Upload
others
View
11
Download
0
Embed Size (px)
Citation preview
Nano & Flexible
Device Materials Lab.77
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
Nano & Flexible
Device Materials Lab.88
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
Nano & Flexible
Device Materials Lab.99
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
Nano & Flexible
Device Materials Lab.1010
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
Nano & Flexible
Device Materials Lab.1111
)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
Nano & Flexible
Device Materials Lab.1212
5.5 Precipitation in Age-Hardening Alloys
5.5.1 Precipitation in Aluminum-Copper Alloys
Transition phases
Phase Transformation In Materials
43210 '"zonesGP
Nano & Flexible
Device Materials Lab.1313
5.5 Precipitation in Age-Hardening Alloys
Phase Transformation In Materials
Nano & Flexible
Device Materials Lab.1414
5.5 Precipitation in Age-Hardening Alloys
Growth of 𝜽′
in the expense of 𝜽"
Phase Transformation In Materials
Nano & Flexible
Device Materials Lab.1515
5.5.3 Quenched in Vacancies
Phase Transformation In Materials
Precipitation Free Zone: PFZ
Nano & Flexible
Device Materials Lab.1616
5.5.4 Age Hardening
Phase Transformation In Materials
Nano & Flexible
Device Materials Lab.1717
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
Nano & Flexible
Device Materials Lab.1818
The Effect of ∆Hmix and T on ∆Gmix
Phase Transformation in Materials
From Ch1
Ω < 0
Ω > 0
Nano & Flexible
Device Materials Lab.1919
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
Nano & Flexible
Device Materials Lab.2020
Spinodal decomposion
Phase Transformation In Materials
Nano & Flexible
Device Materials Lab.2121
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