1. Chapter 10: Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time. Fe g
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(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 engineering non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?

2. Phase transformations are divided into three classifications:
simple diffusion-dependent transformations in which there is no change in either the number or composition of the phases present.( Ex. Solidification of a pure metal, allotropic transformations, recrystallization and grain growth)
another type of diffusion-dependent transformation, there is some alteration in phase compositions and often in the number of phases present; the final microstructure ordinarily consists of two phases ( Ex. The eutectoid reaction)
The third kind of transformation is diffusionless, wherein a
metastable phase is produced.( Ex. martensitic transformation)

3. The progress of a phase transformation may be broken down into two distinct stages:
nucleation: involve the appearance of very small particles, or nuclei of the new phase which are capable of growing. Favorable positions for the formation of these nuclei are imperfection sites, especially grain boundaries.
growth : the nuclei increase in size; during this process, of course, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained.

4. 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)
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
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei,
small crystals

5. 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

6. Homogeneous nucleation
Related to Gibbs free energy G
Free energy is a function of other thermodynamics parameters:
internal energy of the system ( the enthalpy H)
a measurements of the randomness or disorder of the atoms
( the entropy )
Transformation will occur spontaneously only when ∆G has a
negative value

7. There are two contributions to the total free energy change that accompany a solidification transformation:
Free energy difference between the solid and liquid phases(or the volume free energy ∆Cv : negative if the T is below the equilibrium solidification temperature;
- the magnitude = ∆Gv x Volume of the spherical nucleus(4/3πr3 )
The second energy results from the formation of the solid-liquid phase boundary during the solidification transformation( or the surface free energy γ) which is positive
- the magnitude = γ x The surface area of the nucleus(4πr2 )
The total free energy change ∆G = 4/3πr3 ∆Gv + 4πr2 γ
A critical free energy ∆G* occurs at the critical radius and, consequently at the maximum of the curve. This ∆G* corresponds to an activation free energy, which is the free energy required for the formation of a stable nucleus. Equivalent, it may be considered an energy barrier to the nucleation process.

8. 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 radius of nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

9. Since r* and ∆G* appear at the maximum on the free energy-versus-radius curve, we can find r* and ∆G* by derivation equ.
This volume free energy change ∆Gv is the driving force for the solidification transformation, and its magnitude is a function of temperature Tm, the value of ∆Gv is zero, and with diminishing temperature its value becomes increasingly more negative.

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

11. There are two important parameters ( temperature-dependent) influence nucleation:
The number of stable nuclei n* ( having radii greater than r* )
the clustering of atoms by short – range diffusion during the formation of nuclei
Qd – activation energy for diffusion ( temp. independent)
K2 temp.independent constant

12. Nucleation rate - it has units of nuclei per unit volume per second
Nucleation rate expression for homogeneous nucleation
K3 – the number of atoms on a nucleus surface
Comments:
This method may be applied to any shape with the same final result
May be utilized for types of transformations other than solidification
( ex. Solid-vapor, solid-solid)
For solid – solid transformation, there may be volume changes attendant to the formation of new phases, consequently will affect the magnitudes of r* and ∆G*

13. Tm νd N
temperature n*
Supercooling (undercooling): when during the cooling of liquid an appreciable nucleation rate ( i.e., solidification) will begin only after the temperature has been lowered to below the equilibrium solidification
( or melting) temperature Tm .
The degree of supercooling may be significant.
Superheating: Heating to above a phase transition temperature without the occurrence of the transformation.

14. Heterogeneous nucleation
It is a nucleation which occurs at surfaces and interfaces( which is easier than other sites, because of the activation energy ( energy barrier) for nucleation is lowered when nuclei form on preexisting surfaces or interfaces, since the surface free energy is reduced.
liquid θ
solid
S(θ) is a function only of θ ( the shape of nucleus), which will have a numerical value between zero and unity.

15. r* ∆G r
Heterogeneous nucleation occurs more readily

16. Tm
temperature
Nhet
Nhom
Nucleation rate

17. Growth
The growth step in a phase transformation begins once an embryo has exceeded the critical size, r* and becomes a stable nucleus. The nuclei increase in size; during this process, of course, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained
The growth rate G is determined by the rate of diffusion, and its temperature dependence is the same for the diffusion coefficient

18. Overall transformation rateTm
Growth rate, G
temperature
Overall transformation rate
Nucleation rate, N
Rate
Overall transformation rate is equal to some product of N and G.
the size of product phase is particles will depend on transformation temperature.

19. 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

20. Rate of Phase Transformation
All out of material - done
Fixed T
Fraction transformed, y
0.5
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as surface area increases & nuclei grow
t0.5
log t
Logarithm of heating time, t
S.A. = surface area
Avrami rate equation => y = 1- exp (-kt n)
k & n fit for specific sample(time independent constant
fraction transformed
time
The rate of transformation r is taken as the reciprocal of time required to
Proceed halfway completation
By convention r = 1 / t0.5

21. Rate of Phase Transformations
135C
119C
113C
102C
88C
43C 1 10
102
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!

22. Eutectoid Transformation Rate
• Growth of pearlite from austenite: 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.
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

23. 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
• 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

24. 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

25. Microstructure and property changes in Iron – Carbon Alloys
Pearlite
Bainite
Spheroidite
Martensite

26. Isothermal Transformation Diagrams
Consider again the iron–iron carbide eutectoid reaction
which is fundamental to the development of microstructure in steel alloys. Upon cooling, austenite, having an intermediate carbon concentration, transforms to a ferrite phase, having a much lower carbon content, and also cementite, with a much higher carbon concentration. Pearlite is one microstructural product of this transformation
Temperature and time play an important role in the rate of the
austenite-to- pearlite transformation

28. Isothermal Transformation Diagrams
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
T = 675°C
Transformation end y,
% transformed 50
Transformation beginning 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

29. Several constraints are imposed on using diagrams like Figure before:
This particular plot is valid only for an iron–carbon alloy of eutectoid composition; for other compositions, the curves will have different configurations
These plots are accurate only for transformations in which the temperature of the alloy is held constant throughout the duration of the reaction
such as Figure are referred to as isothermal transformation diagrams, or sometimes as time–temperature–transformation
(or T–T–T) plots.

30. 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) A C D
625 B
An actual isothermal heat treatment curve (ABCD) on the TTT diagram g g

31. Coarse pearlite: This microstructure has relatively thick layers of both the -ferrite and Fe3C –phases at temperatures just below the eutectoid
Fine pearlite: The thin-layered structure produced in the vicinity of 540C because of decreasing temperature, and so the decrease of carbon diffusion rate

32. 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
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

33. 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
It occurs at temperatures below those at which pearlite forms; begin-, end-, and half-reaction curves are just extensions of those for the pearlitic transformation
Pearlite forms above the nose—that is, over the temperature range of about 540 to 727. At temperatures between about 215 and 540C Bainite is the transformation product.

34. Spheroidite: Fe-C System
Spheroidite is formed when a steel alloy having either pearlitic or bainitic microstructures is heated to, and left at, a temperature below the eutectoid for a sufficiently long period of time—for example, at about 700C (1300F) for between 18 and 24 h
60 m a
(ferrite)
(cementite)
Fe3C
The Fe3C phase appears as spherelike
particles embedded in a continuous α
phase matrix.
• Spheroidite:
--a grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force)

35. 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%
• g to M transformation..
-- is rapid!(quenching process)
-- % transf. depends on T only
-- time independent

36. Martensite Formation  (FCC)  (BCC) + Fe3C
Is formed when austenitized iron–carbon alloys are rapidly cooled (or quenched) to a relatively low temperature (in the vicinity of the ambient)
 (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
Martensite is a nonequilibrium single-phase structure that results from a diffusionless transformation of austenite(rapid cooling prevent carbon diffusion).

38. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
changes in the positions and shapes of the curves in the isothermal transformation diagrams.
Cr, Ni, Mo, Si, Mn
retard    + Fe3C
transformation

39. CONTINUOUS COOLING TRANSFORMATION DIAGRAMS
An isothermal transformation diagram is valid only for conditions of constant temperature, which diagram must be modified for transformations that occur as the temperature is constantly
changing. For continuous cooling, the time required for a reaction to begin and end is delayed. A plot containing such modified beginning and ending reaction curves is termed a continuous cooling transformation (CCT) diagram.

40. Cooling Curve plot temp vs. time
Actual processes involves cooling – not isothermal
Can’t cool at infinite speed

41. 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

42. 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)

43. 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)

44. Example Problem for Co = 0.45 wt%
100 % martensite – quench = rapid cool
50 % martensite
and 50 % austenite
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) d)

45. Mechanical Prop: Fe-C System
Pearlite:
-- Cementite is much harder but more brittle than ferrite
-- increasing the fraction of Fe3C in a steel alloy while
holding other microstructural elements constant will
result in a harder and stronger material
-- Fine pearlite is harder and stronger than coarse pearlit
because of different in the layer thickness of each of
the ferrite and cementite phases
-- Coarse pearlite is more ductile than fine pearlite,
because of the greater restriction to plastic
deformation of the fine pearlite

46. Spheroidite:
-- Alloys containing pearlitic microstructures have greater strength and hardness than do those with spheroidite. This behavior is explained in terms of reinforcement at, and impedance to, dislocation motion across the ferrite–cementite boundaries as discussed above. There is less boundary area per unit volume in spheroidite, and consequently plastic deformation is not nearly as constrained, which gives rise to a relatively soft and weak material. In fact, of all steel alloys, those that are softest and weakest have a spheroidite microstructure
-- spheroidized steels are extremely ductile, much more than either fine or coarse pearlite .In addition, they are notably tough because any crack can encounter only a very small fraction of the brittle cementite particles as it propagates through the ductile ferrite matrix.

47. Bainite:
-- Because bainitic steels have a finer structure (i.e., smaller -ferrite and Fe3C particles), they are generally stronger and harder than pearlitic ones; yet they exhibit a desirable combination of strength and ductility.
Martinsite:
-- Martensite is the hardest and strongest and, the most brittle; it has, in fact, negligible ductility. Its hardness is dependent on the carbon content, up to about 0.6 wt%. these properties are attributed to the effectiveness of the interstitial carbon
atoms in hindering dislocation motion (as a solid-solution effect) and to the relatively few slip systems (along which dislocations move) for the BCT structure.

48. Mechanical Prop: Fe-C System (1)
Pearlite (med)
• Effect of wt% C C
ementite
(hard)
Pearlite (med)
ferrite (soft)
Co < 0.76 wt% C
Co > 0.76 wt% C
Hypoeutectoid
Hypereutectoid

49. • More wt% C(or equivalent Fe3C): TS and YS increase , %EL decreases.
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
• More wt% C(or equivalent Fe3C): TS and YS increase
, %EL decreases.

50. 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
• Hardness:
fine > coarse > spheroidite
• %RA:
fine < coarse < spheroidite

51. 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
• Hardness: fine pearlite << martensite.

52. Tempering Martensite • •
• reduces brittleness of martensite, enhanced ductility and tough.
• 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
9 mm
produces extremely small Fe3C particles surrounded by a. • •
decreases TS, YS but increases %RA

53. Tempering is accomplished by heating a martensitic steel to a temperature below the eutectoid for a specified time period. Normally, tempering is carried out at temperatures between 250 and 650C ; internal stresses, however, may be relieved at temperatures as low as 200C.This tempering heat treatment allows, by diffusional processes, the formation of tempered martensite,
according to the reaction
The size of the cementite particles influences the mechanical behavior of tempered martensite; increasing the particle size decreases the ferrite–cementite phase boundary area and, consequently, results in a softer and weaker material yet one that is tougher and more ductile
Heat treatment variables are temperature and time, and most treatments are constant-temperature processes. Since carbon diffusion is involved in the martensite-tempered martensite transformation, increasing the temperature will accelerate diffusion, the rate of cementite particle growth, and, subsequently, the rate of softening.

54. 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