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Quasicrystals
Kinds of Quasicrystals Selected AbstractsSpatial mapping on surface light extraction from 2D photonic quasicrystals patterned GaN-based light emittersPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2007ZhenSheng Zhang Abstract We report the observations of surface light extraction enhancement from two-dimensional (2D) photonic crystal (PC) and Photonic Quasicrystal (PQC) patterns on electrical current injected GaN-based light emitters. Spatial mapping of the surface extraction was acquired by a microscopic electrical luminescence setup and a scanning near-field optical microscope (SNOM). Slight difference of mapping profile between twelve-fold PQC and regular triangular PC was obtained. It is shown that 12PQC was more efficient for light extraction. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ChemInform Abstract: Interpenetrating Networks of Three-Dimensional Penrose Tiles in CaAu3Ga, the Structurally Simplest Cubic Approximant of an Icosahedral Quasicrystal.CHEMINFORM, Issue 33 2008Qisheng Lin Abstract ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a "Full Text" option. The original article is trackable via the "References" option. [source] Synthesis and Structure of Five Sc3CuyZn18-y -Type Compositions (0 , y , ,2.2), 1/1 Crystalline Approximants of a New Icosahedral Quasicrystal.CHEMINFORM, Issue 25 2004Direct Example of Tuning on the Basis of Size Effects, Rothery Concepts. Abstract For Abstract see ChemInform Abstract in Full Text. [source] Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho11Mg15Zn74 Quasicrystal from PDF Data.CHEMINFORM, Issue 7 2004S. Bruehne Abstract For Abstract see ChemInform Abstract in Full Text. [source] Design of a Molecular QuasicrystalCHEMPHYSCHEM, Issue 8 2006Zhongfu Zhou Dr. Designer materials: The authors propose a design strategy for a quasicrystalline material composed of discrete molecular entities. The molecular quasicrystal (see figure), which is based on a standard Penrose tiling, is energetically stable and gives rise to a 10-fold symmetric diffraction pattern. The strategy may be further exploited to design molecular quasicrystals based on a range of different types of quasiperiodic arrays. [source] Local 3D real space atomic structure of the simple icosahedral Ho11Mg15Zn74 quasicrystal from PDF dataCRYSTAL RESEARCH AND TECHNOLOGY, Issue 12 2003S. Brühne Abstract We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho11Mg15Zn74 [a(6D) = 5.144(3)Ĺ in a sphere of up to r = 17Ĺ was refined using the atomic pair distribution function (PDF) from in-house X-ray powder diffraction data (MoK,1, Qmax = 13.5Ĺ,1; R = 20.4%). The basic building block is a 105-atom Bergman-Cluster {Ho8Mg12Zn85}. Its center is occupied by a Zn atom , in contrast to a void in face centred icosahedral (fci) Ho9Mg26Zn65. The center is then surrounded by another 12 Zn atoms, forming an icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms arranged on the vertices of a cube which in turn is completed to a pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball of 60 Zn atoms, reflecting the higher Zn content of the si phase compared to the fci phase. In our model, 7% of all atoms are situated in between the clusters. The model corresponds to a hypothetical 1/1-approximant of the icosahedral (i) phase. The local coordinations of the single atoms are of a much distorted Frank-Kasper type and call to mind those present in 0/1-Mg2Zn11. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Reciprocal-space imaging of a real quasicrystal.JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2008A feasibility study with PILATUS 6M How many of the theoretically densely distributed Bragg reflections of a quasicrystal can be observed employing an area detector and synchrotron radiation? How does the reflection density of a real quasicrystal change as a function of exposure time, and what is the minimum distance between reflections? What does the distribution of diffuse scattering look like? To answer these questions, the Bragg reflection density of a perfect icosahedral quasicrystal with composition Al64Cu23Fe13 was measured employing a novel type of single-photon-counting X-ray pixel detector, PILATUS 6M, which allows noise-free data collection with the extraordinarily large dynamic range of 20,bit. The reflection density was found to be two orders of magnitude lower than expected for a strictly quasiperiodic structure. Moreover, diffuse scattering reflects significant structural disorder, breaking six-dimensional F -lattice symmetry. These findings have some implications for the interpretation of physical properties. [source] Composition dependence of positron annihilation lifetime for Al-Pd-Re-Ru quasicrystal and 2/1-AlPdRu approximant crystalPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 10 2007Y. Takagiwa Abstract Quaternary icosahedral Al-Pd-Re-Ru (i -Al71Pd20(Re1,xRux)9 (X = 0.4, 0.55, 0.7, 0.85)) quasicrystals and its 2/1-AlPdRu approximant crystal, 2/1-Al71Pd20Ru9, were investigated by positron annihilation lifetime spectroscopy. The positron annihilation lifetimes measured here are significantly longer than those of defect-free states estimated by compositionally weighting the constituent elements. This result suggests that high densities of structural vacancies exist in both i -Al-Pd-Re-Ru quasicrystals and 2/1-AlPdRu approximant crystal. For i -Al-Pd-Re-Ru quasicrystals, composition dependence of the positron annihilation lifetime is compared with that of the electrical conductivity. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Multiresolution of quasicrystal diffraction spectraACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009Avi Elkharrat A method for analyzing and classifying two-dimensional pure point diffraction spectra (i.e. a set of Bragg peaks) of certain self-similar structures with scaling factor , > 1, such as quasicrystals, is presented. The two-dimensional pure point diffraction spectrum , is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called ,-lattices, we implement a multiresolution analysis of the spectrum ,. This analysis yields a partition of , simultaneously in geometry, in scale and in intensity (the `fingerprint' of the spectrum, not of the diffracting structure itself). The method is tested through numerical explorations of pure point diffraction spectra of various mathematical structures and also with the diffraction pattern of a realistic model of a quasicrystal. [source] The piezoelectric effect of second order in stress or strain: its form for crystals and quasicrystals of any symmetryACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2007Hans Grimmer The restrictions on the coefficients describing physical effects depend on the orientation of the symmetry elements of the crystal or quasicrystal with respect to the Cartesian coordinate system employed. They are given for the piezoelectric effect of second order in stress or strain for all the orientations that can be expressed by the sequence of elements in the Hermann,Mauguin symbol of the point group. In the literature, the restrictions are usually given only for a particular orientation, which sometimes is not specified. [source] A symmetrical indexing scheme for decagonal quasicrystals analogous to Miller,Bravais indexing of hexagonal crystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2007S. Ranganathan The problems of redundancy and superfluous indices in indexing the planes and axes in a decagonal quasicrystal are considered, using a scheme of five coplanar vectors in the quasiperiodic plane and one perpendicular vector. Of all the indexing schemes in use, this scheme offers the maximum advantage. An analogy is drawn to the hexagonal system using Miller,Bravais indices. Based on this, a symmetry-based indexing system for decagonal phases is devised that follows a simplified approximate zone law analogous to the exact zone law for the hexagonal case. The indices based on this scheme will be designated as `Frank indices'. High-symmetry electron diffraction zone-axis patterns as well as powder X-ray diffraction patterns are indexed using Frank indices and compared with those of other indexing schemes. [source] Effect of ionic strength and clay mineralogy on Na,Ca exchange and the SAR,ESP relationshipEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 5 2006P. M. Kopittke Summary The relationship between sodium adsorption ratio (SAR) and exchangeable sodium percentage (ESP) for all soils has traditionally been assumed to be similar to that developed by the United States Salinity Laboratory (USSL) in 1954. However, under certain conditions, this relationship has been shown not to be constant, but to vary with both ionic strength and clay mineralogy. We conducted a detailed experiment to determine the effect of ionic strength on the Na+,Ca2+ exchange of four clay minerals (kaolinite, illite, pyrophyllite, and montmorillonite), with results related to the diffuse double-layer (DDL) model. Clays in which external exchange sites dominated (kaolinite and pyrophyllite) tended to show an overall preference for Na+, with the magnitude of this preference increasing with decreasing ESP. For these external surfaces, increases in ionic strength were found to increase preference for Na+. Although illite (2:1 non-expanding mineral) was expected to be dominated by external surfaces, this clay displayed an overall preference for Ca2+, possibly indicating the opening of quasicrystals and the formation of internal exchange surfaces. For the expanding 2:1 clay, montmorillonite, Na+,Ca2+ exchange varied due to the formation of quasicrystals (and internal exchange surfaces) from individual clay platelets. At small ionic strength and large ESP, the clay platelets dispersed and were dominated by external exchange surfaces (displaying preference for Na+). However, as ionic strength increased and ESP decreased, quasicrystals (and internal exchange surfaces) formed, and preference for Ca2+ increased. Therefore, the relationship between SAR and ESP is not constant and should be determined directly for the soil of interest. [source] Three-Dimensional Nanostructures for PhotonicsADVANCED FUNCTIONAL MATERIALS, Issue 7 2010Georg von Freymann Abstract Recent progress in direct laser writing of three-dimensional (3D) polymer nanostructures for photonics is reviewed. This technology has reached a level of maturity at which it can be considered as the 3D analogue of planar electron-beam lithography. Combined with atomic-layer deposition and/or chemical-vapor deposition of dielectrics,the 3D analogues of planar evaporation technologies, the 3D polymer templates can be converted or inverted into 3D high-refractive-index-contrast nanostructures. Examples discussed in this review include positive and inverse 3D silicon-based woodpile photonic crystals possessing complete photonic bandgaps, novel optical resonator designs within these structures, 3D chiral photonic crystals for polarization-state manipulation, and 3D icosahedral photonic quasicrystals. The latter represent a particularly complex 3D nanostructure. [source] Rhombicuboctahedral Three-Dimensional Photonic QuasicrystalsADVANCED MATERIALS, Issue 21 2010Alexandra Ledermann The aesthetics of quasicrystals has fascinated mankind already for centuries. Numerous examples are known in one and two dimensions, yet in three dimensions only icosahedral quasicrystals have been realized and observed to date in any system, i.e., in man-made, natural, photonic, and phononic quasicrystals. We rationally construct the novel class of three-dimensional rhombicuboctahedral quasicrystals and realize it as polymer microstructure. [source] Ab initio structure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density eliminationJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2010Frank Fleischer Comprehensive tests on the density-modification methods charge flipping [Oszlányi & Süt, (2004). Acta Cryst. A60, 134,141] and low-density elimination [Shiono & Woolfson (1992). Acta Cryst. A48, 451,456] for solving crystal structures are performed on simulated diffraction data of periodic structures and quasicrystals. A novel model-independent figure of merit, which characterizes the reliability of the retrieved phase of each reflection, is introduced and tested. The results of the performance tests show that the quality of the phase retrieval highly depends on the presence or absence of an inversion center and on the algorithm used for solving the structure. Charge flipping has a higher success rate for solving structures, while low-density elimination leads to a higher accuracy in phase retrieval. The best results can be obtained by combining the two methods, i.e. by solving a structure with charge flipping followed by a few cycles of low-density elimination. It is shown that these additional cycles dramatically improve the phases not only of the weak reflections but also of the strong ones. The results can be improved further by averaging the results of several runs and by applying a correction term that compensates for a reduction of the structure-factor amplitudes by averaging of inconsistently observed reflections. It is further shown that in most cases the retrieved phases converge to the best solution obtainable with a given method. [source] Disordered quasicrystals: diffuse scattering in decagonal Al,Ni,FeJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2004E. Weidner High-resolution synchrotron data of near-Bragg diffuse scattering from decagonal Al71.5Ni23.5Fe5 quasicrystals were recorded. A dominant phasonic origin is ruled out because of the absence of a significant G, dependence. An analysis solely in the frame of thermal diffuse scattering (TDS) theory (phonon scattering) showed a good match between experimental and calculated data in the quasiperiodic layers, but with an improbable ratio of elastic constants, c66/c11 = 4.0. In situ high-temperature measurements up to 1000,K revealed an increase of the intensity distribution perpendicular to the scattering vector G. Huang diffuse scattering (HDS) arising from quenched local defects has a general appearance that qualitatively reproduces the observed symmetry and anisotropy. An interpretation based on both TDS and HDS contributions is given. [source] In situ high-temperature powder diffraction study of reversible phase transitions in decagonal Al71.2Co12.8Ni16JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2003Christian Soltmann This experimental work is aimed at confirming and broadening findings of former investigations into the type I,S1 phase transition in Al,Co,Ni quasicrystals. In situ high-temperature synchrotron radiation measurements were carried out on Al71.2Co12.8Ni16 powder samples. The cell parameters were precisely determined at various temperatures in the range 290,1110,K. The data provided a new extended insight into the thermal expansion of Al71.2Co12.8Ni16 and into fundamental properties of the phase transition. [source] Ab-initio simulations of materials using VASP: Density-functional theory and beyondJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2008Jürgen Hafner Abstract During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science,promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Phase imaging using highly coherent X-rays: radiography, tomography, diffraction topographyJOURNAL OF SYNCHROTRON RADIATION, Issue 3 2000José Baruchel Several hard X-rays imaging techniques greatly benefit from the coherence of the beams delivered by the modern synchrotron radiation sources. This is illustrated with examples recorded on the `long' (145,m) ID19 `imaging' beamline of the ESRF. Phase imaging is directly related to the small angular size of the source as seen from one point of the sample (`effective divergence' , microradians). When using the `propagation' technique, phase radiography and tomography are instrumentally very simple. They are often used in the `edge detection' regime, where the jumps of density are clearly observed. The in situ damage assessment of micro-heterogeneous materials is one example of the many applications. Recently a more quantitative approach has been developed, which provides a three-dimensional density mapping of the sample (`holotomography'). The combination of diffraction topography and phase-contrast imaging constitutes a powerful tool. The observation of holes of discrete sizes in quasicrystals, and the investigation of poled ferroelectric materials, result from this combination [source] Bandgap properties of low-index contrast aperiodically ordered photonic quasicrystalsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 11 2009Gianluigi Zito Abstract We numerically analyze, using Finite Difference Time Domain simulations, the bandgap properties of photonic quasicrystals with a low-index contrast. We compared 8-, 10-, and 12-fold symmetry aperiodically ordered lattices with different spatial tiling. Our results show that tiling design, more than symmetry, determines the transmission properties of these structures. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2732,2737, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24724 [source] Composition dependence of positron annihilation lifetime for Al-Pd-Re-Ru quasicrystal and 2/1-AlPdRu approximant crystalPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 10 2007Y. Takagiwa Abstract Quaternary icosahedral Al-Pd-Re-Ru (i -Al71Pd20(Re1,xRux)9 (X = 0.4, 0.55, 0.7, 0.85)) quasicrystals and its 2/1-AlPdRu approximant crystal, 2/1-Al71Pd20Ru9, were investigated by positron annihilation lifetime spectroscopy. The positron annihilation lifetimes measured here are significantly longer than those of defect-free states estimated by compositionally weighting the constituent elements. This result suggests that high densities of structural vacancies exist in both i -Al-Pd-Re-Ru quasicrystals and 2/1-AlPdRu approximant crystal. For i -Al-Pd-Re-Ru quasicrystals, composition dependence of the positron annihilation lifetime is compared with that of the electrical conductivity. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Spatial mapping on surface light extraction from 2D photonic quasicrystals patterned GaN-based light emittersPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2007ZhenSheng Zhang Abstract We report the observations of surface light extraction enhancement from two-dimensional (2D) photonic crystal (PC) and Photonic Quasicrystal (PQC) patterns on electrical current injected GaN-based light emitters. Spatial mapping of the surface extraction was acquired by a microscopic electrical luminescence setup and a scanning near-field optical microscope (SNOM). Slight difference of mapping profile between twelve-fold PQC and regular triangular PC was obtained. It is shown that 12PQC was more efficient for light extraction. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Short-range order diffuse scattering in quasicrystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Akiji Yamamoto A theory for the diffuse scattering intensity owing to short-range order (SRO) in quasicrystals is given. The diffuse scattering intensity can be calculated based on higher-dimensional cluster models of quasicrystals. It is determined by the overlapped area (or volume) of occupation domains separated from each other by distances up to the correlation length and the SRO correlation functions. It is applied to a random atom distribution in phason flip sites in the Penrose pattern. To confirm the validity of the derived formula, analytical and numerical results for this case have been compared. Both results give similar diffuse scattering intensity, suggesting the validity of the theory. [source] Magnetic short-range order diffuse scattering in quasicrystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Akiji Yamamoto An analytical expression is derived for the short-range order (SRO) magnetic neutron diffuse scattering intensity in quasicrystals, and it is applied to a fictitious model of spin-orientation disorder in the Penrose pattern. The SRO diffuse scattering intensity depends on the overlapped volume of the occupation domains which are separated from each other by distances less than the correlation length and the SRO correlation functions. Analytical results for four different spin arrangements in the Penrose pattern are compared with numerical ones. The corresponding analytical and numerical results for all the cases are quite similar, suggesting the validity of the analytical expression. [source] Multiresolution of quasicrystal diffraction spectraACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009Avi Elkharrat A method for analyzing and classifying two-dimensional pure point diffraction spectra (i.e. a set of Bragg peaks) of certain self-similar structures with scaling factor , > 1, such as quasicrystals, is presented. The two-dimensional pure point diffraction spectrum , is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called ,-lattices, we implement a multiresolution analysis of the spectrum ,. This analysis yields a partition of , simultaneously in geometry, in scale and in intensity (the `fingerprint' of the spectrum, not of the diffracting structure itself). The method is tested through numerical explorations of pure point diffraction spectra of various mathematical structures and also with the diffraction pattern of a realistic model of a quasicrystal. [source] Discrete tomography of icosahedral model setsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009Christian Huck The discrete tomography of mathematical quasicrystals with icosahedral symmetry is investigated, placing emphasis on reconstruction and uniqueness problems. The work is motivated by the requirement in materials science for the unique reconstruction of the structures of icosahedral quasicrystals from a small number of images produced by quantitative high-resolution transmission electron microscopy. [source] Elastic properties of two-dimensional quasicrystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2008Hans Grimmer Quasicrystals (QC) with two-dimensional quasiperiodic and one-dimensional periodic structure are considered. Their symmetry can be described by embedding the three-dimensional physical space VE in a five-dimensional superspace V, which is the direct sum of VE and a two-dimensional internal space VI. A displacement v in V can be written as v = u + w, where u,VE and w ,VI. If the QC has a point group P in VE that is crystallographic, it is assumed that w and a vector u,,VE lying in the plane in which the crystal is quasiperiodic transform under equivalent representations of P, inequivalent ones if the point group is 5-, 8-, 10- or 12-gonal. From the Neumann principle follow restrictions on the form of the phonon, phason and phonon,phason coupling contributions to the elastic stiffness matrix that can be determined by combining the restrictions obtained for a set of elements generating the point group of interest. For the phonon part, the restrictions obtained for the generating elements do not depend on the system to which the point group belongs. This remains true for the phason and coupling parts in the case of crystallographic point groups but, in general, breaks down for the non-crystallographic ones. The form of the symmetric 12 × 12 matrix giving the phonon, phason and phonon,phason coupling contributions to the elastic stiffness is presented in graphic notation. [source] The piezoelectric effect of second order in stress or strain: its form for crystals and quasicrystals of any symmetryACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2007Hans Grimmer The restrictions on the coefficients describing physical effects depend on the orientation of the symmetry elements of the crystal or quasicrystal with respect to the Cartesian coordinate system employed. They are given for the piezoelectric effect of second order in stress or strain for all the orientations that can be expressed by the sequence of elements in the Hermann,Mauguin symbol of the point group. In the literature, the restrictions are usually given only for a particular orientation, which sometimes is not specified. [source] Diffraction with a coherent X-ray beam: dynamics and imagingACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2007Frédéric Livet Methods for carrying out coherent X-ray scattering experiments are reviewed. The brilliance of the available synchrotron sources, the characteristics of the existing optics, the various ways of obtaining a beam of controlled coherence properties and the detectors used are summarized. Applications in the study of the dynamics of speckle patterns are described. In the case of soft condensed matter, the movement of inclusions like fillers in polymers or colloidal particles can be observed and these can reflect polymer or liquid-crystal fluctuations. In hard condensed-matter problems, like phase transitions, charge-density waves or phasons in quasicrystals, the study of speckle fluctuations provides new time-resolved methods. In the domain of lensless imaging, the coherent beam gives the modulus of the sample Fourier transform. If oversampling conditions are fulfilled, the phase can be obtained and the image in the direct space can be reconstructed. The forthcoming improvements of all these techniques are discussed. [source] Discrete tomography of planar model setsACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2006Michael Baake Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical quasicrystals. To this end, the class of cyclotomic model sets is introduced, and the corresponding consistency, reconstruction and uniqueness problems of the discrete tomography of these sets are discussed. [source] | |||||||||||||||||||