Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace

Johannes Hielscher,Miriam Martinsons,Michael Schmiedeberg,Sebastian C Kapfer

doi:10.1088/1742-6596/1458/1/012018

Johannes Hielscher, Miriam Martinsons + Show 2 more

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https://doi.org/10.1088/1742-6596/1458/1/012018

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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. Sub- diffusive 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.

Highlights

Intrinsic quasicrystals on the colloidal length scale are of much interest, especially due to the accessibility of microscopic details
The transport in colloidal quasicrystals is carried by phasonic flips, common to all
We have studied the phasonic equilibrium of decagonal quasicrystals governed by a short-ranged pair potential

Summary

Introduction

Intrinsic quasicrystals on the colloidal length scale are of much interest, especially due to the accessibility of microscopic details. G. [1, 2]), thermodynamics and phason elasticity [3] have been studied for two-dimensional (2D) decagonal quasicrystals, the specific role of phasonic excitations is still elusive. Phasonic degrees of freedom are unique to quasicrystals, visible as particle flips in physical space [4, 5]. Phasonic contributions cannot be isolated, and the vastly different time scales between phononic motions and phasonic flips remain a challenge for simulations. Experimental studies on decagonal (3D axial) intermetallic quasicrystals do not detect a significant contribution of phasons to mass transport [8], rather suggest a regular vacancy mechanism for self-diffusion. We present a simple hyperspace model for 2D colloidal quasicrystals without defects (dislocations, vacancies, surfaces), and can identify phason-driven transport. Flip simulations are in quantitative agreement with conventional Brownian Dynamics

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