# Presentation: 004967

## Analysis of Diffusion Path and Interdiffusion Microstructure

- Y. Wang and J. E. Morral
- Department of Materials Science and Engineering
- The Ohio State University
- Work Supported by NSF
- NIST 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

## Horns predicted by DICTRA and Phase Field simulations 

- 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

- Free energy model

## Linear Diffusion Path

- B=5.0 C=1.0 A=5.0

## Single-Horn Diffusion Path

- B=1.0 C=5.0 A=10.0

- (1)

- (2)

## Single-Horn Diffusion Path

- 1

- 2

- 3

- 4

- 1

- 2

- 3

- 4

## Double-Horn Diffusion Path

## Interpretation of Simulation Results

- '<<'<+

- =0.0

- =2000.0

- B=10.0 C=5.0 A=1.0

*c*1 = 25 at%, *c*2 = 40 at%

*c*1 = 32 at%, *c*2 = 60 at%

*J*A

*J*B

- 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 

- +/+ Couple

- >+

- =0.0

- =2000.0

- B=1.0 C=5.0 A=10.0

*c*1 = 25 at%, *c*2 = 40 at%

*c*1 = 32 at%, *c*2 = 60 at%

- (2)

- (1)

*J*A

*J*B

- net flux of (A+B)

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

## Moving Type 0 Boundary

******= 0**

******= 100**

******= 2000**

- 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

## Interdiffusion Microstructure in NI-Al-Cr Diffusion Couple

*Exp. Observation by Nesbitt and Heckel*

- 0 hr

- 4 hr

- 25 hr

- 100 hr
- at 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

*X*Cr =0.25, *X*Al=0.001

## Effect of Cr content on interface migration 

- Annealing time: 25 hours

- (a)

- (b)

- (c)

- Effect of Cr content on interface migration

- 320m

- Ni-Al-Cr at 1200oC

- (d)

- b

- c

- a

- d

## Diffusion path and recess rate - comparison with experiment 

*Exp. measurement by Nesbitt and Heckel*

- Diffusion path and recess rate - comparison with experiment

## (a)

- Annealing time: 25 hours

- (b)

- Effect of Al content on interface migration

- 320m

## Interpretation of Phase Field Simulation - Effect of Coarsening

*t *= 0

*t* = 25*h*

*t* = 100*h*

## Effect of Pure Coarsening

## Interpretation of Phase Field Simulation - Effect of Coarsening

*t *= 0

*t* = 100*h*

*t* = 200*h*

## Interpretation of Phase Field Simulation - Deviation from Local Equilibrium Condition

- A.EngstrÖm, J. E. Morral  and J.Ågren
*Acta mater. 1997*

- 0.15

- 0.20

- 0.10

- 

- 

- _[e0025.mov](file:///../../Current%20Project/MAI/MAI_Ladish_012605/movies/e0025.mov)_

- _[e0045.mov](file:///../../Current%20Project/MAI/MAI_Ladish_012605/movies/e0045.mov)_

## “strange attractors” of the diffusion paths

- 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 arm

- Dendritic core

**Notes:**
People also observed that whenever large concentration gradient exist, it will induce rafting of gamma prime particles along the direction which is perpendicular to the concentration gradient - concentration gradient induced rafting.

## Interdiffusion Induced Rafting 

-  = 0

-  = 40

-  = 220

-  = 400

- Initial Configuration

- Misfitting particle

- Stress-free particles

- No interdiffusion          With interdiffusion

- No interdiffusion         With interdiffusion

- B=5.0 C=1.0 A=5.0

- left: *X*B=0.125, *X*C=0.489
- right: *X*B=0.6 *X*C=0.1

**Notes:**
How large of the lattice mismatch:

## 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 

*M**ij *- chemical mobilities
**ij - gradient coefficients
**I - atomic mobilities
** - molar density

- Diffusion equations

- Thermodynamic parameters

- Kinetics parameters

## Effect of Gradient Term 

*J*