multicomponent diffusion effects in joints of dissimilar ...cecamp/tms2005/agren.pdfin binary...

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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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Content

1. Background2. Multicomponent-multiphase3. Steel composites4. TBC Bond coats5. Kirkendall Effect6. Mobility data

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1. Background

• Engineering materials are multicomponent and often multiphase.

• Coupling effects!

j

n

j

nkjk cDJ ∇−= ∑

−

=

1

1

4


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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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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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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Ni-Al-Cr: Virtual diffusion pathin two-phase field(Engström and Ågren 1996)

2. Multicomponent-multiphase

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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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∑

∑

∑

∑

−

=

−

=

−

=

−

−

=

∂

∂=

∂

∂−=

∂

∂

∂

∂=

∂∂

=

==>

∂∂

−=

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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γγ γ+βγ+β

Zig-Zag diffusion path in two-phase field(Hopfe, Morral et al. 1994)

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“Real” diffusion pathin two-phase fieldEngström and Ågren 1996

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Engström et al. 1996

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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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EMPA

DICTRA

Electron diffraction patternof particles in stainless steelclose to joint: M23C6.

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Image analysis

DICTRA

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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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Diffusion in super alloyNi–Al–Co–Cr–Hf–Mo–Re–Ta–Ti–W in FCCCampbell et al. 2002

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CMSX-4 René-N4

50°h 1050 °CCampbell et al.2002: 8 component system!

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Diffusion in ordered structures(Helander and Ågren 1999)

B2

Fe-Al

A2

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Al-Fe-Ni B2

Experiments fromDayananda

Ni0.55Al0.45

Fe0.59Al0.41

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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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-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)


C-25

-20

-15

-10

-5

0

5

10-8

TABL

E T2


0

1

2

3

4

5

6

7

8

9

10

10-6

ACR(

AL)


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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80

85

90

95

100

105

10-3

X(AL

)


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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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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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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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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Nesbitt and Heckel 1987 Strandlund and Larsson, 2004

Al

Cr

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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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Example of fit to data

At

% C

r an

d A

l

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Conclusions

• Multicomponent diffusion theory is a valuable tool in engineering design.

• Databases much needed.• Fundamental issues:

- Kirkendall effect- Thermal migration - Electro migration- ...

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