# Presentation: 004968

## Phase Field Modeling of Interdiffusion Microstructures

- K. Wu, J. E. Morral and Y. Wang
- Department of Materials Science and Engineering
- The Ohio State University
- Work Supported by NSF
- NIST Diffusion Workshop
- September 16-17, 2003, Gaithersburg, MD

## Examples of Interdiffusion Microstructures

- F-22

- 

- Ni-Al-Cr

**Courtesy of M. Walter**

- Disk alloy (courtesy of M.F. Henry)

- Turbine blade and disk

## Examples of Interdiffusion Microstructures

- Pb and Pb-free solders

- Co2Si/Zn diffusion couple

- SnPb/Cu

- SnBi/Cu

- SnAg/Cu

- Sn/Cu

- (HK Kim and KN Tu)

- (MR Rijnders and FJJ Van Loo)

## Challenges in Modeling Interdiffusion Microstructures

- Multi-component, multi-phase, multi-variant and polycrystalline
- Very complex microstructural features:
- high volume fraction of precipitates
- non-spherical shape and strong spatial correlation
- elastic interactions among precipitates
- Interdiffusion induces both microstructure and phase instabilities.
- Effect of concentration gradient on nucleation, growth and coarsening.
- Roles of defects and coherency/thermal stress on interdiffusion and phase transformation.
- Robustness and computational efficiency of models.

## Methods Available

- One-dimensional diffusion in a common matrix phase
- Precipitates are treated as point sources or sinks of solute
- Mutual interactions between microstructure and interdiffusion and corresponding effects on diffusion path and microstructural evolution are ignored

- Limitations

**You don’t see the microstructure!**

- Advantages
- Simple and efficient: *Error Function* solutions are close forms and *Dictra* is computationally efficient.

## Advanced Microstructure Modeling using Phase Field Method

- Advanced Microstructure Modeling using Phase Field Method

- Y. Jin et. al.

- The phase field method handles well arbitrary microstructures consisting of diffusionally and elastically interacting particles and defects of high volume fraction and accounts self-consistently for topological changes such as particle coalescence.

## Study Interdiffusion Microstructures

- Link to multi-component diffusion and alloy thermodynamic databases
- Break the intrinsic length scale limit
- Interaction between microstructure and interdiffusion processe:
- 	-	Motion of Kirkendall markers, second phase 		particles and Type 0 boundary, non-linear 		diffusion path
- 	-	Interdiffusion microstructure in Ni-Al-Cr 		diffusion couples

## Linking to Thermo. and Kinetic Databases

**Kinetic description**

**Experimental**
**Diffusivity Data**

**Experimental**
**TD Data**

**Mobility**
**Database **

**DICTRA **

**TD**
**Database**** **

**Thermo_Calc **
**or PANDAT**** **

- Chemical Diffusivity of Ti

**Thermodynamic description**

**Phase Field**

**Atomistic **
**Calculations**

**Atomistic **
**Calculations**

**Elastic **
**Properties**

**Interface **
**Properties**

- 1173K

## Linking to CALPHAD Method for Fee Energy

- How to construct non-equilibrium free energy from equilibrium properties?

*f*

*c*

**

*c*

*f*

**= 0

**=**

## Construction of Non-Equilibrium Free Energy

- Equilibrium free energy cannot be incorporated directly in the expression. A1, A2, and A3 need to be fitted to thermodynamic data at different temperature in the whole composition range.
- It is difficult to do for multicomponent systems.

**Indirect Coupling**: Landau polynomial expansion for the free energy:

## Construction of Non-Equilibrium Free Energy

- Equilibrium free energy can be incorporated directly into the non-equilibrium free energy formulation for any multi-component system without any extra effort.

- o

**Direct Coupling**: following the same approach as phase field modeling of solidification (e.g.,WBM or S-SK model)

- Wang et. al, Physica D,1993; 69:189

## Application I: Model System

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

- Free energy model

*Wu et. al. Acta mater. 2001;49:3401*
*Wu et. al. Acta mater, preprint.*

## Phase Field Equations 

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

- Diffusion equations

- Thermodynamic parameters

- Kinetics parameters

## Interaction between Microstructure and Interdiffusion

******= 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
- Diffusion path differs significantly from 1D calcul.

## Size and position changes during interdiffusion

- Diffusion path: comparison with 1D simulation

*Wu et. al. Acta mater. 2001;49:3401*
*Wu et. al. Acta mater, preprint.*

## Diffusion Couple of Different Matrix Phases 

- Diffusion Couple of Different Matrix Phases

- =0.0

- =2000.0

- B=10.0 C=5.0 A=1.0

*X*B = 25 at%, *X*C = 40 at%

*X*B = 32 at%, *X*C = 60 at%

*J*A

*J*B

- net flux of (A+B)

- Kirkendall Effect: Boundary migrates and particles drift due to difference in atomic mobility
- Moving direction opposite to the net flux of A+B
- Non-linear diffusion path penetrating into single phase regions

- <<<

- 

- 

## Effect of Mobility Variation in Different Phases

************= 0**

- M:1=1.0 2=5.0 3=10.0

- Ppt1=1.0 2=5.0 3=5.0

## 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

## Effect of Al content on interface migration 

- Annealing time: 25 hours

- (a)

- (b)

- (c)

- Effect of Al content on interface migration

- c

## (a)

- Annealing time: 25 hours

- (b)

- Effect of Al content on interface migration

- 320m

## Diffusion Path in the Two-Phase Region

*t *= 0

*t* = 25*h*

*t* = 100*h*

## Diffusion Path - Comparison with DICTRA

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

*t *= 0

*t* = 25*h*

*t* = 100*h*

## Two-Phase/Two-Phase Diffusion Couple

*t *= 0

- 10*h*

- 35*h*

## Two-Phase/Two-Phase Diffusion Couple

*t *= 0

*t* = 100*h*

*t* = 200*h*

## Summary 

- Computational methods based on phase field approach and linking to CALPHAD and DICTRA databases have been developed to investigate for the first time effects of microstructure on interdiffusion and interdiffusion on microstructural evolution in the interdiffusion zone.
- Realistic simulations of complicated interdiffusion microstructures in multi-component and multi-phase diffusion couples have been demonstrated.
- Many non-trivial results have been predicted, which are significantly different from earlier work based on 1D models.