Metallic Phase with Long‐Range Orientational Order and No Translational Symmetry

Shechtman, D.; Blech, I. A.; Gratias, D.; Cahn, John W.

doi:10.1002/9781118788295.ch45

Cited by 62 publications

(80 citation statements)

References 8 publications

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“…In principle, there are two possible reasons for a fivefold symmetry. Apart from the quasi crystals first reported by D. Shechtman in19841 the other possibility to obtain a fivefold symmetry is via multiple twinning which was first observed in 1957 and reviewed extensively in 19982. Here the alternating twins enclose angles of 72° to allow a five- or tenfold symmetry23.…”

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confidence: 99%

Bulk Crystallization in a SiO2/Al2O3/Y2O3/AlF3/B2O3/Na2O Glass: Fivefold Pseudo Symmetry due to Monoclinic Growth in a Glassy Matrix Containing Growth Barriers

Wisniewski

Seyring

Patzig

et al. 2016

Sci Rep

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A glass with the mol% composition 17 Y2O3·33 Al2O3·40 SiO2·2 AlF3·3 Na2O·2 CeF3·3 B2O3 is heat treated at 1000 °C for 6–24 h. This results in the surface nucleation and growth of YAG. Nucleation and growth of star-shaped alumina and later of monoclinic β-Y2Si2O7 and orthorhombic δ-Y2Si2O7 are additionally observed in the bulk. Phase identification and localization are performed by electron backscatter diffraction (EBSD) as well as TEM analysis. The monoclinic β-Y2Si2O7 observed in the bulk occurs in the form of large, crystal agglomerates which range from 50 to 120 μm in size. The individual crystals are aligned along the c-axis which is the fastest growing axis. Ten probability maxima are observed in the pole-figures illustrating the rotation of orientations around the c-axes indicating a fivefold symmetry. This symmetry is caused by multiple twinning which results in a high probability of specific orientation relationships with rotation angles of ~36°, ~108° (also referred to as the pentagon angle) and ~144° around the c-axis. All these rotation angles are close to the multiples of 36° which are required for an ideal fivefold symmetry. This is the first report of a fivefold symmetry triggered by the presence of barriers hindering crystal growth.

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confidence: 99%

Bulk Crystallization in a SiO2/Al2O3/Y2O3/AlF3/B2O3/Na2O Glass: Fivefold Pseudo Symmetry due to Monoclinic Growth in a Glassy Matrix Containing Growth Barriers

Wisniewski

Seyring

Patzig

et al. 2016

Sci Rep

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“…Quasicrystals12, short for quasiperiodic crystals, are solids able to violate the conventional rules of crystallography because their structure is “quasiperiodic” rather than periodic; that is, their atomic density can be described by a finite sum of periodic functions with periods whose ratio is irrational. Their diffraction pattern consists of true Bragg peaks whose positions can be expressed as integer linear combinations of D integer linearly independent wavevectors where D is greater than the number of space dimensions.…”

mentioning

confidence: 99%

Icosahedral AlCuFe quasicrystal at high pressure and temperature and its implications for the stability of icosahedrite

Stagno

Bindi

Shibazaki

et al. 2014

Sci Rep

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The first natural-occurring quasicrystal, icosahedrite, was recently discovered in the Khatyrka meteorite, a new CV3 carbonaceous chondrite. Its finding raised fundamental questions regarding the effects of pressure and temperature on the kinetic and thermodynamic stability of the quasicrystal structure relative to possible isochemical crystalline or amorphous phases. Although several studies showed the stability at ambient temperature of synthetic icosahedral AlCuFe up to ~35 GPa, the simultaneous effect of temperature and pressure relevant for the formation of icosahedrite has been never investigated so far. Here we present in situ synchrotron X-ray diffraction experiments on synthetic icosahedral AlCuFe using multianvil device to explore possible temperature-induced phase transformations at pressures of 5 GPa and temperature up to 1773 K. Results show the structural stability of i-AlCuFe phase with a negligible effect of pressure on the volumetric thermal expansion properties. In addition, the structural analysis of the recovered sample excludes the transformation of AlCuFe quasicrystalline phase to possible approximant phases, which is in contrast with previous predictions at ambient pressure. Results from this study extend our knowledge on the stability of icosahedral AlCuFe at higher temperature and pressure than previously examined, and provide a new constraint on the stability of icosahedrite.

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“…[8, 9] Here, group theory is used to describe symmetries and periodicities in the atomic arrangements. When the quasicrystal was discovered,[10] many people believed there must be hidden symmetries or orders, although there is no periodic structure observed in the physical world. Advanced mathematics provides the vocabulary of noncommutative geometry,[11] an advanced notion of an abelian (commutative) group, for an aperiodic system like a quasicrystal,[12] to identify orders hidden in disordered systems (Figure 2).…”

Section: Mathematics For Materialsmentioning

confidence: 99%

Materials inspired by mathematics

Kotani

Ikeda

2016

Science and Technology of Advanced Materials

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Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, ‘data-driven materials design’ has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions.

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Metallic Phase with Long‐Range Orientational Order and No Translational Symmetry

Cited by 62 publications

References 8 publications

Bulk Crystallization in a SiO2/Al2O3/Y2O3/AlF3/B2O3/Na2O Glass: Fivefold Pseudo Symmetry due to Monoclinic Growth in a Glassy Matrix Containing Growth Barriers

Bulk Crystallization in a SiO2/Al2O3/Y2O3/AlF3/B2O3/Na2O Glass: Fivefold Pseudo Symmetry due to Monoclinic Growth in a Glassy Matrix Containing Growth Barriers

Icosahedral AlCuFe quasicrystal at high pressure and temperature and its implications for the stability of icosahedrite

Materials inspired by mathematics

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