Chapter 10:
Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (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 engineer non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?
Chapter 10 - 1
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)
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei,
small crystals
Chapter 10 - 2
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
Chapter 10 - 3
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)
Adapted from Fig.10.2(b), Callister 7e.
Chapter 10 - 4
Solidification
 2 gTm
r* 
H S 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
Chapter 10 - 5
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
Chapter 10 - 6
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
Avrami rate equation => y = 1- exp (-ktn)
fraction
transformed
Adapted from
Fig. 10.10,
Callister 7e.
time
– k & n fit for specific sample
By convention
r = 1 / t0.5
Chapter 10 - 7
Rate of Phase Transformations
135C 119C
1
10
113C 102C
88C
102
43C
Adapted from Fig.
10.11, Callister 7e.
(Fig. 10.11 adapted
from B.F. Decker and
D. Harker,
"Recrystallization in
Rolled Copper", Trans
AIME, 188, 1950, p.
888.)
104
• 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!
Chapter 10 - 8
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
a
pearlite
growth
direction
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)
Adapted from
Fig. 10.12,
Callister 7e.
0
Course pearlite  formed at higher T - softer
Fine pearlite
 formed at low T - harder
Chapter 10 - 9
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
Growth rate increases with T
regime
t 0.5
0
log (time)
Adapted from
Fig. 10.10, Callister 7e.
• Examples:
g
pearlite
colony
T just below TE
Nucleation rate low
Growth rate high
g
T moderately below TE
Nucleation rate med .
Growth rate med.
g
T way below TE
Nucleation rate high
Growth rate low
Chapter 10 - 10
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
Adapted from Fig.
9.24,Callister 7e. (Fig. 9.24
adapted from Binary Alloy
Phase Diagrams, 2nd ed.,
Vol. 1, T.B. Massalski (Ed.in-Chief), ASM International,
Materials Park, OH, 1990.)
6.7
Co , wt%C
Chapter 10 - 11
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
Adapted from Fig. 10.13,Callister 7e.
(Fig. 10.13 adapted from H. Boyer (Ed.)
Atlas of Isothermal Transformation and
Cooling Transformation Diagrams,
American Society for Metals, 1977, p.
369.)
time (s)
Chapter 10 - 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
Austenite
(unstable)
600
g
g
500
TE (727C)
Pearlite
g
g
g
Adapted from Fig.
10.14,Callister 7e.
(Fig. 10.14 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)
Chapter 10 - 13
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
a (ferrite)
TE
P
600
5 mm
100% pearlite
pearlite/bainite boundary
100% bainite
400
Fe3C
(cementite)
B
A
(Adapted from Fig. 10.17, Callister, 7e. (Fig.
10.17 from Metals Handbook, 8th ed.,
Vol. 8, Metallography, Structures, and Phase
Diagrams, American Society for Metals,
Materials Park, OH, 1973.)
200
10-1
10
103
105
time (s)
Adapted from Fig. 10.18, Callister 7e.
(Fig. 10.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling
Transformation Diagrams, American Society for Metals, 1997, p. 28.)
Chapter 10 - 14
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
(Adapted from Fig. 10.19, Callister, 7e.
(Fig. 10.19 copyright United States
Steel Corporation, 1971.)
Chapter 10 - 15
Martensite: Fe-C System
• Martensite:
--g(FCC) to Martensite (BCT)
Fe atom
sites
x
x
x
x
x
60 mm
(involves single atom jumps)
potential
C atom sites
x
(Adapted from Fig.
10.20, Callister, 7e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
400
10-1
(Adapted from Fig. 10.21, Callister, 7e.
(Fig. 10.21 courtesy United States
Steel Corporation.)
• g to M transformation..
B
A
200
TE
P
600
Adapted from
Fig. 10.22,
Callister 7e.
Martensite needles
Austenite
0%
50%
90%
M+A
M+A
M+A
10
103
105
-- is rapid!
-- % transf. depends on T only.
time (s)
Chapter 10 - 16
Martensite Formation
g (FCC)
slow cooling
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
Chapter 10 - 17
Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
transformation
Adapted from Fig. 10.23, Callister 7e.
Chapter 10 - 18
Cooling Curve
plot temp vs. time
Adapted from
Fig. 10.25,
Callister 7e.
Chapter 10 - 19
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) 50% fine pearlite and 50% bainite
b) 100% martensite
c) 50% martensite and 50% austenite
Chapter 10 - 20
Example Problem for Co = 0.45 wt%
a) 50% fine pearlite and 50% bainite
800
first make pearlite
T (°C)
then bainite
A
P
B
600
fine pearlite
 lower T
A+a
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
Adapted from
Fig. 10.29,
Callister 5e.
0
0.1
10
103
time (s)
105
Chapter 10 - 21
Example Problem for Co = 0.45 wt%
b) 100 % martensite – quench = rapid cool
c) 50 % martensite
800
A+a
and 50 %
A
T (°C)
austenite
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
Adapted from
Fig. 10.29,
Callister 5e.
c)
0
0.1
10
103
time (s)
105
Chapter 10 - 22
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 Adapted from Fig. 9.33,Callister 7e.
9.33 copyright 1971 by United
Hypereutectoid (Fig.
States Steel Corporation.)
%EL
Hypo
Hyper
80
100
900
hardness
40
700
50
500
0
0.5
1
0
Adapted from Fig.
10.29, Callister 7e.
(Fig. 10.29 based on
data from Metals
Handbook: Heat
Treating, Vol. 4, 9th
ed., V. Masseria
(Managing Ed.),
American Society for
Metals, 1981, p. 9.)
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.
Chapter 10 - 23
Mechanical Prop: Fe-C System (2)
• Fine vs coarse pearlite vs spheroidite
Hypo
Hyper
90
Hypo
Hyper
fine
pearlite
240
coarse
pearlite
spheroidite
160
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
Adapted from Fig. 10.30, Callister 7e.
(Fig. 10.30 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.)
Chapter 10 - 24
Mechanical Prop: Fe-C System (3)
• Fine Pearlite vs Martensite:
Brinell hardness
Hypo
600
Hyper
martensite
Adapted from Fig. 10.32,
Callister 7e. (Fig. 10.32 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.)
400
200
fine pearlite
0
0
0.5
1
wt% C
• Hardness: fine pearlite << martensite.
Chapter 10 - 25
Tempering Martensite
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
TS(MPa)
YS(MPa)
1800
Adapted from
1400
Fig. 10.34,
Callister 7e.
(Fig. 10.34
1200
adapted from
Fig. furnished
1000
courtesy of
Republic Steel
Corporation.)
800
200
TS
YS
60
50
%RA
40
30
%RA
400
9 mm
1600
Adapted from
Fig. 10.33,
Callister 7e.
(Fig. 10.33
copyright by
United States
Steel
Corporation,
1971.)
600
Tempering T (°C)
• produces extremely small Fe3C particles surrounded by a.
• decreases TS, YS but increases %RA
Chapter 10 - 26
Summary: Processing Options
Austenite (g)
slow
cool
moderate
cool
Adapted from
Fig. 10.36,
Callister 7e.
rapid
quench
Bainite
Martensite
(a + Fe3C layers + a
proeutectoid phase)
(a + Fe3C plates/needles)
(BCT phase
diffusionless
transformation)
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
reheat
Ductility
Strength
Pearlite
Tempered
Martensite
(a + very fine
Fe3C particles)
Chapter 10 - 27
ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems:
Chapter 10 - 28