Dependence of Grain Boundary Mobility on Boundary Plane

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Dependence of Grain Boundary Mobility on Boundary
Plane
Hao Zhang1, Mikhail Mendelev1,2 and David
Srolovitz1
1PRISM, Princeton University 2Ames Laboratory
2
Challenges

• Neither curvature driven boundary migration
  experiments nor simulations yield the fundamental
  kinetic properties for grain boundary migration
• , M
  is the product of the mobility and grain boundary
  stiffness
• Reduced mobility is averaged over all possible
  inclinations
• The migration of a flat boundary is easier to
  analyze, but has several limitations
• Can yield grain boundary mobility dependence on
  inclination
• Is the variation of grain boundary mobility
  correlated with other boundary properties, such
  as grain boundary energy and self-diffusivity?

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Elastically-Driven Migration of a Flat Boundary

• Use elastic driving force
• even cubic crystals are elastically anisotropic
  equal strain ? different strain energy
• driving force for boundary migration difference
  in strain energy density between two grains
• Applied strain
• constant biaxial strain in x and y
• free surface normal to z ? ??iz 0
• Driving Force based on linear Elasticity

S5 (001) tilt boundary
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Measured Driving Force

• Typical strains
• 1-2, out of linear region

• Implies driving force of form

• Measuring 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
• Fit stress
• Driving force

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Determination of Mobility

• Determine mobility by extrapolation to zero
  driving force
• Tension (compression) data approaches from above
  (below)

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Simulation / Bicrystal Geometry
010 S5 36.87º
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Initial Simulation Cell for Different Inclinations
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Mobility vs. Inclination

• No mobility data available at a0, 45º zero
  biaxial strain driving force
• 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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Activation Energy vs. Inclination

• The variation of activation energy for grain
  boundary migration over the inclination region we
  studied is significant
• The variation of mobility becomes weaker than
  expected on the basis of activation energy
  because of the compensation effect
• Activation energy for the symmetric boundary is
  unknown

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Diffusivity vs. Inclination

• Diffusivity shows more anisotropic at low
  temperature than at high temperature
• Most of local minimum corresponds to one of the
  grains normal with low Miller indices
• The a0º has a change from minimum to maximum

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Activation Energy and Compensation Effect

• The activation energy all lie between 0.5 to 0.6
  eV, except for the a0º symmetric boundary(1.1
  eV)
• Compensation effect weaken the diffusivity
  variation based upon the activation energy for
  self-diffusion

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Mobility, Self-diffusion and Energy

• At low temperature, self-diffusion and grain
  boundary energy have similar trend, i.e. change
  from minimum to maximum, but mobility has
  opposite trend.
• Mobility, self-diffusion coefficient and grain
  boundary energy shows local minimum at special
  inclination (one of the plane normal is low
  Miller indices)
• There exists correlation between those three
  quantities in the inclination range of 18º to
  45º.

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Conclusion

• Used stress driven GB motion to determine grain
  boundary mobility as a function of q, a and T
• Mobility is a strong function of inclination and
  temperature
• Grain boundary self-diffusion is sensitive to
  inclinations, i.e. grain boundary structure
• Minima in boundary mobility, self-diffusion
  coefficient and grain boundary energy occurs
  where at least one boundary plane is a low index
  plane
• In the inclination range from 18º to 45º, there
  is a strong correlation between grain boundary
  diffusivity, energy and mobility