Grain Boundary Migration Mechanism: S5 Tilt Boundaries

1. Grain Boundary Migration Mechanism:S5 Tilt Boundaries Hao Zhang, David J. Srolovitz Princeton Institute for the Science and Technology of Materials, Princeton University

2. 11 22 33 Free Surface 22 11 q 33 Grain 2 Z Grain Boundary X Grain 1 Y Free Surface Reminder: elastically driven boundary migration • Drive grain boundary migration with an elastic driving force • even cubic crystals are elastically anisotropic  equal strain different strain energy • measure boundary velocity  deduce mobility • Applied strain • constant biaxial strain in x and y • free surface normal to z iz = 0 • note, typical strains (1-2%)  not linearly elastic • Measure driving force • apply strain εxx=εyy=ε0and σiz= 0 to perfect crystals, measure stress vs. strain and integrate to get the strain contribution to free energy • includes non-linear contributions to elastic energy S5 (001) tilt boundary

3. a a Symmetric boundary Asymmetric boundary a = 14.04º Asymmetric boundary a = 26.57º Reminder: Simulation / Bicrystal Geometry [010] S5 36.87º

4. Reminder: Mobility vs. Inclination • Mobilities vary by a factor of 4 over the range of inclinations studied at lowest temperature • Variation decreases when temperature ↑ (from ~4 to ~2) • Minima in mobility occur where one of the boundary planes has low Miller indices

5. Free Surface Z X Grain 2 Y Grain Boundary Grain 1 tilt axis Free Surface Approach • Look in detail at atomic motions as grain boundary moves a short distance • Focus on one boundary (a=22º), time = 0.3 ns, boundary moves 15 Å • For every 0.2 ps, quench the sample (easier to view structure) – repeat 1500X • X-Z (┴ to boundary) and X-Y (boundary plane) views – remember this Boundary Plane View Color - potential energy Trans-boundary Plane View

6. Interesting Observations 1 Boundary Plane - XY Atomic displacements: Dt=0.4ps, t=30ps Atomic displacements: Dt=5ps • Substantial correlated motions within boundary plane during migration

7. Interesting Observations 2 Trans-boundary plane XZ Atom positions during a period in which boundary moves downward by 1.5 nm Color – von Mises shear stress at atomic position – red=high stress • Regular atomic displacements – periodic array of “hot” points

8. Interesting Observations 3 Trans-boundary plane XZ Atom positions during a period in which boundary moves downward by 1.5 nm Color  time – red=late time, blue=early time • Atomic displacements  symmetry of the transformation

9. Coincidence Site Lattice • Part of the simulation cell in trans-boundary plane view • CSL unit cell • Atomic “jump” direction ▲,○ - indicate which lattice Color – indicates plane A/B Displacements projected onto CSL “Interesting” displacement patterns

10. 4 1 3 2 5 Atomic Path for S5 Tilt Boundary Migration • Translations in the CSL • Types of Atomic Motions • Type I • “Immobile” – coincident sites -1 d1= 0 Å • Type II • In-plane jumps – 2, 4, 5 • d2=d4=1.1 Å, d5=1.6 Å • Type III • Inter-plane jump - 3 • d3=2.0 Å

11. Simulation Confirmation Trans-boundary plane XZ ○ initial average position projected on trans-boundary plane ∆ final average position came from the same atoms in initial Color – indicates plane A/B • The atoms that do not move (Type I) are on the coincident sites • Plane changing motions (Type III), are “usually” as predicted

12. Simulation Confirmation - Type III Displacements Boundary Plane - XY Trans-boundary plane XZ Atomic displacements: Dt=0.4ps, t=30ps Color – von Mises shear stress at atomic position • The red lines on the left ( XY-plane) indicate the Type III displacements • These are the points of maximum shear stress

13. The Big Questions • How are these different types of motions correlated? • which is the chicken and which is the egg? • What triggers the motions that lead to boundary translation? • Can we use this information to explain how mobility varies with boundary structure (inclination)?

14. 4 1 3 2 5 3 3 1 1 2 2 4 4 5 5 1 Type III motion Boundary Plane - XY Transition Sequence Color- time blue- early time Trans-boundary plane XZ Colors  Time Sequence is 1,3,4 then 2 + 5

15. Type II Displacements Trans-boundary plane XZ Atom positions during boundary moves downward by 1.5 nm Color – Voronoi volume change – red= ↑over 10%, blue = ↓over 10% • Excess volume triggers Type II displacement events

16. Connection with Grain Boundary Structure • The higher the boundary volume, the faster the boundary moves • More volume  easier Type II events  faster boundary motion

17. Type III Displacements Boundary Plane - XY Atomic displacements: Dt=5ps

18. Excess Volume Transfer During String Formation Boundary Plane - XY • Colored by Voronoi volume • In crystal, V=11.67Å3 • Excess volume triggers string-like (Type III) displacement sequence • Net effect – transfer volume from one end of the string to the other • Displacive not diffusive volume transport • Should lead to fast diffusion

19. Correlation with Boundary Self-diffusivity • Diffusivity along tilt axis direction is correlated with boundary mobility • Diffusivity along tilt axis – indicative of Type III events • Diffusivity much higher along tilt-axis direction than normal to it

20. How Long are the Strings? Boundary Plane - XY • Display atoms in 0.4 ps time intervals with displacements larger than 1.0 Å • Arrow indicates the direction of motion in the X-Y plane • 3 or 4 atom strings are most common • Some strings as long as the entire simulation cell • -10 atoms

21. 4 1 3 2 5 Another Measure of Simulation Size Effect • What happens if we make the simulation cell thinner in the tilt axis direction? Sequence is 1,3,4 then 2 + 5 • Strings (Type III events) cannot be longer than simulation cell size • The boundary mobility drops rapidly for cell sizes smaller than 6 atom spacings (12 Å)

22. 4 1 3 2 5 Migration Picture Atomic Path • A volume fluctuation occurs at the boundary • A Type II displacement event occurs • Triggers a Type III (string) event • Transfers volume •  Boundary translation Transition Sequence 1,3,4 then 2 + 5