Why are quasicrystals quasiperiodic?

Steurer, Walter

doi:10.1039/c2cs35063g

Cited by 56 publications

(60 citation statements)

References 55 publications

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“…Examples are the k-Al 13 Co 4 compound [7], with (only) 108 at/uc, the O1-AlCuFeCr orthorhombic compound with few hundred at/uc [8], and, even more so, the AlCuTa compound that contains more than 20,000 at/uc [9]. Compounds of the CMA family, the crystal structure of which was fully deciphered from diffraction studies, are now numerous and were the subject of a large number of studies [10]. Some physical properties, especially electron transport, have been determined, and several niche applications have appeared [11,12].…”

Section: Introductionmentioning

confidence: 98%

Indirect assessment of the surface energy of the Al–Cu–Fe quasicrystal

et al. 2016

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This work summarizes an attempt to estimate the surface energy of the stable, icosahedral Al-Cu-Fe quasicrystal (i-ACF hereafter). To this end, samples of i-ACF were prepared by sintering a powder produced by ball milling and heat treating a master ingot of composition Al 59 Cu 25.5 Fe 12.5 B 3 (at.%), icosahedral lattice structure, and containing negligibly small amounts of contaminating crystalline phases. This powder was then sintered in the shape of a cylinder appropriate for pin-on-disk tests in ambient air. Variable amounts of either Sn or Bi were added to the powder prior to sintering. These elements do not dissolve in the quasicrystal and form small pockets of pure Sn or Bi that are either isolated or percolating, depending on the added volume of metal. Analysis of pinon-disk data deduced from tests performed at room temperature allows us to conclude that the surface energy of the quasicrystal itself falls between the respective surface energies of the pure metals: c Bi B c QC B c Sn or 0.5 B c i-ACF B 0.8 J/m 2 .

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Section: Introductionmentioning

confidence: 98%

Indirect assessment of the surface energy of the Al–Cu–Fe quasicrystal

et al. 2016

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“…This information brings us closer towards one of the ultimate goals of materials design: from the desired physical/chemical properties of a material, find its chemical composition and the protocol for preparing it. In the case of QCs most of our goals are at present more basic: first, we want to understand the governing factors for the evolution of quasiperiodic order for a chemical compound of a given composition; in other words, the reason why a structure becomes quasiperiodic (see, e.g., Steurer, 2004Steurer, , 2012. Here it should be mentioned that the structural perfection of QCs can be comparable with that of periodic complex intermetallics in general.…”

Section: Structure Of Quasicrystalsmentioning

confidence: 99%

“…The results could explain why only low-order ACs have been found experimentally so far. The calculations should also allow one to extrapolate the findings to the stability of the corresponding QC (see also Steurer, 2012, and references therein).…”

Section: Open Questions and Challengesmentioning

confidence: 99%

Quasicrystals: What do we know? What do we want to know? What can we know?

Steurer

2018

Acta Crystallogr A Found Adv

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101

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More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso-and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.

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“…10 Liquid crystals can take a quasiperiodic ordering state. 11 Liquids crystals are common in plants with both cellulose and microtubules forming liquid crystalline phases under certain circumstances 12 and DNA itself can generate liquid crystal phases. 13 These, then, provide other possible avenues for the formation of quasicrystals in plants.…”

Section: Fibonacci Phyllotaxy and Fractalsmentioning

confidence: 99%

Fibonacci, quasicrystals and the beauty of flowers

Gardiner

2012

Plant Signaling & Behavior

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T he appearance of Fibonacci sequences and the golden ratio in plant structures is one of the great outstanding puzzles of biology. Here I suggest that quasicrystals, which naturally pack in the golden ratio, may be ubiquitous in biological systems and introduce the golden ratio into plant phyllotaxy. The appearance of golden ratio-based structures as beautiful indicates that the golden ratio may play a role in the development of consciousness and lead to the aesthetic natural selection of flowering plants. Fibonacci and the Golden RatioIn mathematics and the arts, two quantities are in the golden ratio (τ or 1.6180339…) if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is thought to be aesthetically pleasing and thus appears often in art and architecture. The Fibonacci numbers are simply the arithmetic consequence of multiplying each number by τ, and rounding to the nearest integer or, in other words, the next number in the Fibonacci sequence is the sum of the previous two numbers in the sequence thus 1, 1, 2, 3, 5, 8, 13, 21, 34, … The Fibonacci sequence was first discovered by Leonardo da Pisa (also known as Fibonacci) in 1202 and has puzzled scientists for centuries due to its frequent occurrence in nature, including in spiral molluscan shells and plants. The ubiquity of the Fibonacci sequence in nature seems to indicate that it arises through a process that is fundamental to life.

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Why are quasicrystals quasiperiodic?

Cited by 56 publications

References 55 publications

Indirect assessment of the surface energy of the Al–Cu–Fe quasicrystal

Indirect assessment of the surface energy of the Al–Cu–Fe quasicrystal

Quasicrystals: What do we know? What do we want to know? What can we know?

Fibonacci, quasicrystals and the beauty of flowers

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