Acta Crystallographica Section A最新文献

The focusing properties of cylindrically bent crystals in symmetric Laue geometry are discussed using the formalism of Fresnel diffraction and the analytical solution of the Takagi-Taupin equations for a point source on the entrance surface. The existence of a focal shift in the dynamical focusing effect is pointed out and discussed. The present theoretical framework is applied to experiments performed at the energy-dispersive X-ray absorption spectroscopy beamline of the European Synchrotron Radiation Facility concerning the position and the size of the focal spot obtained from a polychromatic source at a large distance from the bent crystal.

Bragg's second law, which deserves to be more widely known, is recounted. The significance of Bragg's law in electron diffraction and microscopy is then discussed, with particular emphasis on differences between X-ray and electron diffraction. As an example of such differences, the critical voltage effect in electron diffraction is described. It is then shown that the lattice imaging of crystals in high-resolution electron microscopy directly reveals the Bragg planes used for the imaging process, exactly as visualized by Bragg in his real-space law. Finally, it is shown how in 2012, for the first time, on the centennial anniversary of Bragg's law, single atoms have been identified in an electron microscope using X-rays emitted from the specimen. Hence atomic resolution X-ray maps of a crystal in real space can be formed which give the positions and identities of the different atoms in the crystal, or of a single impurity atom in the crystal.

We trace the historical development of W. L. Bragg's `law' and the key experimental observation which made it possible using polychromatic radiation at a time when neither X-ray wavelengths nor cell constants were known. This led, through his phasing and solving large mineral structures (without use of a computer), to work on metals, proteins, bubble rafts and his X-ray microscope. The relationship of this to early X-ray microdiffraction is outlined, followed by a brief review of electron microdiffraction methods, where electron-probe sizes smaller than one unit cell can be formed with an interesting `failure' of Bragg's law. We end with a review of recent femtosecond X-ray `snapshot' diffraction from protein nanocrystals, using an X-ray laser which generates pulses so short that they terminate before radiation damage can commence, yet subsequently destroy the sample. In this way, using short pulses instead of freezing, the nexus between dose, resolution and crystal size has been broken, opening the way to time-resolved diffraction without damage for a stream of identical particles.

A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.

The discovery of X-ray diffraction in 1912 by Laue and co-workers had important implications for the physics of diffraction, for the nature of X-radiation and for the structure of matter. Lawrence Bragg made important contributions to early developments in each of these areas, but the most pregnant of his innovations was in structure determination from X-ray diffraction data. He continued to make highly significant contributions to structure determination right on to the first crystal structures of proteins. Crystallography has made substantial contributions to chemistry and biology, and notably so for biological macromolecules.

Tables of the absorption correction A* for cylindrical and spherical crystals were calculated by the Thorkildsen & Larsen [Acta Cryst. (1998), A54, 186-190] analytical method in the range of 0 ≤ μR ≤ 30 and 0 ≤ θ ≤ 90° with accuracies of 10(-6) for cylindrical crystals and 2.0 × 10(-6) for spherical crystals. Bivariate Chebyshev polynomial fitting formulae for A* are also provided for both cases. The maximum fitting error for spherical crystals is 6 × 10(-3) and the average error ranges from 7 × 10(-5) to 3 × 10(-4). All the important tables and the fitting program are provided in the supplementary material.

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that can be realized in the ten orthorhombic trivariant lattice complexes belonging to the space groups of crystal class mmm without mirror symmetry. Altogether, sphere packings of 186 different types have been found; the maximal inherent symmetry is orthorhombic for 124 of these types. In addition, ten types of interpenetrating sphere packings were detected, and in three lattice complexes interpenetrating 6(3) nets occur.

Historians often have debates about the beginning and end of a certain era. The same discussion can be had about the history of aperiodic crystals. There are reasons to claim that in 2012 one may celebrate the 50th anniversary of this field. A short description is given of the development of this branch of crystallography. It is argued that the most important point in its history is the discovery of quasicrystals, which has been recognized by awarding the Nobel Prize in Chemistry 2011 to Dan Shechtman.

New crystallographic tools were developed to access a more precise description of the spin-dependent electron density of magnetic crystals. The method combines experimental information coming from high-resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) in a unified model. A new algorithm that allows for a simultaneous refinement of the charge- and spin-density parameters against XRD and PND data is described. The resulting software MOLLYNX is based on the well known Hansen-Coppens multipolar model, and makes it possible to differentiate the electron spins. This algorithm is validated and demonstrated with a molecular crystal formed by a bimetallic chain, MnCu(pba)(H(2)O)(3)·2H(2)O, for which XRD and PND data are available. The joint refinement provides a more detailed description of the spin density than the refinement from PND data alone.