  Quasicrystals have been observed in a variety of materials ranging from metal
alloys to block copolymers and represent an "intermediate" form of matter
between crystals and amorphous materials (glasses and liquids) in that their
structural and dynamical properties can not readily described in terms of
conventional solid-state models of liquids and solids. In the present work, we
present a comprehensive analysis of basic thermodynamic and dynamic properties
of quasicrystals to better understand the nature of the atomic motion
underlying diffusion and structural relaxation in these materials. As our model
system, we investigate a dodecagonal quasicrystal using molecular dynamics (MD)
simulations in two dimensions (2D), subject to periodic boundary conditions. We
observe a two-stage relaxation dynamics in the self-intermediate scattering
function $F_s(k,t)$ of our quasicrystal material involving a fast
$\beta$-relaxation on a ps timescale 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. Multi-step relaxation
of the intermediate scattering function and string-like collective atomic
motion have similarly been observed ubiquitously in glass-forming liquids at
low temperatures and in crystalline materials at elevated temperatures where
structural relaxation and diffusion are both non-Arrhenius. After examining the
dynamics of our quasi-crystalline material in great detail, we conclude that
its dynamics more closely resemble observations on metallic glass-forming
liquids, in qualitative accord with previous neutron scattering studies.
