12-FOLD Symmetric Quasicrystals (original) (raw)
Related papers
Quasicrystals: A Matter of Definition
Foundations of Physics, 2003
It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.
Some new structural and electronic characteristics of quasicrystals
Bulletin of Materials Science, 1999
The quasicrystals being based on quasiperiodic order other than crystal like periodic translational order and embodying self similarity, present unique condensed matter phases. In addition to their curious structural characteristics the paucity of translational periodicity leads to drastic deviations in their electronic behaviour as compared to crystalline counterparts. This paper describes and discusses some new developments in regard to structural and electronic aspects of quasicrystalline materials. In regard to the structural aspects, two comparatively newer features will be described. One of them relates to the observation of variable strain approximants (VSA) first found in Ti68Fe26NiSi5, qc alloys; the other relates to the structure of decagonal phases. The variable strain approximants correspond to qc phases exhibiting variable strain for the different diffraction spots for the same reciprocal lattice row (possessing linear shifts). The VSA is thought to result from variable...
Quasicrystals and Unit-Cell Twinning
The structure and the corresponding electron diffraction patterns of quasicrystals are explained by unit-cell twinning. The twinning operation is applied to the primitive golden rhombohedra, obtained by a slight deformation of a parent cubic close-packed structure. The deformation is determined by the requirement that the applied multiple twinning fills the space exactly, resembling thus the five-fold rotational symmetry. It is further shown that both, the rotational and translational symmetries are in accord with all rules of classical crystallography and that quasicrystals do not represent an exception to the huge family of solid state structures. The stacking of multiply twinned star polyhedra, called "stellae dodecangulae", keeps the basic golden prolate rhombohedra of adjacent "stellae" in-phase. A strong dynamical scattering accounts for all remaining reflections in the reciprocal space, not being accounted for by the primary diffraction. Simulated diffract...
Tetracoordinated quasicrystals
Physical review. B, Condensed matter, 1991
Current model networks for amorphous Ge contain five-membered rings and pentagonal dodecahedra to explain why in the radial distribution function the third peak of the diamond structure is missing. By presenting an algorithm based on a decoration of the three-dimensional Penrose quasilattice, we prove that this local pentagonal symmetry can be extended globally to an icosahedral quasicrystalline tetracoordinated network. Its structural elements and topological properties coincide with previous hand-built models of random networks. Thus it is suitable for simulating bulk properties of amorphous semiconductors.
Recent research and development on Quasicrystals †
AIMS Materials Science, 2017
Quasicrystals are a kind of unique materials and characterized by the discrete diffraction patterns which cannot be indexed with the conventional three indices but require additional ones [1,2]. They occur in almost every type of solid including organic and inorganic compounds, minerals, metals and alloys, macromolecules and oxides [3,4,5]. It is convenient to describe their structures in higher dimensional space, a conceptual environment, in which threedimensional periodic crystals recover their periodicities [6]. The inconvenience of visualization due to extra dimensions is compensated by the mathematical elegance achieved through recovering periodicity. Studies of quasicrystalline structures have greatly enriched our understanding of the physics and chemistry of atomic orders, and have opened up new perspectives for correlating structure with the properties of complex materials. The ICQ13 conference was attended by 134 participants from all over the world including two participants from India, T.P. Yadav (Banaras Hindu University-Varanasi)
Discussion of electronic properties of quasicrystals
Philosophical Magazine, 2008
This article gives a short review of some important achievements in the field of electronic properties of quasicrystals. It focuses essentially on : the nature of quasicrystals as Hume-Rothery alloys, the energetics of quasicrystals and related phases, the magnetic properties, the localization of electronic states, the transport properties. For each part one emphasizes some promising directions of research. We end by listing some problems that are related to that of electrons in a quasiperiodic potential.
Physical Review Letters, 1986
It is shown that the icosahedral quasicrystal and the recently observed T phase are closely related to each other, The latter is a periodic stacking of two-dimensional quasilattices with mirror symrnetry. Their diffraction patterns, though appearing very different, can be indexed by a set of primary vectors that are only small deformations of each other. Ho~ever, because of the mirror symmetry, their quasilattices are not related by small deformations. A calculation based on the model free energy of Kalugin et ai. shows that this periodic quasicrystal is very competitive with (and in fact energetically more favorable than) the icosahedral quasicrystal.