Statistical dynamical theory of X-ray diffraction in the Bragg case: application to triple-crystal diffractometry

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.

Reconstruction of the projected crystal potential in transmission electron microscopy by means of a maximum-likelihood refinement algorithm

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.

Discrete Fourier transform in arbitrary dimensions by a generalized Beevers–Lipson algorithm

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.

Evaluation of net atomic charges and atomic and molecular electrostatic moments through topo­logical analysis of the experimental charge density

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.

A finite group that derives all the 14 Bravais lattices as its subgroups

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

Enantiomorph determination using inverse reference-beam diffraction images

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.

Triplet-phase measurements using reference-beam X-ray diffraction

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.

Shake-and-Bake applications using simulated reference-beam data for crambin

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

On the extrapolation of the magnitudes |E| of the normalized structure factors E

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

The NaCl- to CsCl-type phase transition discussed on the basis of the cP to cI deformation with the symmetry Cmcm 4(c) m2m

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.

Systematic intensity errors and model imperfection as the consequence of spectral truncation

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.

X-ray dynamical diffraction: the concept of a locally plane wave

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.

Expansion of scalar validation criteria to three dimensions: the R tensor. Erratum

Erratum to Acta Cryst. (2000), A56, 157–162.

The weak hydrogen bond in structural chemistry and biology