diff. in dilute substitutional alloysocw.snu.ac.kr/sites/default/files/note/wk4_1chapter 2... ·...
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Nano & Flexible
Device Materials Lab.11
Diff. In Dilute Substitutional Alloys
XB~0 , XA~1
• Normally DB > DA in dilute sol.
• (solute atom > solvent atom in size )
• Solute – Vacancy pair
Atomic Mobility
• DB = MBRT ( for ideal dilute solution )
• Prove that DB = MBRT [ 1 + ]B
B
Xd
d
ln
ln
Phase Transformation In Materials
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Device Materials Lab.22
Diffusion In Ternary Alloy
Example) Fe-Si-C system (Fe-3.8%Si-0.48%C) vs. (Fe-0.44%C) at 1050
oC
① Si raises the μC (chemical potential of carbon) in solution.
② MSi (sub.)≪ MC (int.), M : mobility
• Interface: local equilibrium
• System: partial equilibrium
Phase Transformation In Materials
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Device Materials Lab.33
High Diffusion path
Defect (grain boundary, dislocation, surface) : more open
structure
⇒ fast diffusion path
)exp(RT
QDD l
lol
)exp(RT
QDD b
bob
)exp(RT
QDD s
sos
Diff. along lattice
Diff. along grain boundary
Diff. along free surface
Ds > Db > Dl
But area fraction → lattice > g.b > surface
Phase Transformation In Materials
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Device Materials Lab.44
Lattice vs. Grain Boundary Diffusion
dx
dCDJ ll
dx
dCDJ bb
dx
dC
d
DD
d
dJJJ lblb )(
)(
∴ dDDD blapparent
dD
D
D
D
l
b
l
app 1or
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Device Materials Lab.5
Where Dbδ > Dld grain boundary diffusion is important
Width of grain boundary: ~ 0.5nm, grain size: 1~1000
㎛
Db > Dl ( always ), Also Qb ~ 0.5Ql in FCC materials
→ Contribution depends on temperature
Dg.b is important
below 0.75 ~ 0.8Tm
High T – lattice diff. Low T – g.b diff.
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Device Materials Lab.66
Diffusion along Pipe
g: Cross-sectional area of pipe per unit area of matrix (δ/dimension)
l
p
l
app
D
Dg
D
D 1
ex) annealed metal ~ 105disl/mm2
Pipe accommodates 10 atoms in the cross-section, matrix contains 1013 atoms mm-2
7
13
6
13
5
1010
10
10
10*10 g
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Device Materials Lab.77
Moving Boundary Problem
Mass balance
)1)(()( dxCCdtJJa
B
b
BBB
x
CD
x
CD
CCdt
dxv
b
B
a
B
a
B
b
B
)(~
)(~
)(
1
x
CDJ
b
BB
)(
~
x
CDJ
a
BB
)(
~
,
Diffusion flux determines velocity (in local equilibrium)
Reaction that passes Interface is important
→ interface (reaction) controlled
Diffusion in Multiple Binary System
Phase Transformation In Materials
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Device Materials Lab.88
Multiphase Binary System (Phase Diagram and Chemical
Potential)
Phase Transformation In Materials
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Device Materials Lab.99
Diffusion in Multiphase System
Phase Transformation In Materials
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Device Materials Lab.1010
Moving boundary problem
Phase Transformation In Materials
CB
x
CBb
CBb
dx
b
a
J J
x
CD
x
CD
CCdt
dxv
b
B
a
B
a
B
b
B
)(~
)(~
)(
1
Velocity of - interface
x
CDJ
b
B
)(
~
x
CDJ
a
B
)(
~
1)(~
)(~
1)(
dt
x
CD
x
CDdxCC
a
B
b
Ba
B
b
B
Amount of accumulated B atoms
volume = dx X 1 (unit area)
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Device Materials Lab.1111
Diffusion Controlled :
Diffusion flux 가 velocity를결정. (local equilibrium에 있을경우)
Interface (reaction) Controlled:
Interface를뛰어넘는계면반응이중요한경우
Phase Transformation In Materials
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Device Materials Lab.1212
Kinetic parameters and measurements
Phase Transformation In Materials
Thermodynamic variables : p, V, T, S, and m
Kinetic parameters : atomic diffusivities, surface and
interface energies, interfacial reaction constants, and
enthalpy (heat) of formation
When the dependence of the layer thickness (x) on time
(t) measured, we can plot x versus t and x versus t1/2
tDx~
42 Ktx
kT
EDD aexp~~
0
kT
EKK aexp0
We can get reaction constant (K), atomic diffusivity (D),
activation energy