Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems (original) (raw)
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Physical Review Letters, 2007
For the study of crystal formation and dynamics we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a decagonal and a dodecagonal quasicrystal are self-assembled. In the case of the quasicrystals the particles reorder by phason flips at elevated temperatures. During annealing the entropically stabilized decagonal quasicrystal undergoes a reversible phase transition at 65% of the melting temperature into an approximant, which is monitored by the rotation of the de Bruijn surface in hyperspace. PACS numbers: 61.50.Ah, 02.70.Ns, 61.44.Br, 64.70.Rh. Self-assembly is the formation of complex patterns out of simple constituents without external interference. It is a truly universal phenomenon, fundamental to all sciences . Although usually the constituents interact only locally, the result is well-ordered over long distances, sometimes with a high global symmetry. In the process of crystallization, particles (atoms, molecules, colloids, etc.) arrange themselves to form periodic or quasiperiodic structures. Here we are interested in structurally complex phases. Examples are metallic crystals with large unit cells -hundreds or thousands of atoms -known as complex metallic alloys . Some consequences of the complexity are the existence of an inherent disorder and the formation of well-defined atomic clusters . Related alloys differ by the cluster arrangement. In the limit of infinitely large unit cells non-periodic order like in quasicrystals [4] is obtained. However self-assembly of complex phases is not unique to alloys. Recently micellar phases of dendrimers were observed to form a mesoscopic quasicrystal , and there are indications that quasicrystals exist in monodisperse colloidal (macroscopic) systems . Since the interaction between colloidal particles can be tuned in various ways, these systems are well-suited for experiments investigating self-assembly in dependence of the potential shape.
Quasicrystals in a monodisperse system
Physical Review E, 1999
We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystalline phase can form for certain values of the square-well parameters. Quenching the liquid phase at a very low temperature, we obtain an amorphous phase. By heating this amorphous phase, we obtain a quasicrystalline structure with five-fold symmetry. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, we conclude that the observed quasicrystal phase can be the stable phase in a specific range of temperatures.
Dynamics of particle flips in two-dimensional quasicrystals
Physical Review B, 2010
The dynamics of quasicrystals is more complicated than the dynamics of periodic solids and difficult to study in experiments. Here, we investigate a decagonal and a dodecagonal quasicrystal using molecular dynamics simulations of the Lennard-Jones-Gauss interaction system. We observe that the short time dynamics is dominated by stochastic particle motion, so-called phason flips, which can be either single-particle jumps or correlated ring-like multi-particle moves. Over long times, the flip mechanism is efficient in reordering the structure of the quasicrystals and can generate diffusion. The temperature dependence of diffusion is well described by an inverse Arrhenius law. We also study the spatial distribution and correlation of mobile particles by analyzing the dynamic propensity.
Stability of two-dimensional soft quasicrystals in systems with two length scales
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
The relative stability of two-dimensional soft quasicrystals in systems with two length scales is examined using a recently developed projection method, which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal, and octagonal quasicrystals, are obtained for a simple model, i.e., the Lifshitz-Petrich free-energy functional, of soft quasicrystals with two length scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.
Numerical simulation of quasicrystals
Journal of Non-Crystalline Solids, 1990
structures can be built by 3D cross sections through 3D atomic motifs in a 6D space. By numerical simulation, we study the stability of a monoatomic model and of an AIMnSi model with interatomic pair potentials. Because all site environments are inequivalent, atoms move from their initial positions. The resulting structures can be related to modifications of the atomic motifs.
Stability of Two-Dimensional Soft Quasicrystals
2015
The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.
Journal of Physics: Condensed Matter
A two-dimensional dodecagonal quasicrystal was previously reported by Dotera et al (2014 Nature 506 208) in a system of particles interacting with a hard core of diameter σ and a repulsive square shoulder of diameter δ σ = 1.40. In the current work, we examine the formation of this quasicrystal using bond orientational order parameters, correlation functions and tiling distributions. We find that this dodecagonal quasicrystal forms from a fluid phase. We further study the effect of the width of the repulsive shoulder by simulating the system over a range of values of δ. For the range of densities and temperatures considered, we observe the formation of the dodecagonal quasicrystal between δ σ = 1.30 and σ 1.44. We also study the effect of shape of the interaction potential by simulating the system using three other interaction potentials with two length scales, namely hard-core plus a linear ramp, modified exponential, or Buckingham (exp-6) potential. We observe the presence of the quasicrystal in all three systems. However, depending on the shape of the potential, the formation of the quasicrystal takes place at lower temperatures (or higher interaction strengths). Using freeenergy calculations, we demonstrate that the quasicrystal is thermodynamically stable in the square-shoulder and linear-ramp system.
Hydrodynamic structure factor for two-dimensional decagonal quasicrystals
physica status solidi (b), 2012
The dynamic and static structure factors for two-dimensional decagonal quasicrystals (QCs) are calculated based on the hydrodynamic model. Explicit formulae with algebraic decay, which is characteristic in lower dimensions, are obtained. The sound-wave and diffusive-mode contributions are analyzed separately. It is shown that the phonon-phason coupling yields the characteristic anisotropy in the structure factors. If one assumes the phasonic diffusion constant of the order of magnitude typical for metallic QCs, however, the phasonic contribution is expected only at very small frequencies and hence more likely to be observed in the time domain than in the frequency domain.