Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace

Abstract

We introduce a novel simulation method that is designed to explore fluctuations of the phasonic degrees of freedom in decagonal colloidal quasicrystals. Specifically, we attain and characterise thermal equilibrium of the phason ensemble via Monte Carlo simulations with particle motions restricted to elementary phasonic flips. We find that, at any temperature, the random tiling ensemble is strongly preferred over the minimum phason-strain quasicrystal. Phasonic flips are the dominant carriers of diffusive mass transport in physical space. Subdiffusive transients suggest cooperative flip behaviour on short time scales. In complementary space, particle mobility is geometrically restricted to a thin ring around the acceptance domain, resulting in self-confinement and persistent phasonic order.

Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals

“…While we can study the dynamics of local phasonic flips over long times in much smaller systems, we cannot explore the phasonic excitations that matter for the long-distance behavior of the correlation functions and that correspond to rearrangements correlated over long distances which are only accessible with large simulation boxes. Simulations where exclusively phasonic flips can occur indicate that phasonic flips are part of thermal equilibrium [59] and the structure can still be dislocation free or at least usually no isolated dislocations occur. Furthermore, the logarithmic decay of the correlations of phasonic displacements [42,43] prohibits a perfect long-range phasonic order.…”

“…over long distances which are only accessible with large simulation boxes. Simulations where exclusively phasonic flips can occur indicate that phasonic flips are part of thermal equilibrium [59] and the structure can still be dislocation free or at least usually no isolated dislocations occur.…”

Efficient algorithm for simulating particles in true quasiperiodic environments

“…One of the reasons why it is interesting to study quasicrystals, is the flexibility they offer due to the variety of symmetries that can be produced, which can be of great importance in the optoelectronics industry [45][46][47], making high symmetry quasicrystals attractive. Another reason why these systems are interesting is the existence of phasons [48][49][50][51][52], that is, thermal excitations that propagate in the lattice without energy cost generating phasonic flips [53], which contribute to the specific heat in a similar way in which the phonons do in the periodic crystals. Just as phonons have a set of d phononic modes, where d is the dimension of the system, phasons also have a set of r − d phasonic modes, where r is the rank of the quasicrystal, i.e., the number of wave vectors linearly independent necessary to generate the reciprocal lattice of the quasiperiodic structure [21,54,55].…”