1. Lecture 9
Phase
Diagrams
8-1

2. Introduction
Phase: A region in a material that differs in structure and function from other regions.
Phase diagrams:
Represents phases present in metal at different conditions (Temperature, pressure and composition).
Indicates equilibrium solid solubility of one element in another.
Indicates temperature range under which solidification occurs.
Indicates temperature at which different phases start to melt.
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3. Phase Diagram of Pure Substances
Pure substance exist as solid, liquid and vapor.
Phases are separated by phase boundaries.
Example : Water, Pure Iron.
Different phases coexist at triple point.
Figure 8.2
Figure 8.1
8-3
After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151

4. Gibbs Phase Rule P = number of phases that coexist in a system
C = Number of components
F = Degrees of freedom
P+F = C+2
For pure water, at triple point, 3 phases coexist.
There is one component (water) in the system.
Therefore 3 + F = F = 0.
Degrees of freedom indicate number of variables that can be changed without changing number of phases.
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5. Used to determine phase transition temperature.
Cooling Curves
Used to determine phase transition temperature.
Temperature and time data of cooling molten metal is recorded and plotted.
Thermal arrest : heat lost = heat supplied by solidifying metal
Alloys solidify over a range of temperature (no thermal arrest)
Pure Metal
Iron

6. Binary Isomorphous Alloy Systems
Mixture of
two systems
Two component
system
Binary alloy
Isomorphous system: Two elements completely soluble in each other in liquid and solid state.
Example: Cu-Ni solution.
Composition at liquid
and solid phases at any
temperature can be
determined by drawing
a tie line.
Figure 8.3
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Adapted from “Metals Handbook,” vol. 8, 8th ed., American society of Metals, 1973, p. 294.

7. Phase Diagram from Cooling Curves
Series of cooling curves at different metal composition are first constructed.
Points of change of slope of cooling curves (thermal arrests) are noted and phase diagram is constructed.
The greater the number of cooling curves the more accurate the phase diagram.
Figure 8.4
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8. The Lever Rule
The Lever rule gives the weight % of phases in any two phase regions.
Wt fraction of solid phase
= Xs = w0 – w1
ws – w1
Wt fraction of liquid phase
= Xl = ws – w0
ws – w1
W0 is the weight percentage of the alloy.
Ws is the weight percentage within the solid phase
Wl is the weight percentage in the liquid phase
Figure 8.5
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9. Non Equilibrium Solidification of Alloys
Very slow cooling (equilibrium) gives rise to cored structure as composition of melt continuously changes.
Rapid cooling delays solidification but also leads to cored structure .
Homogenization: Cast ingots heated
to elevated temperature to eliminate
cored structure.
Temperature of homogenization
must be lower than lowest melting
point of any of the alloy components.
W0=30% Cu
Figure 8.7
Figure 8.8
8-8

10. Binary Eutectic Alloy System
In some binary alloy systems, components have limited solid solubility.
Example : Pb-Sn alloy.
Eutectic composition freezes
at lower temperature than all
other compositions.
This lowest temperature is
called eutectic temperature.
Figure 8.11
Eutectic temperature
Liquid
α solid solution + β solid solution
Cooling
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11. Slow Cooling of 60% Pb – 40% Sn alloy
Liquid at 3000C.
At about 2450C first solid forms – proeutectic solid.
Slightly above 1830C composition of alpha follows solidus and composition of sn varies from 40% to 61.9%.
At eutectic temperature, all the remaining liquid solidifies.
Figure 8.12
Figure 8.13
Further cooling lowers alpha Sn content and beta Pb.
(They try to move to equilibrium)
8-10
From J. Nutting and R. G. Baker, “Microstructure of Metals,” Institute of Metals, London, 1965,p.19.

12. Various Eutectic Structures
Structure depends on factors like minimization of free energy at α / β interface.
Manner in which two phases nucleate and grow also affects structures.
Figure 8.14
8-11
After W. C. Winegard, “An Introduction to the Solidification of Metals,” Institute of Metals, London, 1964.

13. Binary Peritectic Alloy System
Peritectic reaction: Liquid phase reacts with a solid phase to form a new and different solid phase.
Liquid + α β
cooling
Peritectic reaction occurs
when a slowly cooled alloy
of Fe-4.3 wt% Ni passes
through Peritectic
temperature of 1517C.
Peritectic point is invariant.
Figure 8.16
cooling
Liquid(5.4 wt% Ni) + δ (4.0 wt% Ni) γ 4.3 wt % Ni
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14. Peritectic Alloy System
At 42.4 % Ag & 14000C
Phases present Liquid Alpha
Composition % Ag %Ag
Amount of Phases –
55 –
= 74% = 26%
At 42.4% Ag and 11860C – ΔT
Phase Present Beta only
Composition % Ag
Amount of Phase %
At 42.4% Ag and 11860C + ΔT
Composition % Ag %Ag
Amount of Phases –
66.3 – –10.5
= 57% =43%
Figure 8.17
Figure 8.18
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15. Rapid Solidification in Peritectic System
Surrounding or Encasement: During peritectic reaction, L+ α β , the beta phase created surrounds primary alpha.
Beta creates diffusion barrier resulting in coring.
Figure 8.19
Figure 8.20
8-14
After F Rhines, “ Phase Diagrams in Metallurgy,”McGraw- Hill, 1956, p. 86.

16. Binary Monotectic Systems
Monotectic Reaction: Liquid phase transforms into solid phase and another liquid.
L α + L2
Cooling
Two liquids are immiscible.
Example:- Copper – Lead
system at 9550C and 36% Pb.
Table 8.1
Eutectic
Eutectoid
Peritectic
Peritectoid
Monotectic
Figure 8.23
8-15
Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th ed., American Society of Metals, 1973, p. 296.

17. Intermediate Phases and Compounds
Terminal phases: Phases occur at the end of phase diagrams.
Intermediate phases: Phases occur in a composition range inside phase diagram.
Examples: Cu-Zn diagram has both terminal and intermediate phases.
Five invariant peritectic points and one eutectic point.
Figure 8.25
8-16
“Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th ed., American Society of Metals, 1973, p. 301

18. Intermediate Phases in Ceramics
In Al2O2 – SiO2 system, an intermediate phase called Mullite is formed, which includes the compound 3Al2O3.2SiO2.
Figure 8.26
8-17
After A. G. Guy, “Essentials of Materials Science, “McGraw-Hill, 1976

19. Intermediate Compounds
In some phase diagrams, intermediate compound are formed – Stoichiometric
Percent Ionic/Covalent bond depends on electronegativeness
Example:- Mg-Ni phase diagram contains
Mg2Ni : Congruently melting compound
MgNi2 : Incongruently melting compound.
Figure 8.27
8-18
Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 314.

20. Ternary Phase Diagrams
Three components
Constructed by using a equilateral triangle as base.
Pure components at each
end of triangle.
Binary alloy composition
represented on edges.
Figure 8.28
Temperature can be represented as uniform throughout the
Whole Diagram Isothermal section.
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21. Ternary Phase Diagram (Cont..)
Example:- Iron-Chromium-Nickel phase diagrams.
Isothermal reaction at 6500C
for this system
Composition of any metal
at any point on the phase
diagram can be found by
drawing perpendicular
from pure metal corner to
apposite side and calculating
the % length of line at that
point
Figure 8.30
8-20
After “Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 425.