Glass-Like Behavior in General Grain Boundary During Migration
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Hao Zhang 1 , David J. Srolovitz 1,2 1 Princeton University 2 Yeshiva University PowerPoint PPT Presentation


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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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Hao Zhang 1 , David J. Srolovitz 1,2 1 Princeton University 2 Yeshiva University

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Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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)


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

(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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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:


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

“Typical” Strings


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

“Intermittent” Migration Behavior


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

Z

Y

X

X

Y

Z

Movie


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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)


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

GB Position

L

t1

t2

t

Grain Boundary Migration Model

  • Overall Migration

  • Since the migration region follows Arrhenius


Hao zhang 1 david j srolovitz 1 2 1 princeton university 2 yeshiva university

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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