Nanomaterial Phase Field Simulation Workshop in 2008

1. NIST Diffusion Workshop May 12-13, 2008, Gaithersburg, MD Single Phase Layer Formation in Nanostructured Multiphase Layered Structures Ximiao Pan, John E. Morral, Yunzhi Wang Department of Materials Science and Engineering The Ohio State University Columbus, Ohio

2. OUTLINE • Introduction • Particle coarsening in equilibrium layers • Single phase layer formation and horns • Single phase layer growth • Application of the KKS phase field model • Conclusions

3. + + + + + + + Phase field simulation of box with periodic boundary conditions + INTRODUCTIONMultiphase Layer structure A A A A A A A A

4. 2 A A 3 1 INTRODUCTIONRegular Solution Phase Diagram W12 = W23 = 20kJ/mole W13 = 0

5. ~20 m 2.5 m Same matrix No interdiffusion Small effect of particle coarsening PARTICLE COARSENING IN EQUILIBRIUM LAYERSPhase field simulation of nanostructured A/A layers on a tie-line

6. Different matrix No interdiffusion Single phase layers formed by particle coarsening PARTICLE COARSENING IN EQUILIBRIUM LAYERSPhase field simulation of nanostructured J/J layers on a tie-line

7. PARTICLE COARSENING IN EQUILIBRIUM LAYERSPhase field simulation of nanostructured J/J layers on a tie-line

8. Above equilibrium precipitate concentration due to capillarity Concentration gradient leading to layer growth PARTICLE COARSENING IN EQUILIBRIUM LAYERSPhase Field Simulation of nanostructured J/J layers on a tie-line

9. 0.0 1.0 0.1 0.0 0.9 1.0 0.2  0.1  0.8 0.9 0.3 0.2 0.7 0.8 0.4 0.3 0.6 0.7 0.5 0.4 0.5 0.6 0.6 0.5 0.4 0.5 0.7 0.6 0.3 0.4 0.8 0.7 0.2 0.3 0.8 0.9 0.2 0.1 0.9  1.0  0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 SINGLE PHASE LAYER FORMATION AND HORNS1-D simulations of diffusion paths across multiphase layers Constant Dij Atomicmobilities b1= b2= b3 Linear zigzag path Variable Dij Atomicmobilities b1=10, b2= 5, b3=1 Path with horns

10. 1.0 0.0 0.9 0.0 1.0 0.1 0.8 0.1 0.9 0.2 0.7 0.2 0.8 0.3 0.6 0.3 0.7 0.4 0.5 0.4 0.6 0.5 0.4 0.5 0.5 0.6 0.3 0.6 0.4 0.7 0.2 0.7 0.3 0.8 0.1 0.8 0.2 0.9 0.0 0.9 0.1 1.0 1.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Horns with no apparent Single phase layer SINGLE PHASE LAYER FORMATION AND HORNS1-D simulations of variable diffusivity paths with and without single phase layers Variable Dij Atomicmobilities b1=10, b2= 5, b3=1 Path with horns Horns with a Single phase layer

11. 0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 B=10:5:1 0.5 0.5 Flux 0.6 0.4 A2 0.7 0.3 0.8 0.2 A1 0.9 0.1 1.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Distance SINGLE PHASE LAYER FORMATION AND HORNS1-D simulations of variable diffusivity paths with a larger single phase layer

12. SINGLE PHASE LAYER GROWTHInvestigated layer pair compositions

13. SINGLE PHASE LAYER GROWTHTime evolution and diffusion path of layers E/E Diffusion path predicted by 1-D phase field + 1-D phase field

14. 250000 2 =82t 225000 2 EE:W 200000 175000 150000 =47t 2 125000 layer thickness squared (nm) EE:W 100000 75000 50000 25000 0 0 500 1000 1500 2000 2500 3000 dimensionless time SINGLE PHASE LAYER GROWTHLayer growth in E/E in repeated simulations

15. (a) A-A 1 mm (b) B-B (c) C-C (d) D-D 1 mm (e) E-E 1 mm 1 mm 1 mm SINGLE PHASE LAYER GROWTHComparison of phase field simulations after = 3000

16. APPLICATION OF THE KIM/KIM/SUZUKI PHASE FIELD MODELEffect of surface tension and length scale on the interdiffusion microstructure (a) KKS: s≈25 mJ/m2 (b) KKS: s≈50 mJ/m2 (c) KKS: s≈100 mJ/m2 (d )KKS: s≈200 mJ/m2 (e) KKS: s≈400 mJ/m2 (f) Classical model:

17. APPLICATION OF THE KIM/KIM/SUZUKI PHASE FIELD MODELEffect of rescaling the length to make the surface tensions equal and reducing the time to make the microstructures equal

18. CONCLUSIONS In model nanostructured multiphase multilayers • Interdiffusion, capillarity and the Kirkendall effectall play a role in the evolution of single phase layers. • The starting distribution of random precipitates can lead to significant differences in single phase layer growth kinetics. • While 1-D simulations predict that horns may or may not lead to single phase layer formation, non-equilibrium phase field simulations predict single phase layers even when the 1-D models don’t. • The KKS and classical phase field model results were comparable. • The initial precipitate size needs to be taken into account when comparing KKS simulations performed at different length scales.

21. X = 0 g+ g g+ b g+ b g+ b g Single Phase Layers formed by Horns Predicted by DICTRA Diffusion Couple results

22. Ji x Concentration profile x Theory of horns and an example using a finite difference simulation K. Wu, J.E. Morral, and Y. Wang, in press Acta Mater, Oct. 2006