Transcript Single Phase Layer Formation in Nanostructured Multiphase Layered Structures NIST Diffusion Workshop

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
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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
+
+
A
A
+
A
A
Phase field simulation of box
with periodic boundary conditions
INTRODUCTION
Regular Solution Phase Diagram
2
W12 = W23 = 20kJ/mole
A
A
3
1
W13 = 0
PARTICLE COARSENING IN EQUILIBRIUM LAYERS
Phase field simulation of nanostructured
A/A layers on a tie-line
~20 m
2.5 m
~  30
~ = 3000
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
~ = 30
~ = 3000
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
Mole_fraction (C)
1.0
0.8
0.6
0.4
0.2
0.0
0
100
200
300
X_distance
400
500
PARTICLE COARSENING IN EQUILIBRIUM LAYERS
Phase Field Simulation of nanostructured
J/J layers on a tie-line
Above equilibrium precipitate concentration
due to capillarity
0.835
d
0.830
0.830
d
Mole_fraction (C)
0.840
0.825
0.820
0
100
200
300
400
500
400
500
X_distance
0.175
d
0.170
0.169
d
Mole_fraction (C)
0.180
0.165
0.160
0
100
200
300
X_distance
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

0.0
1.0
0.1
0.9
0.2
0.2
0.8
0.3
0.5

0.1
1.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Constant Dij
Atomic mobilities
b1= b2= b3
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
0.5
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
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Variable Dij
Atomic mobilities
b1=10, b2= 5, b3=1
Path with horns
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
0.5
0.6
0.7
0.8
0.6
0.4
0.8
0.7
0.6
0.5
0.4
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
0.3
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
0.0
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
b1=10, b2= 5, b3=1
Path with horns
Horns with a
Single phase layer
SINGLE PHASE LAYER FORMATION AND HORNS
1-D simulations of variable diffusivity paths with a
larger single phase layer
0.0
1.0
0.1
0.9
0.2
0.8
0.3
0.7
0
0.4
0.6
B=10:5:1
0.6
A2
0.7
-1000000
0.5
Flux
flux
0.5
0.8
1000000
0.4
-2000000
0.3
-3000000
0.2
A1
0.9
0.1
1.0
J1
J2
-4000000
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
500
1000
Distance
diffusion distance

 
v Ci  Ci   = J i  J i  

1500
2000
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
1-D
SINGLE PHASE LAYER GROWTH
Layer growth in E/E in repeated simulations
layer thickness squared (nm) 2
250000
225000
200000
175000
150000
125000
100000
75000
50000
25000
0
0
500
1000
1500
2000
2500
dimensionless time
3000
SINGLE PHASE LAYER GROWTH
1 m
Comparison of phase field simulations
~
after  = 3000
1 m
(a) A-A
1 m
(b) B-B
1 m
(c) C-C
1 m
(d) D-D
(e) E-E
APPLICATION OF THE KIM/KIM/SUZUKI PHASE FIELD MODEL
Effect 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:
APPLICATION OF THE KIM/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
s 
t
1

2
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.
1
2
0.50
1000000
0.45
0
-1000000
0.35
flux
concentration
0.40
0.30
-2000000
0.25
-3000000
0.20
J1
J2
-4000000
0.15
0
500
1000
diffusion distance
1500
2000
0
500
1000
diffusion distance
1500
2000
Single Phase Layers formed by Horns
Predicted by DICTRA
Diffusion Couple results
X=0
bb


 b
 
Theory of horns and an example using a finite
difference simulation
Ji
x

dCi 2 dJ i
=
d  d
Concentration
profile
Ci
x
K. Wu, J.E. Morral, and Y. Wang, in press Acta Mater, Oct. 2006