1. Chapter 11: Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time. Fe g
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(cementite) a
(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?

2. 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 T
supercooling (eutectic, eutectoid)
superheating (peritectic)
Small supercooling  slow nucleation rate - few nuclei - large crystals
Large supercooling  rapid nucleation rate - many nuclei - small crystals

3. Solidification: Nucleation Types
Homogeneous nucleation
nuclei form in the bulk of liquid metal
requires considerable supercooling (typically °C)
Heterogeneous nucleation
much easier since stable “nucleating surface” is already present — e.g., mold wall, impurities in liquid phase
only very slight supercooling (0.1-10ºC)

4. Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
g = surface tension
DGT = Total Free Energy
= DGS + DGV
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.11.2(b), Callister & Rethwisch 3e.

5. Solidification Note: Hf and  are weakly dependent on T
Hf = latent heat of solidification
Tm = melting temperature
g = surface free energy
DT = Tm - T = supercooling
r* = critical radius
Note: Hf and  are weakly dependent on T
 r* decreases as T increases
For typical T r* ~ 10 nm

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

7. 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 surface area increases & nuclei grow
t0.5
log t
Adapted from Fig ,
Callister & Rethwisch 3e.
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

8. Temperature Dependence of Transformation Rate1 10
102
104
Adapted from Fig , Callister & Rethwisch 3e.
(Fig 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!

9. Transformations & Undercooling•
Eutectoid transf. (Fe-Fe3C system): g Þ a +
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 g
(austenite) +L
+Fe3C a
L+Fe3C d
(Fe)
C, wt%C
1148°C
T(°C)
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC DT
Undercooling by Ttransf. < 727C
0.76
0.022
Adapted from Fig ,Callister & Rethwisch 3e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

10. The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from Fig , Callister & Rethwisch 3e. g a
pearlite
growth
direction
Austenite (g)
grain
boundary
cementite (Fe3C)
Ferrite (a)
Diffusion of C
during transformation a g
Carbon diffusion
• For this transformation,
rate increases with
[Teutectoid – T ] (i.e., DT).
Adapted from Fig , Callister & Rethwisch 3e.
675°C
(DT smaller) 50
y (% pearlite)
600°C
(DT larger)
650°C
100
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite  formed at lower temperatures – relatively hard

11. Generation of Isothermal Transformation Diagrams
Consider:
• The Fe-Fe3C system, for Co = 0.76 wt% C
• A transformation temperature of 675°C.
100
T = 675°C y,
% transformed 50 2 4 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
Adapted from Fig ,Callister & Rethwisch 3e. (Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

12. 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(°C) 1 10 2 3 4 5
time (s)
Adapted from Fig ,Callister & Rethwisch 3e. (Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) g g

13. 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
Adapted from Fig , Callister & Rethwisch 3e.
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+Fe3C a
L+Fe3C d
(Fe)
C, wt%C
T(°C)
727°C DT
0.76
0.022
1.13
Adapted from Fig , Callister & Rethwisch 3e.
Hypereutectoid composition – proeutectoid cementite

14. Bainite: Another Fe-Fe3C Transformation Product
-- elongated Fe3C particles in a-ferrite matrix
-- diffusion controlled
• Isothermal Transf. Diagram, C0 = 0.76 wt% C
Fe3C
(cementite) a
(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 mm
Adapted from Fig , Callister & Rethwisch 3e. (Fig from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)
Adapted from Fig , Callister & Rethwisch 3e.

15. Spheroidite: Another Microstructure for the Fe-Fe3C System
Adapted from Fig , Callister & Rethwisch 3e. (Fig copyright United States Steel Corporation, 1971.)
60 m a
(ferrite)
(cementite)
Fe3C
• Spheroidite:
-- Fe3C particles within an a-ferrite matrix
-- formation requires diffusion
-- heat bainite or pearlite at temperature just below eutectoid for long times
-- driving force – reduction
of a-ferrite/Fe3C interfacial area

16. Martensite: A Nonequilibrium Transformation Product
-- g(FCC) to Martensite (BCT)
Martensite needles
Austenite
60 m x
potential
C atom sites
Fe atom
sites
Adapted from Fig , Callister & Rethwisch 3e.
Adapted from Fig , Callister & Rethwisch 3e.
• Isothermal Transf. Diagram
• g to martensite (M) transformation..
-- is rapid! (diffusionless)
-- % transf. 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%
Adapted from Fig , Callister & Rethwisch 3e. (Fig courtesy United States Steel Corporation.)

17. Martensite Formation  (FCC)  (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

18. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard    + Fe3C
reaction (and formation of pearlite, bainite)
Adapted from Fig , Callister & Rethwisch 3e.

19. 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
Adapted from Fig ,
Callister & Rethwisch 3e.

20. 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

21. Solution to Part (a) of Example Problem
42% proeutectoid ferrite and 58% coarse pearlite
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Adapted from Fig ,
Callister 5e.
Fe-Fe3C phase diagram, for C0 = 0.45 wt% C
Isothermally treat at ~ 680°C
-- all austenite transforms
to proeutectoid a and
coarse pearlite.
T (°C)

22. Solution to Part (b) of Example Problem
50% fine pearlite and 50% bainite
T (°C)
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Adapted from Fig ,
Callister 5e.
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.

23. Solutions to Parts (c) & (d) of Example Problem
100% martensite – rapidly quench to room temperature
T (°C)
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
Adapted from Fig ,
Callister 5e.
Fe-Fe3C phase diagram, for C0 = 0.45 wt% C
50% martensite
& 50% austenite
-- rapidly quench to ~ 290°C, hold at this T c) d)

24. Mechanical Props: Influence of C Content
Adapted from Fig , Callister & Rethwisch 3e.
C0 > 0.76 wt% C
Hypereutectoid
Pearlite (med) C
ementite
(hard)
Pearlite (med)
ferrite (soft)
C0 < 0.76 wt% C
Adapted from Fig , Callister & Rethwisch 3e.
Hypoeutectoid
Adapted from Fig , Callister & Rethwisch 3e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)
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

25. 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
Adapted from Fig , Callister & Rethwisch 3e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)
• Hardness:
fine > coarse > spheroidite
• %RA:
fine < coarse < spheroidite

26. Mechanical Props: Fine Pearlite vs. Martensite
200
wt% C
0.5 1
400
600
Brinell hardness
martensite
fine pearlite
Hypo
Hyper
Adapted from Fig , Callister & Rethwisch 3e. (Fig adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 36; and R.A. Grange, C.R. Hribal, and L.F. Porter, Metall. Trans. A, Vol. 8A, p )
• Hardness: fine pearlite << martensite.

27. 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
Adapted from Fig , Callister & Rethwisch 3e. (Fig adapted from Fig. furnished courtesy of Republic Steel Corporation.)
Adapted from Fig , Callister & Rethwisch 3e. (Fig copyright by United States Steel Corporation, 1971.)
9 mm •
tempering produces extremely small Fe3C particles surrounded by a. •
tempering decreases TS, YS but increases %RA

28. Summary of Possible Transformations
Adapted from Fig , Callister & Rethwisch 3e.
Austenite (g)
Pearlite
(a + Fe3C layers + a
proeutectoid phase)
slow
cool
Bainite
(a + 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
(a + very fine
Fe3C particles)
reheat

29. Precipitation Hardening
• Particles impede dislocation motion.
• Ex: Al-Cu system
• Procedure: 10 20 30 40 50
wt% Cu L
+L a
a+q q
+L
300
400
500
600
700
(Al)
T(°C)
composition range
available for precipitation hardening
CuAl2 A
-- Pt A: solution heat treat (get a solid solution) B
Pt B
-- Pt B: quench to room temp. (retain a solid solution) C
-- Pt C: reheat to nucleate small q particles within a phase.
Other alloys that precipitation harden: • Cu-Be • Cu-Sn • Mg-Al
Adapted from Fig , Callister & Rethwisch 3e. (Fig adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)
Temp.
Time
Pt A (sol’n heat treat)
Pt C (precipitate )
Adapted from Fig , Callister & Rethwisch 3e.

30. Influence of Precipitation Heat Treatment on TS, %EL
• 2014 Al Alloy:
• Maxima on TS curves.
• Increasing T accelerates
process.
• Minima on %EL curves.
%EL (2 in sample) 10 20 30
1min 1h
1day
1mo
1yr
204°C
149 °C
precipitation heat treat time
precipitation heat treat time
tensile strength (MPa)
200
300
400
100
1min 1h
1day
1mo
1yr
204°C
non-equil.
solid solution
many small
precipitates
“aged”
fewer large
“overaged”
149°C
Adapted from Fig (a) and (b), Callister & Rethwisch 3e. (Fig adapted from Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, p. 41.)

31. Melting & Glass Transition Temps.
What factors affect Tm and Tg?
Both Tm and Tg increase with increasing chain stiffness
Chain stiffness increased by presence of
Bulky sidegroups
Polar groups or sidegroups
Chain double bonds and aromatic chain groups
Regularity of repeat unit arrangements – affects Tm only
Adapted from Fig , Callister & Rethwisch 3e. 31 31

32. Thermoplastics vs. Thermosets
Callister,
Fig. 16.9 T
Molecular weight Tg Tm
mobile
liquid
viscous
rubber
tough
plastic
partially
crystalline
solid
• Thermoplastics:
-- little crosslinking
-- ductile
-- soften w/heating
-- polyethylene
polypropylene
polycarbonate
polystyrene
• Thermosets:
-- significant crosslinking
(10 to 50% of repeat units)
-- hard and brittle
-- do NOT soften w/heating
-- vulcanized rubber, epoxies,
polyester resin, phenolic resin
Adapted from Fig , Callister & Rethwisch 3e. (Fig is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.) 32 32

33. Summary
• Heat treatments of Fe-C alloys produce microstructures including:
-- pearlite, bainite, spheroidite, martensite, tempered martensite
• Precipitation hardening
--hardening, strengthening due to formation of
precipitate particles.
--Al, Mg alloys precipitation hardenable.
• Polymer melting and glass transition temperatures

34. ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems: