Chapter 8:
Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
a
(BCC)
(ferrite)
• How does the rate of transformation depend on
time and T?
• How can we slow down the transformation so that
we can engineer non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?
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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)
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei,
small crystals
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Solidification: Nucleation
Processes
• Homogeneous nucleation
– nuclei form in the bulk of liquid metal
– requires supercooling (typically 80-300°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 0.1-10ºC
supercooling
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Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
GS  4r 2 g
g = surface tension
GT = Total Free Energy
= GS + GV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4
GV  r 3 G
3
G 
volume free energy
unit volume
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
From Fig.8.2(b)
Callister’s Materials Science and Engineering, Adapted Version.
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Solidification
 2gTm
r* 
HS T
r* = critical radius
g = surface free energy
Tm = melting temperature
HS = latent heat of solidification
T = Tm - T = supercooling
Note: HS = strong function of T
g
= weak function of T

r*
decreases as T increases
For typical T
r* ca. 100Å
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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
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Fraction transformed, y
Rate of Phase Transformation
All out of material - done
Fixed T
maximum rate reached – now amount
unconverted decreases so rate slows
0.5
t0.5
rate increases as surface area increases
& nuclei grow
log t
From Fig. 8.10,
Callister’s Materials Science
and Engineering,
Adapted Version.
Avrami rate equation => y = 1- exp (-ktn)
fraction
transformed
time
– k & n fit for specific sample
By convention
r = 1 / t0.5
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Rate of Phase Transformations
135C 119C
1
113C 102C
88C
43C
102
10
104
From Fig. 8.11,
Callister’s Materials
Science and
Engineering,
Adapted Version.
(Fig. 8.11 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!
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Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from
Fig. 9.15,
Callister 7e.
a
a
g a
a
a
a
• Recrystallization
rate increases
with T.
g
cementite (Fe3C)
Ferrite (a)
a
g
pearlite
growth
direction
a
g
a
100
y (% pearlite)
Austenite (g)
grain
boundary
Diffusive flow
of C needed
600°C
(T larger)
50
650°C
675°C
(T smaller)
0
From Fig. 8.12,
Callister’s
Materials
Science and
Engineering,
Adapted
Version.
Course pearlite  formed at higher T - softer
Fine pearlite
 formed at low T - harder
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Nucleation and Growth
• Reaction rate is a result of nucleation and growth
of crystals.
100
% Pearlite
Nucleation rate increases with T
Growth
regime
50 Nucleation
regime
0
t 0.5
Growth rate increases with T
log (time)
• Examples:
g
pearlite
colony
T just below TE
Nucleation rate low
Growth rate high
From Fig. 8.10
Callister’s Materials Science and Engineering,
Adapted Version.
g
g
T moderately below TE
Nucleation rate med .
Growth rate med.
T way below TE
Nucleation rate high
Growth rate low
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Transformations & Undercooling
g  a + Fe3C
• Eutectoid transf. (Fe-C System):
• Can make it occur at:
0.76 wt% C
6.7 wt% C
0.022 wt% C
...727ºC (cool it slowly)
...below 727ºC (“undercool” it!)
T(°C)
1600
d
g +L
g
1200
(austenite)
1000
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727°C
400
0
(Fe)
T
a +Fe3C
Undercooling by Ttransf. < 727C
0.76
600
0.022
a
ferrite
L+Fe3C
1148°C
1
2
3
4
5
6
Fe3C (cementite)
L
1400
From Fig. 7.24
Callister’s Materials Science
and Engineering,
Adapted Version.
(Fig. 7.24 adapted from
Binary Alloy Phase
Diagrams, 2nd ed., Vol. 1,
T.B. Massalski (Ed.-inChief), ASM International,
Materials Park, OH, 1990.)
6.7
Co , wt%C
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Isothermal Transformation Diagrams
y,
% transformed
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
T = 675°C
50
0
10 2
1
T(°C)
Austenite (stable)
10 4
time (s)
TE (727C)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675°C
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
From Fig. 8.13
Callister’s Materials Science and
Engineering,
Adapted Version
(Fig. 8.13 adapted from H. Boyer (Ed.)
Atlas of Isothermal Transformation and
Cooling Transformation Diagrams,
American Society for Metals, 1977, p.
369.)
BITS Pilani, Hyderabad Campus
12
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.
T(°C)
Austenite (stable)
700
600
TE (727C)
Austenite
(unstable)
g
g
500
Pearlite
g
g
g
From Fig. 8.14
Callister’s Materials
Science and Engineering,
Adapted Version.
(Fig. 8.14 adapted from H.
Boyer (Ed.) Atlas of
Isothermal Transformation
and Cooling
Transformation Diagrams,
American Society for
Metals, 1997, p. 28.)
g
400
1
10
10 2
10 3
10 4
10 5
time (s)
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Transformations with
Proeutectoid Materials
CO = 1.13 wt% C
T(°C)
T(°C)
900
d
A
+
C
A
+
P
a
P
g +L
L+Fe3C
(austenite)
1000
g +Fe3C
800
600
500
1
g
10
102
103
time (s)
From Fig. 8.16
Callister’s Materials Science
and Engineering,
Adapted Version.
104
T
400
0
(Fe)
0.76
600
A
1200
1
1.13
700
TE (727°C)
A
L
1400
0.022
800
727°C
a +Fe3C
2
3
4
5
From Fig. 7.24
Callister’s Materials Science
and Engineering,
Adapted Version.
6
Fe3C (cementite)
1600
6.7
Co , wt%C
Hypereutectoid composition – proeutectoid cementite
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Non-Equilibrium Transformation Products: Fe-C
• Bainite:
--a lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
100% pearlite
pearlite/bainite boundary
100% bainite
400
B
A
200
10-1
10
103
a (ferrite)
TE
P
600
Fe3C
(cementite)
5 mm
From Fig. 8.17
Callister’s Materials Science and Engineering,
Adapted Version.
(Fig. 8.17 from Metals Handbook, 8th ed.,
Vol. 8, Metallography, Structures, and Phase
Diagrams, American Society for Metals,
Materials Park, OH, 1973.)
105
time (s)
From Fig. 8.18, Callister’s Materials Science and Engineering, Adapted Version.
(Fig. 8.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling
Transformation Diagrams, American Society for Metals, 1997, p. 28.)
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Spheroidite: Fe-C System
• Spheroidite:
a
(ferrite)
--a grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
Fe3C
--reduces interfacial area (driving force) (cementite)
60 mm
From Fig. 8.19
Callister’s Materials Science and
Engineering, Adapted Version.
(Fig. 8.19 copyright United States
Steel Corporation, 1971.)
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Martensite: Fe-C System
• Martensite:
--g(FCC) to Martensite (BCT)
Fe atom
sites
x
x
x
potential
C atom sites
x
x
x
From Fig. 8.20, Callister’s MSE,
Adapted Version.
60 mm
(involves single atom jumps)
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
P
600
From Fig.
8.22
Callister’s
Materials
Science and
Engineering,
Adapted
Version.
400
200
10-1
TE
B
A
From Fig. 8.21, Callister’s Materials Science and
Engineering, Adapted Version.
(Fig. 8.21 courtesy United States Steel
Corporation.)
• g to M transformation..
0%
50%
90%
M+A
M+A
M+A
10
Martensite needles
Austenite
103
105
-- is rapid!
-- % transf. depends on T only.
time (s)
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Martensite Formation
slow cooling
g (FCC)
a (BCC) + Fe3C
quench
M (BCT)
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation
BCT  few slip planes
BCT if C > 0.15 wt%
 hard, brittle
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Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
transformation
From Fig. 8.23
Callister’s Materials Science and Engineering,
Adapted Version.
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Cooling Curve
plot temp vs. time
From Fig. 8.25,
Callister’s
Materials Science
and Engineering,
Adapted Version.
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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:
a) 42% proeutectoid ferrite and 58% coarse
pearlite
b) 50% fine pearlite and 50% bainite
c) 100% martensite
d) 50% martensite and 50% austenite
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Example Problem for Co = 0.45 wt%
a) 42% proeutectoid ferrite and 58% coarse pearlite
first make ferrite
then pearlite
800
A
T (°C)
P
B
600
course pearlite
 higher T
A+a
A+B
A
400
A+P
50%
M (start)
M (50%)
M (90%)
200
From Fig.
10.29,
Callister 5e.
0
0.1
10
103
time (s)
22
105
BITS Pilani, Hyderabad Campus
Example Problem for Co = 0.45 wt%
b) 50% fine pearlite and 50% bainite
800
first make pearlite
then bainite
A
T (°C)
A+a
P
B
600
A+B
A
fine pearlite
400
 lower T
A+P
50%
M (start)
M (50%)
M (90%)
200
Adapted from
Fig. 10.29,
Callister 5e.
0
0.1
10
103
time (s)
23
105
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Example Problem for Co = 0.45 wt%
c) 100 % martensite – quench = rapid cool
d) 50 % martensite
800
A+a
and 50 %
A
T (°C)
austenite
P
B
600
A+B
A
400
A+P
50%
M (start)
M (50%)
M (90%)
d)
200
Adapted from
Fig. 10.29,
Callister 5e.
c)
0
0.1
10
103
time (s)
24
105
BITS Pilani, Hyderabad Campus
Mechanical Prop: Fe-C System (1)
• Effect of wt% C
Adapted from Fig. 9.30,Callister
7e. (Fig. 9.30 courtesy Republic
Steel Corporation.)
TS(MPa)
1100
YS(MPa)
Co < 0.76 wt% C
Hypoeutectoid
Hypo
Hyper
Co > 0.76 wt% C
Hypereutectoid
%EL
Hypo
From Fig. 7.33, Callister’s Materials
Science and Engineering,
Adapted Version.
(Fig. 7.33 copyright 1971 by United
States Steel Corporation.)
Hyper
80
100
900
hardness
40
700
50
500
0
0.5
1
0
0.76
0
0.76
300
Impact energy (Izod, ft-lb)
Pearlite (med)
ferrite (soft)
Pearlite (med)
Cementite
(hard)
1
0.5
0
wt% C
wt% C
• More wt% C: TS and YS increase, %EL decreases.
25
From Fig. 8.29,
Callister’s Materials
Science and
Engineering,
Adapted Version.
(Fig. 8.29 based on
data from Metals
Handbook: Heat
Treating, Vol. 4, 9th
ed., V. Masseria
(Managing Ed.),
American Society for
Metals, 1981, p. 9.)
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Mechanical Prop: Fe-C System (2)
• Fine vs coarse pearlite vs spheroidite
Hypo
Hyper
90
Hypo
Hyper
fine
pearlite
240
160
coarse
pearlite
spheroidite
80
0
• Hardness:
• %RA:
0.5
1
wt%C
Ductility (%AR)
Brinell hardness
320
spheroidite
60
coarse
pearlite
fine
pearlite
30
0
0
fine > coarse > spheroidite
fine < coarse < spheroidite
0.5
1
wt%C
From Fig. 8.30
Callister’s Materials Science and
Engineering,
Adapted Version.
(Fig. 8.30 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.)
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Mechanical Prop: Fe-C System (3)
• Fine Pearlite vs Martensite:
Brinell hardness
Hypo
600
Hyper
From Fig. 10.32
Callister’s Materials Science and
Engineering,
Adapted Version.
(Fig. 8.32 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. 1776.)
martensite
400
200
0
fine pearlite
0
0.5
1
wt% C
• Hardness: fine pearlite << martensite.
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Tempering Martensite
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
TS(MPa)
YS(MPa)
1800
From Fig. 8.34,
1400
Callister’s
Materials
Science and 1200
Engineering,
Adapted Version.
1000
(Fig. 8.34
adapted from
Fig. furnished 800
courtesy of
Republic Steel
200
Corporation.)
TS
YS
60
50
%RA
40
30
%RA
400
From Fig. 8.33,
Callister’s
Materials
Science and
Engineering,
Adapted Version.
(Fig. 8.33
copyright by
United States
Steel
Corporation,
1971.)
9 mm
1600
600
Tempering T(°C)
• produces extremely small Fe3C particles surrounded by a.
• decreases TS, YS but increases %RA
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Summary: Processing Options
From Fig. 8.36,
Callister’s Materials
Science and
Engineering,
Adapted Version.
Austenite (g)
slow
cool
Bainite
(a + Fe3C layers + a
proeutectoid phase)
Strength
rapid
quench
Martensite
(a + Fe3C plates/needles)
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
(BCT phase
diffusionless
transformation)
reheat
Ductility
Pearlite
moderate
cool
Tempered
Martensite
(a + very fine
Fe3C particles)
General Trends
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