UNIT-II

1(a) Construct phase diagram and explain briefly and list out different types of phase diagram?

A diagram that depicts existence of different phases of a system under equilibrium is termed as
phase diagram.

•It is actually a collection of solubility limit curves. It is also known as equilibrium or

constitutional diagram.

•Equilibrium phase diagrams represent there relationships between temperature, compositions

and the quantities of phases at equilibrium.

These diagrams do not indicate the dynamics when one phase transforms into another.

It shows phases present at different compositions and temperatures under slow cooling
(equilibrium) conditions.

It suggests temperature at which an alloy starts to solidify and the range of solidification.

•It signals the temperature at which different phases start to melt.

•Amount of each phase in a two-phase mixture can be obtained

A single-phase system is called homogeneous,

systems with two or more phases are mixtures or heterogeneous systems.

fig: phase diagram

Equilibrium diagrams may be classified according to the relation of the component in the liquid
and solid states as follows:

-Components completely soluble in the liquid state,

• also completely soluble in the solid state,

•but partly soluble in the solid state (EUTECTIC REACTION Type I).

•but insoluble in the solid state (EUTECTIC REACTION Type II)

•The PERITECTIC Reaction

-Transformation in solid state

•Eutectoid reaction

•Peritectoid reaction

-Types of reactions in binary phase diagrams

•Eutectic Reaction

•Peritectic Reaction

•Eutectoid reaction

•Peritectoid reaction

1b) Define invariant reactions in phase Diagram with examples

According to the Phase Rule, an invariant reaction occurs in a C-component system when (C +
1) phases are at equilibrium at constant pressure.

Examples: Eutectic, peritectic, monotectic, peritectoid and eutectoid reactions are all invariant
and take place at an invariant temperature for the system.
2a).Evaluate Gibbs Phase rule, What are the uses of phase diagram

 The phase rule connects the Degrees of Freedom, the number of Components in a system
and the number of Phases present in a system via a simple equation.
 To understand the phase rule one must understand the variables in the system along with
the degrees of freedom.
 Start with a general definition of the phrase: “degrees of freedom”
 In response to a stimulus the ways in which the system can respond corresponds to the
degrees of freedom of the system


 The Phase rule is best understood by considering examples from actual phase diagrams
 C –No. of Components
 P – No. of Phases
 F – No. of degrees of Freedom
 Variables in the system = Composition variables + Thermodynamic variables
 Composition of a phase specified by (C – 1) variables (e.g. If the composition is
expressed in %ages then the total is 100%
There is one equation connecting the composition variables and we need to specify only
(C-1) composition variables)
 No. of variables required to specify the composition of all Phases: P(C – 1) (as there are P
phases and each phase needs the specification of (C-1) variables)
  Thermodynamic variables = P + T (usually considered) = 2 (at constant Pressure (e.g.
atmospheric pressure) the thermodynamic variable becomes 1)
 Total no. of variables in the system = P(C – 1) + 2
 F < no. of variables F < P(C – 1) + 2

The uses of phase diagram:

The equilibrium diagram is used to obtain following information:

 It shows the various phase present at different composition and temperature.

 It indicate solid solubility of one element in other.
 The understanding of phase diagrams for alloy systems is extremely important because
there is a strong correlation between microstructure and mechanical properties, and the
development of microstructure of an alloy is related to the characteristics of its phase
diagram.
 In addition, phase diagrams provide valuable information about melting, casting,
crystallization, and other phenomena.

2(b) .Define single and multiphase solids with examples

Structurally there are two kinds of metal alloys, Single phase and multiphase. Single-phase
alloys are composed of crystals with the same type of structure. They are formed by "dissolving"
together different elements to produce a solid solution. The crystal structure of a solid solution is
normally that of the base metal.

Ex: liquid crystals; superfluids and supersolids; and the paramagnetic and ferromagnetic phases
of magnetic materials.

A solid solution is a single phase which exists over a range of chemical compositions. Some
minerals are able to tolerate a wide and varied chemistry, whereas others permit only limited
chemical deviation from their ideal chemical formulae.

The definition of a substance that is "multi-phase" is that there is more than one distinct
compound in it and the compounds form distinct regions in the substance with different
properties.

Examples make this clearer. Salt dissolved in water forms a uniform mixture: a salt solution.
There is more than one compound there but they are perfectly mixed.

Ex: Solder, in which the metals lead and tin are present as a mechanical mixture of two separate
phases, is an example of the simplest kind of multiphase alloy.

3(a) What is single component phase diagram? Explain water system with neat diagram

Single component phase diagrams (Unary):

The unary system wherein there is just one component.

When there is only one degree of freedom in a single component phase diagram,

One Component Phase Systems: Water System

In water there is only one component i.e. water and its three phases: ice, water, steam which are
solid, liquid, and gaseous respectively.

All three phases can be represented by the chemical entity H2O. So it is a one-component
system. The conditions of equilibrium between the various phases of a substance can be
represented simultaneously on a single graph which is known as a phase diagram.

The three curves OA, OB and OC represent the equilibrium conditions between two phases solid
with vapour, vapour with liquid and liquid with solid phase of water.

Let us study two phase equilibria one by one.

Curve OA represents the equilibrium between solid and vapour phase of the water. This curve is
known as vapour pressure or sublimation curve. Along the line OA, for every temperature, there
exists a corresponding pressure at which both solid ice and water vapour co-exist in equilibrium.

Applying the phase rule F=C-P+2 but we have c=1 and p=2

F=1-2+2=1 Thus the degree of freedom is 1.

Thus the system is univariant.

Curve OC represents the equilibrium between solid and liquid phase of the water. This curve is
known as fusion pressure or melting point curve. Along this curve there are two phases in
equilibrium that is ice and water. At atmospheric pressure, ice and water can be in equilibrium
only at one temperature i.e. the freezing point of water.We have C=1, P=2 thus, F=C-P+2 = 1.

CURVE OB represents the equilibrium between liquid and vapour. It is known as vaporization
curve. Here also it is necessary to state either temperature or pressure. E.g. - at atmospheric
pressure, water and vapour can exist in equilibrium only at 1 temperature i.e. the boiling pt. of
water.

Water-vapour system has one degree of freedom. F=C-P+2=1

3(b) List out Transformations in the Solid State, Explain allotropic change with diagram

Transformations : Melting: The transition from the solid to the liquid phase.

Freezing: The transition from the liquid phase to the solid phase.

Evaporating: The transition from the liquid phase to the gas phase.

Condensing: The transition from the gas phase to the liquid phase.

There are several equilibrium changes and reactions which take place entirely in the solid state.
They are known as transformations in the solid state.

a. Allotropic change
b. Order-disorder
c. The eutectoid reaction
d. The peritectoid reaction

Allotropic change:

Several metals may exist in more than one type of crystal structure depending upon their
temperature. This property of a metal is called allotropy. Iron, manganese, cobalt and tin have
this property. On equilibrium diagram, allotropic change is indicated by a point on the vertical
line for pure metals

.
4(a) Define congruent-melting alloys, Estimate components for following systems (i) Au-Cu
System, (ii) Ice –water system,(iii) Al2O3-Cr2O3

Congruent-melting alloys :It begins and ends solidification at a constant temperature with no
change in composition, and its cooling curve will show a horizontal line. Such alloys are known
as congruent-melting alloys

The end product of a congruent melting alloy shall have only one phase

Components of a system:

Independent chemical species which comprise the system: These could be: Elements, Ions,
Compounds
i)Au-Cu system : Components →Au, Cu (elements)

ii)Ice-water system : Component →H2O (compound)

iii)Al2O3 –Cr2O3 system : Components → Al2O3 , Cr2O3

4(b) Evaluate cooling curve of binary eutectic system

 Eutectic alloy is the one that undergoes eutectic reaction during cooling.

 Eutectic reaction can be stated as:

Liquid1 Constant Temperature Solid1 + Solid2

 Thus, eutectic alloy when cooled forms two different solid phases.

 Fig. shows typically cooling curve for binary eutectic alloy.

 A binary eutectic alloy thus has two element which are completely soluble in liquid state
but entirely insoluble in the solid state.

 Region AB represent liquid state, solidification starts at B and continue until C, region
CD represent solid state containing.
  Application of Gibb’s phase rule in various regions:

 Region AB

 P+F=C+1

 1+F=2+1

 Therefore, F=2

 Thus F = 2 means any two variables temperature and composition can be varied
without effecting liquid phase of the system.

 (2) Region BC

 P+F=C+1

 3+F=2+1

 Therefore, F=0

 Thus F = 0 means that no variable amongst temperature and pressure can be varied
with out changing the Liquid + Solid phase of system.

 If the temperature is increased the metal goes into liquid state and if the temperature
is lowered it goes into solid state.

 Region CD

 P+F=C+1

 2+F=2+1

 Therefore, F=1

 Thus F = 1 means that only one variable i.e temperature can be varied without
changing solid state of system.

5a) Tabulate types of reactions in binary phase diagrams

Binary Phase diagrams:

Types of reactions in binary phase diagrams

•Eutectic Reaction
•Peritectic Reaction

•Eutectoid reaction

•Peritectoid reaction

Eutectic Reaction:

Peritectic Reaction:

Eutectoid reaction:

Peritectoid reaction:
5b) Explain and draw the equilibrium cooling and heating diagrams of pure metals and alloy
systems..

Cooling curve is the graphical plot of phases of element on temperature v/s time.

The resulting phase during solidification is different for various alloy composition.

The most common cooling curves are:

1. For pure metals

2. For binary solid solution(alloy)

3. For eutectic binary alloy

4. For off-eutectic binary alloy

Cooling Curves for Pure Metals:

7.Evaluate the cooling curve of solidification of a pure metal with diagram

A cooling curve is a graphical plot of the changes in temperature with time for a material over
the entire temperature range. Through which it cools

The transformation from liquid to solid state begins only after it has cooled below its melting
point.

A cooling curve for each mixture is constructed and the initial final phase change temperatures
are determined. Then these temperatures are used for the construction of the phase diagrams.

Under equilibrium conditions, all metals exhibit a definite melting or freezing point. If a cooling
curve is plotted curve is plotted for a pure metal. It will show a horizontal line at the melting or
freezing temperature.
A typical cooling curve of pure metal shown in fig. freezing starts at B and completes at C and
between B and C, the metal is in the liquid plus solid state. Above the temperature indicated by
point B, the metal is in the liquid state and below C, it is in the solid state.

Application of phase rule in various regions:

i) 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.

ii) In region BC: P+F=C+1

2+F=1+1;

Therefore, F=0 (non variant or invariant system)

The meaning of F=0 is that the temperature cannot be varied without changing the liquid and
solid phases existing in the system. If temperature is increased, the metal goes in the liquid state
and if decreased, it goes in the solid state. Hence pure metals solidify at constant temperature.

iii) In region CD: P+F = C+1; 1+F=1+1

Therefore F=1 (univarient system)

 The meaning of F=1 is similar to the previous one i.e temperature can be changed
without changing the solid phase existing in the system.

6a)Draw an equilibrium diagram for an isomorphism system

Solid Solution (Isomorphism System) – Two Metals (or components) Completely Soluble in
the Liquid and Solid States:
The main conditions for complete/unlimited solubility in the solid state (as discussed under solid
solution) are:
(i) Two components should have the same type of crystal.
(ii) Sizes of the atoms should be very similar (the difference in size for iron, nickel, or cobalt
base alloys must not exceed 8 per cent). A difference in size over 15 per cent prevents the
formation of solid solutions due to the extreme distortion of the solvent crystal lattice.
Fig. 2.8 shows the equilibrium diagram for a system of components that are completely mutually
soluble in both the liquid and solid states. The upper line (called liquidus) corresponds to the
temperatures at which the alloys begin to solidify.
The lower line (called solidus) indicates the completion of solidification. In the temperature
interval between the liquidus and solidus the alloys are in semi-solid state, i.e. they consist of
crystals of a solid solution of metals A and B and the liquid alloy.

Let us now consider solidification of an alloy containing 60% B (Fig. 2.8). Freezing starts at
temperature t1, where the first crystal of the solid solution of metals A and B separate from the
liquid alloy. Below temperature t 1, the ‘solid solution’, in equilibrium in the liquid phase, is
determined by the point of intersection of a horizontal line, passing through the given
temperature, with the solidus.

6b) Construct binary phase diagram of Al-Cu and show eutectic point temperature and wt% of
Cu.

Al-Cu phase diagram shown only goes up to around 60%, by weight, of Copper. The Al-Cu
phase diagram is split at around 54wt%Cu by a particular phase. This "split" means that the two
parts of the diagram can be considered separately. The diagram up to the 54% point is very
similar to the "standard" phase diagram.

Consider two Al-Cu alloys, one of composition 33wt%Cu and the other of 20wt%Cu.

Examining the phase diagram:

-the 33wt%Cu alloy is of eutectic composition and

-the 20wt%Cu alloy is hypoeutectic as it is to the left of the eutectic point.

So, first considering the Al-33%Cu alloy:

The eutectic reaction, at 33%Cu can be shown as:

Liquid > alpha + theta

So, the two phases grow simultaneously as an interconnected structure - the eutectic phase

7 Draw and explain the Fe-Fe3c phase diagram invariant reactions?

Phases in Fe–Fe3C Phase Diagram

􀂾 α-ferrite - solid solution of C in BCC Fe
• Stable form of iron at room temperature.
• The maximum solubility of C is 0.022 wt%
• Transforms to FCC γ-austenite at 912 °C
􀂾 γ-austenite - solid solution of C in FCC Fe
• The maximum solubility of C is 2.14 wt %.
• Transforms to BCC δ-ferrite at 1395 °C
• Is not stable below the eutectic temperature
(727 ° C) unless cooled rapidly (Chapter 10)
􀂾 δ-ferrite solid solution of C in BCC Fe
• The same structure as α-ferrite
• Stable only at high T, above 1394 °C
• Melts at 1538 °C
􀂾 Fe3C (iron carbide or cementite)
• This intermetallic compound is metastable, it remains as a compound indefinitely at room T,
but decomposes (very slowly, within several years) into α-Fe and C (graphite) at 650 - 700 °
Fe-C liquid solution:

A few points on Fe–Fe3C system

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
Classification. Three types of ferrous alloys:
• Iron: less than 0.008 wt % C in α−ferrite at room T
• Steels: 0.008 - 2.14 wt % C (usually < 1 wt % ) α-ferrite + Fe3C at room Temperature
• Cast iron: 2.14 - 6.7 wt % (usually < 4.5 wt %)
Invariant reactions:

8) Draw the Eutectoid system diagram and label all points, lines and areas. Explain its important
features.
Microstructure of Eutectoid Steel: Microstructure depends on composition (carbon content) and
heat treatment.

In the discussion, we consider slow cooling in which equilibrium is maintained.

When alloy of eutectoid composition (0.76 wt % C) is cooled down slowly it forms a lamellar or
layered structure of two phases: α-ferrite and cementite (Fe3C). This two phase structure is
called as Pearlite
Microstructure of Hypo-eutectoid Steel: Compositions to the left of eutectoid point, (0.022 -
0.76 wt % C) are termed as hypo-eutectoid (less than eutectoid) Steels.
γ → Proeutectoid α + γ → Proeutectoid α + Pearlite((Eutectoid α + Fe3C))

9a).Explain Lever rule with tie line?

The relative fractions of the phases at a given temperature for an alloy composition Co is
obtained by the lever rule. This rule gives the fraction of a phase by the ratio of the lengths of the
tie line between Co and composition of the other phase to the total length of the tie line. For
example, fraction solid, fs is given by

9b) What are the eutectoid and eutectic reactions in Cu-Ni & Al-Cu binary phase diagram?

• Eutectic reaction is transition between liquid and mixture of two solid phases, α + β at
eutectic concentration CE.

• Eutectic is a Greek word meaning easy to melt

 • The eutectoid (eutectic-like in Greek) reaction is similar to the eutectic reaction but
occurs from one solid phase to two new solid phases.

• Upon cooling, a solid phase transforms into two other solid phases (γ ↔ α + β)

• Eutectic alloy is the one that undergoes eutectic reaction during cooling.

• Eutectic reaction can be stated as:

• Thus, eutectic alloy when cooled forms two different solid phases.

the Al-20wt%Cu alloy is hypoeutectic. The

liquid alloy initially contains a higher percentage
of Al than that corresponding to the eutectic
composition; the primary solid phase that forms is therefore alpha.

Formation of the alpha phase, however, depletes the remaining liquid in Aluminium (Al) and the
liquid composition shifts toward the eutectic composition. When the composition reaches
eutectic (33%Cu for this phase diagram) the remaining liquid follows the eutectic reaction.
So, at room temperature, the microstructure consists of primary alpha dendrites surrounded by a
finely divided eutectic mixture of two solid phases (alpha+theta).

Alloys forming homogeneous solid solutions are widely used as engineering materials.

10)

From the data given below for Cu-Ni system, plot the equilibrium diagram
to scale and label the diagram
Weight 0 20 40 60 80 100
%Ni
Liquidus 108 1200 1275 1345 1440 1455
 Temp oC 4
Solidus 108 1165 1235 1310 1380 1455
TempoC 4
Answer the following for 70% Ni alloy
a) What is the composition of first solid crystallizing out from liquid?
b) What is the composition of last solid formed at the end of
solidification?
What are the amounts of solid and liquid at 1360oC?

Solution: the diagram is plotted to the scale and shown in fig:.the alloy is shown by a vertical
line at 70% Ni. During cooling, solidification starts at point L and finishes at point S.

First solid which separates from Liquid

has a composition given by solidus line
i.e80% Ni and the last liquid which
solidifies has a compostion given by
the liquid line ie 58% Ni shown infig.

At 1360oC,

Amount of solid (75%Ni) = 70-63/75-

63 = 58.3%

And
Amount of liquid (of 63%Ni) =75-70/75-63 = 41.7%

ANS: a) 8 0% Ni

b) 58% Ni
c) Solid =58.3% and liquid =417%

6(A) Differentiate between composite and alloy?

The main difference between alloys and composites are its composition.

Alloy Composite
An alloy is defined as a mixture of a minimum Composites are also a mixture of two or more
of two elements in which one must be metal. elements, for which the metal is not required.
An alloy can either be a homogeneous or a A composite is always a heterogeneous mixture.
heterogeneous mixture.
Alloys are lustrous due to the presence of Composites are not lustrous as they do not
metals in their composition. contain metals in their composition.
Most alloys can conduct electricity. Composites do not conduct electricity except for
 polymeric composites.
Alloys can be found in nature but are very rare Composites can be found naturally almost
everywhere
Ex: steel , brass, bronze Ex: Composite wood, plywood, concrete,
fiberglass

6(B) Evaluate metallic bond and list out characteristics compound

Metallic Bond:

Metallic bonds are the chemical bonds that hold atoms together in metals. They differ from
covalent and ionic bonds because the electrons in metallic bonding are delocalized, that is, they
are not shared between only two atoms. Instead, the electrons in metallic bonds float freely
through the lattice of metal nuclei. This type of bonding gives metals many unique material
properties, including excellent thermal and electrical conductivity, high melting points, and
malleability.

These are formed when the valence electrons of metal atoms are shared by more than one
neighboring atom. The metal atoms are held together by a “sea” of electrons floating around.
Metals consist of a lattice of positive ions through which a cloud of electrons moves. The
positive ions will tend to repel one another, but are held together by the negatively charged
electron cloud. The mobile electrons, known as conduction electrons, can transfer thermal
vibration from one part of the structure to another i.e., metals can conduct heat. They are good
conductors of electricity also.

Fig:Metalic bond

Example:

The metal atoms Na, Cu, Ag, Fe etc., are bound to each
other in their crystals by metallic bond.