Unit 3-k.srinivasulureddy-MMS-metallurgy & material science-snist

Unit - III
Solidification of Metals and Binary Alloys: Concepts of
nucleation & grain growth; directional-solidification; dendritic growth
and equiaxed grain growth. Phase rule, invariant reactions (eutectic,
eutectoid, peritectic, peritectoid; Lever rule, cooling-curves of pure
metals, binary alloys. Binary phase diagrams (Aluminum-Silicon and
Aluminum-Copper, Copper-Zinc, Copper-Tin, Copper-Nickel.
Non ferrous Metals & Alloys: Aluminum based alloys; Cast alloys,
Wrought alloys and their applications. Copper based alloys:
Brasses, Bronzes and their applications. Magnesium based alloys;
Cast alloys, wrought alloys and their applications. Titanium based
alloys: aerospace alloys, bio-compatible alloys. Nimonic alloys -
their compositions and applications. Heat treatment of Non-ferrous
metals, Age hardening, solution hardening.

A phase can be defined as a homogeneous portion of a system that has uniform physical and
chemical characteristics i.e. it is a physically distinct from other phases, chemically
homogeneous and mechanically separable portion of a system.
A component can exist in many phases.
E.g.: Water exists as ice, liquid water, and water vapor.
Carbon exists as graphite and diamond.
➢A solution (liquid or solid) is phase with more than one component; a mixture is a material
with more than one phase. A solution is a mixture where one of the substances dissolves in
the other.
➢In mixtures, there are different phases, each with its own atomic arrangement. It is
possible to have a mixture of two different solutions!
➢ Solute (minor component of two in a solution) does not change the structural pattern of
the solvent, and the composition of any solution can be varied. Ex: Salt water
Salt (Solute) in water(Solvent)

Phase
• A phase is defined as a homogenous portion
of the system having uniform physical and
chemical characteristics.
• Every pure material is considered to be a
single phase.
• Each phase is separated by phase boundaries.
• A phase may contain one or two component.
• A single phase system is called as homogenous
and systems with two or more phases are
heterogeneous systems.

Solubility Limit
• A maximum amount of solute that can be
dissolved in the solvent to form a solid
solution is termed as solubility limit.
• For example, alcohol has unlimited solubility
in water, sugar has limited solubility, and oil is
insoluble in water.
• Cu and Ni are mutually soluble in any amount,
while C has limited solubility in Fe.
• The addition of solute in excess of this limit
results in the formation of two phase solution.

Phase Equilibria: Solubility Limit
Introduction
– Solutions – solid solutions, single phase
– Mixtures – more than one phase
• Solubility Limit:
Max concentration for
which only a single phase
solution occurs.
Question: What is the
solubility limit at 20°C?
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.
65
Sucrose/Water Phase Diagram
Pure
Sugar
Temperature(°C)
0 20 40 60 80 100
Co =Composition (wt% sugar)
L
(liquid solution
i.e., syrup)
Solubility
Limit L
(liquid)
+
S
(solid
sugar)20
40
60
80
10 0
Pure
Water

8
Effect of T & Composition (Co)
• Changing T can change # of phases:
D (100°C,90)
2 phases
B (100°C,70)
1 phase
path A to B.
• Changing Co can change # of phases: path B to D.
A (20°C,70)
2 phases
70 80 1006040200
Temperature(°C)
Co =Composition (wt% sugar)
L
(liquid solution
i.e., syrup)
20
100
40
60
80
0
L
(liquid)
+
S
(solid
sugar)
water-
sugar
system

Solidification ?
➢Solidification, is a phase transition in which a liquid turns into
a solid when its temperature is lowered below its freezing point.
➢During solidification, the liquid changes in to solid as cooling proceeds.
➢The energy of liquid is less than that of the solid above the melting
point. Hence liquid is stable above the melting point.
➢But below the melting point, the energy of liquid becomes more than
that of the solid. Hence below the melting point, the solid becomes more
stable than the liquid.
➢ At temperatures below the freezing/ melting point, the
substance is a solid.

➢ Thermodynamically, both liquid and solid have equal energy at melting
point and therefore both are equally stable at melting point.
➢ Freezing is almost always an exothermic process, meaning that as
liquid changes into solid, heat is released.
➢ This heat must be continually removed from the freezing liquid
otherwise the freezing process will stop.
➢ The energy released upon freezing is latent heat
➢ Some under-cooling is essential for solidification.
➢ Solidification occurs by two process : nucleation and growth.

Nucleation and Growth
Transformation
• Embryo - An embryo is a tiny particle of solid that
forms from the liquid as atoms cluster together.
The embryo is unstable and may either grow in to
a stable nucleus or re-dissolve.
• Nucleus – It is a tiny particle of solid that forms
from the liquid as atoms cluster together.
Because these particles are large enough to be
stable, nucleation has occurred and growth of the
solid can begin.

NUCLEATION
➢The first step of metal solidification is the creation of tiny, stable, nuclei in the
liquid metal.
➢ Cooling the liquid below its equilibrium freezing temperature, or undercooling,
provides the driving force for solidification.
➢ Once a cluster reaches a critical size, it becomes a stable nucleus and continues to
grow.
➢The mold walls and any solid particles present in the liquid make nucleation easier.
Cluster of atoms Embryo Nuclei Crystals Grains
r > r’
r < r’ r’ = critical radius

NUCLEATION & GROWTH
Nucleation and formation of grains
Nucleation – The physical process by which a new phase is produced in a material. In
the case of solidification, this refers to the formation of tiny stable solid particles in
the liquid.
Growth - The physical process by which a new phase increases in size. In the case of
solidification, this refers to the formation of a stable solid particle as the liquid
freezes.

Crystal Nucleation and Growth
Various stages during solidification
of molten metal. Each small square
represents a unit cell.
a) Nucleation of crystals at random
sites in the molten metal. Note that
the crystallographic orientation of
each site is different.
(b) & (c) Growth of crystals as
solidification continuous.
d) Solidified metal, showing grains
and grain boundaries. Note the
different angles at which neighboring
grains meet each other

Nucleation and Growth of Crystals
• At the solidification temperature,
atoms from the liquid, such as molten
metal, begin to bond together and
start to form crystals.
• The moment a crystal begins to grow
is know as nucleus and the point
where it occurs is the nucleation
point.
• When a metal begins to solidify,
multiple crystals begin to grow in the
liquid.
• The final sizes of the individual
crystals depend on the number of
nucleation points.
• The crystals increase in size by the
progressive addition of atoms and
grow until they impinge upon
adjacent growing crystal.
a)Nucleation of crystals,
b) crystal growth,
c) irregular grains form as crystals grow together,
d) grain boundaries as seen in a microscope.

Nucleation is of two types-
➢ Homogeneous nucleation:
Homogeneous Nucleation – Formation of a critically sized solid from the
liquid by clustering together of a large number of atoms at a high
undercooling.
➢ Heterogeneous Nucleation :
Formation of a critically sized solid from the liquid on an impurity surface.
heterogeneous nucleation occurs in a liquid on the surface of its container,
insoluble impurities and other structural materials that lower the critical
free energy required to form a stable nucleus.
In practice, homogeneous nucleation rarely takes place and heterogeneous
nucleation occurs either on the mould walls or on insoluble impurity
particles.
TYPES OF NUCLEATION

COOLING CURVES
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.
COOLING CURVE WITH UNDERCOOLING
Supercooling is the cooling of a liquid below its freezing point without it becoming
solid.

• Homogeneous Nucleation – Formation of a critically sized
solid from the liquid by clustering together of a large
number of atoms at a high undercooling (without an
external interface).

Supercooling
During the cooling of a liquid, solidification (nucleation) will
begin only after the temperature has been lowered below the
equilibrium solidification temperature. This phenomenon is
termed supercooling (or undercooling.)
 The driving force to nucleate increases as T increases
Small supercooling  slow nucleation rate - few nuclei -
large crystals
Large supercooling  rapid nucleation rate- many nuclei -
small crystals

Metal ∆T, 0C
Antimony 135
Germanium 227
Silver 227
Gold 230
Copper 236
Iron 295
Nickel 319
Cobalt 330
Palladium 332
HOMOGENEOUS NUCLEATION
Table: Degree of undercooling (∆T) values for Several metals (Homogeneous Nucleation).

phase transformations
Most phase transformations begin with the formation of numerous small
particles of the new phase that increase in size until the transformation is
complete.
 Nucleation is the process whereby nuclei (seeds) act as templates for
crystal growth.
✓ Homogeneous nucleation - nuclei form uniformly throughout the parent
phase; requires considerable supercooling (typically 80-300°C).
✓ Heterogeneous nucleation - form at structural inhomogeneities (container
surfaces, impurities, grain boundaries, dislocations) in liquid phase much
easier since stable “nucleating surface” is already present; requires slight
supercooling (0.1-10ºC ).

Time-Temperature curve for the solidification of a pure metal
 Undercooling(Supercooling)A-B: It is the gap between the temp. predicted for the
transformation to occur and the temp at which the transformation actually occurs, is
the process of lowering the temperature of a liquid or a gas below its freezing point
without it becoming a solid.
A-B: Undercooling
B-C: Evolution of latent heat after undercooling

➢The first step in the solidification is the formation of nuclei. The nucleus can be
regarded as a small cluster of atoms having the right crystalline arrangement.
➢When the melt is cooled below the melting point, nuclei begin to form in many
parts of the melt at the same time.
➢The rate of nuclei formation depends on the degree of undercoolong or
supercooling and also on the presence of impurities which considerably facilitate
nucleation.
➢At any temperature below the melting point, a nucleus has to be of a certain
minimum size, called the critical size, so that it will grow.
➢Particles smaller than the critical size will be dissolved by the vigorous
bombardment of neighboring atoms and can’t grow are called embryos.

NUCLEATION
➢The volume free energy ΔGV – free energy
difference between the liquid and solid
Δ GV = 4/3πr3ΔGv (- ve)
➢The surface energy ΔGs – the energy needed
to create a surface for the spherical particles
ΔGs = 4πr2γ (+ ve)
γ → specific surface energy of the particle
Total free energy Change, ΔGT = ΔGV + ΔGs
➢ Embryo’s formed may either form into stable
nuclei or may re-dissolve in the liquid.
➢ Beyond the critical radius of the nuclei it will
remain stable and growth occurs
Variation of free energy of a spherical particle as a function of its radius

➢ If a spherical particle of solid of radius r is to form, an interface must be created
between the solid and the surrounding liquid.
 Since ɣ is the energy required to create one unit area of interface, the overall change in
free energy, ΔGv, that accompanies the formation of a spherical solid within the liquid is:
➢The surface energy term (i.e energy needed to create interface or surface energy) is
always positive but the volume energy term(i.e energy released by volume of solidifying
phase or volume energy) will be negative for any phase transformation under
consideration.
➢Since the energy needed to create interface varies as r2 and energy released by volume
of solidifying phase varies as r3 , the variation of these two terms with increasing value of r
is as shown in Fig.
➢Initially for smaller values of r, energy released by volume of solidifying phase is smaller
than the energy needed to create interface but it becomes greater for larger values of r,
since it varies as r3 .
➢Thus the sum of ΔGV goes through a maximum at some critical radius r*.

Surface
free energy
Volume
free energy
Total free
energy
Fig (b) shows the sum of both the terms volume free energy and surface free
energy.
Many clusters will form embryo and dissolve and do not make it to critical radius r*
Few of them survive past the critical radius r*, then growth continue for the nucleus
with decrease in free energy.
Since the maximum free energy occurs at r*, we differentiate ∆G, w.r.t., r, & set the
expression to zero.
Unstable embryos Stable nuclei
Variation of free energy of a spherical particle as a function of its radius

r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Homogeneous Nucleation & Energy Effects
GT = Total Free Energy
= GS + GV
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
 2
4 rGS
 = surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
 GrGV
3
3
4
volumeunit
energyfreevolume
 G

[2]
[3]
[4]
r*
Heat of fusion ∆Hf (energy release upon solidification)
And
Tm-T= Super cooling
Tm= Melting Temp.

Solidification
TH
T
r
S
m



2
*
Note: HS = strong function of T
 = weak function of T
 r* decreases as T increases
HS = latent heat of solidification
Tm = melting temperature
 = surface free energy
T = Tm - T = supercooling
r* = critical radius

As T decreases, both r* and ∆G* become smaller;
LIQUID INSTABILITY at LOWER TEMPERATURES.
➢When the temperature is lowered, the vibrations of atoms gradually decrease,
increasing the chances of survival of small clusters and therefore, the critical size of
nucleus decreases with decreasing temperature or increasing degree of
undercooling.

➢It is also clear that some degree of undercooling is necessary to start
solidification i.e nucleation. The extend of undercooling(i.e temperature A
– temperature B) varies from metal to metal and also depends on the
impurities present in the metal.
*Diffusion is the net movement of molecules or atoms from a region of
high concentration to a region of low concentration.
➢Hence, at lower temperatures nuclei become progressively smaller in
size but the number greatly increases. Growth of nuclei occur by diffusion*
process which is also a function of temperature and hence the rate of
nucleation(N) and rate of growth(G) are functions of temperature.

Heterogeneous nucleation begins on alien surfaces or particles,
or pre-existing nuclei in the old phase. The nuclei can form at
preferential sites(Eg. Mould wall, impurities or catalysts)
Critical radius of the nucleus (r*) for a heterogeneous
nucleation is the same as that for a homogeneous nucleation

HETEROGENEOUS NUCLEATION
Heterogeneous Nucleation
1. Consider the nucleation of a solid from liquid, on a flat surface.
2. Assume that both liquid and solid phases “wet” this flat surface; that is both
of these phases spread out and cover the surface.
3. Interfacial energies: γSL = Solid/Liquid; γIL = Liquid/surface;
γSI = Solid /surface.
4. Taking surface tension force balance: γIL = γSI + γSL cos θ [12]

• Heterogeneous Nucleation – Formation of a critically sized
solid from the liquid on an impurity surface.
• Heterogeneous nucleation occurs in a liquid on the surface of
its container, insoluble impurities and other structural
materials that lower the critical free energy required to form a
stable nucleus
The factors which determine the rate of phase change are:
• (1) the rate of nucleation, N (i.e. the number of nuclei
formed in unit volume in unit time) and
• (2) the rate of growth, G (i.e. the rate of increase in radius
with time)

Heterogeneous Transformation
• In practice, homogeneous nucleation rarely takes
place and heterogeneous nucleation occurs either on
the mould walls or on insoluble impurity particles.
• A reduction in the interfacial energy(Surface energy)
would facilitate nucleation at small values of ∆T.
• This occurs at a mould wall or pre-existing solid
particle

1. The undercooling for Heterogeneous nucleation is only few
degrees, unlike few hundreds for Homogeneous nucleation.
2. The reason for very small undercooling is that the activation
energy (i.e., energy barrier) for nucleation (∆G* ) is lowered
when nuclei form on preexisting surfaces or interfaces, since
the surface free energy (γ ) is reduced.
3. Therefore it is easier to nucleate at surfaces and interfaces than
at other Homogeneous sites.

Nucleation and Grain Growth
• Nucleation
– Homogeneous nucleation: substantial undercooling (0.2Tm)
– Heterogeneous nucleation: nucleation agents (5ºC undercooling)
• Grain growth
– Planar: pure metal
– Dendritic: solid solution
• Grain size
– depends on number of nuclei and cooling rate.
• The solidification of metals occur by nucleation and growth transformation.
• In nucleation and growth transformation, the nuclei of the solid phase are
formed and then they grow.
Grain Growth in pure and solid solutions

• Free energy-versus - embryo/nucleus radius plot for homogeneous and
heterogeneous nucleation – Schematic.
• The lower ∆G* for heterogeneous means that a smaller energy must be overcome
during the nucleation process, (than for homogeneous), and therefore,
heterogeneous nucleation occurs more readily.
NUCLEATION & GROWTH

critical radius versus undercooling
Critical Size of Nucleus:The minimum size that must be formed by atoms
clustering together in the liquid before the solid particle is stable and
begins to grow.

Development of the ingot structure
of a casting during solidification:
(a) Nucleation begins,
(b) the chill zone forms,
(c) preferred growth produces the
columnar zone, and
(d) additional nucleation creates the
equiaxed zone.

Solidification in square moulds
a) Pure metals
b) Solid-solution alloys
c) Structure obtained by
heterogeneous
nucleation of grains
using nucleating
agents

1.Equiaxed zone: A region of randomly oriented grains in the center of a casting
produced as a result of widespread nucleation.
2.Columnar zone: A region of elongated grains having a preferred orientation
that forms as a result of competitive growth during the solidification of a casting.
3.Chill zone: A region of small, randomly oriented grains that forms at the surface
of a casting as a result of heterogeneous nucleation.
4.Dendrite: The treelike structure of the solid that grows when an undercooled
liquid solidifies.
➢ Note down all the definitions and try to understand and identify different
zones as shown in figure solidified solid and the difference between four .

GROWTH
Planar growth Dendritic growth

Directional solidification (DS) and progressive solidification are types
of solidification within castings. Directional solidification is solidification that occurs
from farthest end of the casting and works its way towards the sprue. Directional
solidification can be used as a purification process. Since most impurities will be more
soluble in the liquid than in the solid phase during solidification, impurities will be
"pushed" by the solidification front, causing much of the finished casting to have a lower
concentration of impurities than the feedstock material, while the last solidified metal
will be enriched with impurities. This last part of the metal can be scrapped or recycled.
Progressive solidification, also known as parallel solidification, is solidification
that starts at the walls of the casting and progresses perpendicularly from that
surface
Directional Solidification
Progressive Solidification

➢ Gibb’s phase rule states that under equilibrium conditions, the following
relation must be satisfied.
P + F = C + 2
Where
P= No. 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(i.e elements) in the system and
2 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 a variable. For such cases, Gibbs
phase rule becomes:
✓ P+ F = C + 1
✓ In the above rule, 1 represents any one variable out of the remaining two
i.e temperature and concentration

Schematic cooling curve of a pure metal
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
Cooling curve-Pure metal
Note: For start of solidification or nucleation, undercooling is necessary; but for simplicity, this
is not shown on cooling curves

In region AB:
P+F=C+1
1+F=1+1
So, F=1 (univarient) Temp. can be varied without changing the liquid phase existing in the
system
In region BC:
2+F=1+1
F=0 (nonvarient or invarient system).Temperature can’t be varied without changing the
liquid and solid phases existing in the system. If temp. is increased, the metal goes in the
liquid state and if decreased, it goes in the solid state. Hence pure metals solidify at
constant temp.
In region CD:
1+F=1+1 F=1 (Univarient system)
Temperature can be changed without changing the solid phase existing in the system.

Schematic cooling curve of a solid solution alloy
Binary solid solution alloy
From A to B, the alloy is in the liquid state. Freezing starts at B and completes at C, and
between B and C, the alloy is in the liquid plus solid state. From C to D, there is no change in
the solid state of the alloy

AB: F=2 (bivarient) i.e both temperature and concentration can be varied independently
without changing the liquid phase existing in the system
BC: F=1(univarient) i.e any one variable out of temp. and composition can be changed
independently without altering the liquid and solid phases existing in the system. From this, it is
clear that solid solution allolys solidify over a range of temperature. They have incongruent
melting points i.e melting starts at one temperature and finishes at another temperature.
CD: F=2
P+F=C+1 1+F=2+1, F=3-1=2

Schematic cooling curve of a binary eutectic alloy
Binary eutectic alloys
From A to B, the alloy is in the liquid state. Freezing starts at B and simultaneously two solids
S1 and S2 start separating out from the liquid. This continuous upto C. The alloy gets
completely solidified at C and gives a mixture of S1 and S2. From C to D, there is no change in
the solidified alloy

Lamellar structure
Lamellar structures or microstructures are composed of fine, alternating layers of different
materials in the form of lamellae.

AB: F=2
BC: F=0 (neither temp. nor concentration can be varied without changing the phases
existing in the system. Hence eutectic alloys solidify at constant temperature similar to that
of pure metals.
CD: F=1
➢Binary eutectic is homogeneous mixture of two solids which forms at constant
temperature during cooling and melts at constant temperature during heating. Binary
eutectic transformation can be shown as:
L S1 + S2
➢A eutectic reaction is a three-phase reaction, by which, on cooling, a liquid transforms
into two solid phases at the same time. It is a phase reaction, but a special one. For
example: liquid alloy becomes a solid mixture of alpha and beta at a specific temperature
(rather than over a temperature range). Eutectic meaning Easy melting.
Constant Temp.
➢Where S1 is one solid and S2 is other solid . This mixture appears in a definite
morphological form and is usually lamellar. In certain cases, it may have granular or some
other type of morphology. The temperature at which this transformation occurs is called
eutectic temperature and is the lowest temperature of transformation in the system.

Off-eutectic binary alloy
Eutectic transformation occurs for a definite composition is called eutectic composition. If the
composition of the alloy differs from this, it is called off-eutectic alloy i.e either
hypoeutectic(less than eutectic composition) or hypereutectic(more than eutectic
composition)

➢ A to B alloy is in liquid state. Freezing starts at B and either solid 1 or
solid 2 separates out from the liquid depending on whether the alloy is
hypoeutectic or hypereutectic. This continues upto C.
➢ The remaining liquid at C solidifies at constant temperature and forms a
mixture of S1 and S2. This eutectic transformation starts at C and ends at
D. The alloy completely solidifies at D and there is no change from D to E.
Solidus and Liquidus Temperatures
The start of solidification temperature is called liquidus temperature
because above this the metal or alloy is in the liquid state; where as the
end of solidification temperature is called solidus temperature because
below this , the metal or alloy is in the solid state.
Off-eutectic binary alloy

Liquidus is the lowest temperature at which an alloy is completely liquid;
Solidus is the highest temperature at which an alloy is completely solid.

Cooling Curve for Pure Metals
• Under equilibrium conditions, all metals exhibit a definite
melting or freezing point.
• If a cooling curve is plotted for a pure metal, It will show
a horizontal line at the melting or freezing temperature.

Cooling Curve of Alloys
• In this method, alloys with different compositions are melted and then the
temperature of the mixture is measured at certain time intervals while
cooling back to room temperature.
• A cooling curve for each mixture is constructed and the initial and final
phase change temperatures are determined.

Cooling Curve
• Then these temperatures are used for the construction of the
phase diagrams

Series of cooling curves for different alloys in a completely
soluble system. The dotted lines indicate the form of the phase
diagram

Phase Diagram of Solid Solution

Cooling Curves for Solid Solution

crystal growth and grain formation
• nuclei → crystals → grains
• polycrystalline – solidified metal containing many crystals
• grains – crystals in solidified metal
• grain boundaries – the surfaces between the grains
• two major types of grain structures:
(1) equiaxed grains – crystals grow about equally in all
directions, commonly found adjacent to a cold mold
wall
(2) columnar grains – long, thin, coarse grains, created
when metal solidifies rather slow in the presence of a
steep temperature gradient. columnar grains grow
perpendicular to the mold surface

Dendrites
• In metals, the crystals that form in the liquid during freezing generally
follow a pattern consisting of a main branch with many appendages. A
crystal with this morphology slightly resembles a pine tree and is called a
dendrite, which means branching.
• The formation of dendrites occurs because crystals grow in defined planes
due to the crystal lattice they create.
• The figure shows how a cubic crystal can grow in a melt in three
dimensions, which correspond to the six faces of the cube.
• For clarity of illustration, the adding of unit cells with continued
solidification from the six faces is shown simply as lines.
• Secondary dendrite arms branch off the primary arm, and tertiary arms off
the secondary arms and etcetera.

Dendrites
• During freezing of a polycrystalline material, many dendritic
crystals form and grow until they eventually become large
enough to impinge upon each other.
• Eventually, the interdendritic spaces between the dendrite
arms crystallize to yield a more regular crystal.
• The original dendritic pattern may not be apparent when
examining the microstructure of a material.
• However, dendrites can often be seen in solidification voids
that sometimes occur in castings or welds, as shown in the
next slide..

Equilibrium Phase Diagrams
• What is a phase diagram?
• Phase diagram is a “temperature” versus “composition” plot,
displays several equilibrium phases that are possible to exist at
various given specified ranges of temperature, composition, and
pressure.

• What is an alloy?
• An alloy is a homogeneous solid solution of two* or more metals,
the atoms of one metal substitutes for another metal or occupies
interstitial positions.
Examples:
Brass: Alloy of copper and zinc.
Bronze: Alloy of copper and tin.
Steel: Alloy of iron and carbon.
CMSX4: Alloy of Nickel and Co, Cr, Ta, W, Al, Re, Ti, Mo, Hf
______________________
* At least one is a metal.

• Phase diagrams provide valuable information about
melting,
casting,
crystallization,
heat treatment,
phase transformations, & resulting microstructure, …,
• Phase diagrams are extremely important because there is strong
correlation between the:
(i) phase diagrams,
(ii) microstructure, &
(iii) mechanical properties.

Definitions
(i) Component
Components are pure metals (or compounds) from which an
alloy is formed.
Cu-Zn, Cu-Ni, Fe-C, Al-Cu, Be-Cu,……
(ii) System
A series of possible alloys consisting of the same components is
called a system. Example series of the system is:
10%Cu-90%Ni, is a system.
30%Cu-70%Ni, is a system.
60% Cu-40%Ni, is a system.
(iii) Solubility Limit
A maximum concentration of solute atoms that may dissolve in
the solvent to form a solid solution. Ex. Sugar-water

Phases
A phase is defined as a homogeneous portion of a system that
has uniform physical and chemical characteristics.
(i) Solid is a phase.
(ii) Liquid is a phase.
(iii) Gas is a phase.
(iv) Every pure material is a phase.
(v) Water and ice in a container; Two phases in the container,
because they are physically dissimilar (one is solid & other is
liquid) but identical chemically!.
(vi) Fe exists in two polymorphic forms:
(a) α–Fe (BCC),
(b) γ – Fe (FCC). Both are different phases

Binary Phase Diagrams
1. Temp – Composition plots for alloys consisting of two
components
2. Pressure is considered as one atmosphere.
3. Examples:
Cu-Ni,
Cu-Zn,
Fe-Fe3C, e.t.c.,
Binary Equilibrium Phase Diagrams

Binary Isomorphous Systems
Alloys having complete liquid and solid solubility are called
isomorphous systems. Example: Cu-Ni.
• In Binary phase diagrams,
temperature is plotted on vertical
axis & composition on horizontal
axis.
• “L” is a homogeneous liquid
solution composed of both
copper and nickel.
• α, β, γ, γ’ (Greek) letters are
used to represent solid solutions.
• Liquidus line
• Solidus line
• Mushy state (L + α )
Liquid
α
Composition, wt% NiCu Ni
Temperature,0C

• Cooling curve for pure Cu or Ni
• Cooling curve for Cu-40 wt% Ni
• Heating Cu-50 wt% Ni
1280 0C melting begins.
1320 0C completely liquid.
• What phases are present?
Ex.1. Cu-60 wt% Ni, at “A”, at
1100 0C, is located within the α
region, therefore, only α phase
will be present.
Ex.2.Cu-35 wt% Ni, at “B” 12500C,
will have two phases: α & Liquid
phases in equilibrium.
Liquid
α
Temperature,0C

• How to determine phase
compositions?
(i) Determination of composition in
single phase region, say at position
“A”.
Ex. The position “A” is located in
the single phase region called “α”,
and the composition at “A” is 60 wt%
Ni & 40 wt% Cu.
Liquid
α
Temperature,0C

(ii). Determine composition of the two
phases of the alloy Cu- 35 wt% Ni
present at 1250 0C:
(a) Composition is to be
determined for the specific alloy
is located at position ‘B’, lying
with in the (α + L) region.
(b) Draw a tie line from liquidus
to solidus line through the
point ‘B’.
c. Draw a line perpendicular to the axis of composition through the point of
intersection of the tie line with liquidus.
d. Similarly, draw another line perpendicular to the axis of composition, through
the point of intersection of the tie line with solidus.
Liquid
Composition, wt% Ni
Temperature,0C

Liquid
Composition, wt% Ni
Temperature,0C
(..cont.,)
e. The perpendicular line dropped from
the liquidus line gives composition
of the liquid phase Cu-31.5 wt% Ni.
f. The perpendicular line dropped from
the solidus line gives composition of
the α solid phase Cu-42.5 wt% Ni.

• How to Determine phase amounts?
Single phase region:
For Cu- 60 wt% Ni alloy at 1100 0C
(see previous Fig region designated
by ‘A’), only α phase is present;
hence the alloy is completely 100% α
Two phase region:
(i) For the region designated by
‘B’ at 1250 0C for Cu-35 wt%
Ni alloy, both α phase and ‘L’
liquid phase are present.
(ii) Fraction of each of the α phase & ‘L’ phases can be computed by Lever Rule.
Liquid
Composition, wt% Ni
Temperature,0C

Lever Rule Derivation based on moment equilibrium
WL R = Wα S
We know that: WL + Wα= 1
∴WL = (1 - Wα)
(1 - Wα) R = WαS
R - WαR = WαS
R = WαR +WαS
R = Wα(R + S)
Wα=
𝐑
𝐑+𝐒
WL=
𝐒
𝐑+𝐒
Where,
WL = Weight fraction of liquid.
Wα = Weight fraction of α solid
solution.
CL = Composition of liquid.
Cα = Comp of α solid solution.
B

Determination of phase amounts (..cont.)
Two phase region: (..cont.,)
(iii) From Lever rule,
WL = S / (R + S) =
= (Cα – C0) / (Cα-CL)
WL = (42.5 – 35) / (42.5 – 31.5)
= 0.68
= Weight fraction of liquid ‘L’
(iv) Wα = R / (R + S)
= (C0 – CL) / (Cα – CL)
= (35 – 31.5) / (42.5 – 31.5) = 0.32
= Weight fraction of α solid
Liquid
Composition, wt% Ni
Temperature,0C

Development of Microstructures in Isomorphous Alloys –
Cu-35 wt% Ni alloy is cooled extremely slowly from 1300 0C to allow
diffusion to complete the process of readjustment of composition.
Equilibrium Cooling
Liquid
α
Temperature,0C

• Cu-35 wt% Ni liquid alloy is cooled
from 1300 0C, see point ‘a’ & the
associated microstructure in Fig.
• No microstructural or compositional
change will be realized until we reach
the liquidus line at point ‘b’, ~12600C.
• At point ‘b’, the first solid ‘α’ begins to
form, which has a composition
dictated by the tie line drawn at this
temperature is Cu-46 wt% Ni, but the
composition of liquid is still ~ Cu-35
wt% Ni.
• With continued cooling, both compositions and relative amounts of each of the
phases will change.
Development of Microstructures in Isomorphous Alloys – Equilibrium Cooling

• The compositions of the liquid and ‘α’
phases will follow the liquidus and
solidus lines respectively.
• The fraction of the ‘α’ phase will
increase with continued cooling.
• Overall alloy composition (Cu-35 wt%
Ni) remains unchanged during cooling
even though there is redistribution of
copper and nickel between the
phases.
• At 1250 0C, point ‘c’, the composition
of liquid and ‘α’ phases are Cu-32 wt%
Ni, and Cu-43 wt% Ni respectively.

• The solidification is complete upon
reaching point ‘d’ at ~1220 0C, the
comp. of solid ‘α’ is ~Cu-35 wt% Ni
(the over all alloy comp), while the last
remaining liquid is Cu-24 wt% Ni.
• Upon crossing the solidus line, the
remaining liquid solidifies;
• The final product is a polycrystalline
α-phase solid solution, that has a
uniform Cu-35 wt% Ni composition,
since it was cooled extremely slowly
under equilibrium conditions by
allowing diffusion to complete.
• Subsequent cooling to RT will not
produce any microstructural or
compositional changes (alterations).

Development of Microstructures in Isomorphous Alloys –
• In practical solidification situations, the
cooling rates are rapid enough to cause
nonequilibrium microstructural
development.
• The adjacent Figure shows development
of microstructure during the
nonequilibrium solidification.
• Note that the solidus line got shifted
towards right side represented by dashed
line.
The center of the grain is rich in high m.pt element (Ni) and the area near the GB is
rich with low m.pt element (Cu), leading to formation of cored structure, resulting in
poor mechanical properties.
Nonequilibrium Cooling

• The castings with cored structure when
heated below the solidus line, the grain
boundaries could melt resulting in loss
of mechanical properties.
• Therefore, the castings are given a
homogenization treatment by heating
far below the equilibrium solidus
temperature and held for longer
durations to minimize the segregation
by allowing the atomic diffusion.
Development of Microstructures in Isomorphous Alloys – Nonequilibrium Cooling

Development of Microstructures in Isomorphous Alloys – Nonequilibrium Cooling

Lever Rule
• The composition of various phases in a phase
diagram can be determined by a procedure
called the lever rule.
• Example: Calculate the relative proportions of
the phases in a Cu-Ag alloy of eutectic
composition just below the eutectic
temperature.
Ls
s
Ls
L
CC
CC
LS
L
or
CC
CC
LS
S







00
%2.23
2.919.7
2.919.71







 



CC
CCE

Summary of Important Equilibrium Phase Transformations

(c)2003Brooks/Cole,adivisionofThomsonLearning,Inc.ThomsonLearning™isatrademarkusedhereinunderlicense.
Al – Si eutectic alloy
ll
ll
ll
ll
ll
ll
ll
ll
ll
ll
ll
ll
ll
ll

Al-Si alloys differ from our "standard" phase diagram in that aluminium has zero solid
solubility in silicon at any temperature. This means that there is no beta phase and so
this phase is "replaced" by pure silicon (you can think of it as a beta phase which consists
only of silicon).So, for Al-Si alloys, the eutectic composition is a structure
of alpha+Si rather than alpha+beta.

coarse flakes of Si in the eutectic promote brittleness within these alloys. Most Al-Si
alloys used have a near-eutectic composition since this gives a lower melting point and
makes them cheaper to cast. If these alloys are to be of any great use, we must improve
their properties somehow and deal with the brittle Si flakes.
No etching is required as Si appears grey whilst the alpha phase appears white.
by adding a very small impurity of 0.01%Na the microstructure of the alloy is
changed and its properties are greatly improved.
un-doped alloy doped alloy

Typical eutectic microstructures:
(a) needle-like silicon plates in the aluminum silicon eutectic (x100), and
(b) rounded silicon rods in the modified aluminum-silicon eutectic (x100).

The effect of hardening with phosphorus on the microstructure of hypereutectic
aluminum-silicon alloys:
(a) coarse primary silicon, and
(b) fine primary silicon, as refined by phosphorus addition (x75).

The hypereutectic Al-Si alloys containing primary β will provide the wear-
resistance that at one-third the weight of the steel.
Since the part to be produced is cylindrical in shape, centrifugal
casting (Figure) will be a unique method for producing it.
A typical alloy used to produce aluminum engine components is
Al-17% Si. From Al-Si binary phase diagram (Figure), the total amount of
primary β that can form is calculated at 578o
C, just above the eutectic
temperature:
%0.5100
6.1283.99
12.617Primary% 


NU

• In an eutectic reaction, when a liquid solution of fixed composi-
tion, solidifies at a constant temperature, forms a mixture of two
or more solid phases without an intermediate pasty stage. This
process reverses on heating.
Eutectic

In eutectic system, there is always a specific alloy,
known as eutectic composition, that freezes at a lower
temp. than all other compositions.
At the eutectic temp. two solids form simultaneously
form a single liquid phase.
The eutectic temp. & composition determine a point on
the phase dia, called the eutectic point.

 Binary alloy eutectic system can be classed as:
1. One in which, two metals are completely soluble in the liquid
state but are insoluble in each other in the solid state.
2. two metals are completely soluble in the liquid state but are
partly soluble in each other in the solid state.

1. Two metals completely soluble in the liquid state
but completely insoluble in the solid state.
 Technically, no two metals are completely insoluble in
each other. However, in some cases the solubility is so
restricted that for practical purposes they may be
considered insoluble.

• Alloy-1: 20% Cd and 80% Bi
 Contrary to alloy 3, in this case crystal of pure Bi form first,
enriching the melt with Cd.
 The composition of the melt (or liquid) moves to right until
Ultimately the point E is reached and the remaining liquid solidi-
fies as eutectic (40% Cd and 60% Bi).
• Alloy-2: 40% Cd and 60% Bi (eutectic alloy)
 No solidification occurs until the melt reaches the eutectic
temperature (140°)
 At the eutectic temperature, the two pure metals crystallize
together to give a characteristically line aggregate known as
eutectic.
 Eutectic consists of alternate layers of Cd and Bi which form at
the eutectic temperature (140°C in this case).

 Alloy-3: 80% Cd and 20% Bismuth.
 As the temperature falls to T1, crystal nuclei of pure Cd
begin to form. Since pure Cd is deposited, it follows that
the liquid becomes richer in Bi; the composition of liquid
move s to left 3’ and as indicated by the diagram, no
further Cd deposits until temperature falls to T2.
 At T2 more Cd is deposited and dendrites begin to develop
from the already formed nuclei.
 The growth of the Cd dendrites, on the one hand, and the
consequent enrichment of the remaining liquid in Bi, on
the other, continues until the temperature has fallen to
140°C, the eutectic temperature in this case.
 The remaining liquid then contains 40% Cd and 60% Bi, the
eutectic composition.

2. Two metals completely soluble in the liquid state, but only partly soluble in the
solid state

 Since most metals show some solubility for each other in the solid
state, this type is the most common and, therefore, the most
common alloy system.
 Metals such as Pb-Sn and Pb-Sb are partly soluble in each other in
the solid state.
 Fig. shows the Tin-Lead equilibrium diagram with micro-structures
(of course) obtained under non-equilibrium condition of
solidification.
I. Tin will dissolve up to maximum of 2.6% Pb at the temperature,
forming the solid solution α.
II. Lead will dissolve up to a maximum of (100-80.5) i.e. 19 .5% tin
at the eutectic temperature, giving the solid solution β.
III. Slope of BA and CD indicate that the solubility of Pb in Sn (α)
and that of Sn in Pb (β) decrease as temperature falls
 Consider an alloy of composition Z (70% Pb-30% Sn). As the melt
temperature falls to T1, dendrites of composition Y will deposit.

 The alloy solidifies as a solid solution until at 183°C, the last layer
of solid to form is of composition C (80.5% Pb-19.5% Sn).
 The remaining liquid which has the eutectic composition (38%
Pb-62% Sn) then solidifies by depositing, in the form of a
eutectic, i.e., alternate layers of α and β, of compositions B and C
respectively.
 If cooled slowly to room temperature the compositions of the
solid solutions α and β will follow the line BA and CD, i.e., α will
become progressively poorer in lead and β in tin.
 Take another alloy of composition Z' (95% Pb-5% Sn). When
cooled slowly, solidification starts at R and is complete at P, the
resultant solid being a homogeneous single phase, the β solid
solution.
 As the alloy cools, the solvus line is reached at point Q. The β
solution is now saturated in tin. Below this temperature, under
conditions of slow cooling, the excess tin must come out of
solution. Since tin is soluble in lead, the precipitate does not
come out as the pure metal tin, but rather the α solid solution.

 Eutectoid Transformation:
 Eutectoid reaction is an isothermal reversible reaction in
which a solid phase (usually solid solution) is converted
into two or more intimately mixed solids on cooling, the
number of solids formed being the same as the number of
component in the system.

The peritectoid reaction is the transformation of two solid
into a third solid.

It is the reaction that occurs during the solidification of
some alloys where the liquid phase reacts with a solid
phase to give a solid phase of different structure.
Assuming very slow rates of cooling, the peritectic
reaction will occur only in those Pt-Ag alloys that Contain
between 12 and 69% silver (Ag).
Consider a liquid (melt) of composition Z, i.e., containing
25% Ag. Solidification commences at T1 and dendrites of α,
initially of composition W, begin forming.
Selective crystallization of α continues down to Tp, the
peritectic temperature; when the alloy reaches. this
temperature, it is composed of solid α-dendrites of
composition B and liquid of composition D in the proportion
α : liquid = RD : RB.

 Peritectoid Transformation:
 The peritectoid reaction is the transformation of two solid
into a third solid.

Unit 3-k.srinivasulureddy-MMS-metallurgy & material science-snist

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