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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Multicomponent diffusion effects in joints of dissimilar materials –engineering applications
John Ågren
Dept. of Matls. Sci. & Engg.Royal Institute of TechnologyStockholm, 100 44 Sweden
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Content
1. Background2. Multicomponent-multiphase3. Steel composites4. TBC Bond coats5. Kirkendall Effect6. Mobility data
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
1. Background
• Engineering materials are multicomponent and often multiphase.
• Coupling effects!
j
n
j
nkjk cDJ ∇−= ∑
−
=
1
1
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
DICTRA - Basic calculation procedure
[ ) [ )Jzt
c∂∂
−=∂∂
DATABASESKinetic Thermodynamics
Mobilities Gibbs Energy
Diffusivities
Solve Diffusion
where
2
2
cG
∂∂
Boundary conditions(External or Internal)
All simulations depend on assessed kinetic and thermodynamic data, which are stored in databases
A numerical finite difference scheme is used for solving a system of coupled parabolic partial differential equations
[ ) [ ] [ )zcDJ∂∂
−=
2
2
~cGMDnjk ∂
∂
Why a databasewith Mobilities?
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Why mobilities and not diffusion coefficients?• Individual, intrinsic
Lattice fixed frame of reference, in an n-component system: n-1 for each component, i.e. nx(n-1).
• Self diffusionDiffusion of A in pure A
• tracer diffusion• interdiffusion, chemical diffusion
Number-fixed frame of reference, in an n-component system: n-1 for each component, i.e. (n-1)x(n-1).
j
kkVak
nkj u
MuD∂µ∂
=
AVaAAA RTMD =
AVaAAA RTMD =*
But only n mobilities!
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Ni-Cr-Al diffusion coupleEngström and Ågren 1996
∑−
= ∂∂
−=1
1
n
i
inkik x
cDJ
xα
αα
α : in along diffusion Phase One
C
kk
k
n
si j
iiik
j
kkk
nkj
xx
u
kM
uMuu
uMuD
−=
−= ∑∈
1
and ofmobility theis
where
∂µ∂
∂µ∂
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Ni-Al-Cr: Virtual diffusion pathin two-phase field(Engström and Ågren 1996)
2. Multicomponent-multiphase
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Diffusion in dispersed systems with DICTRA
Assumptions:
Diffusion takes place in the matrix phase only.
Equilibrium holds locally in each node.
SolveDiffusion
Calculatenew averagecompositions
Equilibriumcalculations
New matrixcompositions
Carburisation of high-temperaturealloysInternal oxidation
Interdiffusion in composite materialscoating/substrate systemsweldments between steelsjoints of dissimilar steels
Gradient sintering of cementedcarbide work-tool pices
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
∑
∑
∑
∑
−
=
−
=
−
=
−
−
=
∂
∂=
∂
∂−=
∂
∂
∂
∂=
∂∂
=
==>
∂∂
−=
1
1
1
1
1
1
1321
1
1
i.e.
i.e.)...,,(
element eeach volumin locally mEquilibriu
:in alongdiffusion Phase One
n
i
nkio
j
ieffnkj
oj
n
j
effnkjk
n
j
oj
oj
ii
on
oooii
n
i
inkik
Dcc
D
xc
DJ
xc
cc
xc
cccccc
xc
DJ
x
αα
α
αα
αα
αα
ααα
α
1994) Morral and (Hopfe
Matrix tion Transforma oi
i
cc
∂
∂ α
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
γγ γ+βγ+β
Zig-Zag diffusion path in two-phase field(Hopfe, Morral et al. 1994)
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
“Real” diffusion pathin two-phase fieldEngström and Ågren 1996
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Engström et al. 1996
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
3. Steel composites(Helander et al. 1997)
Low alloy steel0.18C
Stainless steelFe-27Cr-30Ni-3Mo
Tube made by coextrusion and then heat treated 1100 °C, 4h.
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
EMPA
DICTRA
Electron diffraction patternof particles in stainless steelclose to joint: M23C6.
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Image analysis
DICTRA
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
4. TBC Bond coats• The bond coat is the ”buffer” layer between super
alloy and the ceramic top coat (usually YSZ).• Al source to produce TGO layer of Al2O3 to protect
the metal from oxidation.• Bond coat is NiAL+...• One should minimize interdiffusion between bond
coat and super alloy.
Issues:- Diffusion in super-alloy and bond coat- Diffusion in ordered structures B2, L12 etc- Phase equilibria
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Diffusion in super alloyNi–Al–Co–Cr–Hf–Mo–Re–Ta–Ti–W in FCCCampbell et al. 2002
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
CMSX-4 René-N4
50°h 1050 °CCampbell et al.2002: 8 component system!
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Diffusion in ordered structures(Helander and Ågren 1999)
B2
Fe-Al
A2
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Al-Fe-Ni B2
Experiments fromDayananda
Ni0.55Al0.45
Fe0.59Al0.41
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
0
0.1
0.2
0.3
0.4
0.5
X(A
L)
-1000 -500 0 500 1000
Distance from Matano plane (microns)
Janssen (1973)B2
ργ∃∋
FCC
γ’
Distance from Matano plane µm
x Al
AlNi-Ni diffusion couple
Simulations: Helander and Ågren 1999Experiments: Janssen 1973
B2 FCCγ’
B2 FCC
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
-25
-20
-15
-10
-5
0
5
10-8
Flux
es
-500 0 500distance from Matano plane (microm)
C
0
1
2
3
4
5
6
7
8
9
10
10-6
ACR(
AL)
-500 0 500distance from Matano plane (microm)
C-25
-20
-15
-10
-5
0
5
10-8
TABL
E T2
-500 0 500distance from Matano plane (microm)
0
1
2
3
4
5
6
7
8
9
10
10-6
ACR(
AL)
-500 0 500distance from Matano plane (microm)
x based onisoactivity
x ”True” ZFP
ZFP to minimize interdiffusion in Ni-Al-Cr?
Ni
Al
Ni
AlNi-Al0.10Cr0.10 // Ni-AlxCr0.15
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
80
85
90
95
100
105
10-3
X(AL
)
-500 0 500distance from Matano plane (microm)
TIME = 0,3600,36000,360000
80
85
90
95
100
105
10-3
X(AL
)-500 0 500
distance from Matano plane (microm)
TIME = 0,3600,36000,360000
Based onisoactivity
”True” ZFP
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
5. Kirkendall EffectWhen diffusion occurs by a vacancy mechanism opposes the net flux of atoms is opposed by a net flux of vacancies (as regarded in alattice-fixed frame of reference).
0'...'' =+++ VaBA JJJ
zVxxMMJJ AB
m
BAABBA ∂
µµ∂ )()('' −−−=+
:atoms of flow-Net :system binary In
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Two extremes of the Kirkendall effect:
)(1/1
''2 BAm
m
m
JJVV
V
+==−
=
div&&ρ
ρ :change )( density of Rate
)()1(
)(1
''2
''332211
BAmp
p
p
BAmmm
JJVff
f
JJVVV
+−=−
+==++
⇒
div
div
&
&&&&
:) fraction (volume porosity Only 2.
:rate Strain porosity No 1.
εεε
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Borgenstam and Hillert 2000experiments
Fe-32Ni
Strandlund and Larsson 2004simulations
Volu
me
frac
tion p
ore
s
distance m
Fe
100 µm
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Nesbitt and Heckel 1987 Strandlund and Larsson, 2004
Al
Cr
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
6. Mobility data
Al-Cr-NiSimultaneous optimization directly to concentration profiles in ternarysystem with 9 differentdiffusion couples as well as and other pieces of information. Experimental information from Nesbitt et. al. 1987.
Höglund 2004
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Example of fit to data
At
% C
r an
d A
l
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John E. Morral symposiumTMS2005 – San Francisco Feb. 13-17 2005
Conclusions
• Multicomponent diffusion theory is a valuable tool in engineering design.
• Databases much needed.• Fundamental issues:
- Kirkendall effect- Thermal migration - Electro migration- ...