NIST Diffusion Workshop May 12 13 2008 Gaithersburg

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

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

INTRODUCTION Multiphase Layer structure + + A A + + A A Phase field simulation of box with periodic boundary conditions

INTRODUCTION Regular Solution Phase Diagram 2 W 12 = W 23 = 20 k. J/mole A A 3 1 W 13 = 0

PARTICLE COARSENING IN EQUILIBRIUM LAYERS Phase field simulation of nanostructured A/A layers on a tie-line ~20 m 2. 5 m Same matrix No interdiffusion Small effect of particle coarsening

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

PARTICLE COARSENING IN EQUILIBRIUM LAYERS Phase field simulation of nanostructured J/J layers on a tie-line

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

SINGLE PHASE LAYER FORMATION AND HORNS 1 -D simulations of diffusion paths across multiphase layers 0. 0 0. 1 0. 2 0. 0 1. 0 0. 1 0. 9 0. 2 0. 8 0. 3 0. 5 1. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 Constant Dij Atomic mobilities b 1 = b 2 = b 3 Linear zigzag path 0. 8 0. 9 1. 0 0. 3 0. 8 0. 2 0. 9 0. 4 0. 7 0. 3 0. 8 0. 5 0. 6 0. 4 0. 7 0. 6 0. 5 0. 6 0. 7 0. 4 0. 6 0. 9 0. 8 0. 3 0. 7 0. 4 1. 0 0. 9 1. 0 0. 2 0. 1 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 Variable Dij Atomic mobilities b 1=10, b 2= 5, b 3=1 Path with horns 0. 0

SINGLE PHASE LAYER FORMATION AND HORNS 1 -D simulations of variable diffusivity paths with and without single phase layers 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 0 1. 0 0. 1 0. 9 0. 2 0. 8 0. 3 0. 7 0. 4 0. 6 0. 5 0. 6 0. 7 0. 8 0. 6 0. 4 0. 8 0. 7 0. 6 0. 5 0. 4 1. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 0. 3 0. 8 0. 1 Horns with no apparent Single phase layer 0. 9 0. 7 0. 3 0. 2 0. 9 1. 0 0. 2 0. 9 0. 1 1. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 Variable Dij Atomic mobilities b 1=10, b 2= 5, b 3=1 Path with horns Horns with a Single phase layer 0. 0

SINGLE PHASE LAYER FORMATION AND HORNS 1 -D simulations of variable diffusivity paths with a larger single phase layer 0. 0 0. 1 1. 0 0. 9 0. 2 0. 8 0. 3 0. 7 0. 4 B=10: 5: 1 0. 5 0. 6 0. 9 0. 5 A 2 0. 7 0. 8 0. 6 Flux 0. 4 0. 3 A 1 0. 2 0. 1 1. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 0. 0 Distance

SINGLE PHASE LAYER GROWTH Investigated layer pair compositions

SINGLE PHASE LAYER GROWTH Time evolution and diffusion path of layers E/E Diffusion path predicted by phase field + 1 -D

SINGLE PHASE LAYER GROWTH Layer growth in E/E in repeated simulations layer thickness squared (nm)2 250000 225000 2 : W 2 t 8 = EE 200000 175000 150000 2 125000 : W EE 100000 750000 25000 0 0 500 1000 1500 2000 2500 dimensionless time t 7 =4 3000

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

APPLICATION OF THE KIM/SUZUKI PHASE FIELD MODEL Effect of surface tension and length scale on the interdiffusion microstructure (a) KKS: s≈25 m. J/m 2 (b) KKS: s≈50 m. J/m 2 (c) KKS: s≈100 m. J/m 2 (d )KKS: s≈200 m. J/m 2 (e) KKS: s≈400 m. J/m 2 (f) Classical model:

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

CONCLUSIONS In model nanostructured multiphase multilayers • Interdiffusion, capillarity and the Kirkendall effect all 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.

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

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