Possibility of irradiation in quasicrystal–quasicrystal tunneling junctions

We predict the external radiation with a frequency half the frequency of alternating Josephson effect to appear when a constant voltage is applied to a quasicrystal–quasicrystal tunneling junction. Thus the phenomenon typical for superconductor–superconductor junctions can be realized for a non-superconducting object. The physical background for this possibility is the “critical” behavior of the wave functions in quasicrystals and electron scattering on a quasiperiodic potential. The effect opens an avenue for new applications of quasicrystals.     

Modeling of dodecagonal quasicrystal lattices

We consider a method for constructing dodecagonal quasi-lattices, which involves the recurrent multiplication of the initial group of sites that are vertices of a regular dodecagon. The algorithm of modeling of reciprocal lattices of dodecagonal quasicrystals has been analyzed. The proposed modeling method is compared with the traditional projection method. We have performed indexing of the diffraction pattern from dodecagonal quasicrystals, which is analogous to indexing proposed by Cahn for icosahedral quasicrystals. The ambiguity of the choice of the basis vectors of the quasicrystal reciprocal lattice has been considered.     

Phonon-spectrum of an F-type icosahedral quasicrystal

We present calculations for the vibrational properties of F-type icosahedral quasicrystals. Two different approaches are compared, a cluster with complete icosahedral symmetry, and periodic approximants. Though no gaps in the spectra are observed, the well-known rescaling symmetry of ID systems is rediscovered in a generalized way.     

Degenerate quasicrystal of hard triangular bipyramids

We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.     

Optical properties of hybrid periodic/quasiregular dielectric multilayers

Optical properties like transmission, omnidirectional reflection and localization of modes are theoretically investigated in hybrid periodic/quasiregular dielectric heterostructures based on porous silicon. It is shown that the fabrication of this class of multilayers would lead to an improvement of the formation of microcavities, the widening of the incidence angular interval for total reflection as well as the appearance of spatial localization of electric field intensity within specific regions of the structures.     

Properties of elastic waves in quasiregular structures with planar defects

We have studied the elastic waves in quasiregular structures following the Fibonacci and Rudin–Shapiro sequences, and having planar defects, that is breaks of the quasiregular structure in different parts of the system. It is seen that the different kinds of defects produce effects on different ranges of the frequency spectrum, and can introduce more localized states in the gaps, or modify the frequencies of the states in the gaps. We have also studied the phase time and transmission coefficients, thus seeing how these localized modes can be used as frequency filters.     

EFG studies of the AlCuFe quasicrystal and related structures

It is known that the structure and thermal stability of the AlCuFe icosahedral quasicrystalline (i-QC) phase is extremely sensitive to the exact composition. A stable, ideally quasiperiodic phase exists only along a line around Al_62.0Cu_25.5Fe_12.5. The other i-QC samples show structural changes when annealed around 700 °C. The⁵⁷Fe Mössbauer EFG properties and isomer shifts of these various i-QC phases and of the new rhombohedral approximant phase are presented, and compared with the properties of the Al site investigated by NMR. Certain new systematic trends will be presented.     

Dynamical properties of three component Fibonacci quasicrystal

We present a real space renormalization group (RSRG) method to study the lattice dynamics of a three component Fibonacci (3CF) quasicrystal. Phonon dispersion relations corresponding to different models of this lattice are obtained. Some features of the phonon dispersion curves are compared with experiments on real quasicrystal. It is observed that the positions of the strongest Bragg peaks calculated analytically are in perfect agreement with our RSRG calculations. Received 23 October 2000 and Received in final form 11 January 2001     

Phase diagram of a random tiling quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.     

The electronic spectrum of a three-dimensional quasicrystal

The electronic spectrum of an icosahedral quasicrystal with a central-atom decoration of the Amman-Mackay network is investigated in the tight-binding approximation. The quasicrystal is described as a structural limit of the optimal cubic approximants with increasing period. The electronic spectra for the first four optimal cubic approximants do not contain the hierarchical gap structure which is typical for the Cantor set of the spectrum of a one-dimensional quasicrystal. At the same time, as the order of the approximant increases, the spectrum becomes singular throughout the entire energy scale. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 557–562 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Crystalline structures as an approximant of quasicrystal and distortion of B12 icosahedron in boron-rich solids: Search for semiconducting quasicrystal

Analyzing the crystalline structure of α- and β-rhombohedral boron as an approximant structure of a quasicrystal, atomic structures of two unit cells (prolate and oblate rhombohedra) of icosahedral quasicrystal are constructed. According to molecular orbital calculation, a neutral B ₁₂ H ₁₂ icosahedral cluster is distorted to a cubic or rhombohedral type by the Jahn–Teller effect. The distortion of B ₁₂ in the β-rhombohedral boron and K₂B₁₂H₁₂ has the same sign as the lowest energy distortion in the calculation. Among the α-rhombohedral type structures, the distortion of B₁₂ is correlated with the rhombohedral axis angle, and the angle is the closest to the icosahedral angle for B₆O and the distortion is the smallest for B–C. A meta-stable phase has been found on the way towards crystallization of amorphous B–C films.