Grain Boundary Migration Mechanism: S5 Tilt Boundaries

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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
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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 exxeyye0 and siz 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
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Reminder Simulation / Bicrystal Geometry
010 S5 36.87º
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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

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Approach

• Look in detail at atomic motions as grain
  boundary moves a short distance
• Focus on one boundary (a22º), 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
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Interesting Observations 1
Boundary Plane - XY
Atomic displacements Dt0.4ps, t30ps
Atomic displacements Dt5ps

• Substantial correlated motions within boundary
  plane during migration

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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 redhigh stress

• Regular atomic displacements periodic array of
  hot points

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Interesting Observations 3
Trans-boundary plane XZ
Atom positions during a period in which boundary
moves downward by 1.5 nm Color ? time redlate
time, blueearly 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/B
Displacements projected onto CSL Interesting
displacement patterns
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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
• d2d41.1 Å, d51.6 Å
• Type III
• Inter-plane jump - 3
• d32.0 Å

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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

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Simulation Confirmation - Type III Displacements
Boundary Plane - XY
Trans-boundary plane XZ
Atomic displacements Dt0.4ps, t30ps
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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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)?

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Boundary Plane - XY
Transition Sequence
Color- time blue- early time
Trans-boundary plane XZ Colors ? Time
Sequence is 1,3,4 then 2 5
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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

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Connection with Grain Boundary Structure

• 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 Displacements
Boundary Plane - XY
Atomic displacements Dt5ps
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Excess Volume Transfer During String Formation
Boundary Plane - XY

• Colored by Voronoi volume
• In crystal, V11.67Å3

• 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

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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

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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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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)

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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