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```									               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     A      A      A     A

Phase field simulation of box
with periodic boundary conditions
INTRODUCTION
Regular Solution Phase Diagram

2

A            W12 = W23 = 20kJ/mole

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

1.0

0.8
Mole_fraction (C)

0.6

0.4

0.2

0.0
0   100   200   300    400   500
X_distance
PARTICLE COARSENING IN EQUILIBRIUM LAYERS
Phase Field Simulation of nanostructured
J/J layers on a tie-line
Above equilibrium precipitate concentration
due to capillarity
0.840
Mole_fraction (C)

0.835

d
0.830
0.830

d
0.825

0.820
0       100    200     300    400    500
X_distance

0.180
Mole_fraction (C)

0.175
d

0.170       0.169
d

0.165

0.160
0       100    200     300    400    500
X_distance
SINGLE PHASE LAYER FORMATION AND HORNS
1-D simulations of diffusion paths
across multiphase layers
0.0                                                                           0.0
1.0                                                                           1.0
0.1
      0.9                                                              0.1
     0.9
0.2                                                                            0.2
0.8                                                                          0.8
0.3                                                                             0.3
0.7                                                                          0.7
0.4                                                                             0.4
0.6                                                                         0.6
0.5                                                                              0.5
0.5                                                                         0.5
0.6                                                                              0.6
0.4                                                                        0.4
0.7                                                                               0.7
0.3                                                                        0.3
0.8                                                                               0.8
0.2                                                                       0.2
0.9
0.9
                                  0.1                                                                      0.1
1.0                                                                                1.0
0.0                                                                      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

Constant Dij                                                                          Variable Dij
Atomic mobilities                                                                    Atomic mobilities
b1= b2= b3                                                                       b1=10, b2= 5, b3=1
Linear zigzag path                                                                    Path with horns
SINGLE PHASE LAYER FORMATION AND HORNS
1-D simulations of variable diffusivity paths with and
without single phase layers
0.0                                                                        0.0
1.0                                                                        1.0
0.1                                                                        0.1
0.9                                                                        0.9
0.2                                                                        0.2
0.8                                                                        0.8
0.3                                                                        0.3
0.7                                                                        0.7
0.4                                                                        0.4
0.6                                                                        0.6
0.5                                                                        0.5
0.5                                                                        0.5
0.6                                                                        0.6
0.4                                                                        0.4
0.7                                                                        0.7
0.3                                                                        0.3
0.8                                                                        0.8
0.2                                                                        0.2
0.9                                                                        0.9
0.1                                                                        0.1
1.0                                                                        1.0
0.0                                                                        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                               Variable Dij                         Horns with a
Single phase layer                              Atomic mobilities                    Single phase layer
b1=10, b2= 5, b3=1
Path with horns
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                                   1000000

0.3
0.7
0
0.4
0.6
0.5              B=10:5:1               0.5                        -1000000

0.6                                                     Flux

flux
A2     0.4
-2000000
0.7
0.3
0.8                                                                        -3000000
A1                                        0.2
0.9
0.1                           J1
-4000000
1.0                                                                                             J2
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           1500   2000

Distance
diffusion distance


v Ci  Ci   = J i  J i                                       
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

250000
layer thickness squared (nm) 2

225000

200000

175000

150000

125000

100000

75000

50000

25000

0
0   500   1000   1500   2000   2500   3000

dimensionless time
SINGLE PHASE LAYER GROWTH
Comparison of phase field simulations
1 m
~
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
1
s                          t
 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.
0.50       1
1000000
2
0.45
0

0.40
concentration

-1000000
0.35

flux
0.30                                                           -2000000

0.25                                                           -3000000

0.20
-4000000       J1
J2
0.15
0       500         1000           1500   2000                     0        500         1000           1500   2000
diffusion distance                                                  diffusion distance
Single Phase Layers formed by Horns

Predicted by DICTRA       Diffusion Couple results

X=0

 b
 b          b     
Theory of horns and an example using a finite
difference simulation

Ji

x

                                     Concentration
dC i 2 dJ i              Ci
=                                                       profile
d     d
x
K. Wu, J.E. Morral, and Y. Wang, in press Acta Mater, Oct. 2006

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