification of Pure Metal

 Solidification occurs by the nucleation and growth of crystals in the melt.
 In pure metals, the process of solidification starts with formation of nuclei. Nucleus
is small cluster of atoms having crystalline arrangement.
 When the melt is cooled below its melting point, nuclei begin to form in many parts
of the melt.
 The rate of nuclei formation depends on the degree of undercooling or supercooling.
 At any temperature below the melting point, a nucleus must a certain minimum size
to grow further, this minimum size is called critical size.
 The critical size is greatest near the melting point, but the probability of forming
such a large nucleus is less.
 Particles smaller than the critical size will be dissolved by the vigorous
bombardment of neighbouring atoms and can not grow are called embryos.
 When the temperature is lowered, the vibrations of atoms gradually decrease which
increase the chances of survival of small clusters and therefore, the critical size of
nucleus decreases with decreasing temperature or increasing the degree of
undercooling.

 Hence, at lower temperatures nuclei become progressively smaller in size but the
number increases in greater amount.
 Hence, some degree of undercooling is necessary to start solidification i.e.
nucleation.
Fig 2-4 Cooling curve for pure metal
 Fig 2-4 shows cooling curve for pure metal.

 At point A, the pure metal is in liquid state.
 The specific heat is extracted during cooling from point A to B.
 From point B to C undercooling is done to decrease the critical size of nucleus.
 Nucleation begins at point C.
 At point C, the latent heat of fusion is given off and the temperature rises.
 From point C to D, temperature rises due to nucleation which is called recalescence.
 Solidification proceeds isothermally at the melting temperature from point D to E as
the latent heat given off from continued solidification is balanced by the heat lost by
cooling.
 This region between points D and E, where the temperature is constant, is known as
the thermal arrest.

 At point E, solidification completes, and the solid pure metal cools from point E to
room temperature.
2.9 Plotting of Equilibrium Diagrams

 Equilibrium diagrams can be plotted by using several techniques such as thermal
analysis, dilatometry, optical and electron microscopy, X-ray and electron
diffraction, thermodynamic data analysis, electrical resistivity and magnetic
measurements.
 Each method has certain advantages and limitations.
 Most of the times, equilibrium or phase diagrams are plotted by the method of
thermal analysis using the data obtained from cooling curves; and other methods are
generally used to eliminate the ambiguities existing in the diagram plotted by the
thermal analysis method.
 Therefore, the basic method of plotting the diagrams by the use of cooling curves is
explained below:
2.9.1 Plotting of Equilibrium Diagram by Thermal Analysis Method

 Let us consider a binary Cu-Ni system.
 Cu and Ni have 100% solubility in the liquid and solid states and they form series of
solid solutions.
 Following steps are used to obtain the equilibrium diagram.
1. Prepare large number of alloys of varying compositions, say with a variation of
10% Ni and mark them as below:
Material 1 2 3 4 5 6 7 8 9 10 11
No.
% Cu 100 90 80 70 60 50 40 30 20 10 0
% Ni 0 10 20 30 40 50 60 70 80 90 100
No. 1 and 11 are pure metals and No. 2 to 10 are alloys.
2. Plot cooling curves of the above materials. This is shown in Fig 2-5.

Fig 2-5 Cooling curves for Cu-Ni samples
3. Note down the liquidus and solidus temperatures of these materials. Liquidus
temperatures are marked as L1, L2, L3, L4 ... L9, L10, L11, and solidus temperatures
are marked as S1, S2, S3, S4 ... S9, S10, S11; respectively.
4. Since materials 1 and 11 are pure metals, they solidify at constant temperature
and hence their liquidus and solidus temperatures are same i.e. L1 =S1 and L11 =
S11.
5. Transfer these liquidus and solidus temperatures to a temperature Vs
composition graph as shown in Fig 2-6.

Fig 2-6 Equilibrium diagram for Cu-Ni alloy system
6. Corresponding to materials 1 and 11 i.e. for pure Cu and Ni, we get only one
point and for others we get two points because solid solution alloys solidify over
a range of temperature.
7. Draw smooth curves through the points L1 to L11; and S1, to S11, which represent
liquidus and solidus of the diagram.
8. Above liquidus temperatures, all the materials are in the liquid state and below
the solidus temperatures they are in the solid state. Between the liquidus and
solidus temperatures, the alloys are in the liquid as well as solid state.
9. The resulting loop type of curve is called as the phase or equilibrium diagram.
Steps for
plotting of equilibrium diagram of any other system are similar to that
explained above.
2.10 Lever Rule

 Lever rule is used for finding out the amounts of phases existing in a binary system
for a given alloy at any temperature under consideration.

Fig 2-7 Typical isomorphous phase diagram.
 Let us consider an isomorphous system of two metals A and B (Fig 2-7). Let Z be
the composition of the alloy under consideration and T be the temperature at which
the amounts of phases are to be determined.
 At this temperature, the phases are solid and liquid. Let the amount of solid be S and
hence the amount of liquid (L) will be (1 − 𝑆), if the total amount is assumed to be
1.
We know that,
 Now, the amount of B in the liquid or solid phase is equal to the amount of phase
multiplied by its composition in terms of B.
 Here, at temperature T, the composition of solid is D and the composition of liquid
is C. Therefore,

Fig 2-8 Schematic illustration of the lever rule.

Therefore, amount of solid × Arm FD=Amount of liquid × Arm CF
 The tie line CD acts as a lever arm and the point F acts as a fulcrum point as shown
in Fig 2-8. Therefore, it is called lever arm principle or lever rule.
 Therefore, in general Lever arm rule can be stated as;
Amount of solid × its lever arm=Amount of liquid × its lever arm
 At any other temperature, the amounts of solid and liquid phases can be determined
in similar manner.

 The rule also holds good for other phases such as α +β or β + γ and is not restricted
to only solid and liquid phases.
2.11 Iron Carbon Alloy System

 Iron - carbon is a binary alloy system.
 Iron – carbon alloys system is one of the most important alloy system.
 The alloys of iron and carbon are steels and cast irons. These are the primary
structural materials in every technologically advanced sector.
2.11.1 Iron- Iron Carbide Equilibrium Diagram Fe-C or Fe-Fe3c Equilibrium Diagram
or Fe-C or Fe-Fe3c Phase Diagram
 Iron- Iron Carbide Equilibrium Diagram is shown in Fig 2-9.
Fig 2-9 2.11.1 Iron- Iron Carbide Equilibrium Diagram
 The temperature at which the allotropic changes take place in iron is influenced by
alloying elements, the most important of which is carbon.

 The portion of the iron-carbon alloy system is shown in Error! Reference source
not found.. This is the part between pure iron and an interstitial or intermetallic
compound iron carbide Fe3C containing 6.67% carbon by weight.
 The properties of iron carbon-alloy system can be understood with the help of Fe-C
equilibrium diagram. Therefore, it is highly essential to study the Fe-C equilibrium
diagram.
 Fe-Fe3C equilibrium diagram consists of four distinct phases which are α –Ferrite,
γ- Austenite, δ- Ferrite, 4 Cementite. These phases are described as below;
1 α –Ferrite
 α- Ferrite is almost a pure iron.
 It is an essential solid solution of carbon in low temperature B.C.C. α-iron.
 The solubility of carbon in α- iron at room temperature is 0.008% and increases with
increase in temperature to about 0.025% at 727oC.
 It is relatively soft and ductile phase having hardness about 80 BHN.
 It can be extensively cold worked without cracking.
 It is strongly ferromagnetic up to 768oC and becomes paramagnetic at 768oC during
heating.
 The temperature (768oC) at which α- ferrite becomes paramagnetic is called Curie
temperature.
2 γ- Austenite
 γ- Austenite is an interstitial solid solution of carbon in FCC γ-iron.
 The phase is called Austenite in honour of Sir Austin, who was one of the first
metallographer to study its properties.
 It can dissolve up to 2.0% carbon at 1147oC.
 Austenite phase is stable only above 727oC.
 It is soft, ductile, malleable, and paramagnetic phase.
 It can be extensively worked at the temperatures of its existence.
3 δ- Ferrite
 It is an interstitial solid solution of carbon in high temperature BCC δ- iron.
 It is similar to α- Ferrite except its occurrence at high temperature.

4 Cementite (Fe3C) or Iron Carbide or Carbide

 It is an intermetallic compound of iron and carbon with a fixed carbon content of
6.67% by weight.
 It has complex orthorhombic crystal structure with twelve iron atoms and four
carbon atoms in a unit cell.
 It is extremely hard and brittle phase having hardness about 900 BHN.
 It is ferromagnetic upto 210oC and paramagnetic above this temperature.
2.12 Transformations in Fe-Fe3C Diagram

Fe-Fe3C diagram contains three transformations.
1) Peritectic Transformation
2) Eutectic Transformation and
3) Eutectoid Transformation
1 Peritectic Transformation
In general, Peritectic transformation is;
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
𝑆1 + 𝐿 → 𝑆2
Where S1 and S2 are two different solids and L is liquid.

In iron-carbon system, the transformation occurs as below:
In above reaction, δ of 0.1% carbon is added with liquid of 0.55% carbon at the
temperature 14930C to get γ of 0.18% carbon.
The peritectic reaction in iron-iron carbide system is as shown in Fig 2-10.

Fig 2-10 Peritectic Transformation
The amounts of δ and L may be found by applying the Lever rule.
For hypoeutectic steels (< 0.18% carbon), the reaction may be as follows;
For hypereutectic steels (> 0.18% carbon), the reaction may be as follows;
All steels contain carbon in the range of 0.10 to 0.55% as shown in peritectic reaction in
Error! Reference source not found.. When cooled from the liquid state, the
commercial heat treatment is not done in δ- region, we will not refer this region while
study of steels, so no use of changes in properties of steels.
2 Eutectoid Transformation
The eutectoid transformation reaction occurs as follows;
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
𝑆𝑜𝑙𝑖𝑑 1 → 𝑆𝑜𝑙𝑖𝑑2 + 𝑆𝑜𝑙𝑖𝑑3
Where Solid 1, Solid 2, and Solid 3 are various solid phases.
The eutectoid reaction in iron-carbon system is as shown in Figure 2-1.

Figure 2-1 Eutectoid Transformation
The eutectoid transformation in Figure 2-1 is;
The austenite is transformed to mixture of α- ferrite (0.025%C) and cementite (6.67%

carbon). The reaction of eutectoid transformation occurs at constant temperature 727oC.
The austenite of 0.8% carbon decomposes. The eutectoid mixture of ferrite and
cementite is called pearlite.
Pearlite contains alternate lamellae of ferrite and cementite is obtained. The
amount of ferrite and cementite in pearlite at pearlite at room temperature are as follows:
The properties of pearlite depends upon its interlamellar distance. Similar the distance
higher will be the mechanical properties. The interlamellar distance depends upon the
cooling rate and not on the limit. The distance becomes less as the cooling rate increases.
The hardness of pearlite will be 225BHN to 275 BHN.

3 Eutectic Transformation
The eutectic transformation reaction in general as follows;
In iron carbon system, the reaction occurs at 11470C and carbon at 4.3%.
The transformations are as follows;
The liquid transforms to eutectic mixture of austenite (2% carbon) and cementite (6.67%
carbon) is called Ledeburite. The eutectic reaction in iron carbon system as shown in
Figure 2-2 as below;
Figure 2-2 Eutectic Transformation
Austenite from the Ledeburite is not stable at low temperature and gets transformed to
pearlite with slow rates of cooling at 727oC; and hence at room temperature, structure
consists of pearlite and cementite. The mixture of perlite and cementite at room
temperature is called Transformed Ledeburite.
The amount of pearlite and cementite in transformed Ledeburite at room temperature
according to lever rule are as below;

The cementite phase having carbon content 6.67% due to which cementite is hard and
brittle and pearlite is slightly hard and therefore, transformed Ledeburite is hard and
brittle.
Iron carbon equilibrium diagram showing the transformation and occurrence
region of pearlite and Ledeburite is shown in Figure 2-3.
Figure 2-3 Fe-Fe3C Diagram showing Transformations
2.12.2 Critical Temperatures

The temperatures at which the transformations in the solid state take place are called as
critical temperatures or critical points. The various critical temperatures are enlisted in
Table 2-1.

Table 2-1 Critical Temperatures for Iron-Carbon Alloys
Sr. Critical Points (Symbols) Temperature Significance during heating

No. (OC)
1. A0 210 Cementite becomes
(Curie Temperature of paramagnetic
Cementite)
2. A1 727 Pearlite starts transforming to
(Lower critical temperature) austenite
3. A2 768 Ferrite becomes paramagnetic
(Curie temperature of ferrite)
4. A3 727- 910 Completion of ferrite
(Upper critical temperature austenite transformation
for hypoeutectoid steels)
5. Acm 727-1147 Completion of cementite to
(Upper critical temperature austenite
for hypereutectoid steels)
6. A4 1400- 1492 Completion of austenite to δ-
ferrite transformation.
The critical temperatures are shown on Fe-Fe3C phase diagram in Fig 2-11.

Fig 2-11 Fe-Fe3C diagram showing critical temperatures
2.13 Steels and Cast Irons Regions on Fe-Fe3C Diagram

 On the basis of carbon content, iron iron-carbide diagram is divided into two parts;
a) Steels and
b) Cast irons
 The alloys containing less than 2% carbon are known as steels and alloys containing
more than 2% carbon are known as cast irons.
 Steels are further divided by eutectoid carbon content (0.8%C).
 Steels containing less than 0.8% carbon are called hypoeutectoid steels while those
containing between 0.8 and 2.0% carbon are called hypereutectoid steels.
 The cast iron range is also divided by eutectic carbon content (4.3%C).
 Cast irons containing less than 4.3% carbon are known as hypoeutectic cast irons,
whereas those containing more than 4.3% carbon are known as hypereutectoid steels.

Fig 2-12 Steel and CI regions on Fe-Fe3C diagram

2.14 Solidification and Microstructures of Slowly Cooled Steels
Figure 2-4 Solidification of slowly cooled steels
 In Fig 2-12, it shows that, solidification starts at or just below liquidus temperature
i.e. line PQR.
 Below liquidus line PQR, separation of δ-ferrite for a steels of less than 0.55%
carbon and γ-austenite for a steel of carbon between 0.55 to 2.0% take place.
 As the temperature decreases, more and more liquid solidifies and the solidification
completes at the solidus temperature (line PSUV).
 Below line XUV, all the steels have austenitic structure.
 Further decrease in temperature results in solid to solid phase transformation at upper
and lower critical temperatures.
2.14.1 Microstructures of Hypoeutectoid Steels

 Hypoeuctectoid steels contain carbon from 0.008 to 0.8%.
 To study the changes in microstructures of hypoeutectoid steels, let us consider the
composition of 0.2% C as shown in Fig 2-13.

Fig 2-13 Eutectoid transformation for 0.2%C in Fe-Fe3C diagram
 At point 1, α-ferrite starts to separate at the grain boundaries of γ-austenite.

 As the temperature decreases, amount of α-ferrite increases.
 The composition of α-ferrite varies along the line CD.
 The composition of γ-austenite varies along the line CE.
 This continues up to point 2.
 The α-ferrite which is separated before the eutectoid transformation is called primary
or proeutectoid ferrite.
 At point 2, the existing γ-austenite transforms at constant temperature of 727oC to a
lamellar mixture of ferrite and cementite called pearlite by eutectoid transformation
process.
 Cooling from 2 to 3 does not results in significant change in microstructure due to
significant solubility of carbon in α and hence the same structure is observed at room
temperature.
 At room temperature α-ferrite and pearlite are observed.
 The amounts of α-ferrite and pearlite at room temperature are calculated by using
Lever rule.

 As the carbon increases, the amount of proeutectoid ferrite decreases and pearlite
increases.
 For 0.8% carbon, the amount of ferrite becomes 0% and pearlite becomes 100%.
 There is linear relation in amount of carbon content of the steel and the amount of
pearlite & ferrite.
 For 0.008% C, the amount of α-ferrite is 100% and for 0.8%C, the amount of pearlite
is 100%.
 The variation of ferrite and pearlite with carbon is shown in Fig 2-14.
Fig 2-14 variation of pearlite and ferrite with carbon for hypoeutectoid steels
 Ferrite appears white and pearlite appears dark or lamellar under the microscope
with most common etching reagents such as nital and picral.
 Typical microstructures of some of the hypoeutectoid steels are shown in Fig 2-15
to Fig 2-17.
Fig 2-15 Microstructure of ≈ 0.1% Carbon steel light phase being the ferrite and the dark phase being pearlite.

2.14.2 Microstructures of Hypereutectoid Steels

 Hypereutectoid steels contain carbon from 0.8% to 2.0%.
 A typical group such as 1.2%C is marked in Fig 2-18.

Fig 2-18 Cooling of Hypereutectoid steels containing 1.2% C
 When this steel is cooled from point 1, structural changes are occurred.
 At point 1, cementite starts separating out on the grain boundaries of austenite.
 As the temperature decreases amount of cementite increases.
 The composition of austenite varies along line EJ while composition of cementite
does not change as it is an intermetallic compound.
 This continues up to point2.
 The cementite which is separated before eutectoid transformation is called primary
or proeutectoid cementite.
 At point 2, the existing amount of γ-austenite starts to transform into peralite.
 Cooling from point 2 to 3 does not result in significant change in microstructure and
hence the same structure is observed at room temperature.
 The amount of cementite and pearlite can be calculated as;
 As the carbon increases, the amount of Fe3C increases and for a steel containing
maximum amount of carbon i.e. 2.0%, the amount of Fe3C is;

 Free cementite is 0% for 0.8%C steel and increases linearly with increasing carbon
reaching to 20.4% for 2.0% carbon steel.
 The variation of Fe3C and pearlite with carbon is shown in Fig 2-20.
Fig 2-19 Variation of pearlite and cementite with carbon for hypereutectoid steels.
 Cementite appears white at the grain boundaries of pearlite and pearlite appears dark
or lamellar under the microscope with the general etching reagents such as nital and
picral
Fig 2-20 Microstructure of 1.0%C steel slowly cooled from austenitic region showing cementite (white) at the grain
boundaries (Etchant 5% Nital, 100X)
2.15 Non-equilibrium Cooling of Steels

 Due to non-equilibrium cooling i.e. fast cooling of austenite through the critical
range, microstructures produced are quite different from those produced by
equilibrium cooling. This results in significant changes in properties of steels.

 Controlled departures from equilibrium conditions to obtain such different structures

and thereby properties is the object of most of the common heat treatments of steels.
 Eutectoid transformation of austenite to pearlite occurs by nucleation and growth.
 Temperature of transformation has a strong influence on the above mechanisms.
 Faster the cooling, lesser will be the eutectoid transformation temperature with shift
of eutectoid carbon toward the composition of undercooled phase.
 This means that the eutectoid carbon will shift to the lower value for hypoeutectoid
steel and higher values for hypereuctecoid steels. Due to this, in a given steel, the
amount of proeutectoid phase decreases and pearlite increases.
2.16 Classification and Applications of Steels

Steels are classified by various methods and each method is based on a definite criteria.
The various criterions for the basis of classification are as follows;
1) Amount of carbon
2) Amount of carbon and alloying element
3) Amount of deoxidation
4) Grain coursing characteristics
5) Method of manufacture
6) Depth of hardening
7) Forms and use
2.16.1 Classification on the basis of Amount of Carbon

On the basis of carbon, steels are classified into following three types;
a) Low carbon steels
b) Medium carbon steels and
c) High carbon steels
a. Low carbon steels

 Low carbon steels contain carbon from 0.008% to 0.3%
 They are soft, ductile, malleable, tough, machinable, weldable and non-hardenable
by heat treatment.
 They are good for cold working purpose such as rolling into thin sheets required for
galvanizing, tinning or press work.

 They are good for fabrication work by welding, pressing or machining; however,
they cannot be hardened by heat treatment.
 They are used for wires, nails, rivets, screws, panels, welding rods, ship plates, boiler
plates and tubes, fan blades, gears, valves, camshafts, crank shafts, connecting rods,
railway axles, fish plates, cross-heads, tubes for bicycles and automobiles and small
forgings.
 Steels with 0.15 to 0.3% carbon are widely used as structural steels and finds
applications as building bars, grills, beams, angles, channels etc.
b. Medium Carbon Steels

 Medium carbon steels contain carbon from 0.3% to 0.6%
 These steels have intermediate properties to those of low carbon and high carbon
steels.
 They are medium hard, not so ductile and malleable, medium tough, slightly difficult
to machine, weld and harden.
 They require high cooling rates for hardening and the hardness produced after
hardening is not so high,
 The depth of hardening is also less and hence they are of shallow hardening type.
 They are difficult to cold work and hence hot worked.
 They are also called machinery steels.
 They are used for bolts, axles, lock washers, large forging dies, springs, wires, wheel
spokes, hammers, rods, turbine rotors, crank pins, cylinder liners, railway rails and
railway tyres.
c. High Carbon Steels

 High carbon steels contain carbon from 0.6% to 2.0%.
 They are hard, wear resistant, brittle, difficult to machine, difficult to weld and can
be hardened by heat treatment.
 The hardness produced after hardening is high.
 The depth of hardening is also high i.e. the hardenability is more as compared to
medium carbon steels.
 These steels cannot be cold worked and hence are hot worked.
 They are also called as tool steels.

 They are used for forging dies, punches, hammers, springs, clips, clutch discs, car
bumpers, chisels, vice jaws, shear blades, drills, leaf springs, music wires, knives,
razor blades, balls and races for ball bearings, mandrels, cutters, files, wire drawing
dies, reamers and metal cutting saws.
2.16.2 Classification on the basis of alloying elements and carbon

 Alloying elements such as nickel, chromium, manganese, tungsten, molybdenum,
vanadium etc. are added to plain carbon steels in certain amounts to increase the
desired properties.
 Such steels are classified on the basis of total alloy content in the following manner:
a) Low alloy steels – contain alloying element less than 10%
b) High alloy steels - contain alloying element more than 10%
 Steels are also classified on the basis of alloying elements and carbon content as
given in ---;
Alloy steels Contents of carbon and Properties
alloying elements
Low carbon low alloy Carbon < 0.3%, Good strength
steels alloying elements < 10%
Low carbon high alloy Carbon < 0.3%, Good corrosion
steels alloying elements > 10% resistance
Medium carbon low Carbon - 0.3% to 0.6%,
alloy steels alloying elements < 10%
Medium carbon high Carbon - 0.3% to 0.6%,
alloy steels alloying elements > 10%
High carbon low alloy Carbon - 0.6% to 2.0%,
steels alloying elements < 10%
High carbon high alloy Carbon – 0.6% to 2.0%, Excellent hardness and
steels alloying elements > 10% wear resistance at low and
high temperatures
2.16.3 Classification on the basis of Deoxidation

 During the extraction of iron, oxygen gets dissolved into iron.
 This dissolved oxygen during solidification forms blow holes and porosity.
 Hence, it is necessary to remove oxygen.
 Based on the method employed for de-oxidation, steels are classified as:

a. Rimmed Steels
 In rimmed steels, oxygen is not removed by any deoxidation process.
 During solidification, the dissolved oxygen combines with carbon to form CO.
 This CO gas forms blow holes and gets collected at the centre of the ingot i.e. given
steel.
 The outer thin layer of the solid iron thus contains less carbon, more purity and free
from blow holes.
 These blow holes get eliminated during cold working.
 Rimmed steels are not used for forging operation.
b. Killed Steels
 In killed steels, the oxygen is completely removed by addition of deoxidizing agents
such as Al, Si, Mn etc.
 These deoxidants remove free oxygen but form oxide inclusions.
 Killed steel is free from blow holes throughout the cross-section of the ingot.
 These steels can be used for forgings, rolling etc.
c. Semi-killed steels
 In theses steels, part of the dissolved oxygen is removed by addition of de-oxydiseres
and the rest combines with carbon.
 These steels contain oxygen in the form of CO and oxide inclusions.
 Fewer blowholes are observed as compared to rimmed steels.
2.16.4 Classification based on Grain Coarsening Characteristics

 The size of the grain is a function of heating temperature and soaking time at that
temperature.
 Depending on the grain coarsening characteristics, steels are classified as;
a) Coarse grained steels
b) Fine grained steels
2.16.5 Classification based on the Manufacturing Method

 This classification criterion focuses only on the manufacturing method for producing
steels.
 It does not focus on the composition and mechanical properties of steels.

 Steels can be classified as follows;

a) Basic open hearth
b) Electric furnace
c) Basic oxygen process
d) Acid open heart
e) Acid Bessemer
2.16.6 Classification based on depth of Hardening

 Steels are usually hardened before it is put to final use.
 Hence, it is important to know the hardenability of steels.
 Steels can be classified based on its hardening ability as follows;
a. Non-hardenable steels
Contains less carbon and almost no alloying elements.
b. Shallow hardening steels

 It contains medium carbon percentage with or without alloying elements.
 It gets hardened only at the surface and hence is sometimes used for gears, camshafts
and similar applications.
c. Deep hardening steels

 It contains more carbon percentage and alloying elements.
 It is used where depth of hardening required is more and has applications similar to
those of high carbon steel.
2.16.7 Classification based on form and use (Applications)

 Steels are sometimes classified based on their application.
 Following are the types of steels grouped according to its use.
 Their name indicates the specific applications.
a) Boiler steels
b) Case hardening steels
c) Deep drawing steels
d) Corrosion and heat resistant steels
e) Electrical steels

f) Tool steels
g) Free cutting steels
h) Sprig steels
i) Structural steels
j) Die steels
2.17 Specification of Steels

 Steels are specified on the basis of certain criteria like the method of manufacture,
chemical composition, heat treatment, mechanical properties, quality etc.
 Every country has different way of specification. But majority of specification are
based on chemical composition, because the chemical composition gives
information about heat treatment and resulting mechanical properties.
 The knowledge of these specifications helps in selecting proper type of steel from
those available in the market for particular service requirement.
2.17.1 Indian Standard Designation System

 Indian standard code for designation of steel was adopted by the Indian standard
Institution (ISI) in 1961. In 1974, these standards are revised in two parts;
a) Part 1: It covers the designation of steel based on letter symbols.
b) Part 2: It covers the designation of steel based on Numerals, for the purpose
of code designation
 Steel have been classified on the basis of mechanical properties and chemical
composition.
 Code designation on the basis of mechanical properties based on tensile strength or
yield strength.
 Symbol Fe is for minimum tensile strength and FeE to designate minimum yield
strength in N/mm2.
 But when tensile strength and yield strength are in kg/ mm2, it is denoted as ‘St’ and
'St E' respectively.
 Designation of steels on the basis chemical composition consists of mechanical
figures indicating l00 times the average percentage of carbon content.
 Letter ‘C’ is used for plain carbon steels and ‘T’ is used for tool steels.

 Letter C or T is followed by a number indicating ten times the average percentage

of manganese content.
 Symbols S, Se, Te, Pb or P are used to indicate free cutting steels followed by a
figure indicating 100 times the percent content of the respective element.
Examples
Fe 400 Steel with minimum tensile strength of 400 N/mm2.
St 310K Killed steel with minimum tensile strength of 310 kg/mm2
St 42 Steel with minimum tensile strength of 42 kg/mm2
FeE 330 Steel with minimum yield strength of 330 N/mm2
StE 330 Steel with minimum yield strength of 330 Kg/mm2
C20 Steel with average carbon of 0.2 %
25C5 Steel with average carbon of 0.25 % and Mn of 0.5%
8T11 Tool steel with average carbon of 0.8% and 1.1 % Mn
20Ni55Cr50Mo20 Steel with average carbon of 0.20%, Ni- 0.55 %, Chromium-
0.50% and Mo- 0.20 %
2.17.2 AISI/ SAE Designation System

 The SAE system uses a basic four-digit system to designate the chemical
compositions of carbon and alloy steels.
 The first digit (1), of this designation indicates a carbon steel; i.e. carbon steel
comprise 1XXX groups in the SAE-AISI system and are subdivided into four
categories due to the variance in certain fundamental properties among them.
 For many years, certain grades of carbon and alloy steel have been designated by a
four digit AISI / SAE numerical index system that identifies the grades according to
standard chemical compositions, the relationship between AISI and grade
designation has been discontinued.
 From point of edition of the 1995, Iron and Steel Society (ISS) strip steel manual,
the four digit designations are referred to solely as SAE designations.
 The SAE system uses a basic four-digit system to designate the chemical
compositions of carbon and alloy steels. The simple system of designation of steel
is schematically shown;

 Above figure demonstrates the SAE-AISI system uses a four-digit number to

designate a carbon and alloy steel and refers to its specific composition.
 There are certain type of alloy steels that are designated by five digits. (51XXX,
52XXX).
 The first digit of this designation indicates a carbon steel, i.e. carbon steel comprise
1XXX groups in SAE-AISI system and subdivided into four categories due to the
variance in certain fundamental properties among them.
 Thus, the plain carbon steel are comprised within the 10XX series (containing 1.00%
Mn maximum) resulfurized carbon steels within the 11XX series; resulfurized and
rephosphorized carbon steels within the 12XX series and non resulfurized high
manganese (up to 1.65%) carbon steel which are produced for applications requiring
good machinability are comprised with the 15XX series.
 The SAE-AISI system then classifies alloy steels using the same four digit index as
follows;
2 – Nickel steels
3 – Nickel- Chromium steels
4 – Molybdenum steels
5 – Chromium steels
6 – Chromium vanadium steels
7 – Tungsten-Chromium steels
8 – Silicon- Manganese steels
 The second digit of the series indicates the concentration of the major element in
percentiles. The last two digits of the series indicate the 100 times carbon
concentration in percentage.
Examples
SAE 5130 Chromium steel alloy, with 1% Cr and 0.30% C
 Table 2-2 shows the SAE/AISI steel Numbering designation system

 Additional letters added between the second and third digits include B when boron
is added (between 0.0005 and 0.003%) for enhanced hardenability, and L when lead
is added (between 0.15 and 0.35%) for enhanced machinability.
 The prefix M is used to designate merchant quality steel (the least restrictive quality
descriptor for hot-rolled steel bars used in noncritical parts of structures and
machinery).
 The prefix E (electric-furnace steel) and the suffix H (hardenability requirements)
are mainly applicable to alloy steels.

Table 2-2 The SAE/AISI steel numbering designation system
10XX Plain carbon, Mn 1.00% max

11XX Resulfurized free machining
Carbon steels
12XX Resulfurized/rephosphorized free machining
15XX Plain carbon, Mn 1.00-1.65%
Manganese steels 13XX Mn 1.75%
23XX Ni 3.50%
Nickel steels
25XX Ni 5.00%
31XX Ni 1.25%, Cr 0.65-0.80%
32XX Ni 1.75%, Cr 1.07%
Nickel-chromium steels
33XX Ni 3.50%, Cr 1.50-1.57%
34XX Ni 3.00%, Cr 0.77%
40XX Mo 0.20-0.25%
Molybdenum steels
44XX Mo 0.40-0.52%
Chromium-molybdenum steels 41XX Cr 0.50-0.95%, Mo 0.12-0.30%
Nickel-chromium-molybdenum 43XX Ni 1.82%, Cr 0.50-0.80%, Mo 0.25%
steels 47XX Ni 1.05%, Cr 0.45%, Mo 0.20-0.35%
46XX Ni 0.85-1.82%, Mo 0.20-0.25%
Nickel-molybdenum steels
48XX Ni 3.50%, Mo 0.25%
50XX Cr 0.27-0.65%
51XX Cr 0.80-1.05%
Chromium steels 50XXX Cr 0.50%, C 1.00% min
51XXX Cr 1.02%, C 1.00% min
52XXX Cr 1.45%, C 1.00% min
Chromium-vanadium steels 61XX Cr 0.60-0.95%, V 0.10-0.015%
Tungsten-chromium steels 72XX W 1.75%, Cr 0.75%
81XX Ni 0.30%, Cr 0.40%, Mo 0.12%
Nickel-chromium-molybdenum 86XX Ni 0.55%, Cr 0.50%, Mo 0.20%
steels 87XX Ni 0.55%, Cr 0.50%, Mo 0.25%
88XX Ni 0.55%, Cr 0.50%, Mo 0.35%
Silicon-manganese steels 92XX Si 1.40-2.00%, Mn 0.65-0.85%, Cr 0-0.65%
93XX Ni 3.25%, Cr 1.20%, Mo 0.12%
Nickel-chromium-molybdenum 94XX Ni 0.45%, Cr 0.40%, Mo 0.12%
steels 97XX Ni 0.55%, Cr 0.20%, Mo 0.20%
98XX Ni 1.00%, Cr 0.80%, Mo 0.25%

2.17.3 British Standard Designation System

 British system of designation of steel is known as En series. En number of steel has
no relation with the composition or mechanical properties of the steel.
 ---- shows some steels specified by British Standard designation system.
En No. Composition (%)
Carbon Manganese Sulphur Phosphorus Silicon Other
En 1 0.07 to 0.15 0.8 to 1.2 0.2 to 0.3 0.07 0.1
En8 0.35 to 0.45 0.6 to 1.0 0.06 0.06 0.05 to 0.35
En24 0.35 to 0.45 0.45 to 0.70 0.1 to 0.35 Ni- 1.3 to 1.8
Cr- 0.9 to 1.4
Mo- 0.2 to 0.35
En36 0.15 0.3 to 0.6 Ni- 3 to 3.75
Cr- 0.6 to 1.1
Si- 0.1 to 0.35
En42 0.07 to 0.85 0.55 to 0.75 0.05 0.05 0.1 to 0.4

Unit2 - Equilibrium Diagram

Uploaded by

Copyright:

Available Formats

Unit2 - Equilibrium Diagram

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Unit2 - Equilibrium Diagram

Uploaded by

Copyright:

Available Formats

Materials Science and

Chapter 2 Equilibrium Diagrams

Questions asked in University Examinations

Prof. A. H. Kamble, Prof. S. K. Khillare 2-1

2.2 Definition of Terms

2.3 Concept of Alloying

Prof. A. H. Kamble, Prof. S. K. Khillare 2-2

 Alloys are classified as binary alloys, composed of two components; as ternary

Prof. A. H. Kamble, Prof. S. K. Khillare 2-3

2.4.1 Simple Eutectic Solution

2.4.2 Solid Solution

2.4.3 Combination type Solution

2.4.4 Intermetallic Compound

2.5 Solid Solution

Prof. A. H. Kamble, Prof. S. K. Khillare 2-4

2.5.1 Types of Solid Solution

1 Substitutional Solid Solution

Prof. A. H. Kamble, Prof. S. K. Khillare 2-5

Fig 2-1 Ordered substitutional solid solution

Fig 2-2 Disordered substitutional solid solution

2 Interstitial Solid Solution

Prof. A. H. Kamble, Prof. S. K. Khillare 2-6

Fig 2-3 Interstitial solid solution

2.6 Hume Rothery’s Rules of Solid Solubility

1 Crystal structure factor

Prof. A. H. Kamble, Prof. S. K. Khillare 2-7

2 Relative size factor

3 Chemical affinity factor

4 Relative valence factor

2.7 Gibb’s Phase Rule

Prof. A. H. Kamble, Prof. S. K. Khillare 2-8

Significance of Gibb’s Phase rule in metallurgical system

2.8 Solidification of Pure Metal

Prof. A. H. Kamble, Prof. S. K. Khillare 2-9

Fig 2-4 Cooling curve for pure metal

 Fig 2-4 shows cooling curve for pure metal.

Prof. A. H. Kamble, Prof. S. K. Khillare 2-10

2.9 Plotting of Equilibrium Diagrams

2.9.1 Plotting of Equilibrium Diagram by Thermal Analysis Method

Prof. A. H. Kamble, Prof. S. K. Khillare 2-11

Fig 2-5 Cooling curves for Cu-Ni samples

Prof. A. H. Kamble, Prof. S. K. Khillare 2-12

Fig 2-6 Equilibrium diagram for Cu-Ni alloy system

2.10 Lever Rule

Prof. A. H. Kamble, Prof. S. K. Khillare 2-13

Fig 2-7 Typical isomorphous phase diagram.

Prof. A. H. Kamble, Prof. S. K. Khillare 2-14

Fig 2-8 Schematic illustration of the lever rule.

Prof. A. H. Kamble, Prof. S. K. Khillare 2-15

2.11 Iron Carbon Alloy System

Fig 2-9 2.11.1 Iron- Iron Carbide Equilibrium Diagram

Prof. A. H. Kamble, Prof. S. K. Khillare 2-16

Prof. A. H. Kamble, Prof. S. K. Khillare 2-17

4 Cementite (Fe3C) or Iron Carbide or Carbide

2.12 Transformations in Fe-Fe3C Diagram

Where S1 and S2 are two different solids and L is liquid.

Prof. A. H. Kamble, Prof. S. K. Khillare 2-18

Fig 2-10 Peritectic Transformation

The amounts of δ and L may be found by applying the Lever rule.