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					Glass-Like Behavior in General Grain
    Boundary During Migration

          Hao Zhang1, David J. Srolovitz1,2
                 1   Princeton University
                     2   Yeshiva University

         Jack F. Douglas, James A. Warren

     National Institute of Standards and Technology
 Are General Grain Boundaries Glassy?
• General Boundaries
   • Exclude low angle, low S and coherent twin grain boundaries
• Structure
   • “Amorphous-cement” model suggested that the metal grains in cast
     iron were “cemented” together by a thin layer of ‘amorphous’ material
     (Rosenhain and Ewen, J I Met. 10 119,1913)
   • The RDF suggests liquid like structure at high T (Wolf, Phys Rev Lett. 77 2965,
     1996; Curr Opin Solid St M. 5 435, 2001; Acta Mater. 53 1, 2005 )

   • Others show partial crystalline structure (Gleiter, Phys Rev B. 35 9085, 1987;
     Appl Phys Lett. 50 472, 1987; Van Swygenhoven , Phys Rev B. 62 831, 2000 )

• Dynamics
   • Grain boundary viscosity (Ashby, Surf Sci. 31 498, 1972 )
   • Grain boundary migration and diffusion suggests structural transition
     temperature (Wolf, Acta Mater. 53 1, 2005 )
   • self-diffusion in the grain-boundary suggested that the diffusion
     mechanism is similar to that in bulk metallic glasses (Mishin, J Mater Sci. 40
     3155, 2005 )
  Simulation Details
• Molecular dynamics in NVT ensemble
• EAM-type (Voter-Chen) potential for Ni
• [010] tilt general grain boundary with
  q=40.23º
• Periodic boundary conditions in x and y           q
• One grain boundary & two free surfaces
• Fixed strain, xx and yy
                                            Z
• Source of driving force is the elastic
  energy difference due to crystal
                                                X
  anisotropy                                Y
• Driving force is constant during
  simulation
Grain Boundary Migration




• Grain boundary migration tends to be continuous at high
  temperature, while shows “intermittent” at lower temperature
• The waiting period becomes longer as temperature decreasing
Mobility vs. T – Arrhenius?

                                                                 Q 
                                               v / p  M 0 exp  
                                                          *
                                                                        
                                                                   kBT 
                                                              OR
                                                                      QVF     
                                            v / p  M   *
                                                         VF   exp  
                                                                   k T  T  
                                                                               
                                                                   B       0 




• Temperature dependence of grain boundary mobility can be
  nicely fitted into Vogel-Fulcher Form, which is commonly used
  in super-cooled liquid system
• T0 denotes the temperature that mobility disappears
Catch Strings and Determine their Length

   • The atom is treated as mobile if

          0.35r0  ri  t   ri  0   1.2r0


   • Find string pair among mobile atoms using


          min  ri  t   rj  0  , ri  0   rj  t    0.43r0
                                                           

   • The Weight-averaged mean string length:


          n t    n2P  n, t           nP  n, t 
“Typical” Strings
String-like Motion Within Grain Boundary




• String-like cooperative motion within grain boundary is significant
  at low temperature
• The fraction of non-trivial strings in the mobile atoms can be over
  40% at 780K
String Length vs. Temperature
                                •String length distribution
                                 function P(n) follows
                                 exp(-n/<n>)

                                • S grain boundaries
                                 have shorter strings,
                                 therefore they are less
                                 frustrated than general
                                 grain boundaries

                                •String length increases
                                 as temperature
                                 decreasing, similar
                                 behavior is found in
                                 supercooled liquids
“Intermittent” Migration Behavior
Movie




    Z       Y



        X       X
    Y       Z
Migration Mechanism at Low T




                                                    
                            GB



                                   Steps                 Stage I
                            GB




                            GB
                                                         Stage II


• Grain boundary migration at low T is associated with
  nucleation of steps/terrace
Further Observations




• “Selected” migration region can be best described by
  Arrhenius law
• The activation energy is about 0.37 eV (smaller than the
  apparent activation energy)
Grain Boundary Migration Model
• Overall Migration

         L / p             1
v / p           
         t 1  t 2 t 1p / L  1/ M 2




                                   GB Position
• Since the migration region
  follows Arrhenius




                                                               L
                     Q2 
    v2 / p  M exp  
               *
               2          
                     kBT                       t1   t2
                         1                                 t
    v / p 
                         1      Q2 
             t 1p / L  * exp       
                        M2      k BT 
Conclusion
• Temperature dependence of Grain boundary migration in
  general tilt boundaries is found to be described by Vogel-
  Fulcher relation, which is characteristic in glass-forming liquid

• String-like atomic motion in grain boundaries is similar to those
  in liquid system

• It is reasonable to believe that string-like cooperative motion
  dominates the rate of grain boundary migration at low T

• The migration model suggests grain boundary migration is
  controlled by different atomistic mechanisms. The waiting
  period is associated with the nucleation of steps.

				
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posted:8/29/2012
language:English
pages:15