Chapter 9
Phase
Diagrams
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Learning Objectives
1. Isomorphous and eutectic phase diagrams:
a. label various phase regions
b. Label liquidus, solidus, and solvus lines
2. Given a binary phase diagram at equilibrium,
composition of an alloy, its temperature,
determine:
a. phases present
b. compositions of phases
c. mass fractions of phase
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Learning Objectives
3. For some given binary phase diagram
upon heating or cooling, locate
temperatures & compositions and
write reactions of:
Eutectic
Eutectoid
Peritectic
congruent phase transformations
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Learning Objectives
4. Given composition of an Fe–C alloy
containing between 0.022 & 2.14 wt% C:
a. Is alloy hypoeutectoid or
hypereutectoid?
b.name proeutectoid phase
c.compute mass fractions of
proeutectoid phase and pearlite
d.schematic diagram of microstructure at
a temperature just below the
eutectoid.
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Why Study Phase Diagrams?
Design & control of HT procedures
Strong correlation between
microstructure & mechanical properties
Development of microstructure of an
alloy is related to the char of its phase
diagram
Phase Diagram (PD) provides valuable
info about melting, casting, crystallization,
and other phenomena
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9.2 Solubility Limit
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9.3 Phases
A phase: a physically distinct &
homogenous portion in a
material.
Each phase is a homogenous part
of total mass & has its own
characteristics and properties.
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9.3 Phases
Phase Characteristics:
Same structure or atomic arrangement
Same composition & properties
Definite interface between phase and
any surrounding or adjoining phases
Two types of alloys:
single phase
multiple phases
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9.3 Phases
Alloying consists of two basic
forms:
1. Solid solutions
2. Inter-metallic compounds
Solid Solutions (SS): solid material in
which atoms or ions of elements
constituting it are dispersed
uniformly.
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9.3 Phases
A SS is not a mixture
A mixture contains more than one
type of phase whose char are
retained when mixture is formed.
Components of SS completely
dissolve in one another and do
not retain their individual char.
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9.3 Phases
Properties are controlled by creating
point defects such as substititional &
interstitial atoms.
Solute: minor element that is added
to solvent (major element)
When the particular crystal structure
of solvent is maintained during
allying, alloy is called a Solid
Solution.
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9.6 One Component (Unary) Phase Diagrams
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9.7 Binary Isomorphous Systems
A phase diagram (PD) shows the
relationships among temperature,
composition, and phases present in a
particular alloy system under
equilibrium conditions
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9.7 Binary Isomorphous Systems
From PD, we can predict:
how a material will solidify under
equilibrium conditions
what phases for diff temp and
comp.
Equilibrium means that state of a
system remains constant over an
indefinite period of time.
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9.7 Binary
Isomorphous Systems
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9.7 Binary Isomorphous Systems
Only one solid phase forms, the two
components in the system display
complete solid solubility
Liquidus temperature
Solidus temperature
Freezing range: pure metals and
alloys
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9.7 Binary Isomorphous Systems
When temperature of molten metal
is reduced to freezing point:
energy of latent heat of solidification is
given off while temperature remains
constant.
Eventually, solidification is complete
and solid metal continues cooling to RT.
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9.7 Binary Isomorphous Systems
Cooling curve for the
solidification of pure
metals
Alloys solidify over a
range of temperatures
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9.7 Binary Isomorphous Systems
9.8 Interpretation of Phase Diagrams
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% 100
opposite arm of leverPhase
total length of tie line
Phases Present
Determination of Phase Compositions
Determination of Phase Amounts
Example Problem 9.1
Derive the lever rule
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9.8 Interpretation of Phase Diagrams
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Volume Fractions
Conversion between volume and mass fractions
9.9 Development of Microstructure in Isomorphous Alloys
The completely solidified alloy in the phase
diagram shown is a solid solution because:
Alloying element (Cu, solute) is
completely dissolved in host metal (Ni,
solvent)
Each grain has same composition
Atomic radius of Cu is 0.128nm & that of
Ni is 0.125nm,
Both elements are FCC; HRRs are obeyed.
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9.9 Development of Microstructure in Isomorphous Alloys
Two conditions required for growth of solid a:
1. Growth requires that latent heat of fusion
(DHf), which evolves as liquid solidifies,
be removed from solid liquid interface.
2. Diffusion must occur so that compositions
of solid and liquid phases follow solidus
and liquidus curves during cooling. DHf is
removed over a range of temperatures
so that cooling curves shows a change
in slope
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9.9 Development of Microstructure in
Isomorphous Alloys
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Figure 9.4 Schematic
representation of
the development of
microstructure
during equilibrium
solidification of a 35
wt% Ni–65 wt% Cu
alloy.
9.9 Development of Microstructure in Isomorphous Alloys
On cooling from liquidus to 1250oC,
some Ni atoms must diffuse from 1st
solid to new solid, reducing Ni in 1st
solid.
Additional Ni atoms diffuse from
solidifying liquid to new solid.
Meanwhile, Cu atoms have
concentrated –by diffusion – into
remaining liquid.
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9.9 Development of Microstructure in Isomorphous Alloys
The process must continue until we
reach solidus temperature, where
last liquid to freeze, which contains
Cu-28%Ni, solidifies and forms a solid
containing Cu-40%Ni.
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9.9 Development of
Microstructure in Isomorphous Alloys
Figure 9.5 Schematic
representation of the
development of
microstructure during
nonequilibrium
solidification of a 35
wt% Ni–65 wt% Cu
alloy
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9.10 Mechanical Properties of Isomorphous Alloys
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9.11 Binary Eutectic Systems
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9.11 Binary Eutectic Systems
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Example Problem 9.2 Determination of Phases Present and
Computation of Phase Compositions
For a 40 wt% Sn–60 wt% Pb alloy at 150°C,
a. what phase(s) is (are) present?
b. What is (are) the composition(s) of the
phase(s)?
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Example Problem 9.3
Relative Phase Amount Determinations—
Mass and Volume Fractions
For the lead–tin alloy in Example Problem
9.2, calculate the relative amount of each
phase present in terms of
a. mass fraction
b. volume fraction. At 150°C take the
densities of Pb and Sn to be 11.23 and
7.24 g/cm3, respectively.
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9.12 Development
of Microstructure in
Eutectic Alloys
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9.12 Development
of Microstructure in
Eutectic Alloys
9.12 Development of Microstructure in
Eutectic Alloys
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9.12 Development of Microstructure in
Eutectic Alloys
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9.12 Development of Microstructure in
Eutectic Alloys
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9.12 Development of Microstructure in Eutectic Alloys
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9.12 Development of Microstructure in Eutectic Alloys
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9.13 Equilibrium Diagrams Having
Intermediate Phases or Compounds
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9.13 Equilibrium Diagrams Having
Intermediate Phases or Compounds
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9.14 Eutectoid and Peritectic Reactions
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9.15 Congruent Phase Transformations
Congruent
transformations: no
compositional
alterations
allotropic
transformations (Sec
3.6)
melting of pure
materials.
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9.15 Congruent Phase Transformations
Incongruent
transformations: at least one of the
phases will
experience a change
in composition
Eutectic &
eutectoid reactions
melting of an alloy
that belongs to an
isomorphous system
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9.18 The IRON–IRON Carbide (Fe–Fe3C) Phase Diagram
Dr. Mohammad Abuhaiba, PE
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9.18 The IRON–IRON Carbide
(Fe–Fe3C) Phase Diagram
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9.19 Development
of Microstructure in Iron Carbon Alloys
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9.19 Development of Microstructure in Iron Carbon Alloys
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9.19 Development of Microstructure
in Iron Carbon Alloys Hypo-eutectoid Alloys
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9.19 Development of Microstructure in Iron Carbon
Alloys - Hypo-eutectoid Alloys
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9.19 Development of Microstructure in Iron Carbon
Alloys - Hyper-eutectoid Alloys
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EXAMPLE PROBLEM 9.4
Determination of Relative Amounts of Ferrite,
Cementite, and Pearlite Microconstituents
For a 99.65 wt% Fe–0.35 wt% C alloy at a temperature
just below the eutectoid, determine the following:
a. The fractions of total ferrite and cementite phases
b. The fractions of the proeutectoid ferrite and
pearlite
c. The fraction of eutectoid ferrite
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9.20 The Influence of Other Alloying Elements
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Home Work Assignment
1, 6, 11, 16, 21, 26, 32,
39, 44, 49, 54, 59, 65
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