Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems

Abstract

For a three dimensional system we answer two questions, how simple a particle system might be to show the quasicrystal order and, what system features are the most important for quasicrystal formation? One-component system of particles with isotropic pair interaction is one of the simplest ones. We show that such system may be driven to three-dimensional decagonal (10-fold) quasicrystalline state just by purely repulsive, isotropic and monotonic interaction pair potential with two characteristic length scales; no attraction is needed. The second question we answer defining universal (nearly independent from the shape of the pair potential) effective integral parameters related to the first peak of the radial distribution function. The universality is illustrated by demonstrating the quasicrystalline order for a number of particle systems with absolutely different interaction potentials, both purely repulsive and attractive, but with the same effective integral parameters. Simple models like we study qualitatively describe effective interaction in molecular liquids, soft matter systems and metallic alloys for which quasicrystals have been experimentally observed.

8 pages, 5 figures. Published online in Soft Matter, 2015

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Cited by in corpus (12)

• Cooling rate dependence of simulated $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ metallic glass structure
• Non-Close-Packed Three-Dimensional Quasicrystals
• Nucleation instability in super-cooled Cu-Zr-Al glass-forming liquids
• Structure and glass-forming ability of simulated Ni-Zr alloys
• Effects of confinement between attractive and repulsive walls on the thermodynamics of an anomalous fluid
• Programming patchy particles to form three-dimensional dodecagonal quasicrystals
• Simulated Cu-Zr glassy alloys: the impact of composition on icosahedral order
• Crystalline structures of particles interacting through the harmonic-repulsive pair potential
• Investigation of the degree of local structural similarity between the parent-liquid and children-crystal states for a model soft matter system
• Effective potentials induced by mixtures of patchy and hard co-solutes
• Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function
• Polytetrahedral short-range order and crystallization stability in supercooled $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ metallic liquid