Grain Boundary Migration Mechanism S 5 Tilt Boundaries

Grain Boundary Migration Mechanism: S 5 Tilt Boundaries Hao Zhang, David J. Srolovitz Princeton Institute for the Science and Technology of Materials, Princeton University Computational Materials Science Network

Reminder: elastically driven boundary migration • Drive grain boundary migration with an elastic driving force • even cubic crystals are elastically anisotropic X Y Free Surface q 11 22 • Applied strain Grain Boundary 22 • Measure driving force • apply strain εxx=εyy=ε 0 and 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 Computational Materials Science Network 11 Grain 1 • constant biaxial strain in x and y • free surface normal to z iz = 0 • note, typical strains (1 -2%) not linearly elastic 33 Grain 2 equal strain different strain energy • measure boundary velocity deduce mobility Z 33 Free Surface S 5 (001) tilt boundary

Reminder: Simulation / Bicrystal Geometry [010] S 5 36. 87º a Asymmetric boundary a = 26. 57º Asymmetric boundary a = 14. 04º Symmetric boundary Computational Materials Science Network

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 Computational Materials Science Network

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 1500 X • X-Z (┴ to boundary) and X-Y (boundary plane) views – remember this Free Surface Grain 2 Grain Boundary Grain 1 Z X Color - potential energy xis ta Y til Free Surface Boundary Plane View Trans-boundary Plane View Computational Materials Science Network

Interesting Observations 1 Boundary Plane - XY Atomic displacements: Dt=5 ps Dt=0. 4 ps, t=30 ps • Computational Substantial correlated motions within boundary plane during migration 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 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 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 Computational Materials Science Network

Atomic Path for S 5 Tilt Boundary Migration Translations in the CSL Types of Atomic Motions 1 2 3 Type I 4 5 • “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 Computational Materials Science Network

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 Computational Materials Science Network

Simulation Confirmation - Type III Displacements Boundary Plane - XY Trans-boundary plane XZ Atomic displacements: Dt=0. 4 ps, t=30 ps 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 Computational Materials Science Network

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)? Computational Materials Science Network

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

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 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 Computational Materials Science Network

Type III Displacements Boundary Plane - XY Atomic displacements: Dt=5 ps Computational Materials Science Network

Excess Volume Transfer During String Formation Boundary Plane - XY • Colored by Voronoi volume • In crystal, V=11. 67Å3 Computational Materials Science Network • 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

Correlation with Boundary Self-diffusivity • Diffusivity along tilt axis direction is correlated with boundary mobility • Diffusivity along tilt axis – indicative of Type III events • Computational Diffusivity much higher along tilt-axis direction than normal to it 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 Computational Materials Science Network • 3 or 4 atom strings are most common • Some strings as long as the entire simulation cell -10 atoms

Another Measure of Simulation Size Effect • 1 What happens if we make the simulation cell thinner in the tilt axis direction? 2 3 4 5 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) Computational Materials Science Network

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