Hahn-Meitner-Institute Berlin
Diffusion in Al-Ni-Ce Melts
Axel Griesche, Michael-Peter Macht
HMI Berlin, Dept. Materials (SF3)
Günter Frohberg
TU Berlin, Inst. for Material Sciences and Technology, Dept. Metal Physics
DFG-SPP 1120 >Phase Transformations in Multicomponent Melts<
Motivation
• Influence of structure and thermodynamic forces on diffusion in metallic melts?
Dik = (D*i Nk + D*k Ni )Φ M
L.S. Darken, Trans. AIME 180 (1948) 430
in melts?
J.R. Manning, Phys. Rev. 124, 2 (1961) 470
ambiguous result in SnIn melts: M ≠ 1
G. Frohberg in Scientific Results of the German Spacelab Mission D-2, DLR Cologne (1994) 275ff
• AlNi20, AlNi20Ce3, AlNi10Ce3
2
Long-Capillary Technique
∅1,5 mm x 30 mm
80
Ni Ce
10
ICP-MS
70 -1 0 1
0
x [cm]
Corrections: • sample length • effective diffusion time t =0 T = RT ∆C = 10 at% t >0 T > Tliq Dik = fit parameter relative error = ±30...40%
3
CNi CCe [at.-%]
CAl [at.-%]
EDS AAS
90
20
Al
Check for additional Transport
mean square penetration depth -5 [10 m²] Al87Ni10Ce3
4
2 Al/Ni 0 0 1000 2000 3000
diffusion time [s]
• x² = 2Dt ⇒ no additional transport
4
Check for additional Transport
mean square penetration depth -5 [10 m²] AlNi20
4
2 Al/Ni 0 0 1000 2000
diffusion time [s]
• x² = 2Dt + x²0 ⇒ additional transport segregation Al3Ni2
5
Boltzmann-Matano Analysis
1,0
e.g. Al87Ni10Ce3
-0,04
MultiDiFlux
Ji [at.-% µm/s]
Al
rel. Ci
0,8 0,2
Matano planes
JAl JNi
0,00
M.A. Dayananda, Purdue Uni.
Ni
0,0
Ce -2 0 2
0,04
⇒ conc. independence of D
x [cm]
• Matano planes at x = 0 • JAl + JNi = 1
⇒ quasi-binary
6
Thermodynamic Factor Φ
Pandat
R. Schmid-Fetzer / Uni. Clausthal
xNi & xCe [at.-%]
0,2 6 Al Ni 0,0
Φi = 1+ (d ln(γi) / d ln(xi))
Φi [a.u.]
µi = µ0,i + RT ln(ai)
4 2 0 1175 K 0,8 1,0 Ce
xAl [at.-%]
• Φi depends strongly on alloy composition
7
Ni Self Diffusion in AlNi
10
-8
AlNi20 AlNi30
• increase of D*Ni with xAl
AlNi10 Al(Ni)
DNi [m²/s]
Ni
⇒ influence of CSRO
NiAl25
%Al
∆ Garandet, Griesche et al, I. J. Thermophys. 25, 1 (2004) 249
Horbach, Meyer et al., APL 82,1 (2005) 11918
-9
10
0,4
0,8 1000 / T [K ]
-1
1,2
8
T [K]
2000 1750 1E-7 1500
Darken-Test in AlNi20
1250
D [m²/s]
1E-8
Ni Al
• calc. DAlNi = exp. DAlNi
⇒ Darken fulfilled
1E-9
0,6
0,8
1000/T [K ]
∆ Horbach, Meyer et al., APL 82,1 (2005) 11918 exp. interdiffusion, this work calc. w/ Darken-Eq., M=1 9
-1
Darken-Test in Al87Ni10Ce3
15
Al82Ni15Ce vs. Al92Ni5Ce Ni Ce
-2 0 2 EDS Profiler
15
AlNi12Ce1 vs. AlNi8Ce5
10
10
ci [at.-%]
ci [at.-%]
Ni
5
5
Ce
0
0
-2
0
2
x [cm]
x [cm]
15
Al89NiCe1 vs. Al85NiCe5 Ni
PROFILER
J. Morral / Uni. Connecticut
10
ci [at.-%]
5
Ce
0 -2 0 2
• no singularity • poor agreement
x [cm]
⇒ Darken fulfilled?
10
Diffusion in Al77Ni20Ce3
• Ce decreases D*Ni (~30%)
AlNi20
10 D [m ²/s]
-8
⇒ structural change
D AlNi
• DAlNi > DAlCe > DNiCe • DAlNi ≈ 5 D*
⇒ thermodynamic forces
AlNi20 Ce 3
-9
D AlCe
10
D NiCe
0,6
0,8 1000 / T [K ]
-1
1,0
∆
Self Diffusion Ni (Meyer et al.) Interdiffusion
11
Diffusion in Al87Ni10Ce3
• Ce decreases D*Ni (~20%)
⇒ structural change
10 D [m ²/s]
-8
AlNi10 AlNi10 Ce 3 D NiCe
D AlNi D AlCe
• DAlNi > DAlCe > DNiCe • DAlNi ≈ 2 D*
⇒ thermodynamic forces
10
-9
0,6
0,8 1000 / T [K ]
-1
1,0
∆
Self Diffusion Ni (Meyer et al.) Interdiffusion
12
Relationship Diffusion - Thermodynamic Force
ratio Dik / D*
Φ
3,8 4 1,8
AlNi20 AlNi20Ce3 AlNi10Ce3
DAlNi ≈ 3,8 D* DAlNi ≈ 5 D* DAlNi ≈ 2 D*
• Dik ≈ D* Φ
J. Bøttiger et al., Mat. Sci. Eng. A 178 (1994) 65
13
Conclusion
Ce addition decreases D ⇒ change in structure
D* depends strongly on AlNi composition ⇒ CSRO
Φ depends strongly on alloy comp. ⇒ strong atomic interaction
validation of Darken‘s equation in molten AlNi20 qualitative validation of Darken‘s equation in molten AlNiCe?
(check Al77Ni20Ce3)
rule-of-thumb: ratio of Dik / D* correlates with Φ
14
End
Acknowledgement - DFG SPP 1120 - Auswärtiges Amt