Modeling on Diffusion in Ni-base Superalloy

Tao Wang, Long-Qing Chen and Zi-Kui Liu

The Penn State University

April 19th, 2005

Microstructure Evolution of Ni-base Alloys

A real turbine blade made of Ni-base superalloys, a γ (fcc) and γ’ (L12) two phase microstructure from a phase-field simulation, and a schematic phase diagram for the γ and γ’two-phase field.

Evolution Equations in Phase-field Model

⎥⎦

⎤⎢⎣

⎡∂

∂∇∇=⎥

⎦

⎤⎢⎣

⎡∇∇=

∂∂

),(),(),(

tcfM

tcFM

ttc

mim

mim

i

rrr

δδ

Thermodynamic Database

Atomic Mobility Database

Lattice Parameter Database

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂−∇−=−=

∂

∂

),(),(

),(),( 22

tftL

tFL

tt

nnjn

njn

j

rr

rr

φφε

δφδφ

M is diffusion mobility and L is phase field mobility.

Modeling on Atomic Mobility

Ordered Phases:ordi

disii GGG ∆+∆=∆

∑∑≠

−∆=∆j jk

kjkjorderijk

ordi xxyyGG ][ βα

)lnexp(1)exp(00

RTMRTQ

RTRTQ

RTMM iiii

i+−

=−

=

)exp(1RT

GRT

M ii

∆−=

∑∑∑>

∆+∆=∆j jk

kjikj

l

lili GxxGxG ,

A-B binary system:

M: diffusion mobility in phase field

( )ABBABA MxMxxxM +=

Andersson J and Agren J, J Appl Phys, 72 (1992) 1350Helander T and Agren J, Acta Mater, 47 (1999) 1141

Thermodynamic Database

1473K

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

Diffusivity in Ni-Al fcc Phase

Ni-Al

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

Diffusivity in fcc Phase

Ni-Mo Al-Mo

Diffusivity in Stoichiometric Compound (Assessment I)

Diffusivity vs Composition(Assessment I)

Diffusion Mechanism in L12

Major element (Ni)intra-lattice mechanism

Minor element (Al)six-jump cycle mechanismanti-site mechanismanti-site bridge mechanism

Diffusivity of Al (1473K)

Diffusivity of Al (973K)

Atomic Description for Diffusivity

Ni in the fcc Ni Matrix:

Ni in the Ni3Al Matrix:

Al in the fcc Ni Matrix:

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 ω

ωω

=

Numerical Treatment

: anti-site factor.

: reflects the impurity-vacancy and impurity-matrix interactions, assumed to be equal for the diffusion of Al in Ni3Al and fcc Ni.

NiAlAlNi

Ni

NiNi

NiAl

AlNiAl P

DD

DD

≈3

3

)/)(/( 0234 ωωωω

NiAlP

Al

NiAlNi

Al xy

P =

H. Numakura, et al., Phil. Mag. A, 77 (1998) 887

Dictra Modeling on Diffusivity

Ni in the fcc Ni Matrix:

Ni in the Ni3Al Matrix:

Al in the fcc Ni Matrix:

Al in the Ni3Al Matrix:

)exp(RTGD

disNidis

Ni∆−

=

)exp(RTGD

disAldis

Al∆−

=

)exp(3

RTGGD

ordAl

disAlAlNi

Al∆+∆

−=

)exp(3

RTGGD

ordNi

disNiAlNi

Ni∆+∆

−=

Numerical Treatment II

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 ∆−∆−∆+∆=∆ '

Constraint from Diffusion Mechanism

NiAlAlNi

Ni

NiNi

NiAl

AlNiAl P

DD

DD

=3

3

)'exp(3

3

RTGGG

DD

DD ord

NiordAl

AlNiNi

NiNi

NiAl

AlNiAl ∆+∆−∆

−=

⇓

NiAl

ordNi

ordAl P

RTGGG

=∆+∆−∆

− )'exp(

Anti-site Factor

Consider reaction:

Anti-site factor:)( )()()1( 25.075.0325.075.023 fccAlNiAlNiLAlNi ↔

)exp(RTGf

xyP

react

fccAl

NiAlNi

Al∆

−≈≈=

reactordNi

ordAl GGGG ∆=∆+∆−∆ '

Diffusivity in Stoichiometric Compound (Assessment II)

Diffusivity vs Composition(Assessment II)

Optimized Parameters for Ni3Al

ordAlNiAlG∆ ord

NiNiAlG∆ ordAlAlNiG∆ ord

NiAlNiG∆

Assessment I 1.8804e+05 -9.3253e+04 6.0418e+05 -5.8868e+05Assessment II 1.2499e+05 -7.8982e+04 3.6406e+05 -5.3770e+05

Units: J/mole

Diffusion in L12 of the Ni-Al-Mo System

Since Mo prefers to occupy Al-sites in Ni3Al ordered phase, we assume:The effect of Al-Mo ordering can be ignored.The diffusion in the hypothetical Ni3Mo L12ordered phase is similar to that in the Ni3Al phase.The diffusion of Mo in the L12 ordered phase is similar to that of Al.

Diffusivity of Mo in Ni3Al

Phase Field Simulation vs Experimental Investigation

Alloy: Ni-7.7 at.%Al-7.9 at.%MoSystem size: 1024nm×1024nm; Temperature: 1048K; Annealing time: 67hLeft: TEM images; Right: 2D phase-field simulations

Summary

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 anti-site mechanism.Atomic mobility in the L12 phase of Ni-Al-Mo system is evaluated from the experimental information in the literature.Using the above atomic mobility in the fcc and L12 phases, phase field simulations for Ni-Al-Mo alloys have been performed.