A feasible set approach to the crystallographic phase problem

The crystallographic phase problem is recast in terms of feasible sets, facilitating new technique development and improved mathematical understanding.

The Darwin procedure in optics of layered media and the matrix theory

Different formulae of the Darwin theory in the two-beam case are obtained by a uniform view of basic properties of tridiagonal matrices, their determinants (continuants) and their close relationship to continued fractions and difference equations.

Molecular packing groups and ab initio crystal-structure prediction

P1 and space-group-specific methods of ab initio crystal structure prediction are compared, especially with consideration of restrictions introduced by the number of molecules per cell.

Polysomatic series in the structures of complex cuprates

This study has shown that the polysomatic model can be efficiently applied to the structural analysis of complex cuprates. The structure of ladder-type cuprates was analysed in more detail.

Spectral decomposition of the linear elastic tensor for monoclinic symmetry

The spectral decomposition of the compliance fourth-rank tensor related to crystalline or other anisotropic media belonging to the monoclinic crystal system is described.

Modified form factors from multiconfiguration Dirac–Fock wave functions for neutral atoms with Z = 70–100

Modified form factors, to be used in the calculation of the structure factors , are calculated from multiconfiguration relativistic Dirac–Fock wave functions. Tables are presented for neutral elements in the range Z = 70–100.

Determination of mean inner potential of germanium using off-axis electron holography

Off-axis electron holography has been used to determine that the mean inner potential of germanium is 14.3 (2) V using cleaved 90° wedge samples.

Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings

A revised procedure to compute (a program is available) the periodic intensity distribution (PID) function of mica polytypes is given and results are presented in the most suitable axial settings. Symbolism to describe mica polytypes is unified.

Dynamical calculation of crystal truncation rods for surfaces and interfaces using a Cartesian coordinate transformation technique

A dynamical calculation scheme that employs Cartesian coordinates with a z axis normal to the crystal surface to define polarization unit vectors and wavefields is applied to interpret the intensity distribution of crystal truncation rods for surfaces and interfaces.

Three-wave X-ray diffraction: an analysis scheme of the sensitivity in determining triplet phase invariants

A model for analysing the phase sensitivity of the reflection coefficients of a diffracted wave in the case of three-wave X-ray diffraction is proposed. This model considers three-wave diffraction as the interference of the directly excited and the Umweg-excited diffracted waves.

Faster calculation of the full matrix for least-squares refinement

Equations derived from a statistical model for large structures give matrix elements as functions of the lengths and directions of Patterson vectors and the distribution of weights without summation over the individual reflections.

The efficient calculation of the normal matrix in least-squares refinement of macromolecular structures

A method is described whereby the normal matrix of least-squares refinement can be calculated using the fast Fourier transformation to replace all loops over the structure factors.

Room-temperature and low-temperature structure of Nd_1−xCa_xMnO₃ (0.3 ≤ x ≤ 0.5)

Three Nd_1−xCa_xMnO₃ (0.3 ≤ x ≤ 0.5) compounds have been studied at room temperature as well as below the charge ordering temperature by electron microscopy and neutron diffraction.

A new type of constraint in the maximum-entropy method using ambiguous phase information from anomalous-scattering powder data

In an X-ray anomalous-scattering experiment using powder samples, the phases of structure factors cannot be uniquely determined when the crystal is noncentrosymmetric. A new constraint type for this case has been built into the maximum-entropy program MEED, so that now all types of information obtained from such an experiment can be used simultaneously in a MEM calculation of the electron density.

Molecular fragment electric moments derived from the fit of the experimental electrostatic potential. Application to the water molecule

The experimental electrostatic potential is used as an observable property to derive molecular fragment electric moments. The method based on analytical transformations of the real spherical harmonics is presented and applied to a sample of six water molecules.

A likelihood-based search for the macromolecular position in the crystalline unit cell

A generalized likelihood-based search can be used for determining the position of a macromolecule in the cell. In some cases, spurious maxima are eliminated and the signal-to-noise ratio is enhanced in comparison with the straightforward R-factor-based search.

Quasiperiodic packings of fibres with icosahedral symmetry

Quasiperiodic packing of fibres with global icosahedral symmetry are studied and described using a cut and project method.

Progress on the direct-methods solution of macromolecular structures using single-wavelength anomalous-dispersion (SAS) data

A least-squares procedure is described that can in principle resolve the SAS phase ambiguity provided that unbiased ω(h, k) estimates are available. SAS tangent formula methods may be used to either validate or reject the correctness of the anomalously scattering heavy-atom sites.

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. I. Symbols for point-group transformations, families, systems and geometric crystal classes

Crystallographic symbols for use in arbitrary dimensions are considered and recommendations presented together with symbols for orthogonal transformations, geometrical crystal classes and standard settings of lattices. Standard metric tensors recommended for four-, five- and six-dimensional crystal families are given in full.