Slide 1 - CTCMS - NIST by yurtgc548

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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
                                                 Concentration gradient leading to layer growth
                      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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