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

2. Computational Materials Science Network Reminder: elastically driven boundary migration X Y Z Grain Boundary Free Surface Grain 2 Grain 1 11 22 33 11 22 33   5 (001) tilt boundary 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 ε xx =ε yy =ε 0 and σ iz = 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

3. Computational Materials Science Network Symmetric boundary  Asymmetric boundary  = 14.04º Asymmetric boundary  = 26.57º  Reminder: Simulation / Bicrystal Geometry [010]  5 36.87º

4. Computational Materials Science Network 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 Reminder: Mobility vs. Inclination

5. Computational Materials Science Network Approach Look in detail at atomic motions as grain boundary moves a short distance Focus on one boundary (  =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 Trans-boundary Plane View Boundary Plane View X Y Z Grain Boundary Free Surface Grain 2 Grain 1 tilt axis Color - potential energy

6. Computational Materials Science Network Interesting Observations 1 Atomic displacements:  t=5ps Atomic displacements:  t=0.4ps, t=30ps Boundary Plane - XY Substantial correlated motions within boundary plane during migration

7. Computational Materials Science Network 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. Computational Materials Science Network 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. Computational Materials Science Network 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. Computational Materials Science Network Atomic Path for  5 Tilt Boundary Migration Translations in the CSL Types of Atomic Motions Type I “Immobile” – coincident sites -1 d 1 = 0 Å Type II In-plane jumps – 2, 4, 5 d 2 =d 4 =1.1 Å, d 5 =1.6 Å Type III Inter-plane jump - 3 d 3 =2.0 Å 1 2 3 4 5

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

12. Computational Materials Science Network Simulation Confirmation - Type III Displacements Atomic displacements:  t=0.4ps, t=30ps Boundary Plane - XYTrans-boundary plane XZ 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. Computational Materials Science Network 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)? The Big Questions

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

15. Computational Materials Science Network 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. Computational Materials Science Network 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. Computational Materials Science Network Type III Displacements Boundary Plane - XY Atomic displacements:  t=5ps

18. Computational Materials Science Network Excess Volume Transfer During String Formation Colored by Voronoi volume In crystal, V=11.67Å 3 Boundary Plane - XY 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. Computational Materials Science Network 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. Computational Materials Science Network 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. Computational Materials Science Network 1 2 3 4 5 Another Measure of Simulation Size Effect 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) What happens if we make the simulation cell thinner in the tilt axis direction? Sequence is 1,3,4 then 2 + 5

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