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Grain Boundary Migration Mechanism: S5 Tilt Boundaries. Hao Zhang, David J. Srolovitz Princeton Institute for the Science and Technology of Materials, Princeton University. 11. 22. 33. Free Surface. 22. 11. q. 33. Grain 2. Z. Grain Boundary. X. Grain 1. Y. Free Surface. - PowerPoint PPT Presentation
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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
Computational Materials Science Network
Reminder: elastically driven boundary migration
X
Y
Z
Grain Boundary
Free Surface
Free Surface
Grain
2G
rain 1
1122
33
1122
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 εxx=εyy=ε0 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
0
0
1122 )(
dF Grainyy
Grainxx
Grainyy
Grainxx
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Symmetric boundary
Asymmetric boundary = 14.04º
Asymmetric boundary = 26.57º
Reminder: Simulation / Bicrystal Geometry
[010]
5 36.87º
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0 10 20 30 40 500
50
100
150
200
250
1400K 1200K 1000K
Mob
ility
(1
0-9 m
3 /Ns)
• 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
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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 ViewX
Y
Z
Grain Boundary
Free Surface
Free Surface
Grain
2G
rain 1
tilt a
xis Color - potential energy
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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
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Interesting Observations 2Trans-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
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Interesting Observations 3Trans-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
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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/BDisplacements projected onto CSL “Interesting” displacement patterns
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Atomic Path for 5 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
12 3
45
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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
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Simulation Confirmation - Type III Displacements
Atomic displacements: t=0.4ps, t=30ps Boundary Plane - XY Trans-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
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• 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
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1 2 3 45
Transition Sequence
1 2 3 4 5 11 2 3 4 5
Sequence is 1,3,4 then 2 + 5
Trans-boundary plane XZColors Time
Boundary Plane - XYColor- time blue- early time
Type III motion
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Type II DisplacementsTrans-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
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Connection with Grain Boundary Structure
5 10 15 20 25 30 35 40
0.390
0.395
0.400
0.405
0.410
0.415
0.420
0.425
60
80
100
120
140
160
180
Exc
ess
Vol
ume
(A)
Mob
ility
(1
0-9 m
3 /Ns)
ANV /Volume Excess
• The higher the boundary volume, the faster the boundary moves• More volume easier Type II events faster boundary motion
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Type III DisplacementsBoundary Plane - XY
Atomic displacements: t=5ps
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Excess Volume Transfer During String Formation
• Colored by Voronoi volume
• In crystal, V=11.67Å3
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
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Correlation with Boundary Self-diffusivity
5 10 15 20 25 30 35 400.8
1.0
1.2
1.4
1.6
1.8
60
80
100
120
140
160
180
Mob
ility
(1
0-9 m
3 /Ns)
Dy (
10-1
3 cm
3 /s)
• 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
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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
Computational Materials Science Network
1 2 3 45
Another Measure of Simulation Size Effect
10 15 20 25 30 35 401
2
3
4
5
6
Mig
rati
on R
ate
(m/s
)
Thickness (Angstrom)
• 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
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Migration Picture
12 3
45
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 translation1,3,4 then 2 + 5