1. 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, (Sep 2004)
Schall et al., NATURE 440: (Mar 2006)

2. 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

3. 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

4. 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
So this is great! Here we have a novel structure that nevertheless fits neatly into our existing paradigm for 2-D systems. We know a lot about 2-D crystals of spheres, and we can utilize the existing formalisms to approach this new Degenerate Crystal phase. Certainly we can use the standard structure characterization techniques: look for triangular peaks in the lobe pair correlation function, sixfold coordinated lobes. But can we also borrow other properties of close-packed spheres – their material properties, their response to shear, even the mechanisms of melting?not only their static structure, their symmetry, but also their material properties. For example, we know that the creation and motion of dislocations
Crystal
Translational & orientational order
Hexatic
Expon. decaying translational & power law decaying orient. order
Isotropic
No translational & expon. decaying orient. order

5. Important differences between crystals of spheres and DCs
But before we jump right in and assume too many similarities between DCs and crystals of spheres, we need to carefully consider geometric constraints imposed by the particle bonds, which can lead to important differences. One striking example is that while crystals of spheres can easily slip along any crystalline direction, only certain particle orientations allow slip in Degenerate Crystals.
Certain particle orientations block slip.

6. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

7. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

8. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

9. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

10. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

11. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

12. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

13. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

14. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

15. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

16. In thermodynamic crystals, slip occurs via the motion of dislocations.5 7

17. 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

18. Dislocations can only glide short distances between obstacles

19. Dislocations can only glide short distances between obstacles

20. Dislocations can only glide short distances between obstacles
d = maximum glide distance
…so how can dislocations travel long distances, as in shearing or melting?

21. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

22. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

23. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

24. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

25. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

26. Dislocation reactions allow defects to turn, bypassing obstacles
Schematic created using primary author Cris Cecka, see M. Bowick, Science 299 (2003) 1716

27. Dislocation reactions allow defects to turn, bypassing obstacles
Reactions are topologically required to conserve burgers vector. =

28. Experimentally observed dislocation reactions allow turning past obstaclesz 5 5 7 7 7 5
Burgers vector is conserved: =

29. 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:
In crystals of spheres:
Ep N
Es ln(N)

30. 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
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
By what (new?) mechanisms will degenerate crystals melt?

31. 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)

32. Frame 52 of 07_10_08 1.5sphere.2min