Atomistic Mechanisms for Grain Boundary Migration Overview of

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

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

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

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

Steady State Grain Boundary Migration

Bicrystal Geometry [010] S 5 36. 87º a a Asymmetric boundary a = 26. 57º Asymmetric boundary a = 14. 04º Symmetric boundary

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

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

Cahn & Taylor’s Model (2004) initial pure sliding 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:

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

Shear (coupled) Motion - Symmetric Boundary v||=1 m/s • S 5 [010] symmetric tilt boundary (103) at 800 K • 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

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

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

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

Atomistic Jump Picture (2 3)

Macroscopic Migration Picture (Symmetric) v|| 1 v|| 2 v|| 3 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

Shear Motion in Asymmetric Boundaries a=18. 43º a=26. 57º a=36. 87º T=500 K, v||=0. 5 m/s a=9. 46º

Coupled motion at different T (a = 13. 6º)

Shear/coupled motion in General GB

Critical Stresses