5.4 Overall Transformation Kinetics TTT Diagramocw.snu.ac.kr/sites/default/files/NOTE/Wk8_2Chapter...
Transcript of 5.4 Overall Transformation Kinetics TTT Diagramocw.snu.ac.kr/sites/default/files/NOTE/Wk8_2Chapter...
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5.4 Overall Transformation Kinetics – TTT Diagram
TTT Diagram :
the fraction of Transformation (f) as a function of Time and Temperature
Phase Transformation In Materials
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5.4 Overall Transformation Kinetics – TTT Diagram
Johnson-Mehl-Avrami Kolmogorov Equation
specimenofVol
phasenewofVolf
.
.
Assumption :
Reaction produces by nucleation and growth
Nucleation occurs randomly throughout specimen
Reaction product grows radially until impingement
Define volume fraction transformed
f
t
tdτ
τ τ+dτ
specimenofvolume
dduringformed
nucleiofnumber
ttimeatmeasureddduring
nucleatedparticleoneofvol
df
.
Phase Transformation In Materials
𝛼 → 𝛽
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5.4 Johnson-Mehl-Avrami Kolmogorov Equation
0
0
3 )()]([3
4
V
dNVtv
df
v : growth rate (assumed const. )
N : nucleation rate (const. )
33
33
)(3
4
)(3
4
3
4
tvV
vtrV
43
0
33
0
3
3
4
tvNf
d)t(vNf̂df
e
tx
e
volume :
→ do not consider impingement & repeated nucleation
→ only true for f ≪ 1
Phase Transformation In Materials
fe : extended volume fraction
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Johnson-Mehl-Avrami Kolmogorov Equation
edffdf )1( edf
dff 1
43
31 tNvexpf
)tkexp(f n 1 t
1
∝t4
f
····· J-M-A Eq.
k : sensitive to temp. ( N. v )
n : 1 ~ 4
7.05.0 ntk
nkt
/15.0
7.0
4/34/15.0
9.0
vNt
For the case of 50% transform, t0.5
exp (-0.7) = 0.5
i.e.
Example above.
Phase Transformation In Materials
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)pt(expII o
pI)pt(exppIdt
dI)t(N o
pt)ptexp(
p
vIexpf o 1
81
3
3
pt
6
33tp
33
31 tvNexpf o
Other example:
1. Fixed nucleation site and active at the beginning.
2. Nucleation site depends on the time
p: rate at which the individual sites are lost.
limiting cases : small → same as J-M eq.
large → I quickly goes to zero.
Phase Transformation In Materials
Johnson-Mehl-Avrami Kolmogorov Equation
(Io : number of active nucleation site / unit volume)
pt
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5.5 Precipitation in Age-Hardening Alloys
5.5.1 Precipitation in Aluminum-Copper Alloys
Transition phases
Phase Transformation In Materials
43210 '"zonesGP
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5.5 Precipitation in Age-Hardening Alloys
Phase Transformation In Materials
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5.5 Precipitation in Age-Hardening Alloys
Growth of 𝜽′
in the expense of 𝜽"
Phase Transformation In Materials
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5.5.3 Quenched in Vacancies
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Precipitation Free Zone: PFZ
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5.5.4 Age Hardening
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5.5.5 Spinodal Decomposition
No barrier for nucleation
Phase diagram with a miscibility gap
𝑑2𝐺
𝑑𝑋2< 0, chemical spinodal
Phase Transformation In Materials
Ω > 0
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The Effect of ∆Hmix and T on ∆Gmix
Phase Transformation in Materials
From Ch1
Ω < 0
Ω > 0
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5.5.5 Spinodal Decomposition
Composition profiles in an alloy
quenched into the spinodal region
Composition profiles in an alloy
outside the spinodal points
Phase Transformation In Materials
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Spinodal decomposion
Phase Transformation In Materials
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5.5.5 Spinodal Decomposition
The Rate of Transformation
Rate controlled by interdiffusion coefficient D~
D22 4/
D~
)exp(
t Within the spinodal < 0 , composition fluctuation
transf. rate ↑ as λ ↓
- : characteristic time constant
- λ : wavelength of the composition modulation (1-D assumed)
There is a minimum value of below which spinodal decomposion cannot occur
To calculate λ, it is need to take care of 1) interfacial energy 2) coherency strain energy
Phase Transformation In Materials