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

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. (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

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/<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

10. “Intermittent” Migration Behavior

11. Z Y X X Y Z 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. GB Position L t1 t2 t 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.