Structural model for octagonal quasicrystals derived from octagonal symmetry elements arising in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi><mml:mtext>-Mn</mml:mtext></mml:mrow></mml:math>crystallization of a simple monatomic liquid

Elenius, Måns; Zetterling, Fredrik H. M.; Dzugutov, Mikhail; Fredrickson, Daniel C.; Lidin, Sven

doi:10.1103/physrevb.79.144201

Cited by 22 publications

(19 citation statements)

References 40 publications

(42 reference statements)

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Section: Discovery and Dynamics Of The Icosahedral Quasicrystalmentioning

confidence: 99%

“…The shape of the potential is inspired by Friedel oscillations 23,26,28,31 , which are equivalent to the Hume-Rothery mechanism. The oscillating pair potential 32 (OPP) with six parameters mimics the atomic interactions of many metallic systems and, as shown in Supplementary Information, can be simplified to the functional form which combines a short-range repulsion with a damped oscillation of frequency k and phase shift φ that induces an attraction at specific interparticle distances r. Our potential is achieved by terminating the OPP after three wells (at the third maximum) and shifting the potential smoothly to zero to obtain an (in principle) experimentally feasible effective interaction potential; we note possible synthesis routes in our discussion at the end.…”

Section: Discovery and Dynamics Of The Icosahedral Quasicrystalmentioning

confidence: 99%

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Computational self-assembly of a one-component icosahedral quasicrystal

et al. 2014

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Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.

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Section: Discovery and Dynamics Of The Icosahedral Quasicrystalmentioning

confidence: 99%

Section: Discovery and Dynamics Of The Icosahedral Quasicrystalmentioning

confidence: 99%

Computational self-assembly of a one-component icosahedral quasicrystal

et al. 2014

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“…The β-Mn crystal structure with chiral space group P4 1 32 [ Fig. 1a], earlier reported in spheres interacting via an isotropic oscillatory pair potential [31], self-assembles from achiral dodecahedra shapes [27]. However, as expected, the handedness of the crystal could not be controlled and both left-and right-handed crystals were observed with equal probability.…”

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confidence: 52%

Controlling Chirality of Entropic Crystals

et al. 2015

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Colloidal crystal structures with complexity and diversity rivaling atomic and molecular crystals have been predicted and obtained for hard particles by entropy maximization. However, so far homochiral colloidal crystals, which are candidates for photonic metamaterials, are absent. Using Monte Carlo simulations we show that chiral polyhedra exhibiting weak directional entropic forces self-assemble either an achiral crystal or a chiral crystal with limited control over the crystal handedness. Building blocks with stronger faceting exhibit higher selectivity and assemble a chiral crystal with handedness uniquely determined by the particle chirality. Tuning the strength of directional entropic forces by means of particle rounding or the use of depletants allows for reconfiguration between achiral and homochiral crystals. We rationalize our findings by quantifying the chirality strength of each particle, both from particle geometry and potential of mean force and torque diagrams.Controlling -and understanding the origins of-chirality is a major goal in the physical and chemical sciences. It has longstanding implications that range from the design of effective pharmaceuticals to explaining biological homochirality and the beginnings of life [1]. In recent years the expectation that chiral materials can provide a route for photonic metamaterials [2] has renewed the interest in chirality, now from a materials design perspective. A key remaining challenge for the development of metamaterials [3] is the ability to use scalable techniques to create crystals with unique chirality. Of particular importance are enantioselective processes, which select a pre-defined handedness of the crystal, thereby maximizing optical activity. [17][18][19][20], the final chiral structures have, so far, been restricted to liquid crystalline and low-dimensional arrangements. Growth of three-dimensional homochiral colloidal crystals has yet to be demonstrated. In fact, the only examples of chiral crystals with realized applications as polarization sensitive devices [21,22] were fabricated via non-scalable processes such as direct laser writing, hampering large scale production.Recent work has shown that hard polyhedra can selfassemble into a great diversity of crystals, liquid crystals, and quasicrystals via entropy maximization [23][24][25][26][27][28], a mechanism that can be understood as resulting from emergent directional entropic forces (DEFs) between neighboring particles due to crowding [25,29,30]. Even chiral crystals have been assembled. The β-Mn crystal structure with chiral space group P4 1 32 [ Fig. 1a], earlier reported in spheres interacting via an isotropic oscillatory pair potential [31], self-assembles from achiral dodecahedra shapes [27]. However, as expected, the handedness of the crystal could not be controlled and both left-and right-handed crystals were observed with equal probability. Given the ability of entropic interactions to imitate the plethora of complex structures achievable from atomistic interactions, the abs...

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“…Indeed, -Mn is the approximant structure of an octagonal quasicrystal with two-dimensional quasiperiodicity and a structure corresponding to an Ammann-Beenker-type tessellation (Elenius et al, 2009). Indeed, -Mn is the approximant structure of an octagonal quasicrystal with two-dimensional quasiperiodicity and a structure corresponding to an Ammann-Beenker-type tessellation (Elenius et al, 2009).…”

Section: Construction Of An Artificial Permutation Structurementioning

confidence: 99%

Quantitative crystal structure descriptors from multiplicative congruential generators

Hornfeck¹

2012

Acta Cryst Sect A

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Special types of number-theoretic relations, termed multiplicative congruential generators (MCGs), exhibit an intrinsic sublattice structure. This has considerable implications within the crystallographic realm, namely for the coordinate description of crystal structures for which MCGs allow for a concise way of encoding the numerical structural information. Thus, a conceptual framework is established, with some focus on layered superstructures, which proposes the use of MCGs as a tool for the quantitative description of crystal structures. The multiplicative congruential method eventually affords an algorithmic generation of three-dimensional crystal structures with a near-uniform distribution of atoms, whereas a linearization procedure facilitates their combinatorial enumeration and classification. The outlook for homometric structures and dual-space crystallography is given. Some generalizations and extensions are formulated in addition, revealing the connections of MCGs with geometric algebra, discrete dynamical systems (iterative maps), as well as certain quasicrystal approximants.

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Structural model for octagonal quasicrystals derived from octagonal symmetry elements arising inβ-Mncrystallization of a simple monatomic liquid

Cited by 22 publications

References 40 publications

Computational self-assembly of a one-component icosahedral quasicrystal

Computational self-assembly of a one-component icosahedral quasicrystal

Controlling Chirality of Entropic Crystals

Quantitative crystal structure descriptors from multiplicative congruential generators

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