1

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

2

Diffusion in the fcc Disordered Phase of the Ni-Al-Mo System

3

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

4

Thermodynamic Database

Ø S. Zhou et al., in submission, (2005)

n 1473K

5

Diffusivity in Ni-Al fcc Phase

Ø A. Engstrom, J. Agren, Z.Metallkd., 97 (1996) 92

n Ni-Al

6

Diffusivity in fcc Phase

n Ni-Mo n Al-Mo

7

Diffusion in the L12 Ordered Phase of the Ni-Al System

8

Modeling the Ordered Phase

Ø T. Helander and J. Agren, Acta Mater., 47 (1999) 1141

ordi

disii GGG ∆+∆=∆

∑∑≠

−∆=∆j jk

kjkjorderijk

ordi xxyyGG ][ βα

9

Diffusivity in Stoichiometric Compound (Assessment I)

10

Diffusivity vs Composition(Assessment I)

11

Diffusion in L12 Ordered Phase

The movements of vacancies should not destroy the ordered structure.

12

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

13

Diffusivity of Al (1473K)

14

Diffusivity of Al (973K)

15

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.

16

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 =

17

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∆+∆

−=

18

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 ∆−∆−∆+∆=∆ '

19

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 ∆+∆−∆

−=

⇓

20

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∆

−≈≈=

21

Diffusivity in Stoichiometric Compound (Assessment II)

22

Diffusivity vs Composition(Assessment II)

23

Diffusion in the L12 Ordered Phase of the Ni-Al-Mo System

24

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.

25

Diffusivity of Mo in Ni3Al

26

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.