Transcript Dislocations & Colloids Dislocations: Line defects in 3D xtals. Point defects in 2D xstals (Often difficult to study in atomic systems) Colloids: small.

Dislocations & Colloids
Dislocations: 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: 319323 (Mar 2006)
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
Degenerate Crystal*
• Particle centers form
a sparse, aperiodic
decoration of a
Kagomé lattice
• Particle lobes tile a
triangular lattice
• Particle orientations
uniformly populate 3
lattice directions
*K.W. Wojciechowski et al., PRL1991
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
Hexatic
Isotropic
Translational &
orientational order
Expon. decaying translational &
power law decaying orient. order
No translational & expon.
decaying orient. order
Important differences between
crystals of spheres and DCs
Certain particle orientations block slip.
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
In thermodynamic crystals, slip
occurs via the motion of dislocations.
7
5
Observed mechanisms for dislocation
nucleation and glide in DCs
5
7
A dislocation glides
via the shifting of
two particles, one
that slides and one
that swings to let
the defect pass.
Dislocations can only glide short
distances between obstacles
Dislocations can only glide short
distances between obstacles
Dislocations can only glide short
distances between obstacles
d = 4.6±0.2
d = maximum
glide distance
d=7
…so how can dislocations
travel long distances, as in
shearing or melting?
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
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
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
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
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
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
Dislocation reactions allow defects
to turn, bypassing obstacles
=
+
Reactions are topologically required
to conserve burgers vector.
Experimentally observed dislocation
reactions allow turning past obstacles
5
5
z
7
7
5
Burgers vector is conserved:
=
+
7
Using dislocation reactions,
is long-range transport feasible?
Estimate energetic cost assuming:
• Two dislocations separate by N lattice constants in an otherwise perfect crystal.
• They glide along a zig-zag pathway, using dislocation reactions to turn at obstacles.
• Extra dislocations created by reactions are stationary.
~d
N
The energetic cost for
this separation is:
Ep
N
In crystals of
spheres:
Es
ln(N)
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.
How do degenerate crystals
respond to imposed shear?
Melting
Free Energy:
F = E(N) – TS(N)
Spheres
Peanuts
Both terms grow
like ln(N):
If the separation energy
increases linearly with N:
S(N)
ln(N)
S(N)
ln(N)
Es(N)
ln(N)
Ep(N)
N
By what (new?)
mechanisms
will degenerate
crystals melt?
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)
Gerbode et al., PRL (2008)
Angie Wolfgang
Cornell University)
(Physics,
Frame 52 of 07_10_08 1.5sphere.2min