Dislocation-free growth of quasicrystals from two seeds due to additional phasonic degrees of freedom

Abstract

We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.

Quasi-periodic Geometry for Architectural Acoustics

“…These systems could potentially provide a rich source of performative geometries for innovating new structures, systems, materials, patterns, surfaces and forms. One intriguing potential of their unique quasi-periodic formations is the ability to orchestrate the flow of light or sound energy, which could find applications across a wide range of light and soundbased technologies (Roichman and Grier 2005;Steurer and Widmer 2007;Mikhael et al 2010;Schmiedeberg and Stark 2012;Martinsons et al 2014;Dong et al 2015;Boriskina 2015;Schmiedeberg et al 2017). In this context, this paper is focused specifically on investigating aspects of the acoustical diffusion behavior of quasi-periodic formations.…”

Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids

“…Modeling quasicrystals and their evolution using the PFC approach shows great promise. Recent works have considered quasicrystal growth modes [23], interfaces between quasicrystalline grains from multiple separate seeds [24], monolayers on quasicrystalline surfaces [25] and even three-dimensional quasicrystalline systems [26]. On the other hand, where periodic crystals display an endlessly repeating motif quasicrystals do not obey this rule which drastically complicates both the detection of a lattice orientation and grain extraction with the current methods [11,13,19].…”

Formation of a single quasicrystal upon collision of multiple grains

“…Although past studies on QC growth mechanisms extend our understanding of phason contributions to stability in a bulk QC 1,2,9 , studies on phason contributions to the formation and motion of grain boundaries (GBs) remain limited 10 . Yet the latter is critically important from a practical standpoint since the formation of polycrystals is unavoidable due to finite nucleation rates below the melting point.…”

“…Recently, Schmiedeberg et al 10 conducted phase field crystal simulations to determine whether and when a GB may form between two QCs. In general, they observe that grain coalescence occurs more readily in dodecagonal QCs than in periodic crystals.…”