1. CHAPTER 2 (CONTD.)
Binary Phase System
1. Description of Binary Phase Diagram
2. Construction of Binary Phase Diagram
3. Interpretation of Binary Phase Diagram
i. Modified Gibb’s Phase Rule
ii. Tie-Line
iii. Lever Rule
4. Problems based on Binary Phase Diagram
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2. BINARY PHASE DIAGRAMS (ISOMORPHOUS PHASE DIAGRAM)
This is a two component system.
In this phase diagram, temperature and
composition are variable parameters, and pressure
is held constant normally 1 atm.
Temperature is taken on Y-axis and various
compositions of the two components on X-axis.
Ni-Cu, Au-Ag, Cr-Mo are examples of binary
phase diagram.
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Fig: Binary Phase Diagram
Liquidus
Solidus
A
B
3. Description of Binary Phase Diagram
For all combinations of temperature and composition
above liquidus curve (AB), the mixture is in the liquid
state.
Liquidus temperature as the temperature above which a
material is completely liquid.
The solidus temperature is the temperature below which
the alloy is 100% solid.
For all combinations of temperature and composition
below solidus curve (BA), the mixture is in the solid state.
state.
Point A and B represent the melting temperatures of
individual alloy.
The temperature difference between the liquidus and the
solidus is the freezing range of the alloy.MTE/III SEMESTER/MSE/MTE 2101 3
Liquidus
Solidus
A
B
Fig: Binary Phase Diagram
4. Construction of Binary Phase Diagram
Phase diagrams for a binary alloy system can be obtained from
cooling curves of the system at various compositions of the two
components.
Let us consider two metals A and B.
Curve A and B represent the cooling curve of pure metal A and
Curve U,V,W,X represent cooling curves of alloy of A and B at
different compositions.
NOTE: Phase diagram show the relationship of phases at equilibrium
conditions. This means the phases present at particular temperature
and composition don't change with time.
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U
V
W
X
Fig: Cooling curves of metal A and B, alloy mixture of A
and B
5. These temperature points are re-plotted (projected from the cooling curves) on a temperature versus
composition diagram by taking temperature on the Y axis and composition of the alloys on X axis.
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6. Interpretation of Binary Phase Diagram – Using Phase Rule, Tie-Line and Lever Rule
For a binary system of known composition and temperature that is at equilibrium, at least three kinds
information are available: (1) the phases that are present, (2) the compositions of these phases, and (3)
the percentages or fractions of the phases.
For determining the degrees of freedom in a binary phase diagram, Modified Gibb’s Phase Rule ( P+F
= C+1) is used. (Pressure is assumed to be 1 atm)
To determine the phase composition present at any point, Tie Line is used.
To determine the amount of each phase present at any point, Lever Rule is used.
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8. Modified Gibb’s Phase Rule:
Points A and B represent the melting temperatures of A and B. The degrees of freedom, F = 0 at these
points because number of phases, P=2, Number of components, C=1.
These points are called as “Invariant Points”.
Region 1:
Single phase homogeneous region.
Number of Components, C =2 (i.e. Liq.A and Liq.B)
Number of Phases, P = 1 (i.e. Liquid Phase)
Applying Modified Gibb’s Phase Rule(P+F = C+1):
Number of Degrees of Freedom, F = 2
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9. Region 2:
Mixture of solid and liquid phase.
Number of Components, C = 2. (i.e. Liq + α)
Number of Phases, P = 2. (i.e. Liquid and Solid)
Applying Modified Gibb’s Phase Rule(P+F = C+1):
Number of Degrees of Freedom, F = 1
Region 3:
Single phase solid region.
Similar to region 1.
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10. Let us consider an alloy consisting of 60% A and 40% B.
At point L, the mixture is a single phase homogeneous liquid at T₁°C.
At point N, the mixture is fully in solid state at T₃°C.
At point M, where solidification is in progress, there is a two phase mixture of solid and liquid, both of
metals A and B.
Two questions arise: 1. What are solid and liquid composition?
2. What are the amounts of solid and liquid phase?
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11. Phase Composition (Tie - Line):
At point M, a horizontal “tie line” or “constant temperature line” is drawn which intersects the liquidus
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12. Amount of each phase present (Lever Rule):
Lever Rule states that,” The relative amount of each phase is directly proportional to the length of
opposite lever arm”.
The tie-line OMP has two arms OM and MP which intersects the liquidus and solidus curves.
According to Lever Rule, the length MP touching the solidus proportional to the amount of liquid
present at M and the length OM touching the liquidus is proportional to the amount of solid phase
present at M.
Therefore,
Amount of liquid phase at M =
𝑴𝑷
𝑶𝑷
× 100 =
[𝟗𝟎−𝟒𝟎]
[𝟗𝟎−𝟐𝟎]
× 100 = 71.42% .
Amount of solid phase at M =
𝑶𝑴
𝑶𝑷
× 100 =
[𝟒𝟎−𝟐𝟎]
[𝟗𝟎−𝟐𝟎]
× 100 = 28.58% .
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13. PROBLEMS BASED ON BINARY PHASE SYSTEM
Q1.) Determine the degrees of freedom in a Cu-
40% Ni alloy at (a) 1300°C, (b) 1250°C, and (c)
1200°C.
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Reference: Example 10.6; The Science and Engineering of Materials, Donald
Askeland and Pradeep Phule
14. Q2.) Determine the composition of each phase in a Cu-
40% Ni alloy at 1300°C, 1270°C, 1250°C, and 1200°C.
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Reference: Example 10.7; The Science and Engineering of Materials,
Donald Askeland and Pradeep Phule
15. Q3.) Calculate the amounts of and L at 1250°C in the
Cu-40% Ni alloy shown in Figure.
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Reference: Example 10.8; The Science and Engineering of Materials, Donald Askeland and
Pradeep Phule