Download Paired with Lecture

Hypoeutectoid Steel
T(°C)
1600
d
g g
g g
g +L
g
1200
(austenite)
g g
g g
1000
g
a
g g
800
a
w a =s/(r +s) 600
w g =(1- wa )
a
727°C
r s
RS
400
0
(Fe)
pearlite
a + Fe3C
1
C0
w pearlite = w g
w a =S/(R+S)
w Fe3 =(1-w a )
C
L+Fe3C
g + Fe3C
0.76
ag
a
1148°C
pearlite
2
3
4
5
6
Fe3C (cementite)
L
1400
6.7
Co , wt% C
100 mm
proeutectoid ferrite
Proeuctectoid Ferrite – Pearlite
0.38 wt% C: Plain Carbon – Medium Carbon Steel
Hypereutectoid Steel
T(°C)
1600
d
Fe3C
g
g
g +L
g
1200
(austenite)
g
g
1000
g g
g g
r
800
w Fe3C =r/(r +s)
w g =(1-w Fe3C )
a R
600
400
0
(Fe)
pearlite
1148°C
L+Fe3C
g +Fe3C
0.76
g
g
g
g
s
S
1 Co
w pearlite = w g
w a =S/(R+S)
w Fe3C =(1-w a )
a +Fe3C
2
3
4
5
6
Fe3C (cementite)
L
1400
6.7
Co , wt%C
60 mm
pearlite
proeutectoid Fe3C
Adapted from Fig. 9.33,Callister 7e.
Proeutectoid Cementite - Pearlite
1.4 wt% C: Plain Carbon – High Carbon Steel
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
Phase Transformations
Phase transformations involve some form of change in the microstructure
Let’s categorize with 3 types:
1. 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
2. Diffusion-dependent transformations in which there is a change in the phase
compositions and or number of phases present
Examples:
 Eutectoid reaction
 Peritectic reaction
3. Diffusion-less transformations, in which a metastable phase is produced
Examples:
 Martensitic and Bainitic transformations
Nucleation
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 DT
– supercooling (eutectic, eutectoid reactions)
Small supercooling  few nuclei - large crystals
Large supercooling  rapid nucleation - many nuclei,
small crystals
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
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
Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
Surface area of sphere
an interface)
DGS  4r 2g
g = surface tension
DGT = Total Free Energy
= DGS + DGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
embryo
nucleus
DGV 
DG 
4 3
r DG
3
volume free energy
unit volume
DGn = free energy difference between the parent and daughter phase
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Solidification
 2 gTm
r* 
DH S DT
r* = critical radius
g = surface free energy
Tm = melting temperature
DHS = latent heat of solidification
DT = Tm - T = supercooling
Note: DHS = strong function of DT
g

r*
= weak function of DT
decreases as DT increases
For typical DT
r* ca. 100Å
T1 > T2
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
Heterogenous Nucleation
Young’s Law:
g ml  g sm  g sl cos
(g ml  g sm )
cos 
g sl
Heterogeneous Nucleation
DGhet  Vs DGv  Aslg sl  Asmg sm  Asmg ml
 4 3

DGhet     r DGv  4 r 2g sl  S ( )
 3

(1  cos  ) 2
S ( )  (2  cos  )
4
2g sl
DG v
 1 6g 3
sl
DG*  
 3DG 2

v
r* 
Note: DG*het = DGhom S()

S( )


Heterogeneous vs Homogenous
DG*het = DGhom S()
Lower activation energy barrier
 Less undercooling required
 Faster transformation rate
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
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
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
– k & n fit for specific sample
By convention
r = 1 / t0.5
time
Rate of Phase Transformations
135C 119C
1
10
113C 102C
88C
102
43C
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!
Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from
Fig. 9.15,
Callister 7e.
a
a
g a
a
a
a
• Transformation
rate increases
with DT.
g
cementite (Fe3C)
Ferrite (a)
a
g
a
pearlite
growth
direction
a
100
y (% pearlite)
Austenite (g)
grain
boundary
Diffusive flow
of C needed
600°C
(DT larger)
50
650°C
675°C
(DT smaller)
0
Course pearlite  formed at higher T - softer
Fine pearlite
 formed at low T - harder
g
Nucleation and Growth
Reaction rate is a result of nucleation and growth of crystals.
100
% Pearlite
Nucleation rate increases with DT
Growth
regime
50 Nucleation
Growth rate increases with T
regime
t 0.5
0
log (time)
• 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
Consider Eutectoid Transformation …
g  a + Fe3C
Eutectoid transformation (Fe-C):
0.76 wt% C
6.7 wt% C
0.022 wt% C
1600
d
L
1400
g +L
g
1200
(austenite)
1000
L+Fe3C
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727°C
400
0
(Fe)
DT
a +Fe3C
Undercooling by DTtransf. < 727C
0.76
600
0.022
a
ferrite
1148°C
1
2
3
4
5
6
Fe3C (cementite)
T(°C)
6.7
Co , wt%C
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
time (s)
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
g
400
1
10
10 2
10 3
time (s)
10 4
10 5