1. Chapter 11: Phase Diagrams
ISSUES TO ADDRESS...
• When we combine two elements...
what is the resulting equilibrium state?
• In particular, if we specify...
-- the composition (e.g., wt% Cu - wt% Ni), and
-- the temperature (T )
then...
How many phases form?
What is the composition of each phase?
What is the amount of each phase?
Phase B
Phase A
Nickel atom
Copper atom

2. Phase Equilibria: Solubility Limit
• Solution – solid, liquid, or gas solutions, single phase
• Mixture – more than one phase
• Solubility Limit:
Maximum concentration for
which only a single phase solution exists.
Sugar/Water Phase Diagram
Sugar
Temperature (°C) 20 40 60 80
100 C
= Composition (wt% sugar) L
(liquid solution
i.e., syrup)
Solubility
Limit
(liquid) + S
(solid
sugar) 4 6 8 10
Water
Adapted from Fig. 11.1,
Callister & Rethwisch 9e.
Question: What is the
solubility limit for sugar in
water at 20°C? 65
Answer: 65 wt% sugar.
At 20°C, if C < 65 wt% sugar: syrup
At 20°C, if C > 65 wt% sugar:
syrup + sugar

3. Components and Phases • Components: • Phases: β (lighter phase) α
The elements or compounds which are present in the alloy
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that form (e.g., α and β).
Aluminum-
Copper
Alloy β
(lighter
phase) α
(darker
phase)
Adapted from chapter-opening photograph, Chapter 9, Callister, Materials Science & Engineering: An Introduction, 3e.

4. Phase Diagrams • Indicate phases as a function of T, C, and P.
• For this course:
- binary systems: just 2 components.
- independent variables: T and C (P = 1 atm is almost always used).
wt% Ni 20 40 60 80
100
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid) α
(FCC solid
solution) L +
liquidus
solidus
• 2 phases:
Phase
Diagram
for Cu-Ni
system L
(liquid) α
(FCC solid solution)
• 3 different phase fields: L
L + α α
Fig. 11.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, Reprinted
by permission of ASM International, Materials
Park, OH.)

5. Ex: Cooling of a Cu-Ni Alloy
• Phase diagram:
Cu-Ni system.
T(°C)
L (liquid)
L: 35 wt%Ni
Cu-Ni
system
• Consider
microstuctural
changes that
accompany the
cooling of a
C0 = 35 wt% Ni alloy α
α: 46 wt% Ni
L: 35 wt% Ni
130 A + L B 46 35 C 43 32
α: 43 wt% Ni
L: 32 wt% Ni D 24 36 α
L: 24 wt% Ni
α: 36 wt% Ni +
120 L E α
(solid)
α: 35 wt% Ni
110 20 3 35 4 5 C0
wt% Ni
Adapted from Fig. 11.4, Callister & Rethwisch 9e.

6. Binary-Eutectic Systems
has a special composition
with a min. melting T.
2 components
Cu-Ag
system
T(°C)
Ex.: Cu-Ag system
1200
• 3 single phase regions
(L, α, β)
L (liquid)
1000 α L + α
• Limited solubility:
α: mostly Cu
β: mostly Ag L + β
800
779°C β TE
8.0
71.9
91.2
600
• TE
: No liquid below TE α + β
: Composition at
temperature TE
• CE
400
200 20 40 60 CE 80
100
• Eutectic reaction
L(CE) α(CαE) + β(CβE)
C, wt% Ag
Fig. 11.6, Callister & Rethwisch 9e [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.].
cooling
heating

7. EX 2: Pb-Sn Eutectic System
• For a 40 wt% Sn-60 wt% Pb alloy at 220°C, determine:
-- the phases present:
Pb-Sn
system
Answer: α + L L + β α
200
T(°C)
C, wt% Sn 20 60 80
100
300
L (liquid)
183°C
-- the phase compositions
Answer: Cα = 17 wt% Sn
CL = 46 wt% Sn
-- the relative amount of each phase
220 17 Cα R 40 C0 S 46 CL
Answer: W α =
CL - C0
CL - Cα 6 29
= 0.21
Fig. 11.7, Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] WL =
C0 - Cα
CL - Cα 23 29
= 0.79

8. Microstructural Developments in Eutectic Systems II
L: C0 wt% Sn
• For alloys for which
2 wt% Sn < C0 < 18.3 wt% Sn
• Result:
at temperatures in α + β range
-- polycrystalline with α grains
and small β-phase particles
Pb-Sn
system L + α
200
T(°C) C ,
wt% Sn 10
18.3 20 C0
300
100 30 β
400
(sol. limit at TE) TE 2
(sol. limit at T
room ) L α
α: C0 wt% Sn α β
Fig , Callister & Rethwisch 9e.

9. Microstructural Developments in Eutectic Systems III
• For alloy of composition C0 = CE
• Result: Eutectic microstructure (lamellar structure)
-- alternating layers (lamellae) of α and β phases.
Fig , Callister & Rethwisch 9e. (From Metals Handbook, 9th edition, Vol. 9,
Metallography and Microstructures, 1985.
Reproduced by permission of ASM International, Materials Park, OH.)
160 μm
Micrograph of Pb-Sn
eutectic
microstructure
Pb-Sn
system
Lβ
αβ
200
T(°C)
C, wt% Sn 20 60 80
100
300 L α β +
183°C 40 TE
L: C0 wt% Sn CE
61.9
18.3
α: 18.3 wt%Sn
97.8
β: 97.8 wt% Sn
Fig , Callister & Rethwisch 9e.

10. Microstructural Developments in Eutectic Systems IV
• For alloys for which 18.3 wt% Sn < C0 < 61.9 wt% Sn
• Result: α phase particles and a eutectic microconstituent WL
= (1- W α )
= 0.50 Cα
= 18.3 wt% Sn CL
= 61.9 wt% Sn S R + Wα =
• Just above TE :
Fig , Callister & Rethwisch 9e.
Pb-Sn
system L + β
200
T(°C)
C, wt% Sn 20 60 80
100
300 α 40 TE
L: C0
wt% Sn L α L α
18.3
61.9 S R
97.8 S R
primary α
eutectic β
• Just below TE : C α
= 18.3 wt% Sn β
= 97.8 wt% Sn S R + W =
= 0.73
= 0.27

11. Eutectic, Eutectoid, & Peritectic
Eutectic - liquid transforms to two solid phases
L α + β (For Pb-Sn, 183°C, 61.9 wt% Sn)
cool
heat
Eutectoid – one solid phase transforms to two other solid phases
S S1+S3
γ α + Fe3C (For Fe-C, 727°C, 0.76 wt% C)
intermetallic compound - cementite
cool
heat
cool
heat
Peritectic - liquid and one solid phase transform to a second solid phase
S1 + L S2
δ + L γ (For Fe-C, 1493°C, 0.16 wt% C)

12. Eutectoid & Peritectic
Peritectic transformation γ + L δ
Cu-Zn Phase diagram
Eutectoid transformation δ γ + e
Fig , Callister & Rethwisch 9e.
[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 2, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]

13. Phase Rule Phase Rule: 상태조건 T,P,C와 미세조직상과 관련
미세조직형성을 알기 위해서 상태도를 알아야 하며, 이를 위해 상률을 알아야 한다
F = C – P + 2 (T & P)
1기압: F = C – P + 1

14. fig_09_24
fig_09_24

15. Iron-Carbon (Fe-C) Phase Diagram
• 2 important
Fig , Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite) +L
+Fe3C α + δ
(Fe)
C, wt% C
1148°C
T(°C)
727°C = T
eutectoid
points
- Eutectic (A): L Þ γ +
Fe3C A
- Eutectoid (B): γ Þ α +
Fe3C
L+Fe3C γ
Result: Pearlite = alternating
layers of α and Fe3C phases
120 μm
Fig , Callister & Rethwisch 9e. (From Metals Handbook, Vol. 9, 9th ed.,
Metallography and Microstructures, 1985.
Reproduced by permission of ASM International, Materials Park, OH.)
0.76 B
Fe3C (cementite-hard) α
(ferrite-soft)
4.30

16. Hypoeutectoid Steel a T(°C) δ L +L γ (austenite) Fe3C (cementite) α
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite) +L
+ Fe3C α
L+Fe3C δ
(Fe)
C, wt% C
1148°C
T(°C) a
727°C
(Fe-C
System) C0
0.76 γ γ
Adapted from Figs and 11.28, Callister & Rethwisch 9e.
[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] γ α α
pearlite
Adapted from Fig , Callister & Rethwisch 9e. (Photomicrograph courtesy of Republic Steel Corporation.)
proeutectoid ferrite
pearlite
100 μm
Hypoeutectoid
steel

17. Hypoeutectoid Steel T(°C) δ L +L γ (austenite) Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite) +L
+ Fe3C α
L+Fe3C δ
(Fe)
C, wt% C
1148°C
T(°C)
727°C
(Fe-C
System) C0
0.76 γ α
Adapted from Figs and 11.28, Callister & Rethwisch 9e.
[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]
Wα = s/(r + s)
Wγ =(1 - Wα) s r α
pearlite R S
Wpearlite = Wγ
Wα’ = S/(R + S)
W =(1 – Wα’)
Fe3C
Adapted from Fig , Callister & Rethwisch 9e. (Photomicrograph courtesy of Republic Steel Corporation.)
proeutectoid ferrite
pearlite
100 μm
Hypoeutectoid
steel

18. Hypereutectoid Steel T(°C) δ L +L γ γ (austenite) Fe3C (cementite) γ γ
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite) +L
+ Fe3C α
L+Fe3C δ
(Fe)
C, wt% C
1148°C
T(°C)
727°C
(Fe-C
System) C0 γ γ
Adapted from Figs and 11.31, Callister & Rethwisch 9e.
[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]
Fe3C γ
pearlite C0
0.76
Adapted from Fig , Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.)
proeutectoid Fe3C
60 μm
Hypereutectoid
steel
pearlite

19. Hypereutectoid Steel Fe3C (cementite) L γ (austenite) +L α δ T(°C) γ x
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite) +L
+ Fe3C α
L+Fe3C δ
(Fe)
C, wt% C
1148°C
T(°C)
727°C
(Fe-C
System) C0
Fe3C γ
Adapted from Figs and 11.31, Callister & Rethwisch 9e.
[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]
W =(1-Wγ)
Wγ =x/(v + x)
Fe3C x v
pearlite V X C0
0.76
Wpearlite = Wγ
Wα = X/(V + X)
W =(1 - Wα)
Fe3C’
Adapted from Fig , Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.)
proeutectoid Fe3C
60 μm
Hypereutectoid
steel
pearlite

20. Alloying with Other Elements
• Teutectoid changes:
Fig , Callister & Rethwisch 9e. (From Edgar C. Bain, Functions of the Alloying Elements
in Steel, Reproduced by permission of ASM
International, Materials Park, OH.) T
Eutectoid
(ºC)
wt. % of alloying elements Ti Ni Mo Si W Cr Mn
• Ceutectoid changes:
Fig ,Callister & Rethwisch 9e. (From Edgar C. Bain, Functions of the Alloying Elements in Steel, Reproduced by permission of ASM International, Materials Park, OH.)
wt. % of alloying elements C
eutectoid
(wt% C) Ni Ti Cr Si Mn W Mo

21. Summary • Phase diagrams are useful tools to determine:
-- the number and types of phases present,
-- the composition of each phase,
-- and the weight fraction of each phase
given the temperature and composition of the system.
• The microstructure of an alloy depends on
-- its composition, and
-- whether or not cooling rate allows for maintenance of equilibrium.
• Important phase diagram phase transformations include eutectic, eutectoid, and peritectic.