issue contents

ISSN: 2053-2733

May 2000 issue

Highlighted illustration

Cover illustration: Unit cell of a self-intersecting minimal surface with symmetry I432. The surface subdivides R3 into two congruent three-periodic mutually interpenetrating labyrinths with symmetry P4232. Lines of self-intersection are marked in red. See Koch [Acta Cryst. (2000), A56, 15-23].

research papers

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The statistical dynamical theory of X-ray diffraction is developed for a crystal containing statistically distributed microdefects. Fourier-component equations for coherent and diffuse (incoherent) scattered waves have been obtained in the case of so-called triple-crystal diffractometry. New correlation lengths and areas are introduced for characterization of the scattered volume.

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The algorithm takes an exit wave function as input and refines a starting potential, which is set up using the weak-phase-object model or the electron-channelling approximation. The reconstruction is successful even under the strongly nonlinear dynamical diffraction conditions at larger specimen thicknesses and on large areas containing defects in crystalline materials.

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An algorithm is proposed that can perform discrete Fourier transforms in arbitrary dimensions with a single piece of computer code. It will find applications in the calculation of Fourier maps and in the maximum-entropy method for aperiodic crystals.

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The atoms in molecules (AIM) theory has been used to derive atomic charges, atomic volumes and molecular dipole moments from theoretical (both single-molecule and periodic) and experimental charge densities on p-nitroaniline, using the programs TOPOND and TOPXD, respectively. The latter is a new program for topological analysis of densities described by the Coppens–Hansen multipole formalism.

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A finite group was discovered that includes all the types of Bravais lattices as its subgroups. Its elements are represented by 6\times6 matrices whose components are complex in general. The order of the group is 2799360.

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It is shown that a pair of reference-beam oscillating-crystal diffraction images related by an inverse-beam geometry can provide the enantiomorphic phase information that is needed for solving noncentrosymmetric crystal structures.

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The article presents a detailed theoretical and experimental description of a recently developed reference-beam diffraction technique for direct measurements of a large number of triplet phases in a crystallography experiment.

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Tests with simulated data for crambin suggest that reference-beam diffraction will expedite direct-methods applications at resolutions lower than 1.2 Å.

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A new procedure for estimating the values of nonmeasured diffraction amplitudes is given.

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Deformations of homogeneous sphere packings in Cmcm 4(c) are employed to describe the transitions from a cubic P to a cubic I lattice, from a cubic body-centred structure to a hexagonal close packing and from a hexagonal primitive structure to a hexagonal close packing. The transformation from an NaCl-type to a CsCl-type structure is described by the deformation of a heterogeneous sphere packing in Pmmn.

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The large wavelength dispersion of 0.14 in graphite-monochromated Mo radiation causes scan-angle-induced spectral truncation errors in the observed Bragg intensities. Since the systematic intensity error increases with θ, the X-ray model becomes biased and leads to values of the atomic displacement parameters that are too large.

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It is shown that, under certain conditions, the intensity received by a point located on the exit surface of a crystal is described by the diffraction of a locally plane wave. It is possible to visualize the rocking curve of a crystal as a function of the position along the exit surface. This represents a topographic method to obtain the reflectivity curve of the crystal instead of the usual goniometric method.

addenda and errata

Acta Cryst. (2000). A56, 317
doi: 10.1107/S0108767300004153

books received

Acta Cryst. (2000). A56, 318
doi: 10.1107/S0108767300004165
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