Acta Crystallographica Section A最新文献

A previous paper detailed a novel algorithm, ε-machine spectral reconstruction theory (εMSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction patterns [Varn et al. (2013). Acta Cryst. A69, 197-206]. Here εMSR is applied to simulated diffraction patterns from four close-packed crystals. It is found that, for stacking structures with a memory length of three or less, εMSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ε-machine. For stacking structures with a memory length larger than three, εMSR returns a model that captures many important features of the original stacking structure. These include multiple stacking faults and multiple crystal structures. Further, it is found that εMSR is able to discover stacking structure in even highly disordered crystals. In order to address issues concerning the long-range order observed in many classes of layered materials, several length parameters are defined, calculable from the ε-machine, and their relevance is discussed.

The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters.

A new study of the σA parameter has been undertaken to understand its behaviour when the diffraction amplitude distributions are far from the standard Wilson distributions. The study has led to the formulation of a new statistical interpretation of σA, expressed in terms of a correlation factor. The new formulas allow a more accurate use of σA in electron-density modification procedures.

Femtosecond X-ray pulses from X-ray free-electron laser sources make it feasible to conduct room-temperature solution scattering experiments far below molecular rotational diffusion timescales. Owing to the ultra-short duration of each snapshot in these fluctuation scattering experiments, the particles are effectively frozen in space during the X-ray exposure. In contrast to standard small-angle scattering experiments, the resulting scattering patterns are anisotropic. The intensity fluctuations observed in the diffraction images can be used to obtain structural information embedded in the average angular correlation of the Fourier transform of the scattering species, of which standard small-angle scattering data are a subset. The additional information contained in the data of these fluctuation scattering experiments can be used to determine the structure of macromolecules in solution without imposing symmetry or spatial restraints during model reconstruction, reducing ambiguities normally observed in solution scattering studies. In this communication, a method that utilizes fluctuation X-ray scattering data to determine low-resolution solution structures is presented. The method is validated with theoretical data calculated from several representative molecules and applied to the reconstruction of nanoparticles from experimental data collected at the Linac Coherent Light Source.

New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part P(s). Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms.

This paper studies the symmetry group of two special types of carbon nanotori. The construction is motivated by a group-theoretical result.

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions.

δ Recycling is a simple procedure for directly extracting phase information from Patterson-type functions [Rius (2012). Acta Cryst. A68, 399-400]. This new phasing method has a clear theoretical basis and was developed with ideal single-crystal X-ray diffraction data. On the other hand, introduction of the automated diffraction tomography (ADT) technique has represented a significant advance in electron diffraction data collection [Kolb et al. (2007). Ultramicroscopy, 107, 507-513]. When combined with precession electron diffraction, it delivers quasi-kinematical intensity data even for complex inorganic compounds, so that single-crystal diffraction data of nanometric volumes are now available for structure determination by direct methods. To check the tolerance of δ recycling to missing data-collection corrections and to deviations from kinematical behaviour of ADT intensities, δ recycling has been applied to differently shaped nanocrystals of various inorganic materials. The results confirm that it can phase ADT data very efficiently. In some cases even more complete structure models than those derived from conventional direct methods and least-squares refinement have been found. During this study it has been demonstrated that the Wilson-plot scaling procedure is largely insensitive to sample thickness variations and missing absorption corrections affecting electron ADT intensities.