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Atomistic Mechanisms for Grain Boundary Migration

Atomistic Mechanisms for 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. Z. v(y). Curvature-driven Grain Boundary Migration. U-shaped half loop geometry.

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Atomistic Mechanisms for Grain Boundary Migration

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  1. Atomistic Mechanisms for 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. Z v(y) Curvature-driven Grain Boundary Migration • U-shaped half loop geometry • Local Velocity • FCC Aluminum <111> Tilt Grain Boundary • EAM – Al • Periodic along X and Z • Steady-state Velocity

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

  4. 11 22 33 Free Surface 22 11 q 33 Grain 2 Z Grain Boundary X Grain 1 Y Free Surface 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: S5 (001) tilt boundary

  5. Steady State Grain Boundary Migration

  6. a a Symmetric boundary Asymmetric boundary a = 14.04º Asymmetric boundary a = 26.57º Bicrystal Geometry [010] S5 36.87º

  7. Mobility vs. Inclination • 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 H. Zhang et al.Scripta Materialia, 52: 1193; 2005

  8. Mobility, Diffusivity & Energy • 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 >18º M. Mendelev et al.JMR, 20: 1146; 2005

  9. Cahn & Taylor’s Model (2004) pure sliding initial pure shear combination • 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, vn. The coefficient b is independent of grain boundary inclination. • Coupling coefficient b:

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

  11. v||=1m/s Shear (coupled) Motion - Symmetric Boundary • S5 [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

  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|| v|| v|| Macroscopic Migration Picture (Symmetric) 3 2 1 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. a=18.43º a=9.46º a=26.57º a=36.87º Shear Motion in Asymmetric Boundaries T=500K, v||=0.5m/s

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

  19. Shear/coupled motion in General GB

  20. Critical Stresses

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