dislocations & colloidsdislocations & colloids dislocations: line defects in 3d xtals. point...
TRANSCRIPT
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Dislocations & ColloidsDislocations: Line defects in 3D xtals. Point defects in 2D xstals
(Often difficult to study in atomic systems)
Colloids: small particles that are Brownian and therefore thermal
(Form crystals, easy to see, slow)
Schall et al., SCIENCE 305,
1944-1948 (Sep 2004)
Schall et al., NATURE 440: 319-
323 (Mar 2006)
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Restricted Dislocation Mobility
in Colloidal Peanut Crystals
Itai Cohen
Sharon J. Gerbode
Stephanie H. Lee
Chekesha M. Liddell
Physics
Materials Science and Engineering
Cornell University, Ithaca NY 900nm
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Degenerate Crystal*
*K.W. Wojciechowski et al., PRL1991
• Particle centers form
a sparse, aperiodic
decoration of a
Kagomé lattice
• Particle lobes tile a
triangular lattice
• Particle orientations
uniformly populate 3
lattice directions
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Familiar turf: 2-D crystals of spheres
Vast existing body of knowledge on hard spheres:
• Standard structure characterization – triangular peaks
in g(r) and sixfold coordination
• Plasticity, yield, and other material properties are well
described by established theories of dislocation motion
(Taylor, Orowan, Polanyi, 1934)
• 2-D melting is extensively studied: KTHNY theory of
dislocation and disclination unbinding
Crystal
Translational &
orientational order
Hexatic
Expon. decaying translational &
power law decaying orient. order
Isotropic
No translational & expon.
decaying orient. order
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Important differences between
crystals of spheres and DCs
Certain particle orientations block slip.
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In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
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In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
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Observed mechanisms for dislocation
nucleation and glide in DCs
A dislocation glides
via the shifting of
two particles, one
that slides and one
that swings to let
the defect pass.
5
7
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Dislocations can only glide short
distances between obstacles
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Dislocations can only glide short
distances between obstacles
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d=7d=7
d = maximum
glide distance
…so how can dislocations
travel long distances, as in
shearing or melting?
d = 4.6±0.2
Dislocations can only glide short
distances between obstacles
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Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
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Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
![Page 23: Dislocations & ColloidsDislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals ... • Plasticity, yield, and other material properties are well](https://reader030.vdocument.in/reader030/viewer/2022040109/5e74f87fafd85c35a8413438/html5/thumbnails/23.jpg)
Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
![Page 24: Dislocations & ColloidsDislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals ... • Plasticity, yield, and other material properties are well](https://reader030.vdocument.in/reader030/viewer/2022040109/5e74f87fafd85c35a8413438/html5/thumbnails/24.jpg)
Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
![Page 25: Dislocations & ColloidsDislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals ... • Plasticity, yield, and other material properties are well](https://reader030.vdocument.in/reader030/viewer/2022040109/5e74f87fafd85c35a8413438/html5/thumbnails/25.jpg)
Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
![Page 26: Dislocations & ColloidsDislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals ... • Plasticity, yield, and other material properties are well](https://reader030.vdocument.in/reader030/viewer/2022040109/5e74f87fafd85c35a8413438/html5/thumbnails/26.jpg)
Dislocation reactions allow defects
to turn, bypassing obstacles
Schematic created using
http://physics.syr.edu/thomson/thomsonapplet.htm
primary author Cris Cecka, [email protected]
see M. Bowick, Science 299 (2003) 1716
![Page 27: Dislocations & ColloidsDislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals ... • Plasticity, yield, and other material properties are well](https://reader030.vdocument.in/reader030/viewer/2022040109/5e74f87fafd85c35a8413438/html5/thumbnails/27.jpg)
Dislocation reactions allow defects
to turn, bypassing obstacles
= +Reactions are topologically required
to conserve burgers vector.
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Experimentally observed dislocation
reactions allow turning past obstacles
z
7
5
5
5
7
7
= +
Burgers vector is conserved:
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Estimate energetic cost assuming:
Using dislocation reactions,
is long-range transport feasible?
• Extra dislocations created by reactions are stationary.
• Two dislocations separate by N lattice constants in an otherwise perfect crystal.
The energetic cost for
this separation is:In crystals of
spheres:
• They glide along a zig-zag pathway, using dislocation reactions to turn at obstacles.
N
~ d
Ep N Es ln(N)
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We are left with some compelling questions …
Shear Response
Since glide along a straight path is forbidden, slip is
blocked and degenerate crystals will be stiff.
By what (new?)
mechanisms
will degenerate
crystals melt?
Melting
Free Energy: F = E(N) – TS(N)
Spheres
S(N) ln(N)
Es(N) ln(N)
Both terms grow
like ln(N):
If the separation energy
increases linearly with N:
S(N) ln(N)
Ep(N) N
Peanuts
How do degenerate crystals
respond to imposed shear?
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Simple geometric constraints can
dramatically alter material properties
• Degenerate crystals of peanut particles are
structurally similar to crystals of spheres.
• The pairing of particle lobes creates
obstacles that block dislocation glide.
• Restricted dislocation motion alters the
plasticity and the melting mechanisms.
• Connection to crumpling?
Thank you:
Fernando Escobedo (Chem.
& Biomolecular Eng., Cornell
University)
Angie Wolfgang (Physics,
Cornell University)Gerbode et al., PRL (2008)
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Frame 52 of 07_10_08 1.5sphere.2min