Restricted Dislocation Motion in Crystals of Colloidal Dimer Particles

At high area fractions, monolayers of colloidal dimer particles form a degenerate crystal (DC) structure in which the particle lobes occupy triangular lattice sites while the particles are oriented randomly along any of the three lattice directions. We report that dislocation glide in DCs is blocked by certain particle orientations. The mean number of lattice constants between such obstacles is ${\overline{Z}}_{\exp }=4.6\pm 0.2$ in experimentally observed DC grains and ${\overline{Z}}_{\mathrm{sim}}=6.18\pm 0.01$ in simulated monocrystalline DCs. Dislocation propagation beyond these obstacles is observed to proceed through dislocation reactions. We estimate that the energetic cost of dislocation pair separation via such reactions in an otherwise defect free DC grows linearly with final separation, hinting that the material properties of DCs may be dramatically different from those of 2-D crystals of spheres.

Figure 1

Before-and-after micrographs illustrating observed dislocation nucleation and glide moves. Particle lobes have been marked with dots, nearest neighbor bonds are indicated by lines, and dislocations consisting of paired fivefold and sevenfold coordinated lobes have been highlighted. (a), (b) One rotating dimer particle (highlighted with a thick black dumbbell) nucleates a pair of dislocations. (c), (d) A dislocation glides down by three rows through a combination of one sliding move (upper dumbbell) followed by one swinging move (lower dumbbell).

Figure 2

Schematic of mechanisms for dislocation nucleation and glide in monolayers of spheres (a)–(c) and dimer particles (d)–(f). (a), (b) Displacing two spheres (gray) creates a pair of dislocations, each containing one fivefold and one sevenfold coordinated particle. (b), (c) The pair glides apart when the sevenfold particles shift parallel to their Burgers vectors (outlined arrows) while all other particles retain their crystalline positions. (d) A dislocation pair in a DC is created by rotating one particle (gray) so that its lobes move similarly to the gray spheres in (a). Glide proceeds through the motion of the lobes marked with arrows, either by swinging (blue particle) or sliding (green particle). (e) Nucleation and glide have the net effect of shifting the left side of the crystal upward and the right side downward. This slip leaves swinging and sliding particles intact, indicating accommodation of the dislocation glide. The red particles, however, would have to be severed by this deformation. Since the colloidal particles in our suspensions do not break, the required dislocation motion is blocked by such particle orientations. (f) The sequence of green and blue particles is a zipper of length $Z=4$. This zipper length sets the maximum separation attainable using glide.

Figure 3

Probability distribution of zipper lengths in both experimental (empty squares) and simulated (solid triangles) DCs. Counting statistics determine the error bars, which for the simulations are smaller than the symbols. The average zipper length measured from experimental DC grains is ${\overline{Z}}_{\exp }=4.6\pm 0.2$. Zippers in simulated crystals with ${10}^4$ lattice sites are only slightly longer: ${\overline{Z}}_{\mathrm{sim}}=6.18\pm 0.01$. The dotted line is the best fit exponential for $Z>6$, having the form $\rho (Z)=0.37e^{-Z/4.4}$. The inset shows the ensemble of glide-permitting particle orientations given nucleation via clockwise rotation of the gray particle. Particle configurations including a subset of these orientations enable glide via swinging (blue/dark gray) or sliding (green/light gray).

Figure 4

An observed dislocation reaction allowing a dislocation to hop from one zipper to another. Only the relevant defects have been highlighted, and their Burgers vectors are indicated by outlined arrows. (a) A dislocation gliding down from the upper right is one lobe from the end of its zipper. (b) The dislocation has reacted and proceeds by gliding down another zipper extending horizontally to the left. A second dislocation, visible to the lower right of the reaction site, was emitted to conserve total Burgers vector.