1. Atomistic Mechanisms for Atomistic Mechanisms for Grain Boundary Migration Grain Boundary Migration  Overview of Atomistic Simulations of Grain Boundary Migration Hao Zhang 1, David J. Srolovitz 1,2 1 Princeton University 2 Yeshiva University

2. U-shaped half loop geometry FCC Aluminum Tilt Grain Boundary EAM – Al Periodic along X and Z Curvature-driven Grain Boundary Migration v(y) Z Local Velocity Steady-state Velocity

3. Reduced mobility increases with increasing temperature Mobility shows maxima at low Σ misorientations Reduced Mobility vs. Misorientation

4. Stress-Driven Boundary Migration Molecular dynamics in NVT ensemble EAM-type (Voter-Chen) potential for Ni Periodic boundary conditions in x and y One grain boundary & two free surfaces Fixed biaxial strain,  =  xx =  yy Source of driving force is the elastic energy difference due to crystal anisotropy Driving force is constant during simulation Linear elasticity: At large strains, deviations from linearity occur, determine driving force from the difference of the strain energy in the 2 grains: X Y Z Grain Boundary Free Surface Grain 2 Grain 1 11 22 33 11 22 33   5 (001) tilt boundary

5. Steady State Grain Boundary Migration

6. Symmetric boundary  Asymmetric boundary  = 14.04º Asymmetric boundary  = 26.57º  Bicrystal Geometry [010]  5 36.87º

7. No mobility data available at a=0, 45º; zero driving force Mobilities vary by a factor of 4 over the range of inclinations studied at lowest temperature Variation increases when temperature ↓ (from ~2 to ~4) Minima in mobility occur where one of the boundary planes has low Miller indices Mobility vs. Inclination H. Zhang et al. Scripta Materialia, 52: 1193; 2005

8. At low T, self-diffusivity & grain boundary energy increase with increasing inclination Mobility, self-diffusion coefficient and grain boundary energy exhibit local minimum at special inclination (at least one low index boundary plane) All three quantities are correlated for a >18 º Mobility, Diffusivity & Energy M. Mendelev et al. JMR, 20: 1146; 2005

9. Cahn & Taylor’s Model (2004) Boundary migration can also produce a coupled tangential motion of the two crystals relative to each other In the absence of grain boundary sliding, the velocity parallel to the grain boundary, v ||, is proportional to the grain boundary migration velocity, v n. The coefficient  is independent of grain boundary inclination. Coupling coefficient  : initial pure shear pure sliding combination

10. Suzuki & Mishin’s Simulation (2005) v || [001] Symmetric tilt boundaries Fix the bottom and shear the top with v || = 1m/s Grain boundary migrates ↑ or ↓

11. Shear (coupled) Motion - Symmetric Boundary  5 [010] symmetric tilt boundary (103) at 800K The step height = 1.11Ǻ ((103) plane spacing is 1.13Ǻ), therefore, the migration is plane by plane Both Ashby and Cahn give the correct prediction for symmetric grain boundary v || =1m/s

12. Critical Stress for Shear (coupled) Motion When the shear strain of lower grain reaches ~0.4%, migration was ignited. The average critical stress is ~0.64 GPa. This migration is difussionless

13. Atomistic Migration Detail 1  2: Atomic configurations apart by ~122 ps The displacements represent elastic deformation; no indication of grain boundary sliding.

14. Atomistic Migration Detail (Cont’d) 2  3: Atomic configurations apart by 5.6 ps Coupled sliding and migration  shear Grain boundary migrates from blue line to red line Top crystal uniformly slides right – releases elastic strain

15. Atomistic Jump Picture (2  3)

16. v || 1 2 3 Macroscopic Migration Picture (Symmetric) 1  2: Elastic deformation, Stress ↑ 2  3: Reach critical stress, two grains slide relatively to each other; stress release; boundary migrates Fixed ratio of migration/sliding  shear

17. Shear Motion in Asymmetric Boundaries T=500K, v || =0.5m/s  =9.46º  =18.43º  =26.57º  =36.87º

18. Coupled motion at different T (  = 13.6º)

19. Shear/coupled motion in General GB

20. Critical Stresses