On a Realistic Growth Mechanism for Quasicrystals

Abstract

Simple rules are discussed that can guide under realistic conditions the growth of quasicrystals. We propose a two-step mechanism where the well-known overlap rules for the fundamental atomic clusters are complemented by the new layer-continuation rule. This rule demands that the sets of atomic layers, crisscrossing each atomic cluster according to its eigensymmetry, have to be continued across all other clusters formed during the growth process. On one hand, this combined growth rule is local because each fundamental cluster al-* Prof. Dr. W. Steurer Fax: +41-44-632-1133 E-Mail: steurer@mat.ethz.ch [a]

Computational self-assembly of a one-component icosahedral quasicrystal

“…Note that although metallic quasicrystals occur exclusively in binary and higher intermetallic compounds, they are often understood as comprised of identical clusters. An effective cluster interaction could be modelled with a potential similar to the one employed here 37 .…”

“…Computer simulations of IQCs should account for the observation that they can form on short timescales via rapid solidification 7 . Fast growth is possible only if there is an efficient way to add particles to the nucleus [36][37][38] and if the periodic boundary conditions of the simulation do not impose constraints on the growing crystal and inhibit the relaxation of defects. For a specific choice of the potential parameters (k, φ), we initialize the particles in a random arrangement at a low density and slowly decrease the temperature until a roughly spherical solid forms directly from the gas phase (Fig.…”

GummeltversusLück decagon covering and beyond. Implications for decagonal quasicrystals

“…2 and 3 of Steurer & Deloudi (2014); Steurer & Cervellino (2001)]. One has to keep in mind that DQCs are three-dimensional structures, and that the periodic direction also influences the long-range order (Steurer & Cervellino, 2001;Steurer, 2011).…”

“…However, matching and overlapping rules alone are not growth rules; they cannot force quasiperiodic growth but they essentially prove the quasiperiodicity of a structure [see e.g. Steurer (2011)].…”

Why are quasicrystals quasiperiodic?

“…Consequently, those slightly puckered layers connect the periodic and the quasiperiodic directions. This coupling constrains the evolution of quasiperiodic order during QC growth (see Steurer 47 any deviation from it would hinder the growth of the inclined atomic layers. Consequently, 2D growth models or 3D models assuming stackings of largely independent 2D quasiperiodic layers are not realistic.…”