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

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 )

Simulation Details (001) q 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 q (001) X Z Y

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

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

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:

“Typical” Strings

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

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

“Intermittent” Migration Behavior

Movie X Y Z X Z Y

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

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)

Grain Boundary Migration Model Overall Migration t GB Position t1 t2 L Since the migration region follows Arrhenius Mention the simple check at High temperature 1200-1400K, Q=0.37eV

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.