Diffusion in fcc and L1 2 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
1
Diffusion in the fcc Disordered Phase of the Ni-Al-Mo System
2
Modeling on Atomic Mobility
M i0 − Qi 1 − Qi + RT ln M i0 Mi = exp( )= exp( ) RT RT RT RT 1 − ∆G i Mi = exp( ) RT RT
∆Gi = ∑ xl ∆Gil + ∑∑ x j xk ∆Gi j ,k
l j k> j
Ø
J. Andersson and J. Agren, J. Appl. Phys., 72 (1992) 1350
3
Thermodynamic Database
n Ø
1473K
4
S. Zhou et al., in submission, (2005)
Diffusivity in Ni-Al fcc Phase
n
Ni-Al
5
Ø
A. Engstrom, J. Agren, Z.Metallkd., 97 (1996) 92
Diffusivity in fcc Phase
n
Ni-Mo
n
Al-Mo
6
Diffusion in the L1 2 Ordered Phase of the Ni-Al System
7
Modeling the Ordered Phase
∆Gi = ∆G
dis i
+ ∆G
ord i
order β ∆Giord = ∑∑ ∆Gijk [ y α y k − x j xk ] j j k≠ j
Ø
T. Helander and J. Agren, Acta Mater., 47 (1999) 1141
8
Diffusivity in Stoichiometric Compound (Assessment I)
9
Diffusivity vs Composition (Assessment I)
10
Diffusion in L1 2 Ordered Phase
The movements of vacancies should not destroy the ordered structure.
11
Diffusion Mechanism in L12
n
v
Major element (Ni)
intra-lattice mechanism
n
v v v
Minor element (Al)
six-jump cycle mechanism anti-site mechanism anti-site bridge mechanism
I think you need extra illustration to show the 3 mechanisms
12
Diffusivity of Al (1473K)
13
Diffusivity of Al (973K)
14
Atomic Description for Diffusivity
n
Ni in the fcc Ni Matrix:
D
Ni Ni
=a C ω
2 Ni Ni V
Ni 0
f
Ni
There is no explanation of ωo,ω1,ω2,ω3, etc.
n
Ni in the Ni3 Al Matrix:
D
Ni3 Al Ni
n
Al in the fcc Ni Matrix: Ni
D
Ni Al
2 2 Ni = aNi3 Al CV 3 Alω0Ni3 Al f 3
2 Ni Ni V
Ni3 Al
=a C
n
Al in the Ni3 Al Matrix:
Ni DAl 3 Al
ω4 ω 2Ni f ω 3Ni
Ni
2 2 ω 4Ni3 Al Ni3 Al Ni = a Ni3 Al CV 3 Al Ni3 Al ω2 f 3 ω3
Ni3 Al
Ni PAl
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Numerical Treatment
n
(ω 4 / ω3 )(ω 2 / ω0 ) : reflects the impurity-vacancy and impurity-matrix interactions, assumed to be equal for the diffusion of Al in Ni3Al and fcc Ni.
Ni PAl P : anti-site factor.
n
Ni Al
Ni y Al = x Al
Ni Ni DAl 3 Al DNi Ni ≈ PAl Ni Ni DAl DNi 3 Al
Ø
H. Numakura, et al., Phil. Mag. A, 77 (1998) 887
16
Dictra Modeling on Diffusivity
n
Ni in the fcc Ni Matrix: dis
D
dis Ni
n
Ni in the Ni3 Al Matrix:
Ni DNi 3 Al
− ∆GNi = exp( ) RT
dis ord ∆GNi + ∆GNi = exp( − ) RT
n
Al in the fcc Ni Matrix: dis
D
dis Al
n
Al in the Ni3 Al Matrix:
Ni DAl 3 Al
− ∆GAl = exp( ) RT
dis ord ∆GAl + ∆GAl = exp( − ) RT
17
Numerical Treatment II
Ni Ni ord ord DAl 3 Al DNi ∆GAl − ∆GNi + ∆G ' = exp( − ) Ni3 Al Ni DAl DNi RT
n
dis Ni Ni dis Where ∆G ' = ∆G Al + ∆GNi − ∆G Al − ∆GNi , which can be calculated from the mobility descriptions of the related disordered phase.
18
Constraint from Diffusion Mechanism
Ni Ni DAl 3 Al DNi Ni = PAl Ni Ni DAl DNi 3 Al Ni Ni ord ord DAl 3 Al DNi ∆GAl − ∆GNi + ∆G ' = exp( − ) Ni3 Al Ni DAl DNi RT
⇓
ord ord ∆G Al − ∆GNi + ∆G' Ni exp(− ) = PAl RT
19
Anti-site Factor
n
Consider reaction:
Ni3 Al ( L12 ) ↔ ( Ni0.75 Al0.25 ) 3 ( Ni0.75 Al0.25 ) ( fcc)
n
Anti-site factor:
Ni y Al ∆G react Ni PAl = ≈ f fcc ≈ exp(− ) x Al RT
n
Energy of reaction can be calculated based on the thermodynamic database.
20
Diffusivity in Stoichiometric Compound (Assessment II)
21
Diffusivity vs Composition (Assessment II)
22
Diffusion in the L1 2 Ordered Phase of the Ni-Al-Mo System
23
Assumptions
Since Mo prefers to occupy Al-sites in Ni3Al ordered phase, we assume: n The diffusion of Mo in the L1 2 ordered is similar to that of Al. n The diffusion in the hypothetical Ni3Mo L1 2 ordered phase is similar to that in the Ni3Al phase. n The effect of Al-Mo ordering can be ignored.
24
Diffusivity of Mo in Ni3Al
25
Summary
n
n
n
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. 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. The anti-site mechanism is found to be dominant for Al diffusion in L12. The atomic mobility modeling is then refined based on the antisite mechanism. Atomic mobility in the L1 2 phase of Ni-Al-Mo system is evaluated from the experimental information in the literature.
26