No abstract

Quasicrystals are structures that are not periodic but possess a long range positional order. They can have any rotational symmetry including those that are forbidden in periodic crystals. The symmetry is classied by the point group and the rank D. In quasicrystals, phasons as additional hydrodynamic modes cause correlated rearrangements of the particles. The number of phasonic degrees of freedom depends on the rank. For colloidal quasicrystals that are induced by laser elds, specic phasonic displacements can be realized by changing the phases of the laser beams in a well-determined way. The arising trajectories of colloids in two-dimensional light-induced colloidal quasicrystals with rank D = 4 have already been analyzed in detail. Here, we analyze the colloidal trajectories in two-dimensional quasicrystals with 14-fold symmetry having rank D = 6. We observe complex paths of the colloids consisting of straight and winding lines as well as jumps.

We explore the behavior of two-dimensional patchy colloidal particles with 8 or 10 symmetrically arranged patches by employing Monte-Carlo simulations. The particles interact according to an isotropic pair potential that possesses only one typical length. The patches lead to additional attractions that are anisotropic and depend on the relative orientation of two neighboring particles. We investigate the assembled structures with a special interest in quasicrystals. We found that the patch width is of great importance: Only in case of narrow patch widths we are able to observe metastable octagonal and decagonal quasicrystals, while dodecagonal quasicrystals can also occur for broad patches. These results are important to understand the role of interactions with preferred binding angles in order to obtain quasicrystals. Our findings suggest that in case of sharp binding angles, as they occur in metallic alloys, octagonal and decagonal symmetries might be observed more often than in systems with less sharp binding angles as it is the case in soft matter systems where dodecagonal quasicrystals dominate.

Phasons are additional degrees of freedom which occur in quasicrystals alongside the phonons known from conventional periodic crystals. The rearrangements of particles that are associated with a phason mode are hard to interpret in physical space. We reconstruct the quasicrystal structure by an embedding into extended higher-dimensional space, where phasons correspond to displacements perpendicular to the physical space. In dislocation-free decagonal colloidal quasicrystals annealed with Brownian dynamics simulations, we identify thermal phonon and phason modes. Finite phononic strain is pinned by phasonic excitations even after cooling down to zero temperature. For the phasonic displacements underlying the flip pattern, the reconstruction method gives an approximation within the limits of a multi-mode harmonic ansatz, and points to fundamental limitations of a harmonic picture for phasonic excitations in intrinsic colloidal quasicrystals.

The growth of quasicrystals, i.e. structures with long-range positional order but no periodic translational symmetry, is more complex than the growth of periodic crystals. By employing Brownian dynamics simulations in two dimensions for colloidal particles that interact according to an isotropic pair potential with two incommensurate lengths, we study the growth of quasicrystalline structures by sequentially depositing particles at their surface. We quantify the occurrence of quasicrystalline order as a function of the temperature and the rate of added particles. In addition, we explore defects like local triangular order or gaps within the quasicrystalline structure. Furthermore, we analyze the shapes of the surfaces in grown structures which tend to build straight lines along the symmetry axes of the quasicrystal. Finally, we identify phasonic flips which are rearrangements of the particles due to additional degrees of freedom. The number of phasonic flips decreases with the distance to the surface.