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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Isomorphous Systems
Isomorphous:
Two elements are completely soluble in each other in solid and
liquid states; substitutional solid state solution can be formed;
single type of crystal structure exists.
Hume-Rothery Rules:
(1) atoms have similar radii;
(2) both pure materials have same crystal structure;
(3) similar electronegativity (otherwise may form a compound
instead);
(4) solute should have higher valence.
Example:
Cu-Ni (slow cooling conditions), Mo-Nb, Mo-V, ...
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Isomorphous Systems
Information from this diagram:
• Pure Ni melts at 1455
o
C
• Pure Cu melts at 1085
o
C
• Pure component melts at a
fixed temperature, an alloy
melts in a temperature range.
• Cu-80at%Ni starts to melt at
1382
o
C (solidus), and becomes
complete liquid at 1398
o
C
(liquidus)
• Liquid and solid coexist
between the liquidus and
solidus temperatures
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Information Obtained from both the Phase
Diagram and the G-x Diagram:
At the given temperature T=1300
o
C
1. On the left of x
L
, Liquid is most stable
2. On the right of x
a
, a phase is stable
3. Between x
L
and x
a
the two-phase mixture is
stable
x
L
x
a
( )
LL
B
L
A
L
B
L
B
L
A
L
A
L
B
L
B
L
A
L
A
L
xxxxxxRTGxGxG
++++= lnln
( )
aaaaaaaaaaaa
BABBAABBAA
xxxxxxRTGxGxG ++++= lnln
Phase Diagram vs. Gibbs Energy Curve
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x
L
x
a
x
L
x
a
Phase Diagram vs. Gibbs Energy Curve
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Details Refer to:
1. Database: Database_Isomorphous_Cu-Ni.tdb
2. Tutorial Video: Binary_Isomorphous
Calculated Phase Diagram
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Finding the amounts of phases
in a two-phase region:
1. Locate composition and
temperature in diagram
2. In two-phase region draw the
tie line
3. Fraction of a phase is
determined by taking the
length of the tie line to the
phase boundary for the other
phase, and divided by the
total length of tie line
L
L
CC
CC
SR
S
F
−
−
=
+
=
a
a
0
L
L
CC
CC
SR
R
F
−
−
=
+
=
a
a
0
R
S
Lever Rule
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Equilibrium Solidification
L
(50%Ni)
a
(50%Ni)
L
(41%Ni)
a
(53%Ni)
L
(45%Ni)
a
(57%Ni)
L
(50%Ni)
a
(61%Ni)
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Non-Equilibrium Solidification
a
(61%Ni)
L
(50%Ni)
L
(44%Ni)
a
(57%Ni)
L
(33%Ni)
a
(50%Ni)
a
(46%Ni)
L
(38%Ni)
a
(54%Ni)
L
(50%Ni)
As-cast 70%Cu – 30%Ni alloy
showing a cored structure
Non-equilibrium
solidus due to
undercooling of the
liquid phase and
low diffusion in the
solid phase
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Non-Equilibrium and Equilibrium Micro-structures
Non-Equilibrium Structure
Fast cooling rate
C
a
changes during solidification
Equilibrium Structure
Very slow cooling rate
Uniform C
a
during solidification
Coring can be eliminated by means of a homogenization heat
treatment carried out at temperatures below the alloy’s solidus
Heat Treatment
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Eutectic Systems
Information from this diagram:
• Eutectic reaction occurs at
779
o
C and 60.5 at% Ag:
L ↔ a
1
+ a
2
.
• Alloy (4.8%<x
Ag
<87.7%) starts
to melt at eutectic reaction
temperature 779
o
C and
becomes complete liquid at
liquidus.
• Alloy (x
Ag
<4.8% or x
Ag
>87.7%)
transforms from two phases to
single phase when crossing
solvus from lower temperature,
starts to melt at solidus, and
becomes complete liquid at
liquidus.
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How Is A Eutectic Phase Diagram Calculated?
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How Is A Eutectic Phase Diagram Calculated?
Details Refer to:
1. Database: Database_Eutectic_Cu-Ag.tdb
2. Tutorial Video: Binary_Eutectic
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Eutectic Phase Diagram Calculation (Another Example)
Details Refer to:
1. Database: Database_Eutectic_Pb-Sn.tdb
2. Tutorial Video: Binary_Eutectic
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Sn) at% 89( Sn) at% (31 Sn) at% 76(
a
+L
cooling
heating
Microstructure of a Eutectic Alloy, C
0
=C
E
=76 at% Sn
L
(76%Sn)
L
(76%Sn)
a
(31%Sn)
(98%Sn)
a
(31%Sn)
(98%Sn)
The dark layers are Pb-rich
α phase, and the light
layers are Sn-rich β phase.
Photo copyright by Metals Handbook Vol. 9, 1985.
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Lamellar Eutectic Microstructure
❑A two-phase lamellar
microstructure resulting
from the solidification of a
liquid having the eutectic
composition.
Eutectic
growth
direction
Liquid
a
a
a
a
Pb
Pb
Pb
Pb
Pb
Sn
Sn
Sn
Sn
❑Compositions of α and β
phases are very different.
Solidification involves
redistribution of Pb and Sn
atoms by atomic diffusion.
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Microstructure of a Solid Solution Alloy, C
0
< 2 at% Sn
L
(C
0
)
L
a
a
(C
0
)
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Microstructure of An Alloy That Exceeds Solubility Limit,
2 < C
0
< 31 at% Sn
L
(C
0
)
L
a
a
(C
0
)
a
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Microstructure of a Hypoeutectic Alloy, 31 < C
0
< 76 at% Sn
L
L
a
L
a
L
Primary a
Eutectic a
Eutectic
Precipitate
The dark layers are Pb-rich α phase,
and the light layers are Sn-rich β phase.
Photo copyright by Metals
Handbook Vol. 9, 1985.
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Scheil (Non-Equilibrium) Solidification Simulation
Assumptions for Scheil Simulation:
•Planar solid/liquid interface and negligible undercooling
•Local equilibrium at the solid/liquid interface
•Complete diffusion in liquid phase
•No diffusion in solid phase
•Density of liquid equals density of solid
In Reality:
•Planar/sphere/… S/L interface and considerable undercooling
•Large diffusion in liquid phase
•Limited diffusion in solid phase
•Density of liquid does not equal to density of solid
Scheil simulation is good for fast cooling of systems with small amount.
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Scheil (Non-Equilibrium) Solidification Simulation
When the alloy hits the eutectic
temperature at 187
o
C, the liquid
transforms to a + mixture and
remains at the same temperature
until all the liquid is gone.
The final a phase fraction contains
two parts: primary a phase (~62%)
and eutectic a phase in the
eutectic mixture (~38%).
f(a) = 62%+38%*33% = 74%
f() = 38%*67% = 26%
For the Alloy Pb-45at%Sn, the
liquid starts to solidify at 252
o
C
and the a phase is the product.
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Eutectoid Systems
Information from this diagram:
• Fe-C stable phase boundaries
are represented by pink dot
lines, and Fe-Fe
3
C metastable
phase boundaries are
represented by blue solid lines.
• Fe
3
C phase is a line compound
(6.7 wt% of Carbon) without
any solubility.
• Carbon is an interstitial
impurity in iron and forms a
solid solution with the a, g, d
phases.
• Eutectoid reaction is a solid
state reaction with no liquid
involved: g ↔ a + Fe
3
C.
Photo copyright by United States Steel Corporation.
a, Ferrite
g, Austenite
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Formation of Pearlite
Due to the eutectoid reaction: g ↔ a + Fe
3
C, pearlite structure is formed.
Pearlite: alternating layers of a and Fe
3
C phases, not a single phase.
Growth
direction of
pearlite
Austenite
(g)
Austenite
(g)
Cementite
(Fe
3
C)
Ferrite(a)
Ferrite(a)
Ferrite(a)
Ferrite(a)
a
a
Carbon
diffusion
Austenite
grain
boundary
g
g
g
a
Fe
3
C
• Nucleating at g grain boundaries.
• Growth by diffusion of carbon to achieve the compositions of a and Fe
3
C
(with structure changes).
• According to lever rule, the amount of a is much larger than that of Fe
3
C,
resulting in a much thicker a lamellae.
Photo copyright by Metals Handbook Vol. 9, 1985.
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g
g
g
g
g
g
a
g
g
g
a
Proeutectoid a
Eutectoid a
Fe
3
C
Proeutectoid Microstructure
Photo copyright by Republic Steel Corporation.
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g
g
g
g
g
g
Fe
3
C
g
g
g
Fe
3
C
Hypereutectoid Microstructure
Fe
3
C
Pearlite
Photo copyright by United States Steel Corporation.
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Peritectic Systems
Information from this diagram:
• Peritectic reaction occurs at
1186
o
C and 80 at% Ag:
L + g
1
↔ g
2
.
• Alloy (22%<x
Ag
<59%) starts to
melt at peritectic reaction
temperature 1186
o
C and
becomes complete liquid at
liquidus.
• Alloy (x
Ag
<22% or x
Ag
>59%)
starts to melt at solidus, and
becomes complete liquid at
liquidus.
Details Refer to:
1. Database: Database_Peritectic_Ag-Pt.tdb
2. Tutorial Video: Binary_Peritectic
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How Is A Peritectic Phase Diagram Calculated?
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Microstructure in a Peritectic System, 22<C
0
<59 at% Ag
L
L
g
1
g
1
g
2
L
g
1
g
2
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Microstructure in a Peritectic System, C
0
=59 at% Ag
L
L
g
1
L
g
1
g
2
g
2
g
2
Precipitate g
1
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Microstructure in a Peritectic System, 59<C
0
<80 at% Ag
L
L
g
1
L
g
1
g
2
g
2
L
g
2
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Peritectic Systems (Another Example)
Information from this diagram:
• Peritectic reaction occurs at
1620
o
C and 86.9 at% Ni:
L + a ↔ .
• Alloy (18.4%<x
Ni
<82.6%) starts
to melt at peritectic reaction
temperature 1620
o
C and
becomes complete liquid at
liquidus.
• Alloy (x
Ni
<18.4% or x
Ni
>86.9%)
starts to melt at solidus, and
becomes complete liquid at
liquidus.
Details Refer to:
1. Database: Database_Peritectic_Ni-Re.tdb
2. Tutorial Video: Binary_Peritectic
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Phase Diagram vs. Gibbs Energy Curve
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Information from this diagram:
• Peritectoid reaction is a solid
state reaction without any
liquid involved.
• Peritectoid reaction occurs at
358
o
C and 18.6 - 24.8 at% Al:
a + x ↔ m.
Peritectoid Systems
Details Refer to:
1. Database: Database_Peritectoid_Ag-Al.tdb
2. Tutorial Video: Binary_Peritectoid
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Peritectoid Systems
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Peritectoid Systems
Photos from Phase Diagrams in Metallurgy, F.N. Rhines.
a
m
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Monotectic Systems
Information from this diagram:
• Monotectic reaction occurs at
663
o
C and 6 at% In:
L
1
↔ a + L
2
.
• Alloys of all compositions start
to melt at eutectic temperature
156
o
C: L ↔ a + .
• Alloy (x
In
<6at% or x
In
>88at%)
becomes complete liquid at
liquidus.
• Alloy (6at%<x
In
<88at%)
becomes complete liquid
mixture (two liquids with
different compositions) at
663
o
C.
Details Refer to:
1. Database: Database_Monotectic_Al-In.tdb
2. Tutorial Video: Binary_Monotectic
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How Is A Monotectic Phase Diagram Calculated?
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Microstructure of Al-In System
Al-rich
In-rich
Al
64
In
36
Photo from J Mater Sci (2012) 47:8360–8366.
The Al
64
In
36
(at.%) alloy in a graphite
container solidified at about 0.25 K/s
resulting in one layer on top of another.
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Monotectic Phase Diagram (Another Example)
Details Refer to:
1. Database: Database_Monotectic_Cu-Pb.tdb
2. Tutorial Video: Binary_Monotectic
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Types of Binary Phase Diagrams
• Isomorphous Systems
• Eutectic Systems
• Eutectoid Systems
• Peritectic Systems
• Peritectoid Systems
• Monotectic Systems
• Syntectic Systems
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Syntectic Systems
Information from this diagram:
• Syntectic reaction occurs at
557
o
C: L
1
+ L
2
↔ NaZn
13
.
• Alloys (x
Zn
<92.3at%) start to
melt at eutectic temperature
98
o
C: L ↔ a+NaZn
13
.
• Alloys (x
Zn
>92.3at%) start to
melt at eutectic temperature
419
o
C: L ↔ +NaZn
13
.
• Alloy (x
Zn
<9.4at% or
x
Zn
>94.4at%) becomes
complete liquid at liquidus.
• Alloy (9.4at%<x
Zn
<94.4at%)
becomes complete liquid
mixture (two liquids with
different compositions) at
557
o
C.
Details Refer to:
1. Database: Database_Syntectic_Na-Zn.tdb
2. Tutorial Video: Binary_Syntectic
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Reaction
Symbolic
equation
Schematic
presentation
Example
Eutectic
L↔
α+ β
Cu
-Ag, Pb-Sn, Al-Si
Eutectoid
α↔β+ γ
Fe
-C
Peritectic
L+
α↔β
Cu
-Fe, Pb-In
Peritectoid
α+ β↔γ
Al
-Cu
Monotectic
L
1
↔L
2
+ α
Cu
-Pb, Al-In
Monotectoid
α
1
↔α
2
+ β
Al
-Zn
Syntectic
L
1
+ L
2
↔α
Na
-Zn
L
a
a
g
L
a
a
g
a
L
2
L
1
a
L
2
L
1
Summary of Invariant Reactions in Binary Systems
a
2
a
1
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Binary Phase Diagrams
Use of regular solution model parameters to
generate different types of binary phase diagram
•Hypothetical elements A and B both present Fcc (a) structure in
their solid states.
•Both liquid and solid phases are described using regular solution
models.
( )
LL
B
L
A
L
B
L
B
L
A
L
A
L
B
L
B
L
A
L
A
L
xxxxxxRTGxGxG
0
,o,o
lnln
++++=
( )
aaaaaaaaaaa
0
,o,o
lnln
BABBAAB
L
BAA
xxxxxxRTGxGxG ++++=
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Phase Diagram Using Regular Solution Parameters
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Phase Diagram Using Regular Solution Parameters
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Phase Diagram Using Regular Solution Parameters
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Phase Diagram Using Regular Solution Parameters
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Acknowledgement
• Many of the slides are reproduced based on the
book: Materials Science and Engineering: An
Introduction, 8
th
Edition, William D. Callister, Jr.
David G. Rethwisch.
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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.