Structure Of Icosahedral Quasicrystals Research Articles

Crystal-chemical model of atomic interactions. 4. Prognostic ability: crystals and quasicrystals

Abstract The idea of structural ensembles is introduced in the framework of the crystal-chemical model of atomic interactions (CCMAI). The atomic ensemble is treated as a minimal portion of atoms, which predetermines the crystal structure. Inorganic crystal structures such as graphite, white tin, PbO are considered. It is supposed that both atoms and localized electron pairs form these structures. On the basis of CCMAI the hypothetical structure of icosahedral quasicrystals is worked out. In accordance with this hypothesis the initial cluster (or simply cluster) of the quasicrystal has a double-shell structure and each shell has an icosahedral form; the thickness of a shell is equal to the diameter of one atom; the number of atoms in one shell is 10n2 + 2, where n is the number of the shell. The quasicrystal has two subsystems of atoms. One of them consists of the central atoms of clusters and the atoms included in the first shells of clusters. The 13-atom icosahedral bodies form a crystal lattice with space group Fd3. All icosahedra of this atomic subsystem have a perfect form and all of them are perfectly oriented with respective to each other. The first atomic subsystem is responsible for the diffraction of electrons and X-rays. The second atomic subsystem includes atoms of the second shells of clusters. This subsystem has no translational symmetry, but it is partially ordered.

Three-dimensional penrose tiling under phason strain field I

From the 3DPT point of view this paper focuses on the change of quasilattice under phason strain, and indicates that linear phason strain field makes the projecting region rotate. Cooperating this with diffraction message, we can get useful information about the icosahedral quasicrystal structure. At the same time, we also give phason strain a geometric picture.

Mode locking in quasicrystals.

Possible modulated structures of icosahedral quasicrystals are investigated. The modulated phases are regarded as lower symmetric phases where the global icosahedral symmetry of quasicrystals is broken due to mode locking of phason degrees of freedom. With the help of group theory, nonvanishing phason fields are calculated for all the possible symmetry breaking. A modified projection scheme in the presence of nonvanishing phason fields is obtained for modulated quasicrystalline structures with tetrahedral, pentagonal, and trigonal symmetries. Three possible ways of generating a rational approximation of the icosahedral quasicrystal are discussed in connection with the phason degrees of freedom.

Analytical formulation of icosahedral quasi-crystal structures

Analytical formulations of icosahedral quasi-crystal structure treated as the projection from a six-dimensional hypercubic crystal and its Fourier transform have been derived with a three-dimensional orthogonal coordinate system. Each coordinate axis consists of two basic lengths related to each other by a multiplier equal to the golden ratio. The relationship between icosahedral and orthogonal coordinates in both real and reciprocal spaces is demonstrated. The expression obtained for the icosahedral structure is identical with the density-wave description.

On the Glass Formation in Systems Forming Icosahedral Quasicrystals

AbstractRapidly solidified micron and submicron size droplets of Al-14 a/o Mn have been used to study the possibility of glass formation and nucleation behavior of icosahedral phase. Homogeneous nucleation of icosahedral phase is assumed, based on the high grain density (>1015 mm−3). Extremely low nucleation resistance of icosahedral phase can be understood when possible topological similarities between liquid and icosahedral quasicrystal structures are considered. Configurationally frozen liquid in Al-Mn and similar alloy systems is questionable, implying that Al-Mn “glass” probably has a microquasicrystalline structure.