Diffusion in fcc and L1 Phases of Ni-Al-Mocecamp/TMS2005/Tao02162005TMS_… · Diffusion in fcc and...
Transcript of Diffusion in fcc and L1 Phases of Ni-Al-Mocecamp/TMS2005/Tao02162005TMS_… · Diffusion in fcc and...
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Diffusion in fcc and L12 Phases of Ni-Al-Mo
Tao Wang, Shi-Huai Zhou, Jing-Zhi Zhu, Long-Qing Chen and Zi-Kui Liu
The Penn State University
February 16, 2005
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Diffusion in the fcc Disordered Phase of the Ni-Al-Mo System
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Modeling on Atomic Mobility
)exp(1
RTG
RTM i
i
∆−=
∑∑∑>
∆+∆=∆j jk
kjikj
l
lili GxxGxG ,
)ln
exp(1
)exp(00
RTMRTQ
RTRTQ
RTM
M iiiii
+−=
−=
Ø J. Andersson and J. Agren, J. Appl. Phys., 72 (1992) 1350
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Thermodynamic Database
Ø S. Zhou et al., in submission, (2005)
n 1473K
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Diffusivity in Ni-Al fcc Phase
Ø A. Engstrom, J. Agren, Z.Metallkd., 97 (1996) 92
n Ni-Al
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Diffusivity in fcc Phase
n Ni-Mo n Al-Mo
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Diffusion in the L12 Ordered Phase of the Ni-Al System
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Modeling the Ordered Phase
Ø T. Helander and J. Agren, Acta Mater., 47 (1999) 1141
ordi
disii GGG ∆+∆=∆
∑∑≠
−∆=∆j jk
kjkjorderijk
ordi xxyyGG ][ βα
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Diffusivity in Stoichiometric Compound (Assessment I)
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Diffusivity vs Composition(Assessment I)
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Diffusion in L12 Ordered Phase
The movements of vacancies should not destroy the ordered structure.
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Diffusion Mechanism in L12
n Major element (Ni)v intra-lattice mechanism
n Minor element (Al)v six-jump cycle mechanismv anti-site mechanismv anti-site bridge mechanism
I think you need extra illustration to show the 3 mechanisms
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Diffusivity of Al (1473K)
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Diffusivity of Al (973K)
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Atomic Description for Diffusivity
n Ni in the fcc Ni Matrix:
n Ni in the Ni3Al Matrix:
n Al in the fcc Ni Matrix:
n Al in the Ni3Al Matrix:
NiNiNiVNi
NiNi fCaD 0
2 ω=
AlNiAlNiAlNiVAlNi
AlNiNi fCaD 333
3
30
2
32
ω=
NiNiNi
NiNi
VNiNiAl fCaD 2
3
42 ωωω
=
NiAl
AlNiAlNiAlNi
AlNiAlNi
VAlNiAlNi
Al PfCaD 33
3
33
3
32
3
42
32
ωωω
=
There is no explanation of ωo,ω1,ω2,ω3, etc.
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Numerical Treatment
n : reflects the impurity-vacancy and impurity-matrix interactions, assumed to be equal for the diffusion of Al in Ni3Al and fcc Ni.
n : anti-site factor.
Ø H. Numakura, et al., Phil. Mag. A, 77 (1998) 887
NiAlAlNi
Ni
NiNi
NiAl
AlNiAl P
DD
DD
≈3
3
)/)(/( 0234 ωωωω
NiAlP
Al
NiAlNi
Al xy
P =
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Dictra Modeling on Diffusivity
n Ni in the fcc Ni Matrix:
n Ni in the Ni3Al Matrix:
n Al in the fcc Ni Matrix:
n Al in the Ni3Al Matrix:
)exp(RTG
DdisNidis
Ni
∆−=
)exp(RTG
DdisAldis
Al∆−
=
)exp(3
RTGG
DordAl
disAlAlNi
Al∆+∆
−=
)exp(3
RTGG
DordNi
disNiAlNi
Ni∆+∆
−=
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Numerical Treatment II
n Where , which can be calculated from the mobility descriptions of the related disordered phase.
)'
exp(3
3
RTGGG
DD
DD ord
NiordAl
AlNiNi
NiNi
NiAl
AlNiAl ∆+∆−∆
−=
disNi
NiAl
NiNi
disAl GGGGG ∆−∆−∆+∆=∆ '
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Constraint from Diffusion Mechanism
NiAl
ordNi
ordAl P
RTGGG
=∆+∆−∆
− )'
exp(
NiAlAlNi
Ni
NiNi
NiAl
AlNiAl P
DD
DD
=3
3
)'
exp(3
3
RTGGG
DD
DD ord
NiordAl
AlNiNi
NiNi
NiAl
AlNiAl ∆+∆−∆
−=
⇓
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Anti-site Factor
n Consider reaction:
n Anti-site factor:
n Energy of reaction can be calculated based on the thermodynamic database.
)( )()()1( 25.075.0325.075.023 fccAlNiAlNiLAlNi ↔
)exp(RTG
fxy
Preact
fccAl
NiAlNi
Al∆
−≈≈=
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Diffusivity in Stoichiometric Compound (Assessment II)
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Diffusivity vs Composition(Assessment II)
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Diffusion in the L12 Ordered Phase of the Ni-Al-Mo System
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Assumptions
Since Mo prefers to occupy Al-sites in Ni3Al ordered phase, we assume:
n The diffusion of Mo in the L12 ordered is similar to that of Al.
n The diffusion in the hypothetical Ni3Mo L12ordered phase is similar to that in the Ni3Al phase.
n The effect of Al-Mo ordering can be ignored.
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Diffusivity of Mo in Ni3Al
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Summary
n The atomic mobility modeling of Ni-Mo and Al-Mo fcc phases has been carried out based on the available experimental data. By combining them with previous work on Ni-Al, the mobility database for the fcc phase of the Ni-Al-Mo system has been developed.
n The effect of chemical ordering on atomic mobility is described by a phenomenological model. The available experimental data for Ni3Al are used to evaluate the model parameters.
n The anti-site mechanism is found to be dominant for Al diffusion in L12. The atomic mobility modeling is then refined based on the anti-site mechanism.
n Atomic mobility in the L12 phase of Ni-Al-Mo system is evaluated from the experimental information in the literature.