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 T ?
• How can we slow down the transformation so that
we can engineering non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?

2. Kinetics : the science of time-dependent phase
transformations
TTT diagram : temperature, time and transformation
◈ Time-the third dimension
The time required for a liquid phase to transform to the solid phase is a strong function of temperature.

3. To understand the “ knee-shaped” transformation curve, some fundamental concepts of kinetics theory are needed
핵의 생성(nucleation)
homogeneous nucleation : the precipitation occurs within
a completely homogeneous medium
heterogeneous nucleation : the precipitation occurs at
some structural imperfection

4. Classical nucleation theory
Total change in energy

5. critical radius for homogeneous nucleation
The rate of nucleation
① The driving force for solidification increases with decreasing temperature, and the rate of nucleation increases sharply.
② The clustering of atoms to form a nucleus decrease in rate with decreasing temperature (diffusion)
③ The overall nucleation rate reflects these two factors
(① & ②)

6. The growth rate (핵의 성장)

7. -The overall transformation rate : product of

8. ◈ The TTT Diagram
- Temperature, time, and transformation

9. Phase Transformations
Nucleation
nuclei (seeds) act as template to grow crystals
for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss
once nucleated, grow until reach equilibrium
Driving force to nucleate increases as we increase T
supercooling (eutectic, eutectoid)
superheating (peritectic)
In Chapter 9 we looked at the equilibrium phase diagram . This indicated phase structure if we wait long enough. But due to slow diffusion may not reach equilibrium We need to consider time- kinetics - energy of phase boundaries may be high. – also nucleation
Transformation rate
How fast do the phase transformations occur?
First need nuclei (seeds) to form for the rest of the material to crystallize
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei,
small crystals

10. Solidification: Nucleation Processes
Homogeneous nucleation
nuclei form in the bulk of liquid metal
requires supercooling (typically °C max)
Heterogeneous nucleation
much easier since stable “nucleus” is already present
Could be wall of mold or impurities in the liquid phase
allows solidification with only ºC supercooling

11. Solidification Note: HS = strong function of T
HS = latent heat of solidification
Tm = melting temperature
g = surface free energy
DT = Tm - T = supercooling
r* = critical radius
Note: HS = strong function of T
 = weak function of T
 r* decreases as T increases

12. Rate of Phase Transformations
Kinetics - measure approach to equilibrium vs. time
Hold temperature constant & measure conversion vs. time
How is conversion measured?
X-ray diffraction – have to do many samples
electrical conductivity – follow one sample
sound waves – one sample

13. Rate of Phase Transformation
All out of material - done
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 7e.
Avrami rate equation => y = 1- exp (-ktn)
k & n fit for specific sample
S.A. = surface area
fraction transformed
time
By convention r = 1 / t0.5

14. Rate of Phase Transformations
135C
119C
113C
102C
88C
43C 1 10
102
104
Adapted from Fig , Callister 7e. (Fig adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)
In general, rate increases as T 
r = 1/t0.5 = A e -Q/RT
R = gas constant
T = temperature (K)
A = preexponential factor
Q = activation energy
Arrhenius expression
r often small: equilibrium not possible!

15. Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from Fig. 9.15, Callister 7e. g a
pearlite
growth
direction
Austenite (g)
grain
boundary
cementite (Fe3C)
Ferrite (a)
Diffusive flow
of C needed a g
• Recrystallization
rate increases
with DT.
Adapted from Fig , Callister 7e.
675°C
(DT smaller) 50
y (% pearlite)
600°C
(DT larger)
650°C
100
Course pearlite  formed at higher T - softer
Fine pearlite  formed at low T - harder

16. Nucleation and Growth
• Reaction rate is a result of nucleation and growth
of crystals.
% Pearlite 50
100
Nucleation
regime
Growth
log (time) t
0.5
Nucleation rate increases with T
Growth rate increases with T
Adapted from
Fig , Callister 7e.
• Examples:
T just below TE
Nucleation rate low
Growth rate high g
pearlite
colony
T moderately below TE g
Nucleation rate med .
Growth rate med.
Nucleation rate high
T way below TE g
Growth rate low

17. Transformations & Undercooling•
Eutectoid
transf. (Fe-C System): g Þ a +
Fe3C •
Can make it occur at:
0.76 wt% C
6.7 wt% C
...727ºC (cool it slowly)
0.022 wt% C
...below 727ºC (“undercool” it!)
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)
Co , wt%C
1148°C
T(°C)
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC DT
Undercooling by DTtransf. < 727C
0.76
0.022
Adapted from Fig. 9.24,Callister 7e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

18. Isothermal Transformation Diagrams
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 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 7e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

19. Effect of Cooling History in Fe-C System
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
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 7e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) g g

20. Transformations with Proeutectoid Materials
CO = 1.13 wt% C
TE (727°C)
T(°C)
time (s) A + C P 1 10
102
103
104
500
700
900
600
800
Adapted from Fig , Callister 7e.
Adapted from Fig. 9.24, Callister 7e.
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)
Co , wt%C
T(°C)
727°C DT
0.76
0.022
1.13
Hypereutectoid composition – proeutectoid cementite

21. Non-Equilibrium Transformation Products: Fe-C
• Bainite:
--a lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
Fe3C
(cementite) a
(ferrite) 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50%
pearlite/bainite boundary A
100% pearlite
100% bainite
5 mm
(Adapted from Fig , Callister, 7e. (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 7e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

22. Spheroidite: Fe-C System
(Adapted from Fig , Callister, 7e. (Fig copyright United States Steel Corporation, 1971.)
60 m a
(ferrite)
(cementite)
Fe3C
• Spheroidite:
--a grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force)

23. Martensite: Fe-C System
--g(FCC) to Martensite (BCT)
Martensite needles
Austenite
60 m x
potential
C atom sites
Fe atom
sites
(involves single atom jumps)
(Adapted from Fig , Callister, 7e.
• Isothermal Transf. Diagram 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, 7e. (Fig courtesy United States Steel Corporation.)
Adapted from Fig , Callister 7e.
• g to M transformation..
-- is rapid!
-- % transf. depends on T only.

24. Martensite Formation  (FCC)  (BCC) + Fe3C slow cooling quench
M (BCT)
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation BCT if C > 0.15 wt%
BCT  few slip planes  hard, brittle

25. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard    + Fe3C
transformation
Adapted from Fig , Callister 7e.

26. Cooling Curve plot temp vs. time
Actual processes involves cooling – not isothermal
Can’t cool at infinite speed
Adapted from Fig ,
Callister 7e.

27. Dynamic Phase Transformations
On the isothermal transformation diagram for 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

28. Example Problem for Co = 0.45 wt%
42% proeutectoid ferrite and 58% coarse pearlite
first make ferrite
then pearlite
course pearlite
 higher T
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%)
T (°C)
Adapted from Fig ,
Callister 5e.

29. Example Problem for Co = 0.45 wt%
50% fine pearlite and 50% bainite
first make pearlite
then bainite
fine pearlite
 lower T
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%)
T (°C)
Adapted from Fig ,
Callister 5e.

30. Example Problem for Co = 0.45 wt%
100 % martensite – quench = rapid cool
50 % martensite
and 50 % austenite
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%) c)
T (°C) d)
Adapted from Fig ,
Callister 5e.

31. Mechanical Prop: Fe-C System (1)
• Effect of wt% C
Pearlite (med)
Pearlite (med) C
ementite
ferrite (soft)
(hard)
Co < 0.76 wt% C
Co > 0.76 wt% C
Adapted from Fig. 9.30,Callister
7e. (Fig courtesy Republic Steel Corporation.)
Adapted from Fig. 9.33,Callister 7e. (Fig copyright 1971 by United States Steel Corporation.)
Hypoeutectoid
Hypereutectoid
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
Adapted from Fig , Callister 7e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)
• More wt% C: TS and YS increase
, %EL decreases.

32. Mechanical Prop: Fe-C System (2)
• Fine vs coarse pearlite vs spheroidite 80
160
240
320
wt%C
0.5 1
Brinell hardness
fine
pearlite
coarse
spheroidite
Hypo
Hyper 30 60 90
wt%C
Ductility (%AR)
fine
pearlite
coarse
spheroidite
Hypo
Hyper
0.5 1
Adapted from Fig , Callister 7e. (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

33. Mechanical Prop: Fe-C System (3)
• Fine Pearlite vs Martensite:
200
wt% C
0.5 1
400
600
Brinell hardness
martensite
fine pearlite
Hypo
Hyper
Adapted from Fig , Callister 7e. (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.

34. Tempering Martensite • • • reduces brittleness of martensite,
• reduces internal stress 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 7e. (Fig adapted from Fig. furnished courtesy of Republic Steel Corporation.)
Adapted from Fig , Callister 7e. (Fig copyright by United States Steel Corporation, 1971.)
9 mm
produces extremely small Fe3C particles surrounded by a. • •
decreases TS, YS but increases %RA

35. Summary: Processing Options
Austenite (g)
Bainite
(a + Fe3C plates/needles)
Pearlite
(a + Fe3C layers + a
proeutectoid phase)
Martensite
(BCT phase
diffusionless
transformation)
Tempered
(a + very fine
Fe3C particles)
slow
cool
moderate
rapid
quench
reheat
Strength
Ductility
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
Adapted from Fig , Callister 7e.

36. PRECIPITATION HARDENING
• Particles impede dislocations.
• Ex: Al-Cu system
• Procedure:
--Pt A: solution heat treat
(get a solid solution)
--Pt B: quench to room temp.
--Pt C: reheat to nucleate
small q crystals within
a crystals.
• Other precipitation
systems:
• Cu-Be
• Cu-Sn
• Mg-Al
Adapted from Fig , Callister 6e. (Fig adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)
Adapted from Fig , Callister 6e. 20

37. PRECIPITATE EFFECT ON TS, %EL
• 2014 Al Alloy:
• TS peaks with
precipitation time.
• Increasing T accelerates
process.
• %EL reaches minimum
with precipitation time.
Adapted from Fig (a) and (b), Callister 6e. (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.) 21

38. STRENGTHENING STRATEGY : PRECIPITATION STRENGTHENING
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
• Result: 24

39. APPLICATION: PRECIPITATION STRENGTHENING
• Internal wing structure on Boeing 767
Adapted from Fig. 11.0, Callister 5e.
(Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
• Aluminum is strengthened with precipitates formed
by alloying.
1.5mm
Adapted from Fig , Callister 6e.
(Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 26