Crystallography of quasi-crystals

Janssen, Τ.

doi:10.1107/s0108767386099324

Cited by 258 publications

(127 citation statements)

References 16 publications

Supporting

Mentioning

120

Contrasting

Order By: Relevance

“…However, in contrast to other types of QCs that show periodic order in at least one direction, i-QCs cannot make effective use of two-dimensional (2D) imaging techniques such as high-resolution electron microscopy or high-angle annular dark-field scanning transmission electron microscopy for their structural characterization 4 . The i-QCs' structure determination is best achieved in the context of hyperspace crystallography 5,6 , where the structure can be described as a periodic crystal in higher dimensions. For i-QCs, the periodic space is 6D and decomposes into two orthogonal 3D subspaces: the parallel (physical) space and the perpendicular (complementary) space.…”

mentioning

confidence: 99%

Atomic structure of the binary icosahedral Yb–Cd quasicrystal

et al. 2006

View full text Add to dashboard Cite

Icosahedral quasicrystals (i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs form as ternary alloys suffering from chemical disorder. Here, we present the first detailed structure solution of i-YbCd 5.7 , one of the very few stable binary i-QCs, by means of X-ray structure determination. Three building units with unique atomic decorations arrange quasiperiodically and fill the space. These also serve as building units in the periodic approximant crystals. The structure is not only chemically feasible, but also provides a seamless structural understanding of the i-YbCd 5.7 phase and its series of related i-QCs and approximant crystals, revealing hierarchic features that are of considerable physical interest.Icosahedral quasicrystals (i-QCs) are the only class to show quasiperiodicity in three dimensions 1,2 . Obviously, structural knowledge is essential for understanding the physical properties, stability and tailoring applications of these exotic materials 3 . However, in contrast to other types of QCs that show periodic order in at least one direction, i-QCs cannot make effective use of two-dimensional (2D) imaging techniques such as high-resolution electron microscopy or high-angle annular dark-field scanning transmission electron microscopy for their structural characterization 4 . The i-QCs' structure determination is best achieved in the context of hyperspace crystallography 5,6 , where the structure can be described as a periodic crystal in higher dimensions. For i-QCs, the periodic space is 6D and decomposes into two orthogonal 3D subspaces: the parallel (physical) space and the perpendicular (complementary) space. The 6D unit cell is decorated by 3D objects known as 'occupation domains' (OD), the 3D QCs being obtained as a section of this decorated 6D lattice. This approach allows modelling and refinement of the structure against experimental diffraction data in a way similar to that achieved for 3D periodic crystals 6 . Although much progress has been achieved recently, for instance in the i-AlPdMn phase 7 , the models proposed so far are still being debated 8 . Indeed, the amount of observed diffraction data is in general rather limited, which precludes a detailed refinement of the chemical order in ternary QCs. Therefore, the atomic order in i-QCs remains a challenging and outstanding question. The recent discovery of the first stable binary icosahedral YbCd 5.7 QCs 9,10 has been a breakthrough and led to discoveries of a whole series of related ternary i-QCs 11 . This i-QC offers a unique opportunity for the structural analysis of i-QCs. Indeed, the i-YbCd 5.7 phase can be obtained as high-quality single grains. Furthermore, it is binary and exhibits very good X-ray contrast between Cd (Z = 48) and Yb (Z = 70) atoms.Finally, there is a series of periodic 'approximant crystals' (ACs) to the QC, having almost the same chemical composition and for...

show abstract

mentioning

confidence: 99%

Atomic structure of the binary icosahedral Yb–Cd quasicrystal

et al. 2006

View full text Add to dashboard Cite

show abstract

“…The corresponding periodic density function consists of -like distributions on submanifolds, commonly referred to as atomic surfaces' (Janssen, 1986;Bak, 1986). This brings up again the question of optimality of the weight factors w K from (8).…”

Section: Quasicrystals and Incommensurate Structuresmentioning

confidence: 99%

A new phasing method based on the principle of minimum charge

Kalugin

2001

Acta Cryst Sect A

View full text Add to dashboard Cite

A new method for phase determination in X‐ray crystallography is proposed. The method is based on the so‐called `minimum‐charge' principle, recently suggested by Elser [Acta Cryst. (1999), A55, 489–499]. The electron‐density function is sought in the form = , where is an ‐component real function. The norm is minimized under the constraint imposed by the measured data on the amplitudes of Fourier harmonics of . Compared with the straightforward implementation of the `minimum‐charge' scheme, the method attenuates the Gibbs phenomenon and is also capable of extrapolation of the diffraction data beyond the set of measured amplitudes. The method is applicable to quasicrystals under the condition that the number of components of the function is bigger than the dimensionality of the `atomic surface'. It has been successfully tested on synthetic data for a Fibonacci chain and octagonal tiling. In the latter case, the reconstructed density map shows the shape of the atomic surface, despite relatively low resolution data.

show abstract

“…Quasicrystals have inherent potentials that have been subject of important theoretical developments in both solid-state physics and photonics engineering [1][2][3][4][5]. Quasicrystals were discovered in nature first in AlMn metallic alloys, and exhibit a lot of unique electronic properties [6].…”

Section: Introductionmentioning

confidence: 99%

Band Structure and Dispersion Properties of Photonic Quasicrystals

Rostami¹,

Matloub²

2009

PIER M

View full text Add to dashboard Cite

Abstract-In this paper, for developing analytical and semi-analytical methods to evaluate band structure in photonic quasicrystals the perturbation theory is examined. It is shown that more isotropic and complete photonic band gap can be observed under low dielectric contrast for photonic quasicrystals in comparison with ordinary crystals and because of this feature of photonic quasicrystals, perturbation theory is suitable for evaluation of these structures. In this work, we show that using perturbation semianalytical method one can obtain complete band structure for quasicrystals that are interesting for terahertz technology especially and microwave and optical engineering too. Also, we investigate that complete band gap is appeared in quasicrystals in low refractive index contrast and with increasing number of fold in quasicrystals gap size and isotropy are increased.

show abstract

Crystallography of quasi-crystals

Cited by 258 publications

References 16 publications

Atomic structure of the binary icosahedral Yb–Cd quasicrystal

Atomic structure of the binary icosahedral Yb–Cd quasicrystal

A new phasing method based on the principle of minimum charge

Band Structure and Dispersion Properties of Photonic Quasicrystals

Contact Info

Product

Resources

About