1. TMS Annual Meeting, Orlando, 2007 1 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 Glass-Like Behavior in General Grain Boundary During Migration

2. TMS Annual Meeting, Orlando, 2007 2 Are General Grain Boundaries Glassy? General Boundaries General Boundaries Exclude low angle, low  and coherent twin grain boundariesExclude low angle, low  and coherent twin grain boundaries Structure 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 )“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 )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 )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 Dynamics Grain boundary viscosity ( Ashby, Surf Sci. 31 498, 1972 )Grain boundary viscosity ( Ashby, Surf Sci. 31 498, 1972 ) Grain boundary migration and diffusion suggests structural transition temperature ( Wolf, Acta Mater. 53 1, 2005 )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 )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. TMS Annual Meeting, Orlando, 2007 3 Simulation Details Molecular dynamics in NVT ensembleMolecular dynamics in NVT ensemble EAM-type (Voter-Chen) potential for NiEAM-type (Voter-Chen) potential for Ni [010] tilt general grain boundary with  =40.23º[010] tilt general grain boundary with  =40.23º Periodic boundary conditions in x and yPeriodic boundary conditions in x and y One grain boundary & two free surfacesOne grain boundary & two free surfaces Fixed strain,  xx and  yyFixed strain,  xx and  yy Source of driving force is the elastic energy difference due to crystal anisotropySource of driving force is the elastic energy difference due to crystal anisotropy Driving force is constant during simulationDriving force is constant during simulation  (001) X Z Y

4. TMS Annual Meeting, Orlando, 2007 4 Grain Boundary Migration Grain boundary migration tends to be continuous at high temperature, while shows “intermittent” at lower temperatureGrain boundary migration tends to be continuous at high temperature, while shows “intermittent” at lower temperature The waiting period becomes longer as temperature decreasingThe waiting period becomes longer as temperature decreasing

5. TMS Annual Meeting, Orlando, 2007 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 systemTemperature dependence of grain boundary mobility can be nicely fitted into Vogel-Fulcher Form, which is commonly used in super-cooled liquid system T 0 denotes the temperature that mobility disappears T 0 denotes the temperature that mobility disappears

6. TMS Annual Meeting, Orlando, 2007 6 The atom is treated as mobile ifThe atom is treated as mobile if Find string pair among mobile atoms usingFind string pair among mobile atoms using The Weight-averaged mean string length:The Weight-averaged mean string length: Catch Strings and Determine their Length

7. TMS Annual Meeting, Orlando, 2007 7 “Typical” Strings

8. TMS Annual Meeting, Orlando, 2007 8 String-like Motion Within Grain Boundary String-like cooperative motion within grain boundary is significant at low temperatureString-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 780KThe fraction of non-trivial strings in the mobile atoms can be over 40% at 780K

9. TMS Annual Meeting, Orlando, 2007 9 String Length vs. Temperature String length distribution function P(n) follows exp(-n/ )String length distribution function P(n) follows exp(-n/ )  grain boundaries have shorter strings, therefore they are less frustrated than general grain boundaries  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 liquidsString length increases as temperature decreasing, similar behavior is found in supercooled liquids

10. TMS Annual Meeting, Orlando, 2007 10 “Intermittent” Migration Behavior

11. TMS Annual Meeting, Orlando, 2007 11 X Z Y X Y Z Movie

12. TMS Annual Meeting, Orlando, 2007 12 GB Steps Stage I Stage II Migration Mechanism at Low T Grain boundary migration at low T is associated with nucleation of steps/terraceGrain boundary migration at low T is associated with nucleation of steps/terrace GB GB

13. TMS Annual Meeting, Orlando, 2007 13 Further Observations “Selected” migration region can be best described by Arrhenius law“Selected” migration region can be best described by Arrhenius law The activation energy is about 0.37 eV (smaller than the apparent activation energy)The activation energy is about 0.37 eV (smaller than the apparent activation energy)

14. TMS Annual Meeting, Orlando, 2007 14 t GB Position 11 22 L Overall Migration Overall Migration Since the migration region follows Arrhenius Since the migration region follows Arrhenius Grain Boundary Migration Model

15. TMS Annual Meeting, Orlando, 2007 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 liquidTemperature 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 systemString-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 TIt 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.The migration model suggests grain boundary migration is controlled by different atomistic mechanisms. The waiting period is associated with the nucleation of steps.