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Analysis of Diffusion Path and Interdiffusion Microstructure

Y. Wang and J. E. MorralDepartment of Materials Science and Engineering

The Ohio State University

Work Supported by NSFNIST Diffusion Workshop

April 19-20, 2005, Gaithersburg, MD

Outline• Discontinuities in interdiffusion microstructure and “horns”

in the diffusion path• Motion of Type-0 boundaries and its effect on the shape

of diffusion path• Variation in microstructure and diffusion path caused by

deviation from local-equilibrium conditions and by precipitate coarsening

• Special points on the phase diagram that act as “strange attractors” of the diffusion paths

• Development of various morphological instabilities including concentration-gradient induced rafting

These phenomena are associated with intimate thermodynamic and kinetic coupling in multi-component diffusion and interactions between interdiffusion and microstructural evolution in multi-phase regions

Understanding the “Horns” in Diffusion Path

Horns predicted by DICTRA and Phase Field simulations

Schwind, Helendar and Argren, Scripta mater. 2001 Wu, Morral and Wang, Acta mater. 2001

A-B-C Model System

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

A B

C

’

Free energy model

Gm RT XA ln XA XB ln XB XC ln Xc I XA XC XB XC

Linear Diffusion Path

dc d

2

dJd

dc 2dc 1

dJ2

ddJ1

d

J1 D11c1

J2 D21c1

D21 RTc 2 A B

D11 RT B c1 A B

B=5.0 C=1.0 A=5.0

Single-Horn Diffusion Path

J1 D11c1

J2 D21c1

D21 RTc 2 A B

D11 RT B c1 A B

B=1.0 C=5.0 A=10.0(1)

(2)

Single-Horn Diffusion Path

12

34

1

2

3 4

dc 2dc 1

dJ2

ddJ1

d

Double-Horn Diffusion Path

0.000 0.001 0.002 0.003 0.004

0.00E+000

2.00E-010

4.00E-010

6.00E-010

8.00E-010

1.00E-009

1.20E-009

JM(A

l)

Distance x(m)

20.0 20.2 20.4 20.6 20.8 21.015

16

17

18

19

20

21

C(C

r)

C(Al)

0.000 0.001 0.002 0.003 0.004

0.00E+000

5.00E-010

1.00E-009

1.50E-009

2.00E-009

JM(C

r)

Distance x(m)

Interpretation of Simulation Results

'<<'<+

=0.0

=2000.0

B=10.0 C=5.0 A=1.0

c1 = 25 at%, c2 = 40 at% c1 = 32 at%, c2 = 60 at%

JA

JB

net flux of (A+B)

(2)

(1)

Simulations have stimulated the development of theoretical understanding and new theoretical principles have guided the interpretation of simulation results

Wu, Morral and Wang, Acta mater. 49, 3401 – 3408 (2001)

Yong-Ho Sohn and M. Dayananda

+/+ Couple

>+

=0.0

=2000.0

B=1.0 C=5.0 A=10.0

c1 = 25 at%, c2 = 40 at% c1 = 32 at%, c2 = 60 at%

(2)

(1)

JAJB

net flux of (A+B)

Wu, Morral and Wang, Acta mater. 49, 3401 – 3408 (2001)

= 0

= 100

= 2000

Moving Type 0 Boundary

4608x64 size simulation, 1024x256 size output

1=1.0 2=5.0 3=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

K. Wu, J. E. Marrol and Y. Wang, Acta mater. 52:1917-1925 (2004)

Size and position changes during

interdiffusion

Diffusion path: comparison with 1D simulation

Exp. Observation by Nesbitt and Heckel

Interdiffusion Microstructure in NI-Al-Cr Diffusion Couple0 hr

4 hr

25 hr

320m

100 hrat 1200oC

Ni-Al-Cr at 1200oC

• Free energy data from Huang and Chang

• Mobilities in from A.EngstrÖm and J.Ågren

• Diffusivities in from Hopfe, Son, Morral and Roming

200m

XCr =0.25, XAl=0.001

Annealing time: 25 hours

(a)

(b)

(c)

Effect of Cr content on interface migration

320m

Ni-Al-Cr at 1200oC

(d)

b ca d

Exp. measurement by Nesbitt and Heckel

Diffusion path and recess rate - comparison with experiment

Annealing time: 25 hours

(a)

(b)

Effect of Al content on interface migration

320m

ab

Interpretation of Phase Field Simulation - Effect of Coarsening

t = 0

t = 25h

t = 100h

Effect of Pure Coarsening

t = 0

t = 100h

t = 200h

Interpretation of Phase Field Simulation - Effect of Coarsening

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

Interpretation of Phase Field Simulation - Deviation from Local Equilibrium Condition

0.15

0.20

0.10

e0025.mov e0045.mov

Lawrence A. Carol, Michigan Tech. 1985

“strange attractors” of the diffusion paths

Concentration-Gradient Induced Rafting

Hazotte and Lacaze, Scripta metall.

Aging of initially as cast alloy (1100oC for 1500 hr.)

Interdendritic zone

Secondary dendritic arm

Secondary dendritic armDendritic core

Interdiffusion Induced Rafting = 0

= 40

= 220

= 400

Initial Configuration

Misfitting particle Stress-free particles

No interdiffusion With interdiffusionNo interdiffusion With interdiffusion

B=5.0 C=1.0 A=5.0

left: XB=0.125, XC=0.489right: XB=0.6 XC=0.1

Summary – Predicting of Interdiffusion Microstructure

• DICTRA and Phase Field share the same thermodynamic and diffusivity databases

• DICTRA directly outputs diffusion path on phase diagram and runs on PC, but is an1D program, assumes local-equilibrium, treats precipitates as point sources or sinks, and is accurate when most diffusion occurs in a single, matrix phase, no metastable states, and for limited boundary conditions

• Phase Field directly outputs microstructure, does not require local-equilibrium, can treat diffusion couples of different matrix phase, is able to consider a wide variety of boundary conditions, and allows for studies of effects of precipitates morphology on interdiffusion and interdiffusion on microstructural evolution. But many critical issues remain•Computation efficiency•How to determine accurately the average compositions in the two-phase regions

•How to analyze the diffusion path using statistically meaningful microstructures and computationally tractable system sizes without artificial Gibbs-Thompson effect

• Incorporation of nucleation – work in progress

Phase Field Equations

XB

t M11 B A M12 C A

XC

t M21 B A M22 C A

B A BB A

B 2 112 XB 212

2 XC

C A CB A

B 2 212 XB 2 22

2 XC

Mij - chemical mobilities

ij - gradient coefficients

I - atomic mobilities

- molar density

Diffusion equations

Thermodynamic parameters

Kinetics parametersM11 XB 1 XB 2B XBXCC XB XA A M12 M21 XB XC 1 XB B 1 XC C XA A M22 XC XBXC B 1 XC 2C XC XA A

Effect of Gradient Term

3c

J

B A BB A

B 2 112c1 212

2c2