Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals

Steurer, Walter

doi:10.1524/zkri.219.7.391.35643

Cited by 241 publications

(109 citation statements)

References 416 publications

(454 reference statements)

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“…The discovery of a DDQC phase in the (nominally) single-component IL-5.1 diblock copolymer melt marks only the third experimental single-component system to exhibit quasicrystalline order, joining supramolecular wedge-shaped dendrimers (3,22,23) and linear poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) tetrablock terpolymers (8); quasicrystals have only been reported in multicomponent hard materials such as binary metal alloys (24). Diblock copolymers are perhaps the simplest of these systems and are the most amenable to statistical mechanical theory.…”

Section: Discussionmentioning

confidence: 99%

Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

182

264

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We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T ODT = 66°C) using small-angle X-ray scattering (SAXS) measurements. Between T ODT and the order-order transition temperature T OOT = 42°C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T OOT the Frank-Kasper σ phase is the stable morphology. At T < 40°C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35°C and more than 10 and 200 d at 25°C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below T OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40°C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.quasicrystals | Frank-Kasper phases | block polymers T he discovery of aperiodic order, today referred to as quasicrystalline order, in rapidly cooled Al-Mn alloys by Shechtman and coworkers in 1984 heralded a paradigm shift in the understanding of what constitutes long-range order in matter (1, 2). More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3-8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.Block polymers are uniquely tunable self-assembling soft materials in which the nanoscale morphology, characteristic length scale, chemical and physical properties, and dynamics can be precisely controlled through the judicious choice of block repeat unit chemistries, block molecular weights, and molecular architecture (9, 10). Such exquisite control over structure, and the associated dynamics, makes block polymers ideal model materials for fundamental inquiries into the formation and stability of soft quasicrystals. In this article, we report the discovery of a long-lived metastable dodecagonal quasicrystalline phase (DDQC) in a (nominally) single-component poly(1,4-is...

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Section: Discussionmentioning

confidence: 99%

Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

182

264

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“…Based on all the previous research done so far in the system Al--Co--Ni (cf. Steurer, 2004) we assume that the cluster picture helps in understanding the formation of DQCs. We conclude, however, that the crystal-chemically relevant cluster is much smaller than the usually employed %20 A Gummelt cluster.…”

Section: Discussionmentioning

confidence: 99%

“…5). Mostly low-order rational (stable) approximants have been discovered up to now (for a list of approximants in the system Al--Co--Ni, see Steurer, 2004). Approximants in the wider sense of the word posses periodic crystal structures consisting of the same atomic clusters as QCs.…”

Section: Approximants and Clustersmentioning

confidence: 99%

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Reflections on symmetry and formation of axial quasicrystals

Steurer¹

2006

Zeitschrift Für Kristallographie - Crystalline Materials

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Abstract. Some ideas are presented on the geometrical factors governing structure and formation of axial quasicrystals with 5-and 7-fold symmetry, respectively. First, the importance of thin atomic layers is discussed for the growth of decagonal quasicrystals. They are the only longrange ordered structural units carrying information on the local non-crystallographic symmetry of the constituent clusters. Second, the consequences of local polysynthetic twinning for the formation of pentagonal and heptagonal quasicrystals are demonstrated. Third, the special relationship of the b-phase, (Co,Ni) 1Àx Al 1þx , to the decagonal phase and its periodic average structure is discussed as well as its role as template for the formation and growth of decagonal Al--Co--Ni.

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“…The discovery of icosahedral QCs was followed by discoveries of axial QCs (periodic in one dimension) with decagonal, pentagonal, octagonal, dodecagonal and enneagonal symmetries. [3] The discovery of an Al-Fe-Si glass, which solidifies from melt, opens the possibility of an ordered structure of infinite rotations. [4] Most thermodynamically stable QCs, are ternary or higher order, but some binary QCs appear to be stable as well, at least at finite temperatures.…”

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confidence: 99%

A Warm Welcome to Quasicrystals

Bendersky

Burton

2012

J. Phase Equilib. Diffus.

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The ultimate recognition of quasicrystals (QC) as legitimate members of the Materials Kingdom finally arrived with the 2011 Nobel Prize in Chemistry awarded to material scientist Dan Shechtman for the discovery of an icosahedral Al-Mn phase. [1] Before this discovery thermodynamic and structural properties of materials were studied for either isotropic substances (gases, liquids or glasses as frozen liquids; the disordered systems with infinite space group symmetry) or periodic structures (ordered, 230 crystallographic space groups). The discovery of QC significantly increased the classes of materials that must be investigated for their structural, thermodynamic and physical properties; and also to determine their (meta)stability fields in phase diagrams.Mathematical descriptions of QCs as 3D structures with quasiperiodic lattices that can be generated by projection from higher-dimension periodic lattices (e.g. a 6D hypercube for an icosahedral phase) opened the possibility of filling the gap between isotropic and periodic structures with an infinite number of ordered non-periodic structures. ''The aperiodic zoo'' of tiles includes not only the famous pentagonal Penrose tile, but also tiles with higher than six-fold rotations, e.g. octagonal and seven-fold symmetries; even ordered tiling of infinite order rotations, the pinwheel tiling, is possible. [2] The first QC was discovered as a metastable phase of icosahedral symmetry in the Al-Mn system. Since then, numerous stable and metastable icosahedral QCs have been found, mostly as intermetallic phases, but also in minerals, liquid crystals, polymers and nanoparticles. The discovery of icosahedral QCs was followed by discoveries of axial QCs (periodic in one dimension) with decagonal, pentagonal, octagonal, dodecagonal and enneagonal symmetries. [3] The discovery of an Al-Fe-Si glass, which solidifies from melt, opens the possibility of an ordered structure of infinite rotations. [4] Most thermodynamically stable QCs, are ternary or higher order, but some binary QCs appear to be stable as well, at least at finite temperatures. Stable QCs allow quantitative structural studies, and determinations of their thermodynamic functions and phase equilibria. The first stable icosahedral QC was synthesized in the Al-Cu-Fe ternary; a stable axial decagonal QC was discovered in Al-Co-Cu; and the first stable binary icosahedral QCs were found in Ca-Cd and Yb-Cd. The stabilities of QCs are dominated by the electron/atom ratio rather than bulk composition; thus most QCs can be considered to be Hume-Rothery compounds.Translational aperiodicity presents fundamental challenges to electronic structure calculations (e.g. DFT) for QCs. [5] Even loworder periodic approximants [e.g. the Frank-Kasper phase: (Al,Zn) 49 Mg 32 ] are very complex crystal structures, typically with hundreds atoms per unit cell, and the atoms/cell ratio increases by a factor of % 4.17 for each step in the approximants hierarchy. Thus, very large complex models are typically required to obtain good approximati...

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Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals

Cited by 241 publications

References 416 publications

Dodecagonal quasicrystalline order in a diblock copolymer melt

Dodecagonal quasicrystalline order in a diblock copolymer melt

Reflections on symmetry and formation of axial quasicrystals

A Warm Welcome to Quasicrystals

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