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)

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*

*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

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

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

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

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

Dislocations can only glide short

distances between obstacles

Dislocations can only glide short

distances between obstacles

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

Dislocation reactions allow defects

to turn, bypassing obstacles

Schematic created using

http://physics.syr.edu/thomson/thomsonapplet.htm

primary author Cris Cecka, ccecka@stanford.edu

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, ccecka@stanford.edu

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, ccecka@stanford.edu

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, ccecka@stanford.edu

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, ccecka@stanford.edu

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, ccecka@stanford.edu

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

z

7

5

5

5

7

7

= +

Burgers vector is conserved:

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)

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?

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)

Frame 52 of 07_10_08 1.5sphere.2min