1. Hypoeutectoid Steel T(°C) d L +L g (austenite) Fe3C (cementite) a
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)
727°C C0
0.76 g g r s w a = /( + ) g
(1-
proeutectoid ferrite
pearlite
100 mm R S a w = /( + )
Fe3C
(1- g

2. Proeuctectoid Ferrite – Pearlite
0.38 wt% C: Plain Carbon – Medium Carbon Steel

3. Hypereutectoid Steel Fe3C (cementite) L g (austenite) +L a d T(°C) g g
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) g g s r w
Fe3C = /( + ) g
=(1-
Adapted from Fig. 9.33,Callister 7e.
proeutectoid Fe3C
60 mm
pearlite R S w a = /( + )
Fe3C
(1- g Co
0.76

4. Proeutectoid Cementite - Pearlite
1.4 wt% C: Plain Carbon – High Carbon Steel

5. Phase Transformations
We just studied Phase Diagrams which are thermodynamic maps which tell us the equilibrium phases present at any specific combination of temperature, pressure, and composition
These phase diagrams are based on the concept of Gibbs Free Energy, DG, which we have briefly introduced before:
DG is the thermodynamic driving force for a reaction
If DG is negative then there is a probability that a reaction will occur.
The more negative DG becomes, the more driving force there is for the reaction
Thermodynamics tells us the probability of a reaction but not the rate – the rate of a reaction is determined by Kinetics
Now we are going to shift perspectives and discuss the details of how we transform from one phase to another

6. Phase Transformations
Phase transformations involve some form of change in the microstructure
Let’s categorize with 3 types:
Simple diffusion-dependent transformations in which there is no change in the number or composition of the phases present
Examples:
Solidification of a pure metal
Allotropic transformations
Recrystallization and Grain Growth
Diffusion-dependent transformations in which there is a change in the phase compositions and or number of phases present
Eutectoid reaction
Peritectic reaction
Diffusion-less transformations, in which a metastable phase is produced
Martensitic and Bainitic transformations

7. Nucleation Driving force to nucleate increases as we increase T
During Phase transformation – new phase formed with different physical/ chemical characteristics than the parent phase
Diffusion based Phase Transformations do not occur instantaneously – nucleated
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 reactions)
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

8. 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

9. Consider Solidification First
Let’s assume spherical nuclei
Why?
Sphere has the smallest surface area/ surface energy for a given volume
Let’s Determine the equations that define behavior

10. Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
g = surface tension
Surface area of sphere
DGT = Total Free Energy
= DGS + DGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
embryo
nucleus
DGn = free energy difference between the parent and daughter phase
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

11. Solidification r* = critical radius g = surface free energy
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
T1 > T2
 = weak function of T
 r* decreases as T increases
For typical T r* ca. 100Å

12. Other Effects of Temperature
Number of stable nuclei follows Arrhenius behavior (like vacancy densities)
Clustering of atoms by short range diffusion – Diffusivity has Arrhenius behavior
Maximum Nucleation Rate occurs at intercept of two curves

13. Heterogenous Nucleation
Young’s Law:

14. Heterogeneous Nucleation
The formation of the embryo will be associated with an excess free energy. Notice first two contributions are positive (arising from the creation of interfaces) and third contribution is negative (arising from the destruction of the mould/liquid interface under the spherical cap)
Note: DG*het = DGhom S(q)

15. Heterogeneous vs Homogenous
DG*het = DGhom S(q)
Lower activation energy barrier
Less undercooling required
Faster transformation rate

16. Nucleation vs Growth Rates
Growth is determined by long range diffusion
Arrhenius activation energy behavior
Overall transformation is equal to the product of Ġ and Ń
Rate = 1/time

17. Kinetics of Phase Transformation
Discussed Thermodynamic driving forces in detail
Kinetics – measures the approach to equilibrium vs. time
Hold temperature constant & measure conversion vs. time

18. 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
Avrami rate equation => y = 1- exp (-ktn)
k & n fit for specific sample
S.A. = surface area
time
fraction transformed
By convention r = 1 / t0.5

19. 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 = pre-exponential factor
Q = activation energy
Arrhenius expression
r often small: equilibrium not possible!

20. Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from Fig. 9.15, Callister 7e. g a
pearlite
growth
direction
Austenite (g)
grain
boundary
cementite (Fe3C)
Ferrite (a)
Diffusive flow
of C needed a g
• Transformation
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

21. 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

22. Consider Eutectoid Transformation …
transformation (Fe-C): g Þ a +
Fe3C
0.76 wt% C
6.7 wt% C
0.022 wt% C
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

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

24. 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) g g