Acta Crystallographica Section A最新文献

The use of Pólya's theorem in crystallography and other applications has greatly simplified many counting and coloring problems. Given a group of equivalences acting on a set, Pólya's theorem equates the number of unique subsets with the orbits of the group action. For a lattice and a given group of periodic equivalences, the number of nonequivalent subsets of the lattice can be solved using Pólya's counting on the group of relevant symmetries acting on the lattice. When equivalence is defined via a sublattice, the use of Pólya's theorem is equivalent to knowing the cycle index of the action of the group elements on a related finite group structure. A simple algebraic method is presented to determine the cycle index for a group element acting on a lattice subject to certain periodicity arguments.

A framework is presented based on color symmetry theory that will facilitate the determination of the subgroup structure of a crystallographic Coxeter group. It is shown that the method may be extended to characterize torsion-free subgroups. The approach is to treat these groups as groups of symmetries of tessellations in space by fundamental polyhedra.

Algorithms for constructing aperiodic structures produce templates for the nanofabrication of arrays for applications in photonics, phononics and plasmonics. Here a general multidimensional recursion rule is presented for the regular paperfolding structure by straightforward generalization of the one-dimensional rule. As an illustrative example the two-dimensional version of the paperfolding structure is explicitly constructed, its symbolic complexity referred to rectangles computed and its Fourier transform shown. The paperfolding structures readily yield novel 'paperfolding' tilings. Explicit formulas are put forward to count the number of folds in any dimension. Finally, possible generalizations of the dragon curve are discussed.

White-beam X-ray Laue microdiffraction allows fast mapping of crystal orientation and strain fields in polycrystals, with a submicron spatial resolution in two dimensions. In the well crystallized parts of the grains, the analysis of Laue-spot positions provides the local deviatoric strain tensor. The hydrostatic part of the strain tensor may also be obtained, at the cost of a longer measuring time, by measuring the energy profiles of the Laue spots using a variable-energy monochromatic beam. A new `rainbow' method is presented, which allows measurement of the energy profiles of the Laue spots while remaining in the white-beam mode. It offers mostly the same information as the latter monochromatic method, but with two advantages: (i) the simultaneous measurement of the energy profiles and the Laue pattern; (ii) rapid access to energy profiles of a larger number of spots, for equivalent scans on the angle of the optical element. The method proceeds in the opposite way compared to a monochromator-based method, by simultaneously removing several sharp energy bands from the incident beam, instead of selecting a single one. It uses a diamond single crystal placed upstream of the sample. Each Laue diffraction by diamond lattice planes attenuates the corresponding energy in the incident spectrum. By rotating the crystal, the filtered-out energies can be varied in a controlled manner, allowing one to determine the extinction energies of several Laue spots of the studied sample. The energies filtered out by the diamond crystal are obtained by measuring its Laue pattern with another two-dimensional detector, at each rotation step. This article demonstrates the feasibility of the method and its validation through the measurement of a known lattice parameter.

Electron diffraction is a unique tool for analysing the crystal structures of very small crystals. In particular, precession electron diffraction has been shown to be a useful method for ab initio structure solution. In this work it is demonstrated that precession electron diffraction data can also be successfully used for structure refinement, if the dynamical theory of diffraction is used for the calculation of diffracted intensities. The method is demonstrated on data from three materials - silicon, orthopyroxene (Mg,Fe)(2)Si(2)O(6) and gallium-indium tin oxide (Ga,In)(4)Sn(2)O(10). In particular, it is shown that atomic occupancies of mixed crystallographic sites can be refined to an accuracy approaching X-ray or neutron diffraction methods. In comparison with conventional electron diffraction data, the refinement against precession diffraction data yields significantly lower figures of merit, higher accuracy of refined parameters, much broader radii of convergence, especially for the thickness and orientation of the sample, and significantly reduced correlations between the structure parameters. The full dynamical refinement is compared with refinement using kinematical and two-beam approximations, and is shown to be superior to the latter two.

In previous publications [Varn et al. (2002). Phys. Rev. B, 66, 174110; Varn et al. (2007). Acta Cryst. B63, 169-182] we introduced and applied a new technique for discovering and describing planar disorder in close-packed structures directly from their diffraction patterns. Here, we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. We show that the resulting statistical model of the stacking structure - called the ε-machine - allows the calculation of measures of memory, structural complexity and configurational entropy. The methods developed here can be adapted to a wide range of experimental systems in which power spectra data are available.

The affine extensions (there are 55 different ones) of the icosahedral group developed by T. Keef and R. Twarock of the York Centre for Complex Systems Analysis of the University of York [see in particular Keef et al. (2013). Acta Cryst. A69, 140-150], and applied to the investigation of the architecture of a number of icosahedral viruses, are here considered in the framework of molecular crystallography. The basic ideas of such molecular description involve positions with rational indices which approximate backbone positions in viral polypeptide and RNA chains. The test case of the Pariacoto virus suggests that the best-fit algorithm used in the York group's approach should be adapted to a more specific toolkit suited for the investigation of the architecture of icosahedral viruses. Typical problems which could be solved by means of such a toolkit are exemplified and put in the perspective of viral properties.

Understanding the fundamental principles of virus architecture is one of the most important challenges in biology and medicine. Crick and Watson were the first to propose that viruses exhibit symmetry in the organization of their protein containers for reasons of genetic economy. Based on this, Caspar and Klug introduced quasi-equivalence theory to predict the relative locations of the coat proteins within these containers and classified virus structure in terms of T-numbers. Here it is shown that quasi-equivalence is part of a wider set of structural constraints on virus structure. These constraints can be formulated using an extension of the underlying symmetry group and this is demonstrated with a number of case studies. This new concept in virus biology provides for the first time predictive information on the structural constraints on coat protein and genome topography, and reveals a previously unrecognized structural interdependence of the shapes and sizes of different viral components. It opens up the possibility of distinguishing the structures of different viruses with the same T-number, suggesting a refined viral structure classification scheme. It can moreover be used as a basis for models of virus function, e.g. to characterize the start and end configurations of a structural transition important for infection.

The results of experimental and theoretical studies into the influence of ultrasound on the propagation of neutron waves in a thick Ge crystal are presented. The neutron intensity profiles were measured for the case of Laue diffraction inside the Borrmann fan. At low amplitudes of ultrasonic waves interference effects (diffraction intensity beatings) were observed. The observations were possible because of the uniform acoustic-field distribution through the whole bulk of the crystal. As distinct from the classical Shull experiments, wide analysing slits or position-sensitive detectors were used. To explain the results obtained, a modified theory for the spatial distribution of neutron diffraction intensities in the presence of acoustic excitation of the crystal is proposed. A good agreement between experiment and theory is obtained. At high amplitudes of ultrasonic waves the transition to kinematic scattering was not observed, despite the large strains in the crystalline lattice created by ultrasound. This could be connected with the formation of a superlattice having a standing wave period. A strong rise in the diffraction intensity and a sharp constriction of the neutron beam at the centre of the Borrmann fan were observed. This new effect could be used for the creation of ultrasound-controlled monochromators.

Expressions for absorption and the secondary scattering intensity ratio are presented for a small beam impinging off-center of a spherical amorphous sample. Large gradients in the absorption correction are observed from small offsets from the central axis. Additionally, the secondary scattering intensity ratio causes an intensity asymmetry in the detector image. The secondary scattering intensity ratio is presented in integral form and must be computed numerically. An analytic, small-angle, asymptotic series solution for the integral form of the absorption correction is also presented.