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Reading 2-D Ternary Phase Diagrams
• Isothermal Section
• Isopleth
• Liquidus Projection
• Lever Rule in Ternary Field
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Reading 2-D Ternary Phase Diagrams
• Isothermal Section:
• Fixed Temperature
A
B
C
X
A
X
C
X
B
X
B
X
A
X
C
A
B
C
X
B
X
C
X
A
=1-X
B
-X
C
• Composition represented on
equilateral Triangle
• For low concentration of one
component, use a right-
angled triangle (e.g. Fe-Cr-C)
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Reading 2-D Ternary Phase Diagrams
• Isothermal Section:
• Phase boundary (Blue)
• Tie-line (Green)
• Tie-triangle (Red)
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Reading 2-D Ternary Phase Diagrams
• Isopleth:
• Y-axis: temperature
• X-axis: composition
• Tie-line may not lie
on the section
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Reading 2-D Ternary Phase Diagrams
• Liquidus Projection:
• Univariant line (Blue)
• Isothermal line (Green)
• Primary phase region
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Reading 2-D Ternary Phase Diagrams
• Isothermal Section:
• Lever rule on tie-line
a
g
Alloy
In Alloy P, two phases are in equilibrium:
Fraction of a = Length(PN) / Length(MN)
Fraction of γ = Length(MP) / Length(MN)
M
N
P
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Reading 2-D Ternary Phase Diagrams
• Isothermal Section:
• Lever rule on tie-triangle
In Alloy P, three phases are in equilibrium:
Fraction of a = Area(PON) / Area(MNO)
Fraction of β = Area(PMN) / Area(MNO)
Fraction of γ = Area(POM) / Area(MNO)
a
g
Alloy
M
N
P
O
b
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Isomorphous Systems - Case I
Case I: Three binaries are all isomorphous with
Cigar shape phase boundaries.
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Isomorphous Systems - Case I
Case I: Isothermal sections in decreasing T order.
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Isomorphous Systems - Case I
Case I: Liquidus projection has no univariant line.
Liquidus Projection in 2-D view Liquidus Projection in 3-D view
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Isomorphous Systems - Case I
Case I: Isopleths parallel to the B-C binary
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Isomorphous Systems - Case I
Case I: Isopleths in 3-D view
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Isomorphous Systems - Case I
Case I: Gibbs energy surface for Liquid at 700
o
C
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Isomorphous Systems - Case II
Case II: Three binaries are all isomorphous with 2
Cigar shape phase boundaries and 1 maximum.
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Isomorphous Systems - Case II
Case II: Isothermal sections in decreasing T order.
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Isomorphous Systems - Case II
Case II: Liquidus projection has no univariant line.
Liquidus Projection in 2-D view Liquidus Projection in 3-D view
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Isomorphous Systems - Case II
Case II: Isopleths parallel to the B-C binary
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Isomorphous Systems - Case II
Case II: Isopleths in 3-D view
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Isomorphous Systems - Case II
Case II: Gibbs energy surface for Liquid at 700
o
C
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Isomorphous Systems - Case III
Case III: Three binaries are the same as those in
case I. There is a maximum melting point in the
ternary phase field.
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Isomorphous Systems - Case III
Case III: Liquidus projection has no univariant line.
Liquidus Projection in 2-D view Liquidus Projection in 3-D view
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Isomorphous Systems - Case III
Case III: Isopleths parallel to the B-C binary
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Isomorphous Systems - Case III
Case III: Isopleths in 3-D view
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Ternary Three-Phase Equilibrium - Case I
Case I: Two eutectic binary systems and one
isomorphous with Cigar shape phase boundary.
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Ternary Three-Phase Equilibrium - Case I
Case I: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case I
Case I: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case I
Liquidus has one univariant line starting from A-B
binary and ending at B-C binary, which separates
2 primary phase fields, Fcc and Bcc.
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Ternary Three-Phase Equilibrium - Case I
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case I
Liquid+Fcc+Bcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case I
Isopleth through B-A
0.5
C
0.5
(Green line in 3D view)
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Ternary Three-Phase Equilibrium - Case II
Case II: Two peritectic binary systems and one
isomorphous with Cigar shape phase boundary.
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Ternary Three-Phase Equilibrium - Case II
Case II: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case II
Liquidus has one univariant line starting from A-B
binary and ending at B-C binary, which separates
2 primary phase fields, Fcc and Bcc.
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Ternary Three-Phase Equilibrium - Case II
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case II
Liquid+Fcc+Bcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case II
Isopleth through B-A
0.5
C
0.5
(Green line in 3D view)
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Ternary Three-Phase Equilibrium - Case III
Case III: One peritectic binary, one eutectic
binary and one isomorphous with Cigar shape
phase boundary.
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Ternary Three-Phase Equilibrium - Case III
Case III: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case III
Liquidus has one univariant line starting from A-B
binary and ending at B-C binary, which separates
2 primary phase fields, Fcc and Bcc.
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Ternary Three-Phase Equilibrium - Case III
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case III
Liquid+Fcc+Bcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case III
Isopleth through B-A
0.5
C
0.5
(Green line in 3D view)
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Ternary Three-Phase Equilibrium - Case IV
Case IV: One eutectic binary and Two isomorphous
with Cigar shape phase boundary.
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Ternary Three-Phase Equilibrium - Case IV
Case IV: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case IV
Liquidus has one univariant line starting from A-
B binary and ending at a minimum in the ternary
field, and only one primary phase field, Fcc.
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Ternary Three-Phase Equilibrium - Case IV
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
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Ternary Three-Phase Equilibrium - Case IV
Liquid+Fcc+Fcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
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Ternary Three-Phase Equilibrium - Case IV
Isopleth through B-A
0.9
C
0.1
(Green line in 3D view)
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Ternary Three-Phase Equilibrium - Case V
Case V: One eutectic binary and Two isomorphous
with Cigar shape phase boundary.
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Ternary Three-Phase Equilibrium - Case V
Case V: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case V
Liquidus has one univariant line starting from a
maximum in the ternary field and ending at A-C
binary, and only one primary phase field, Fcc.
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Ternary Three-Phase Equilibrium - Case V
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
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Ternary Three-Phase Equilibrium - Case V
Liquid+Fcc+Fcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
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Ternary Three-Phase Equilibrium - Case V
Isopleth through B
0.05
C
0.95
-A
0.95
B
0.05
(Green line in
3D view)
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Ternary Three-Phase Equilibrium - Case VI
Case VI: Two eutectic binary systems and one
isomorphous with Cigar shape phase boundary.
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Ternary Three-Phase Equilibrium - Case VI
Case VI: Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case VI
Liquidus lines start from a maximum in the ternary
field, go separately in opposite directions and end at
the two eutectic reactions in the binaries. Two
primary phase fields, Fcc and Bcc.
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Ternary Three-Phase Equilibrium - Case VI
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case VI
Liquid+Fcc+Fcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case VI
Isopleth through B-A
0.5
C
0.5
(Green line in 3D view)
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Ternary Three-Phase Equilibrium - Case VII
Case VII: The binaries are the same as those in Case
VI. Isothermal sections in decreasing T order.
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Ternary Three-Phase Equilibrium - Case VII
Liquidus lines start from the two eutectic reactions in
the binaries, join together at a minimum in the
ternary field. Two primary phase fields, Fcc and Bcc.
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Ternary Three-Phase Equilibrium - Case VII
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case VII
Liquid+Fcc+Fcc Tie-triangle changes in ternary field
Liquid phase: Fuchsia
Fcc phase: Red
Bcc phase: Orange
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Ternary Three-Phase Equilibrium - Case VII
Isopleth through B-A
0.5
C
0.5
(Green line in 3D view)
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Ternary Four-Phase Equilibrium – Class I
Class I: Three eutectic binary systems.
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Ternary Four-Phase Equilibrium – Class I
Class I: Isothermal sections in decreasing T order.
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Ternary Four-Phase Equilibrium – Class I
Liquidus lines start from the three eutectic reactions in
the binaries, join together at one point in the ternary
field. Three primary phase fields, Fcc, Bcc and Hcp.
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Ternary Four-Phase Equilibrium – Class I
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Aqua
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Ternary Four-Phase Equilibrium – Class I
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Green
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Ternary Four-Phase Equilibrium – Class I
Isopleths through 40 at.% C and 50 at.% C
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Ternary Four-Phase Equilibrium – Class I
Isopleths through B-A
0.6
C
0.4
and B-A
0.415
C
0.585
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Ternary Four-Phase Equilibrium – Class I
Characteristics to determine whether it is a Class
I four-phase equilibrium:
Before Reaction: 3 three-phase triangles
After Reaction: 1 three-phase triangle
Class I reaction: Φ => a + β + γ
Φ+a+β
Φ+a+γ
Φ+β+γ
Before Reaction
a
β
γ
Φ
a+β+γ
After Reaction
a
β
γ
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Ternary Four-Phase Equilibrium – Class I
Class I, Case 2: Four-phase equilibrium with two
liquids involved, One monotectic, one eutectic
and one isomorphous binary systems.
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Ternary Four-Phase Equilibrium – Class I
Class I: Isothermal sections in decreasing T order.
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Ternary Four-Phase Equilibrium – Class I
Class I: Enlarged isothermal sections before and
after the Class I invariant reaction.
L
1
=> L
2
+ Bcc + Fcc
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Ternary Four-Phase Equilibrium – Class I
Liquidus lines are separated into two parts:
A-rich part starts from the monotectic and eutectic reactions in A-B binary
and the liquid miscibility gap in ternary field, join together at the invariant
reaction.
A-poor part starts from the monotectic reaction in A-B binary, joins with the
liquid miscibility gap in ternary field and then ends in eutectic reaction in B-
C binary.
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Ternary Four-Phase Equilibrium – Class I
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Aqua
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Ternary Four-Phase Equilibrium – Class I
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Fuchsia
Invariant: Green
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Ternary Four-Phase Equilibrium – Class II
Class II: Two eutectic binary and one peritectic
binary systems.
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Ternary Four-Phase Equilibrium – Class II
Class II: Isothermal sections in decreasing T order.
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Ternary Four-Phase Equilibrium – Class II
Liquidus lines start from the peritectic reaction in A-B binary
and the eutectic reaction in A-C binary, join together at one
point in the ternary field and then go to the eutectic reaction
in B-C binary. Three primary phase fields, Fcc, Bcc and Hcp.
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Ternary Four-Phase Equilibrium – Class II
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Aqua
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Ternary Four-Phase Equilibrium – Class II
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Green
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Ternary Four-Phase Equilibrium – Class II
Isopleths through 25 at.% A and 20 at.% A
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Ternary Four-Phase Equilibrium – Class II
Characteristics to determine whether it is a Class
II four-phase equilibrium:
Before Reaction: 2 three-phase triangles
After Reaction: 2 three-phase triangles
Class II reaction: Φ + a => β + γ
Φ+a+β
Φ+a+γ
Before Reaction
a
β
γ
Φ
Φ+β+γ
a+β+γ
After Reaction
a
β
γ
Φ
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Ternary Four-Phase Equilibrium – Class II
Class II, Case 2: Four phase equilibrium with two
liquids involved, One monotectic, one eutectic
and one isomorphous binary systems.
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Ternary Four-Phase Equilibrium – Class II
Class II: Isothermal sections in decreasing T order.
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Ternary Four-Phase Equilibrium – Class II
Class II: Enlarged isothermal sections before and
after the type II invariant reaction.
L
1
+ Bcc => L
2
+ Fcc
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Ternary Four-Phase Equilibrium – Class II
Liquidus lines are separated into two parts:
A-rich part starts from the monotectic and eutectic reactions in A-B binary,
join together at the invariant reaction and then ends at the liquid miscibility
gap in ternary field.
A-poor part starts from the monotectic reaction in A-B binary, separate into
two directions after invariant reaction, one ends at the liquid miscibility gap
in ternary field and the other ends in eutectic reaction in B-C binary.
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Ternary Four-Phase Equilibrium – Class II
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Aqua
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Ternary Four-Phase Equilibrium – Class II
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Fuchsia
Invariant: Green
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Ternary Four-Phase Equilibrium – Class III
Class III: One eutectic binary and two peritectic
binary systems.
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Ternary Four-Phase Equilibrium – Class III
Class III: Isothermal sections in decreasing T order.
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Ternary Four-Phase Equilibrium – Class III
Liquidus lines start from the eutectic reaction in A-B binary,
split into two directions in the ternary field and end at the
peritectic reactions in A-C and B-C binaries. Three primary
phase fields, Fcc, Bcc and Hcp.
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Ternary Four-Phase Equilibrium – Class III
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Aqua
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Ternary Four-Phase Equilibrium – Class III
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Invariant: Green
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Ternary Four-Phase Equilibrium – Class III
Isopleths through 65 at.% C and 72 at.% C
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Ternary Four-Phase Equilibrium – Class III
Characteristics to determine whether it is a Class
III four-phase equilibrium:
Before Reaction: 1 three-phase triangle
After Reaction: 3 three-phase triangles
Class III reaction: a + β + γ => Φ
Φ+a+β
Φ+a+γ
Φ+β+γ
After Reaction
a
β
γ
Φ
a+β+γ
Before Reaction
a
β
γ
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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Congruent Transformation – Case I
Case I: Congruent melting in one binary and form
a pseudo-binary in the ternary field.
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Congruent Transformation – Case I
Case I: Isothermal sections in decreasing T order.
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Congruent Transformation – Case I
Case I: Isothermal sections in decreasing T order.
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Congruent Transformation – Case I
The isopleth through A
0.5
B
0.5
-C is a pseudo-binary system.
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Congruent Transformation – Case I
The isopleth through A
0.5
B
0.5
-C cuts the liquidus projection
into two parts and each one contains a class I four-phase
equilibrium. The red point is a maximum in the liquidus
surface.
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Congruent Transformation – Case I
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
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Congruent Transformation – Case I
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
Tie-triangle: Green
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Congruent Transformation – Case II
Case II: Congruent melting in one binary but do
not form a pseudo-binary in the ternary field.
Binaries are the same as in Case I.
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Congruent Transformation – Case II
Case II: Isothermal sections in decreasing T order.
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Congruent Transformation – Case II
Case II: Isothermal sections in decreasing T order.
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Congruent Transformation – Case II
The isopleth through A
0.5
B
0.5
-C is not a pseudo-binary system.
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Congruent Transformation – Case II
The liquidus projection contains one class I four-phase
equilibrium and one class II four-phase equilibrium.
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Congruent Transformation – Case II
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
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Congruent Transformation – Case II
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
Tie-triangle: Green
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Congruent Transformation – Case III
Case III: Binaries are all eutectic systems, and
there is a ternary compound which melts
congruently in the ternary field.
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Congruent Transformation – Case III
Case III: Isothermal sections in decreasing T order.
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Congruent Transformation – Case III
Case III: Isothermal sections in decreasing T order.
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Congruent Transformation – Case III
The delta primary phase appears as an island in the ternary
field and there are three class I four-phase equilibria. The red
points are three maximums in the liquidus surface.
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Congruent Transformation – Case III
Ternary phase fields in 3-D view
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
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Congruent Transformation – Case III
Liquid involved Tie-triangle changes in ternary field
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Invariant: Aqua
Tie-triangle: Green
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Types of Ternary Phase Diagrams
• Isomorphous System
• Ternary Three-phase Equilibrium
• Ternary Four-phase Equilibrium
• Class I Reaction
• Class II Reaction
• Class III Reaction
• Congruent Transformation
• A Complex System
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A Complex Ternary System
A complex ternary system involving all three
classes of four-phase equilibrium.
Binaries contain three solid solution phases: Fcc,
Bcc, and Hcp, and three intermetallic compounds:
Delta, Gamma and Epsilon.
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Congruent Transformation – Case III
Isothermal sections showing the invariant reaction 1 in detail.
Class I: Delta => Liquid + Gamma + Bcc
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Congruent Transformation – Case III
Isothermal sections showing the invariant reaction 2 in detail.
Class II: Liquid + Bcc => Gamma + Hcp
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Congruent Transformation – Case III
Isothermal sections showing the invariant reaction 3 in detail.
Class I: Liquid => Gamma + Fcc + Hcp
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Congruent Transformation – Case III
Isothermal sections showing the invariant reaction 4 in detail.
This reaction occurs in the solid state.
Class III: Gamma + Bcc + Hcp => Epsilon
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Congruent Transformation – Case III
There are three four-phase equilibria on the liquidus surface,
two Class I reactions and one Class II reaction.
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A Complex Ternary System
Ternary phase fields in 3-D view above 440
o
C
Liquid phase: Blue
Fcc phase: Red
Bcc phase: Orange
Hcp phase: Fuchsia
Delta phase: Pink
Gamma phase: Green
Invariant: Aqua
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A Complex Ternary System
Ternary phase fields in 3-D view below 440
o
C
Bcc phase: Orange
Hcp phase: Fuchsia
Epsilon phase: Olive
Gamma phase: Green
Invariant: Aqua
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Acknowledgement
• Many of the slides are reproduced based on the
book: Phase Diagrams in Metallurgy, Frederick
N. Rhines.
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For Download
• The PowerPoint file and related thermodynamic
database files are available for downloading
under the directory: Resources/Downloads.
• Thank you for your interest.