1. Introduction to Materials Science and Engineering
Chapter 10: Phase Transformation
(Textbook Chapter 12)

2. ISSUES TO ADDRESS... • Transforming one phase into another takes time.Fe γ
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(cementite) α
(ferrite) +
(BCC)
• How does the rate of transformation depend on
time and temperature ?
• Is it possible to slow down transformations so that non-equilibrium structures are formed?
• Are the mechanical properties of non-equilibrium
structures more desirable than equilibrium ones?

3. Phase Transformations
Nucleation
nuclei (seeds) act as templates on which crystals grow
for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss
once nucleated, growth proceeds until equilibrium is attained
Driving force to nucleate increases as we increase ΔT
supercooling (eutectic, eutectoid)
superheating (peritectic)
Small supercooling  slow nucleation rate - few nuclei - large crystals
Large supercooling  rapid nucleation rate - many nuclei - small crystals

4. Solidification: Nucleation Types
Homogeneous nucleation
nuclei form in the bulk of liquid metal
requires considerable supercooling (typically °C)
Fig_12_01

5. Solidification: Nucleation Types
Heterogeneous nucleation
much easier since stable “nucleating surface” is already present — e.g., mold wall, impurities in liquid phase
only very slight supercooling ( C)
Fig_12_05

6. Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
g = surface tension
ΔGT = Total Free Energy
= ΔGS + ΔGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
r* = critical nucleus: for r < r* nuclei shrink; for r > r* nuclei grow (to reduce energy)
Adapted from Fig.12.2(b), Callister & Rethwisch 9e.

7. Homogeneous Nucleation & Energy Effects
Fig_12_03
For typical DT, r* ~ 10 nm.

8. Homogeneous Nucleation & Energy Effects
The number of stable nuclei n* having radius greater than r*, is expressed as
Fig_12_04

9. Hetrogeneous Nucleation & Energy Effects
Fig_12_05
Fig_12_06

10. Growth
Fig_12_08

11. Kinetic Considerations of Solid-State Transformation
Kinetics - study of reaction rates of phase transformations
To determine reaction rate – measure degree of transformation as function of time (while holding temp constant)
measure propagation of sound waves – on single specimen
electrical conductivity measurements – on single specimen
X-ray diffraction – many specimens required
How is the degree of transformation measured?

12. Rate of Phase Transformation
transformation complete
Fixed T
Fraction transformed, y
0.5
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as interfacial surface area increases & nuclei grow
t0.5
log t
Fig ,
Callister & Rethwisch 9e.
Avrami equation => y = 1- exp (-kt n)
k & n are transformation specific parameters
S.A. = surface area
fraction transformed
time
By convention rate = 1 / t0.5

13. Temperature Dependence of Transformation Rate1 10
102
104
Fig , Callister & Rethwisch 9e.
(Reprinted with permission from Metallurgical Transactions, Vol. 188, 1950, a publication of The Metallurgical Society of AIME, Warrendale, PA. Adapted from B. F. Decker and D. Harker, “Recrystallization in Rolled Copper,” Trans. AIME, 188, 1950, p. 888.)
For the recrystallization of Cu, since rate = 1/t0.5 rate increases with increasing temperature
Rate often so slow that attainment of equilibrium state not possible!

14. Transformations & Undercooling•
Eutectoid transf. (Fe-Fe3C system): γ Þ α +
Fe3C •
For transf. to occur, must
cool to below 727°C
(i.e., must “undercool”)
0.76 wt% C
6.7 wt% C
0.022 wt% C
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite)
γ +L
γ +Fe3C
α +Fe3C
L+Fe3C δ
(Fe)
C, wt%C
1148°C
T(°C) α
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727°C ΔT
Undercooling by Ttransf. < 727°C
0.76
0.022
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.]

15. The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from Fig , Callister & Rethwisch 9e. γ α
pearlite
growth
direction
Austenite (γ)
grain
boundary
cementite (Fe3C)
Ferrite (α)
Diffusion of C
during transformation α γ
Carbon diffusion
• For this transformation,
rate increases with
[Teutectoid – T ] (i.e., ΔT).
Adapted from Fig , Callister & Rethwisch 9e.
675°C
(ΔT smaller) 50
y (% pearlite)
600°C
(ΔT larger)
650°C
100
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite  formed at lower temperatures – relatively hard

16. Generation of Isothermal Transformation Diagrams
Consider:
• The Fe-Fe3C system, for C0 = 0.76 wt% C
• A transformation temperature of 675ºC.
100
T = 675°C y,
% transformed 50 2 4
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.] 1 10 10
time (s)
400
500
600
700 1 10 2 3 4 5
0%pearlite
100%
50%
Austenite (stable)
TE (727°C)
Austenite
(unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C

17. Austenite-to-Pearlite Isothermal Transformation
• Eutectoid composition, C0 = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C
• Hold T (625°C) constant (isothermal treatment)
400
500
600
700
0%pearlite
100%
50%
Austenite (stable)
TE (727°C)
Austenite
(unstable)
Pearlite
T(ºC) 1 10 2 3 4 5
time (s)
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.] γ γ

18. Transformations Involving Noneutectoid Compositions
Consider C0 = 1.13 wt% C a
TE (727°C)
T(°C)
time (s) A + C P 1 10
102
103
104
500
700
900
600
800
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L γ
(austenite)
γ +L
γ +Fe3C
α +Fe3C
L+Fe3C δ
(Fe)
C, wt%C
T(°C)
727°C
0.76
0.022
1.13
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.]
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.]
Hypereutectoid composition – proeutectoid cementite

19. Bainite: Another Fe-Fe3C Transformation Product
-- elongated Fe3C particles in α-ferrite matrix
-- diffusion controlled
• Isothermal Transf. Diagram, C0 = 0.76 wt% C
Fe3C
(cementite) α
(ferrite) 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50% A
100% pearlite
100% bainite
5 μm
Fig , Callister & Rethwisch 9e. (From Metals Handbook, Vol. 8, 8th edition,
Metallography, Structures and Phase Diagrams,
1973. Reproduced by permission of ASM
International, Materials Park, OH.)
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.]

20. Spheroidite: Another Microstructure for the Fe-Fe3C System
Fig , Callister & Rethwisch 9e. (Copyright United States Steel Corporation, 1971.)
60 μm α
(ferrite)
(cementite)
Fe3C
• Spheroidite:
-- Fe3C particles within an α-ferrite matrix
-- formation requires diffusion
-- heat bainite or pearlite at temperature just below eutectoid for long times
-- driving force – reduction
of α-ferrite/Fe3C interfacial area

21. Martensite: A Nonequilibrium Transformation Product
-- γ(FCC) to Martensite (BCT)
Martensite needles
Austenite
60 μm x
potential
C atom sites
Fe atom
sites
Adapted from Fig , Callister & Rethwisch 9e.
Adapted from Fig , Callister & Rethwisch 9e.
• Isothermal Transf. Diagram
• γ to martensite (M) transformation.
-- is rapid! (diffusionless)
-- % transformation depends only on T to which rapidly cooled 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50% A
M + A
90%
Fig , Callister & Rethwisch 9e. (Courtesy United States Steel Corporation.)

22. Martensite Formation γ (FCC) α (BCC) + Fe3C slow cooling quench
M (BCT)
tempering
Martensite (M) – single phase
– has body centered tetragonal (BCT) crystal structure
Diffusionless transformation BCT if C0 > 0.15 wt% C
BCT  few slip planes  hard, brittle

23. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
reaction (and formation of pearlite, bainite)
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.]

24. Continuous Cooling Transformation Diagrams
Cooling curve
Conversion of isothermal transformation diagram to continuous cooling transformation diagram
Actual processes involves cooling – not isothermal
Can’t cool at infinite speed
Fig , Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, Reproduced by permission of ASM International, Materials Park, OH.]

25. Isothermal Heat Treatment Example Problems
On the isothermal transformation diagram for a 0.45 wt% C, Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures:
42% proeutectoid ferrite and 58% coarse pearlite
50% fine pearlite and 50% bainite
100% martensite
50% martensite and 50% austenite

26. Solution to Part (a) of Example Problem
42% proeutectoid ferrite and 58% coarse pearlite
A + B
A + P
A + α A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Fe-Fe3C phase diagram, for C0 = 0.45 wt% C
Isothermally treat at ~ 680°C
-- all austenite transforms
to proeutectoid α and
coarse pearlite.
T (°C)
Figure 12.39, Callister & Rethwisch 9e.
(Adapted from Atlas of Time-Temperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, Reprinted by permission of ASM International, Materials Park, OH.)

27. Solution to Part (b) of Example Problem
50% fine pearlite and 50% bainite
T (ºC)
A + B
A + P
A + α A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Fe-Fe3C phase diagram, for C0 = 0.45 wt% C
Isothermally treat at ~ 590°C
– 50% of austenite transforms
to fine pearlite.
Then isothermally treat
at ~ 470°C
– all remaining austenite
transforms to bainite.
Figure 12.39, Callister & Rethwisch 9e.
(Adapted from Atlas of Time-Temperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, Reprinted by permission of ASM International, Materials Park, OH.)

28. Solutions to Parts (c) & (d) of Example Problem
100% martensite – rapidly quench to room temperature
T (°C)
A + B
A + P
A + α A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Fe-Fe3C phase diagram, for C0 = 0.45 wt% C
50% martensite
& 50% austenite
-- rapidly quench to ~ 290°C, hold at this temperature c) d)
Figure 12.39, Callister & Rethwisch 9e.
(Adapted from Atlas of Time-Temperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, Reprinted by permission of ASM International, Materials Park, OH.)

29. Mechanical Props: Influence of C Content
Fig , Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.)
C0 > 0.76 wt% C
Hypereutectoid
Pearlite (med) C
ementite
(hard)
Pearlite (med)
ferrite (soft)
C0 < 0.76 wt% C
Fig , Callister & Rethwisch 9e. (Courtesy of Republic Steel Corporation.)
Hypoeutectoid
Fig , Callister & Rethwisch 9e.
[Data taken from Metals Handbook: Heat Treating, Vol. 4, 9th edition, V. Masseria (Managing Editor), Reproduced by permission of ASM International, Materials Park, OH.]
300
500
700
900
1100
YS(MPa)
TS(MPa)
wt% C
0.5 1
hardness
0.76
Hypo
Hyper
wt% C
0.5 1 50
100
%EL
Impact energy (Izod, ft-lb) 40 80
0.76
Hypo
Hyper
• Increase C content: TS and YS increase, %EL decreases

30. Mechanical Props: Fine Pearlite vs. Coarse Pearlite vs. Spheroidite80
160
240
320
wt%C
0.5 1
Brinell hardness
fine
pearlite
coarse
spheroidite
Hypo
Hyper 30 60 90
wt%C
Ductility (%RA)
fine
pearlite
coarse
spheroidite
Hypo
Hyper
0.5 1
Fig , Callister & Rethwisch 9e. [Data taken from Metals Handbook: Heat Treating, Vol. 4, 9th edition, V. Masseria (Managing Editor), Reproduced by permission of ASM International, Materials Park, OH.]
• Hardness:
fine > coarse > spheroidite
• %RA:
fine < coarse < spheroidite

31. Mechanical Props: Fine Pearlite vs. Martensite
200
wt% C
0.5 1
400
600
Brinell hardness
martensite
fine pearlite
Hypo
Hyper
Fig , Callister & Rethwisch 9e. (Adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, 1939; and R. A. Grange, C. R. Hribal, and L. F. Porter, Metall. Trans. A, Vol. 8A. Reproduced by permission of ASM International, Materials Park, OH.)
• Hardness: fine pearlite << martensite.

32. Tempered Martensite • •
Heat treat martensite to form tempered martensite
• tempered martensite less brittle than martensite
• tempering reduces internal stresses caused by quenching
YS(MPa)
TS(MPa)
800
1000
1200
1400
1600
1800 30 40 50 60
200
400
600
Tempering T (°C)
%RA TS YS
Fig , Callister & Rethwisch 9e. (Adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, Reproduced by permission of ASM International, Materials Park, OH.)
Figure 12.33, Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.)
9 μm •
tempering produces extremely small Fe3C particles surrounded by α. •
tempering decreases TS, YS but increases %RA

33. Summary of Possible Transformations
Adapted from Fig , Callister & Rethwisch 9e.
Austenite (γ)
Pearlite
(α + Fe3C layers + a
proeutectoid phase)
slow
cool
Bainite
(α + elong. Fe3C particles)
moderate
cool
Martensite
(BCT phase
diffusionless
transformation)
rapid
quench
Strength
Ductility
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
Tempered
Martensite
(α + very fine
Fe3C particles)
reheat