Hao Zhang1, David J. Srolovitz1,2

1
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
2
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 )

3
Simulation Details

• Molecular dynamics in NVT ensemble
• EAM-type (Voter-Chen) potential for Ni
• 010 tilt general grain boundary with q40.23º
• Periodic boundary conditions in x and y
• One grain boundary two free surfaces
• Fixed strain, ?xx and ?yy
• Source of driving force is the elastic energy
  difference due to crystal anisotropy
• Driving force is constant during simulation

4
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

5
Mobility vs. T Arrhenius?
OR

• 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

6
Catch Strings and Determine their Length

• The atom is treated as mobile if
• Find string pair among mobile atoms using
• The Weight-averaged mean string length

7
Typical Strings
8
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

9
String Length vs. Temperature

• String length distribution function P(n) follows
  exp(-n/ltngt)
• 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

10
Intermittent Migration Behavior
11
Movie
12
Migration Mechanism at Low T
GB
Stage I
Steps
GB
GB
Stage II

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

13
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)

14
Grain Boundary Migration Model

• Overall Migration

• Since the migration region follows Arrhenius

15
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.