To superspace and beyond

The significance of an algorithm developed by H. T. Stokes & B. J. Campbell [Acta Cryst. (2017), A73, 4–13] is discussed. The algorithm promises to be a key tool for understanding the structure–property relationships of the many technologically important materials that display incommensurate modulations in their atomic and/or magnetic structure.

A general algorithm for generating isotropy subgroups in superspace

Irreducible representations can now be used to derive the isotropy subgroups at irrational wavevectors, making it relatively easy to explore the (3 + d)-dimensional superspace-group symmetries that arise from incommensurate modulations of a parent crystal structure. A general algorithm capable of arbitrary superpositions of multiple incommensurate and commensurate order parameters is presented.

2-Periodic self-dual tilings

All uninodal, binodal and trinodal 2-periodic self-dual tilings are enumerated and described.

How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

The critical photon fluence for reconstructing objects from noisy diffraction patterns is computed by a maximum-likelihood estimator, for the optical near- and far-field regimes, of random binary bitmap images as a function of contrast value.

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. II

Computer simulations of six-beam (000, 220, 242, 044, −224, −202) X-ray diffraction in a perfect silicon crystal of large thickness are performed. Both the plane-wave angular dependence and the six-beam section topographs are investigated.

Sphere packings as a tool for the description of martensitic phase transformations

Martensitic phase transformations are described by means of group–subgroup relations and sphere-packing considerations.

Revisiting La_0.5Sr_1.5MnO₄ lattice distortion and charge ordering with multi-beam resonant diffraction

Sinusoidal wave type distortions of La_0.5Sr_1.5MnO₄ in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction and dynamical theory.

Constraint-induced direct phasing method

A constraint-induced direct phasing method has been developed to improve structure-solution determination for low-resolution X-ray powder diffraction data.

Lattice reduction using a Euclidean algorithm

The reduction of a crystal lattice is considered. The reduction associated with the existence of a commensurate translation that leaves the crystal invariant is addressed, and a practical scheme for it is provided.

MPF, a multipurpose figure of merit for phasing procedures

A new figure of merit, MPF, has been devised. It may be usefully applied in different contexts of a phasing procedure.

Ordering of convex polyhedra and the Fedorov algorithm

The relation between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the ordering of convex n-acra is found. A method to weakly order the convex n-acra by the maximum extra valencies of their vertices is suggested.

Basic Elements of Crystallography

X-Ray Crystallography