Microstructural Evolution in InterdiffusionZone and Its Effect on Diffusion Path

K. Wu, J. E. Morral and Y. Wang

Department of Materials Science and EngineeringThe Ohio State University

Work Supported by NSFTMS05 Annual Meeting

Feb. 13-17, 2005, San Francisco, California

Experimental Observation of InterdiffusionMicrostructure and Diffusion Path

Xin Qiao. M.S. Thesis. University of Connecticut. 1998

γ+β<γ>γ+β>γ+γ’

Kirkendall porosity

IMS

1999 OSU-MSE Distinguished Alumnus Lecture J.E. Morral

The Multicomponent Mountain

?

Composition VectorComposition Vector

Amount of InterdiffusionSquare root diffusivity

Diffusivity measurementsZero-Flux Planes

Kirkendall porosityZigzag diffusion paths

Three types of boundaryShort hand notation

Interdiffusion microstructure mapsFive-line nodes

Predict InterdiffusionMicrostructure

IMS

1999 OSU-MSE Distinguished Alumnus Lecture J.E. Morral

The Other Side of the MulticomponentMountain

?

High Temp. Coatings

Diffusion bondingSoldering and Brazing

Phase TransformationsCarburizing, Nitriding

Powder Processing

Predict InterdiffusionMicrostructure

IMS

1999 OSU-MSE Distinguished Alumnus Lecture J.E. Morral

Climbing the Multicomponent Mountain with John

?

Composition VectorComposition Vector

Amount of InterdiffusionSquare root diffusivity

Diffusivity measurementsZero-Flux Planes

Kirkendall porosityZigzag diffusion paths

Three types of boundaryShort hand notation

Interdiffusion microstructure mapsFive-line nodes

Predict InterdiffusionMicrostructure

Phase Field

Coupling interdiffusion with microtructural evolution:• Effect of two-phase

microstructure on interdiffusionand diffusion path

• Interdiffusion induced phase and microstructure instabilities

• Effect of concentration gradient on nucleation, growth and coarsening

• Effect of phase transformation on interdiffusion

• Roles of coherency/thermal stress on interdiffusion and phase transformation

• One-dimensional diffusion in a common matrix phase

• Precipitates are treated as stationary point sources or sinks of solute

• Mutual interactions between microstructure and interdiffusion and corresponding effects on diffusion path and microstructural evolution are ignored

Simple Model System

• Elements A and B form ideal solution while elements A and C or B and C form regular solutions

A B

C

α

α’

Acta Mater., 49(2001), 3401-3408

Free energy model

( ) ( )ln ln lnm A A B B C c A C B CG RT X X X X X X I X X X X= + + + +

Wu et. al. Acta mater. 2001;49:3401Wu et. al. Acta mater, 2004; 52:1917

Phase Field Equations

( ) ( )11 12B

B A C AX M Mt

µ µ µ µ∂ ⎡ ⎤ ⎡ ⎤= ∇ ∇ − + ∇ ∇ −⎣ ⎦ ⎣ ⎦∂

( ) ( )21 22C

B A C AX M Mt

µ µ µ µ∂ ⎡ ⎤ ⎡ ⎤= ∇ ∇ − + ∇ ∇ −⎣ ⎦ ⎣ ⎦∂

µB − µA = µBB − µA

B − 2κ 11∇2 XB − 2κ12∇2 XC

µC − µA = µCB − µA

B − 2κ 21∇2 XB − 2κ 22∇

2 XC

Mij - chemical mobilities

κij - gradient coefficients

βI - atomic mobilities

ρ - molar density

Diffusion equations

Gradient thermodynamics

Kinetics parameters( )

( ) ( )

( )

211

12 21

222

1

1 1

1

B B B B C C B A A

B C B B C C A A

C B C B C C C A A

M X X X X X X

M M X X X X X

M X X X X X X

ρ β β β

ρ β β β

ρ β β β

⎡ ⎤= − + +⎣ ⎦= = − − − − +⎡ ⎤⎣ ⎦

⎡ ⎤= + − +⎣ ⎦

Wu et. al. Acta mater. 2001;49:3401Wu et. al. Acta mater, 2004; 52:1917

τ = 0

τ = 100

τ = 2000

Interaction between Microstructure and Interdiffusion – Type 0 boundary

4608x64 size simulation, 1024x256 size output

βB=1.0 βC=5.0 βA=10.0

• Ppt and Type 0 boundary migrate as a results of Kirkendall effect

• Type 0 boundary becomes diffuse

• Kirkendall markers move along curved path and marker plane bends around precipitates

• Diffusion path differs significantly from 1D calcul.

• Ppt and Type 0 boundary migrate as a results of Kirkendall effect

• Type 0 boundary becomes diffuse

• Kirkendall markers move along curved path and marker plane bends around precipitates

• Diffusion path differs significantly from 1D calcul.

Size and position changes during interdiffusion

Diffusion path: comparison with 1D simulation

1

Wu et. al. Acta mater. 2001;49:3401Wu et. al. Acta mater, 2004; 52:1917

Real Alloy System: Ni-Al-Cr

Exp. Observation by Nesbitt and Heckel in Met Trans. A (1986)18A: 2087-2094

ExperimentalData

ExperimentalData

MobilityDatabase Mobility

Database

TDDatabase

TDDatabase

Chemical Diffusivity of Al

Thermodynamic description

Phase Field

Interface Properties

Interface Properties

Elastic PropertiesElastic

Properties

Other properties

Database development

Atomistic CalculationsAtomistic

Calculations

DICTRA DICTRA

Thermo_Calc or PANDAT

Thermo_Calc or PANDAT

DICTRA

Phase FieldModel

γ-surfacesγ-surfaces

Optimizer

Constitutiveequation

construction

Constitutiveequation

construction

Phase field model

development

Kinetic description

Linking to Thermo. and Kinetic Databases and Atomistic Calculations

Scripta mater. 50(2004)471-476; ibid,50(2004)1145-1150

Quantitative comparison with DICTRA

Dissolution

Growth

Q. Chen et. al. Scripta mater. 50 (2004)471-476

Exp. Observation by Nesbitt and Heckel

Interdiffusion Microstructure and Diffusion Path0 hr

4 hr

25 hr

320µm

100 hrat 1200oC

Ni-Al-Cr at 1200oC

• Free energy data from Huang and Chang

• Mobilities in γ from A.EngstrÖm and J.Ågren

• Diffusivities in β from Hopfe, Son, Morral and Roming

• Free energy data from Huang and Chang

• Mobilities in γ from A.EngstrÖm and J.Ågren

• Diffusivities in β from Hopfe, Son, Morral and Roming

200µm

XCr =0.25, XAl=0.001

γ+β < γ

Annealing time: 25 hours

(a)

(b)

(c)

Effect of Cr content on interface migrationEffect of Cr content on interface migration

320µm

Ni-Al-Cr at 1200oC

(d)

b ca d

γ+β < γ

Exp. measurement by Nesbitt and Heckel

Diffusion path and recess rate -comparison with experiment

Diffusion path and recess rate -comparison with experiment

Annealing time: 25 hours

(a)

(b)

(c)

Effect of Al content on interface migrationEffect of Al content on interface migration320µm

a

cb

c

γ+β < γ

Annealing time: 25 hours

(a)

(b)

Effect of Al content on interface migrationEffect of Al content on interface migration

320µm

ab

γ+β > γ

γ+β < γ

Shape of the Diffusion Path

t = 0

t = 25h

t = 100h pure coarseningγ+β > γ

500µm

β- γ+

Shape of Diffusion Path - Comparison with DICTRA

0.15

0.20

0.10

γ+β

γ

A.EngstrÖm, J. E. Morral and J.ÅgrenActa mater. 1997

Growth vs. Nucleation

γ+β > γγ+β < γ

Summary – Remaining Challenges

• Incorporation of nucleation• Breaking the intrinsic length scale limit of quantitative

phase field modeling- effect of surface energy, e.g.,

coarsening and coalescence

• Quantitative comparison with experiment- accuracy of thermodynamic and mobility databases- accurate determination of average composition of multiphase

microstructure in both simulation and experiment- Accurate determination of boundary position

c

η

C. Shen et al., Scripta mater. (2004) 50:1023-1028; ibid, 1029-1034.