Atomistic mechanisms of dynamics in a two-dimensional dodecagonal quasicrystal

Quasicrystals have been observed in a variety of materials ranging from metal alloys to block copolymers. However, their structural and dynamical properties cannot be readily described in terms of conventional solid-state models of liquids and solids. We may expect the dynamics of this specific class of quasicrystalline materials to be more like glass-forming liquids in the sense of exhibiting large fluctuations in the local mobility ("dynamic heterogeneity") and non-Arrhenius temperature dependence of relaxation and diffusion. In this work, we investigate a model dodecagonal quasicrystal material in two dimensions (2D) using molecular dynamics (MD) simulations, with a focus on heterogeneous dynamics and non-Arrhenius relaxation and diffusion. As observed in glass-forming liquids and heated crystals, we observe a two-stage relaxation dynamics in the self-intermediate scattering function $F_s(k,t)$ of our quasicrystal material. It involves a fast $\beta$-relaxation and $\alpha$ relaxation process having a highly temperature dependent relaxation time whose activation energy varies in concert with the extent of string-like collective motion, a phenomenon recognized to occur in glass-forming liquids at low temperatures and crystalline materials at elevated temperatures. After examining the dynamics of our dodecagonal quasicrystalline material in great detail, we conclude that the dynamics of these materials more closely resembles observations on metallic glass-forming liquids than crystalline materials.