Chapter 11:
Phase Transformations
ISSUES TO ADDRESS...
• ____________ 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 ________________ depend on
time and temperature?
• Is it possible to slow down transformations so that
non-equilibrium _________________ are formed?
• Are the mechanical properties of non-equilibrium
structures more desirable than ___________ ones?
Chapter 11 - 1
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
– ___________ (eutectic, eutectoid)
– ___________ (peritectic)
Small supercooling  ________________ - few nuclei - ____ crystals
Large supercooling  ________________ - many nuclei - ____ crystals
Chapter 11 - 2
Solidification: Nucleation Types
• Homogeneous nucleation
– nuclei form in the bulk of liquid _______
– requires considerable _____________
(typically 80-300°C)
• _________________ nucleation
– much easier since ______ “nucleating surface” is
already present—e.g., mold wall, impurities in
liquid phase
– only very slight _____________ (0.1-10ºC)
Chapter 11 - 3
Homogeneous Nucleation & Energy Effects
Surface Free Energy - ___________
the nuclei (it takes energy to make
an _____________)
DGS = 4pr 2 g
g = surface _____________
GT = Total ______________
= GS + GV
Volume (Bulk) Free Energy –
________ the ______ (releases energy)
4
DGV = pr 3 DGu
3
DGu =
volume free energy
unit volume
r* = critical nucleus: for r < r* nuclei ______; for r >r* nuclei grow (to reduce energy)
Adapted from Fig.11.2(b), Callister & Rethwisch 4e.
Chapter 11 - 4
Solidification
- 2gTm
r* =
DHf DT
r* = critical radius
g = surface free energy
Tm = melting temperature
Hf = latent heat of _____________
T = Tm - T = supercooling
Note: Hf and g are ___________ dependent on T

r*
_____________ as T increases
For typical T
r* ~ 10 nm
Chapter 11 - 5
Rate of Phase Transformations
Kinetics - study of reaction rates of phase
transformations
• To determine reaction rate – measure degree
of ______________ as function of time (while
holding temp constant)
How is degree of ___________ measured?
____________ – many specimens required
electrical conductivity measurements –
on ________ specimen
measure __________ of sound waves –
on single specimen
Chapter 11 - 6
Fraction transformed, y
Rate of Phase Transformation
____________________
Fixed T
__________ rate reached – now amount
unconverted __________ so rate slows
0.5
t0.5
rate ________ as surface area increases
& nuclei _________
log t
Avrami equation => y = 1- exp (-kt n)
fraction
transformed
Adapted from
Fig. 11.10,
Callister &
Rethwisch 4e.
time
– k & n are ____________ specific parameters
By convention
rate = 1 / t0.5
Chapter 11 - 7
Temperature Dependence of
Transformation Rate
135C 119C
1
10
113C 102C
102
88C
43C
104
Adapted from Fig.
11.11, Callister &
Rethwisch 4e.
(Fig. 11.11 adapted
from B.F. Decker and
D. Harker,
"Recrystallization in
Rolled Copper", Trans
AIME, 188, 1950, p.
888.)
• For the ________________ of Cu, since
rate = 1/t0.5
rate _________ with ___________ temperature
• Rate often so ______ that attainment of ___________
state not possible!
Chapter 11 - 8
Transformations & Undercooling
g  a + Fe3C
• _________ transf. (Fe-Fe3C system):
0.76 wt% C
6.7 wt% C
• For transf. to occur, must
0.022 wt% C
cool to below ________
(i.e., must “_________”)
T(ºC)
1600
d
1200
L+Fe3C
1148ºC
1000
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727ºC
400
0
(Fe)
T
a +Fe3C
Undercooling by Ttransf. < 727C
0.76
600
0.022
a
ferrite
g +L
g
(austenite)
1
2
3
4
5
6
Fe3C (cementite)
L
1400
Adapted from Fig.
10.28,Callister & Rethwisch
4e. (Fig. 10.28 adapted from
Binary Alloy Phase
Diagrams, 2nd ed., Vol. 1,
T.B. Massalski (Ed.-inChief), ASM International,
Materials Park, OH, 1990.)
6.7
C, wt%C
Chapter 11 - 9
The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from
Fig. 10.15,
Callister &
Rethwisch 4e.
a
a
g a
a
a
a
g
• For this transformation,
cementite (Fe3C)
Ferrite (a)
rate ___________ with
___________________.
a
g
pearlite
growth
direction
a
a
100
y (% pearlite)
Austenite (g)
grain
boundary
Diffusion of C
during transformation
600ºC
(T larger)
50
0
650ºC
675ºC
(T smaller)
g
Carbon
diffusion
Adapted from
Fig. 11.12,
Callister &
Rethwisch 4e.
Coarse _______  formed at higher temperatures – relatively _____
Fine ________  formed at lower temperatures – relatively ______
Chapter 11 - 10
Generation of Isothermal Transformation
Diagrams
Consider:
y,
% transformed
• The Fe-Fe3C system, for Co = _____ wt% C
• A transformation temperature of ________.
100
T = 675ºC
50
0
10 2
1
T(ºC)
Austenite (stable)
10 4
time (s)
TE (727ºC)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675ºC
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
Adapted from Fig. 11.13,Callister &
Rethwisch 4e. (Fig. 11.13 adapted from H.
Boyer (Ed.) Atlas of Isothermal
Transformation and Cooling
Transformation Diagrams, American
Society for Metals, 1977, p. 369.)
Chapter 11 - 11
Austenite-to-Pearlite Isothermal Transformation
•
•
•
•
Eutectoid composition, Co = 0.76 wt% C
Begin at T > ________
Rapidly ___________________
Hold T (625°C) ___________ (__________ treatment)
T(ºC)
Austenite (stable)
700
Austenite
(unstable)
600
g
g
500
TE (727ºC)
Pearlite
g
g
g
Adapted from Fig.
11.14,Callister &
Rethwisch 4e. (Fig. 11.14
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 11 - 12
Transformations Involving
Noneutectoid Compositions
Consider C0 = 1.13 wt% C
T(ºC)
T(ºC)
900
d
A
+
1200
C
A
+
P
a
P
L+Fe3C
(austenite)
1000
g +Fe3C
800
600
500
1
g +L
g
10
102
103
time (s)
Adapted from Fig. 11.16,
Callister & Rethwisch 4e.
104
T
400
0
(Fe)
0.76
600
A
TE (727ºC)
A
1.13
700
L
1400
0.022
800
1
727ºC
a +Fe3C
2
3
4
5
Adapted from Fig. 10.28,
Callister & Rethwisch 4e.
6
Fe3C (cementite)
1600
6.7
C, wt%C
Hypereutectoid composition – ___________ cementite
Chapter 11 - 13
Bainite: Another Fe-Fe3C
Transformation Product
• _________:
--elongated Fe3C _________ in
a-ferrite ________
--__________ controlled
• Isothermal Transf. ___________,
Co = 0.76 wt% C
800
Austenite (stable)
T(ºC)
A
5 mm
100% pearlite
100% bainite
400
B
A
a (ferrite)
TE
P
600
Fe3C
(cementite)
Adapted from Fig. 11.17, Callister &
Rethwisch 4e. (Fig. 11.17 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
Adapted from Fig. 11.18,
Callister & Rethwisch 4e.
105
time (s)
Chapter 11 - 14
Spheroidite: Another Microstructure
for the Fe-Fe3C System
a
--Fe3C particles within _______________ (ferrite)
• Spheroidite:
--formation requires ____________
--heat ____________________________ Fe3C
just below eutectoid for long times (cementite)
--driving force – reduction
of a-ferrite/Fe3C ___________ area
60 mm
Adapted from Fig. 11.19, Callister &
Rethwisch 4e. (Fig. 11.19 copyright
United States Steel Corporation,
1971.)
Chapter 11 - 15
Martensite: A Nonequilibrium
Transformation Product
• ___________:
Fe atom
sites
x
x
x
x
x
60 mm
-- g(FCC) to ____________ (BCT)
potential
C atom sites
x
Adapted from Fig. 11.21,
Callister & Rethwisch 4e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(ºC)
A
400
10-1
Adapted from Fig. 11.22, Callister &
Rethwisch 4e. (Fig. 11.22 courtesy
United States Steel Corporation.)
• g to ________ (M) transformation.
B
A
200
TE
P
600
Adapted from
Fig. 11.23,
Callister &
Rethwisch 4e.
Martensite needles
Austenite
0%
50%
90%
M+A
M+A
M+A
10
103
105
-- is rapid! (_______________)
-- % transf. depends only on __ to
which rapidly __________
time (s)
Chapter 11 - 16
Martensite Formation
g (FCC)
slow cooling
a (BCC) + Fe3C
quench
M (BCT)
_________
_________(M) – single phase
– has body centered tetragonal (BCT)
crystal structure
_________ transformation
BCT  few slip planes
BCT if C0 > 0.15 wt% C
 hard, brittle
Chapter 11 - 17
Phase Transformations of Alloys
Effect of adding other __________
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
reaction (and formation of
_________________)
Adapted from Fig. 11.24,
Callister & Rethwisch 4e.
Chapter 11 - 18
Continuous Cooling
Transformation Diagrams
Conversion of isothermal
_____________________
continuous cooling
_____________________
Adapted from Fig. 11.26,
Callister & Rethwisch 4e.
Cooling curve
Chapter 11 - 19
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:
a) 42% proeutectoid ferrite and 58% coarse
pearlite
b) 50% fine pearlite and 50% bainite
c) 100% martensite
d) 50% martensite and 50% austenite
Chapter 11 - 20
Solution to Part (a) of Example
Problem
a) 42% proeutectoid ferrite and 58% coarse pearlite
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
Isothermally treat at _______
800
A
-- all __________ transformsT (ºC)
to proeutectoid a and
coarse pearlite.
600
Wpearlite
Co - 0.022
=
0.76 - 0.022
A+a
P
B
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
Wa = 1 - 0.58 = _____
Adapted from Fig. 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 21
Solution to Part (b) of Example
Problem
b) 50% fine pearlite and 50% bainite
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
800
Isothermally treat at ~590°C T (ºC)
– __________________________
to fine pearlite.
A
P
B
600
Then _________________ treat
at ~470°C
400
– all remaining _____________
transforms to __________.
A+a
A+P
A+B
A
50%
M (start)
M (50%)
M (90%)
200
Adapted from Fig. 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 22
Solutions to Parts (c) & (d) of Example
Problem
c) 100% __________ – rapidly quench to ______
Fe-Fe3C phase diagram,
_____________
for C0 = 0.45 wt% C
d) 50% _________ 800
T (ºC)
& 50% _________
-- rapidly quench to
__________, hold at this
temperature
A
A+a
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
c)
Adapted from Fig. 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 23
Mechanical Props: Influence of C Content
Adapted from Fig. 10.34,
Callister & Rethwisch 4e.
TS(MPa)
1100
YS(MPa)
C0 < 0.76 wt% C
Hypoeutectoid
Hypo
Hyper
C0 > 0.76 wt% C
Hypereutectoid
Hypo
%EL
Adapted from Fig. 10.37,
Callister & Rethwisch 4e.
Hyper
80
100
900
hardness
40
700
50
500
0
0.5
1
wt% C
0
0
0.5
0.76
0
0.76
300
Impact energy (Izod, ft-lb)
Pearlite (med)
ferrite (soft)
__________ (med)
__________
(hard)
Adapted from Fig.
11.30, Callister &
Rethwisch 4e. (Fig.
11.30 based on data
from Metals
Handbook: Heat
Treating, Vol. 4, 9th
ed., V. Masseria
(Managing Ed.),
American Society for
Metals, 1981, p. 9.)
1
wt% C
• Increase C content: TS and YS increase, %EL decreases
Chapter 11 - 24
Mechanical Props: Fine Pearlite vs.
Coarse Pearlite vs. Spheroidite
Brinell hardness
320
Hyper
fine
pearlite
240
coarse
pearlite
spheroidite
160
80
0
• Hardness:
• %RA:
0.5
1
wt%C
90
Ductility (%RA)
Hypo
Hypo
spheroidite
60
coarse
pearlite
fine
pearlite
30
0
Hyper
0
_______________________
_______________________
0.5
1
wt%C
Adapted from Fig. 11.31, Callister &
Rethwisch 4e. (Fig. 11.31 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 11 - 25
Mechanical Props: Fine Pearlite vs.
Martensite
Brinell hardness
Hypo
600
Hyper
martensite
Adapted from Fig. 11.33, Callister
& Rethwisch 4e. (Fig. 11.33
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: ______________________.
Chapter 11 - 26
Tempered Martensite
Heat treat martensite to form tempered martensite
• tempered martensite ______ brittle than martensite
• tempering reduces internal stresses caused by _________
TS(MPa)
YS(MPa)
1800
Adapted from
Fig. 11.35,
1400
Callister &
Rethwisch 4e.
1200
(Fig. 11.35
adapted from
Fig. furnished 1000
courtesy of
Republic Steel
800
Corporation.)
200
TS
YS
60
50
%RA
40
30
%RA
400
9 mm
1600
Adapted from Fig.
11.34, Callister &
Rethwisch 4e. (Fig.
11.34 copyright by
United States Steel
Corporation, 1971.)
600
Tempering T (ºC)
• tempering produces extremely small Fe3C particles surrounded by a.
• tempering ___________ TS, YS but __________ %RA
Chapter 11 - 27
Summary of Possible Transformations
Austenite (g)
slow
cool
Bainite
Strength
(a + Fe3C layers + a
proeutectoid phase)
(a + elong. Fe3C particles)
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
rapid
quench
Martensite
(BCT phase
diffusionless
transformation)
reheat
Ductility
Pearlite
moderate
cool
Adapted from
Fig. 11.37,
Callister &
Rethwisch 4e.
Tempered
Martensite
(a + very fine
Fe3C particles)
Chapter 11 - 28
Precipitation Hardening
• Particles impede ___________ motion.
700
• Ex: Al-Cu system
T(ºC)
• Procedure:
600
a+L
a
L
CuAl2
q+L
--Pt A: _______________
A
500
(get a solid solution)
q
a+q
--Pt B: _______ to room temp.
400 C
(retain a solid solution)
--Pt C: ________ to nucleate 300
small q __________ within (Al) 0 B 10 20 30 40 50
wt% Cu
composition range
a phase.
• Other alloys that precipitation
harden: Temp.
• Cu-Be
• Cu-Sn
• Mg-Al
Adapted from Fig.
11.22, Callister &
Rethwisch 4e.
Pt A (sol’n heat treat)
available for precipitation hardening
Adapted from Fig. 11.43, Callister & Rethwisch 4e.
(Fig. 11.43 adapted from J.L. Murray, International
Metals Review 30, p.5, 1985.)
Pt C (precipitate q)
Pt B
Time
Chapter 11 - 29
Influence of Precipitation Heat
Treatment on TS, %EL
• 2014 Al Alloy:
400
300
200
100
149ºC
204ºC
1min
1h 1day 1mo 1yr
precipitation heat treat time
• ________ on %EL curves.
%EL (2 in sample)
tensile strength (MPa)
• ________ on TS curves.
• __________ T accelerates
process.
30
20
10
0
204°C
149°C
1min
1h 1day 1mo 1yr
precipitation heat treat time
Adapted from Fig. 11.46 (a) and (b), Callister & Rethwisch 4e. (Fig. 11.46 adapted from Metals
Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker Chapter 11 - 30
(Managing Ed.), American Society for Metals, 1979. p. 41.)
Melting & Glass Transition Temps.
What _______________________?
•
•
•
Both Tm and Tg _________ with
increasing chain stiffness
Chain stiffness ___________ by
presence of
1. Bulky sidegroups
2. Polar groups or sidegroups
3. Chain double bonds and
aromatic chain groups
_____________ of repeat unit
arrangements – affects Tm only
Adapted from Fig. 11.48,
Callister & Rethwisch 4e.
Chapter 11 - 31
Thermoplastics vs. Thermosets
• Thermoplastics:
-- little __________
-- ductile
-- soften w/heating
-- polyethylene
polypropylene
polycarbonate
polystyrene
• _____________:
T
viscous
liquid
mobile
liquid
Callister,
rubber
Fig. 16.9
tough
plastic
crystalline
solid
partially
crystalline
solid
Molecular weight
Adapted from Fig. 11.49, Callister & Rethwisch 4e. (Fig.
-- significant _____________ 11.49 is from F.W. Billmeyer, Jr., Textbook of Polymer
(10 to 50% of repeat units) Science, 3rd ed., John Wiley and Sons, Inc., 1984.)
-- hard and brittle
-- do NOT soften w/heating
-- ____________ rubber, epoxies,
polyester resin, phenolic resin
Chapter 11 - 32
Tm
Tg
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
Chapter 11 - 33