This document summarizes key concepts about phase transformations from Chapter 10 of an materials science textbook. It discusses (1) how the rate of phase transformations depends on time and temperature, (2) different non-equilibrium structures that can form like bainite and martensite, and (3) how the mechanical properties vary for different phase structures and compositions. Examples of the iron-carbon phase diagram and transformations are analyzed in detail.

1. Chapter 10 - 1
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 engineer non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?
Fe
γ
(Austenite)
Eutectoid
transformation
C FCC
Fe3C
(cementite)
α
(ferrite)
+
(BCC)
Chapter 10:
Phase Transformations

2. Chapter 10 - 2
Phase Transformation and Structure
Processing
Structure Properties
Phase Transformation  Altering Structure
Changing Temperature (on phase diagram)

3. Chapter 10 - 3
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

4. Chapter 10 - 4
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

5. Chapter 10 - 5
Rate of Phase Transformations
Kinetics - measure approach to equilibrium vs. time
• Hold temperature constant
& measure conversion vs. time
sound waves – one sample
electrical conductivity – follow one sample
X-ray diffraction – have to do many samples
How is conversion measured?

6. Chapter 10 - 6
Rate of Phase Transformation
Avrami rate equation => y = 1- exp (-ktn
)
– k & n fit for specific sample (from experiments)
All out of material - done
log t
Fractiontransformed,y
Fixed T
fraction
transformed
time
0.5
By convention r = 1 / t0.5
maximum rate reached – now amount
unconverted decreases so rate slows
t0.5
rate increases as surface area increases
& nuclei grow

7. Chapter 10 - 7
Rate of Phase Transformations
• 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!
135°C 119°C 113°C 102°C 88°C 43°C
1 10 102
104
∆T
supercooling

8. Chapter 10 - 8
Eutectoid Transformation Rate
Course pearlite  formed at higher T - softer
Fine pearlite  formed at low T - harder
Diffusive flow
of C needed
α
α
γ
γ
α
• Growth of pearlite from austenite:
γα
α
α
α
α
α
pearlite
growth
direction
Austenite (γ)
grain
boundary
cementite (Fe3C)
Ferrite (α)
γ
• Recrystallization
rate increases
with ∆T. 675°C
(∆T smaller)
0
50
y(%pearlite)
600°C
(∆T larger)
650°C
100

9. Chapter 10 - 9
• Reaction rate is a result of nucleation and growth of crystals.
• Examples:
Nucleation and Growth
% Pearlite
0
50
100
Nucleation
regime
Growth
regime
log(time)t0.5
Nucleation rate increases with ∆T
Growth rate increases with T
T just below TE
Nucleation rate low
Growth rate high
γ
pearlite
colony
T moderately below TE
γ
Nucleation rate medium.
Growth rate medium.
Nucleation rate high
T way below TE
γ
Growth rate low

10. Chapter 10 -10
Transformations & Undercooling
• Can make it occur at:
...727ºC (cool it slowly)
...below 727ºC (“undercool” it!)
• Eutectoid transf. (Fe-C System): γ ⇒ α + Fe3C
0.76 wt% C
0.022 wt% C
6.7 wt% C
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ +Fe3C
α +Fe3C
L+Fe3C
δ
(Fe) Co, wt%C
1148°C
T(°C)
α
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
∆T
Undercooling by ∆Ttransf. < 727°C
0.76
0.022

11. Chapter 10 -11
Isothermal Transformation Diagrams
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
50
0
1 102 104
T = 675°C
y,
%transformed
time (s)
400
500
600
700
1 10 102 103 104 105
0%pearlite
100%
50%
Austenite (stable)
TE (727°C)Austenite
(unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C

12. Chapter 10 -12
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
Effect of Cooling History in Fe-C System
400
500
600
700
0%pearlite
100%
50%
Austenite (stable)
TE (727°C)
Austenite
(unstable)
Pearlite
T(°C)
1 10 102 103 104 105
time (s)
γ γ
γ
γ γ
γ

13. Chapter 10 -13
Transformations with
Proeutectoid Materials
Hypereutectoid composition – proeutectoid cementite
α
CO = 1.13 wt% C
TE (727°C)
T(°C)
time (s)
A
A
A
+
C
P
1 10 102
103
104
500
700
900
600
800
A
+
P
Adapted from Fig. 10.16,
Callister 7e.
Adapted from Fig. 9.24,
Callister 7e.
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ +Fe3C
α+Fe3C
L+Fe3C
δ
(Fe)
Co, wt%C
T(°C)
727°C
∆T
0.76
0.022
1.13

14. Chapter 10 -14
Non-Equilibrium Structure of Fe-C
• Bainite:
− α lathes (strips) with long rods of Fe3C
- Needles of Fe3C in α
- Very fine structure
--diffusion controlled.
Obtained from moderate cooling
i.e. no enough time for diffusion
Fe3C
(cementite)
5 µm
α (ferrite)

15. Chapter 10 -15
• Spheroidite:
--α grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force)
Spheroidite: Fe-C System
60 µm
α
(ferrite)
(cementite)
Fe3C

16. Chapter 10 -16
• Martensite:
--γ (FCC) to Martensite (BCT)
NON-Equilibrium
single phase
Hard and Brittle
• γ to M transformation..
-- is rapid!
-- % transf. depends on T only.
Martensite: Fe-C System
Martensite needles
Austenite
60µm
x
x x
x
x
x
potential
C atom sites
Fe atom
sites
(involves single atom jumps)

17. Chapter 10 -17
γ (FCC) α (BCC) + Fe3C
Martensite Formation
slow cooling
tempering
quench
M (BCT)
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation BCT if C > 0.15 wt%
BCT  few slip planes  hard, brittle

18. Chapter 10 -18
Mechanical Prop: Effect Of Carbon Content
Increasing wt% C: TS and YS increase
%EL decreases
.
• Effect of wt% C
Co < 0.76 wt% C
Hypoeutectoid
Pearlite (med)
ferrite (soft)
Co > 0.76 wt% C
Hypereutectoid
Pearlite (med)
Cementite
(hard)
300
500
700
900
1100
YS(MPa)
TS(MPa)
wt% C
0 0.5 1
hardness
0.76
Hypo Hyper
wt% C
0 0.5 1
0
50
100
%EL
Impactenergy(Izod,ft-lb)
0
40
80
0.76
Hypo Hyper

19. Chapter 10 -19
Mechanical Prop: Effect Of Size
• Fine vs coarse pearlite vs spheroidite
• Hardness:
• %RA:
fine > coarse > spheroidite
fine < coarse < spheroidite
80
160
240
320
wt%C
0 0.5 1
Brinellhardness
fine
pearlite
coarse
pearlite
spheroidite
Hypo Hyper
0
30
60
90
wt%C
Ductility(%RA)
fine
pearlite
coarse
pearlite
spheroidite
Hypo Hyper
0 0.5 1

20. Chapter 10 -20
Mechanical Prop: Effect Of Structure Type
• Fine Pearlite vs Martensite:
• Hardness: fine pearlite << martensite.
0
200
wt% C
0 0.5 1
400
600
Brinellhardness
martensite
fine pearlite
Hypo Hyper

21. Chapter 10 -21
Tempering Martensite
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
• decreases TS, YS but increases %RA
• produces extremely small Fe3C particles surrounded by α.
9µm
YS(MPa)
TS(MPa)
800
1000
1200
1400
1600
1800
30
40
50
60
200 400 600
Tempering T (°C)
%RA
TS
YS
%RA

22. Chapter 10 -22
Summary: Processing Options
Austenite (γ)
Bainite
(α + Fe3C plates/needles)
Pearlite
(α + Fe3C layers + a
proeutectoid phase)
Martensite
(BCT phase
diffusionless
transformation)
Tempered
Martensite
(α + very fine
Fe3C particles)
slow
cool
moderate
cool
rapid
quench
reheat
reheat
Spheroidite
The most ductile

23. Chapter 10 -23
Summary:
Structures versus Mechanical Properties
Strength
Ductility
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends

24. Chapter 10 -24
Annealing: Heat to Tanneal, then cool slowly.
Based on discussion in Section 11.7, Callister 7e.
Thermal Processing of Metals
Types of
Annealing
• Process Anneal:
Negate effect of
cold working by
(recovery/
recrystallization)
• Stress Relief: Reduce
stress caused by:
-plastic deformation
-nonuniform cooling
-phase transform.
• Normalize (steels):
Deform steel with large
grains, then normalize
to make grains small.
• Full Anneal (steels):
Make soft steels for
good forming by heating
to get γ, then cool in
furnace to get coarse P.
• Spheroidize (steels):
Make very soft steels for
good machining. Heat just
below TE & hold for
15-25 h.

25. Chapter 10 -25
a) Annealing
b) Quenching
Heat Treatments
c)
c) Tempered
Martensite
Adapted from Fig. 10.22, Callister 7e.
time (s)
10 10
3
10
5
10
-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%
50%
A
A
M + A
M + A
0%
50%
90%
a)b)

26. Chapter 10 -26
Hardenability--Steels
• Ability to form martensite
• Jominy end quench test to measure hardenability.
• Hardness versus distance from the quenched end.
Adapted from Fig. 11.11,
Callister 7e. (Fig. 11.11
adapted from A.G. Guy,
Essentials of Materials
Science, McGraw-Hill Book
Company, New York,
1978.)
Adapted from Fig. 11.12,
Callister 7e.
24°C water
specimen
(heated to γ
phase field)
flat ground
Rockwell C
hardness tests
Hardness,HRC
Distance from quenched end

27. Chapter 10 -27
• The cooling rate varies with position.
Adapted from Fig. 11.13, Callister 7e.
(Fig. 11.13 adapted from H. Boyer (Ed.)
Atlas of Isothermal Transformation and
Cooling Transformation Diagrams,
American Society for Metals, 1977, p.
376.)
Why Hardness Changes W/Position
distance from quenched end (in)
Hardness,HRC
20
40
60
0 1 2 3
600
400
200
A → M
A
→
P
0.1 1 10 100 1000
T(°C)
M(start)
Time (s)
0
0%
100%
M(finish)
M
artensite
M
artensite
+
Pearlite
Fine
Pearlite
Pearlite

28. Chapter 10 -28
Hardenability vs Alloy Composition
• Jominy end quench
results, C = 0.4 wt% C
• "Alloy Steels"
(4140, 4340, 5140, 8640)
--contain Ni, Cr, Mo
(0.2 to 2wt%)
--these elements shift
the "nose".
--martensite is easier
to form.
Adapted from Fig. 11.14, Callister 7e.
(Fig. 11.14 adapted from figure furnished
courtesy Republic Steel Corporation.)
Cooling rate (°C/s)
Hardness,HRC
20
40
60
100 20 30 40 50
Distance from quenched end (mm)
210100 3
4140
8640
5140
1040
50
80
100
%M4340
T(°C)
10
-1
10 10
3
10
50
200
400
600
800
Time (s)
M(start)
M(90%)
shift from
A to B due
to alloying
BA
TE

29. Chapter 10 -29
• Effect of quenching medium:
Medium
air
oil
water
Severity of Quench
low
moderate
high
Hardness
low
moderate
high
• Effect of geometry:
When surface-to-volume ratio increases:
--cooling rate increases
--hardness increases
Position
center
surface
Cooling rate
low
high
Hardness
low
high
Quenching Medium & Geometry

30. Chapter 10 -30
0 10 20 30 40 50
wt% Cu
L
α+Lα
α+θ
θ
θ+L
300
400
500
600
700
(Al)
T(°C)
composition range
needed for precipitation hardening
CuAl2
A
Adapted from Fig. 11.24, Callister 7e. (Fig. 11.24 adapted from
J.L. Murray, International Metals Review 30, p.5, 1985.)
Precipitation Hardening
• Particles impede dislocations.
• Ex: Al-Cu system
• Procedure:
Adapted from Fig.
11.22, Callister 7e.
--Pt B: quench to room temp.
--Pt C: reheat to nucleate
small θ crystals within
α crystals.
• Other precipitation
systems:
• Cu-Be
• Cu-Sn
• Mg-Al
Temp.
Time
--Pt A: solution heat treat
(get α solid solution)
Pt A (sol’n heat treat)
B
Pt B
C
Pt C (precipitate θ)

31. Chapter 10 -31
• 2014 Al Alloy:
• TS peaks with
precipitation time.
• Increasing T accelerates
process.
Adapted from Fig. 11.27 (a) and (b), Callister 7e. (Fig. 11.27 adapted from Metals Handbook:
Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing
Ed.), American Society for Metals, 1979. p. 41.)
Precipitate Effect on TS, %EL
precipitation heat treat time
tensilestrength(MPa)
200
300
400
100
1min 1h 1day 1mo 1yr
204°C
non-equil.
solidsolution
manysmall
precipitates“aged”
fewerlarge
precipitates
“overaged”
149°C
• %EL reaches minimum
with precipitation time.
%EL(2insample)
10
20
30
0
1min 1h 1day 1mo 1yr
204°C 149°C
precipitation heat treat time

32. Chapter 10 -32
Metal Alloy Crystal Stucture
Alloys
• substitutional alloys
– can be ordered or disordered
– disordered solid solution
– ordered - periodic substitution
example: CuAu FCC
Cu
Au

33. Chapter 10 -33
• Interstitial alloys (compounds)
– one metal much larger than the other
– smaller metal goes in ordered way into
interstitial “holes” in the structure of larger
metal
– Ex: Cementite – Fe3C
Metal Alloy Crystal Stucture

34. Chapter 10 -34
Metal Alloy Crystal Stucture
• Consider FCC structure --- what types of
holes are there?
Octahedron - octahedral site = OH Tetrahedron - tetrahedral site = TD

35. Chapter 10 -35
Metal Alloy Crystal Stucture
• Interstitials such as H, N, B, C
• FCC has 4 atoms per unit cell
metal atoms
2
1
2
1
2
1
2
1
TD sites
4
3
4
1
,4
3
4
1
,
4
3
4
1
,4
3
4
1
,
8 TD sites
OH sites
2
1
2
1
2
1
2
1
2
1
4 OH sites

36. Chapter 10 -36
• Steels: increase TS, Hardness (and cost) by adding
--C (low alloy steels)
--Cr, V, Ni, Mo, W (high alloy steels)
--ductility usually decreases w/additions.
• Non-ferrous:
--Cu, Al, Ti, Mg, Refractory, and noble metals.
• Fabrication techniques:
--forming, casting, joining.
• Hardenability
--increases with alloy content.
• Precipitation hardening
--effective means to increase strength in
Al, Cu, and Mg alloys.
Summary