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