Non-close-packed three-dimensional quasicrystals

Abstract

Quasicrystals are frequently encountered in condensed matter. They are important candidates for equilibrium phases from the atomic scale to the nanoscale. Here, we investigate the computational self-assembly of four quasicrystals in a single model system of identical particles interacting with a tunable isotropic pair potential. We reproduce a known icosahedral quasicrystal and report a decagonal quasicrystal, a dodecagonal quasicrystal, and an octagonal quasicrystal. The quasicrystals have low coordination number or occur in systems with mesoscale density variations. We also report a network gel phase.

Crystalline structures of particles interacting through the harmonic-repulsive pair potential

“…The stability of single component systems against crystallization is unusual because single component supercooled liquids usually readily crystallize [1,2,6]. In particular, several binary models have been intentionally developed to avoid crystallization and allow numerical investigations of the deeply supercooled model liquids [70,71] However, recently there have been observations of the unusual stabilities of the single components liquids against crystallization [38,69]. Our observations of the stability of the single component systems appear to be similar to the observations made in [38,69].…”

“…Finally, we would like to note that the columnar organization of the observed crystal structure resembles (from a local perspective) the organization of particles in some columnar quasicrystals [33,[36][37][38].…”

“…In particular, several binary models have been intentionally developed to avoid crystallization and allow numerical investigations of the deeply supercooled model liquids [70,71] However, recently there have been observations of the unusual stabilities of the single components liquids against crystallization [38,69]. Our observations of the stability of the single component systems appear to be similar to the observations made in [38,69]. At the same time, it appears to be of interest to note that the pair potential used in our study is noticeably simpler than the potentials studied in [38,69].…”

“…Discovery of quasicrystals lead, in particular, to the systematic studies of the single component systems consisting of the particles interacting through sphericallysymmetric pair potentials whose shape is more complex than the shape of the simple "traditional" pair potentials [28][29][30][31][32][33][34][35][36][37][38]. The goal of the related studies is often to clarify the relationship between the shape of the potential and the structural/dynamic properties of the systems of particles interacting through such potentials.…”

Simulated nanoparticle assembly using protoparticles (SNAP)

“…This exchange can be further optimised when we recognise that many surface atoms behave similarly (particularly when they occupy a common {hkl} plane) and replace surface atoms with regions of the surface that are uniquely characterised by common surface properties. This type of coarse-graining simplification shares similarities with coarse-grained molecular dynamics (MD) [12][13][14][15][16] used to represent biomolecules with a reduced number of degrees of freedom [17][18][19][20]; as well as finite element methods [21][22][23], discrete element methods [24,25] and other methods used to represent anisotropic granular material [26][27][28][29][30][31][32][33]. This means that thousands of nanoparticles containing hundreds of atoms can be replaced by tens of thousands of nanoparticles containing tens of artificial entities that encapsulate all of the essential properties and interactions relevant at the scale of the simulation.…”