1. Chapter 10: Phase Transformations – adding Time to Phase Diagrams
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
• 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? Fe g
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(cementite) a
(ferrite) +
(BCC)

2. 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, the “seed” must grow until they reach equilibrium

3. Phase Transformations
Driving force to nucleate increases as we increase T
supercooling (eutectic, eutectoid)
superheating (peritectic)
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei, small crystals
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

4. 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

5. 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: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Adapted from Fig.10.2(b), Callister 7e.

6. Solidification Note: HS = strong function of T
 = weak function of T
HS = latent heat of solidification
Tm = melting temperature
g = surface free energy
DT = Tm - T = supercooling
r* = critical radius
 r* decreases as T increases
For typical T r* ca. 100Å (10 nm)

7. Rate of Phase Transformations
Kinetics - measures 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 (ultrasonic insitu) – one sample

8. Rate of Phase Transformation
All out of material – “done!”
Fixed Temp.
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as surface area increases & nuclei grow
Log Time
t0.5
Adapted from Fig ,
Callister 7e.
Modeled by the Avrami Rate Equation:
S.A. = surface area

9. Avrami Equation Avrami rate equation => y = 1- exp (-ktn)
k & n are fit for specific sample
By convention we define: r = 1 / t as the rate which is defined as the inverse of the time to complete half of the transformation
The initial slow rate can be attributed to the time required for a significant number of nuclei of the new phase to form and begin growing.
During the intermediate period the transformation is rapid as the nuclei grow into particles and consume the old phase while nuclei continue to form in the remaining parent phase.
Once the transformation begins to near completion there is little untransformed material for nuclei to form in and the production of new particles begins to slow. Further, the articles already existing begin to touch one another, forming a boundary where growth stops.

10. 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’ rate factor
Q = activation energy
r is often small so equilibrium is not possible!
Arrhenius expression

11. 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.)

12. 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

13. 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

14. 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.)

15. 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

16. 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

17. 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.)

18. TTT Curves showing the Bainite Transformation (a) Plain Carbon Steels; (b) Alloy Steel w/ distinct Bainite “Nose”
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

19. 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 (below the AC1 critical temperature)
--driven by a reduction in interfacial area of Carbide

20. 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.

22. Transformation to Martensite
Martensite formation requires that the steel be subject to a minimum – Critical – Cooling Rate (this value is ‘ITT’ or ‘CCT’ chart dependent for alloy of interest)
For most alloys it indicates a quench into a RT oil or water bath

23. 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

24. Martensite Transformation Crystallography: FCC Austenite to BCT Martensite
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

25. Austenite to Martensite: Size Issues and Material Response
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

26. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard    + Fe3C
transformation delaying the time to entering the diffusion controlled transformation reactions – thus promoting “Hardenability’ or Martensite development
Adapted from Fig , Callister 7e.

27. Continuous Cooling Transformations (CCT)
Isothermal Transformations are “Costly” requiring careful “gymnastics” with heated (and cooling) products
CC Transformations change the observed behavior concerning transformation
With Plain Carbon Steels when cooled “continuously” we find that the Bainite Transformation is suppress(see Figure 10.26)

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

29. CCT for Eutectoid Steel
Figure: 10-26

30. CCT for Eutectoid Steel
f10_27_pg338.jpg

31. Alloy Steel CCT Curve – note distinct Bainite Nose
Adapted from Fig , Callister 7e.

32. 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

33. Example Problem for Co = 0.45 wt%
42% proeutectoid ferrite and 58% coarse pearlite
first make ferrite
then pearlite
coarse 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.

34. 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)
NOTE: This “2nd step” is sometimes referred to as an “Austempering” step, quenching into a heated salt bath held at the temperature of need
Adapted from Fig , Callister 5e.

35. Example Problem for Co = 0.45 wt%
100 % martensite: 240C/s d)
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)
50%martensite/50%(retained) austenite
Adapted from Fig , Callister 5e.

36. CT for CrMo Med-carbon steel
Hardness of cooled samples at various cooling rates in bubbles -- Dashed lines are IT solid lines are CT regions

37. 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.

38. 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

39. 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.

40. 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

41. Temper Martensite Embrittlement – an issue in Certain Steels
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.
Suspected to be due to the deposition of very fine carbides during 2nd and 3rd phase tempering along original austenite G. B. from the transformation of retained austenite,

42. 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.