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Glass-Like Behavior in General Grain Boundary During Migration. Hao Zhang 1 , David J. Srolovitz 1,2 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

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slide1
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

slide2
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)
slide3
(001)

q

(001)

Z

X

Y

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
  • 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
slide4
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
slide5
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
slide6
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:
slide8
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
slide9
String Length vs. Temperature
  • String length distribution function P(n) follows exp(-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
slide11
Z

Y

X

X

Y

Z

Movie

slide12
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
slide13
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)
slide14
GB Position

L

t1

t2

t

Grain Boundary Migration Model

  • Overall Migration
  • Since the migration region follows Arrhenius
slide15
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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