Pierre J. Becker (1942–2024)

In memory of Pierre J. Becker.

Atomic pair distribution functions from textured polycrystalline samples: fundamentals

The basic equations for the atomic pair distribution function of a sample that has a crystallographic texture (preferred orientation) are derived.

Towards a taxonomy of nets: supersymmetric 2- and 3-periodic structures in three-dimensional Euclidean space

We describe the supersymmetric nets, including some that are interlinked and interwoven.

Computing the bridge length: the key ingredient in a continuous isometry classification of periodic point sets

We describe an efficient algorithm to compute the bridge length estimating the size of a complete isoset invariant, which classifies all periodic point sets under Euclidean motion.

X-ray dynamical diffraction wavefront division interferometer (double-slit diffraction) with an asymmetric monochromator

The determination of the parameters of an X-ray asymmetrically cut monochromator for the experimental realization of an X-ray dynamical diffraction interferometer with wavefront division (X-ray double-slit experiment) is presented.

Digital distance in the kisrhombille grid with the edge neighborhood

The kisrhombille tiling is the dual of one of the eight semi-regular tilings and is composed of right-angled triangles in 12 different orientations. In this paper, two triangles are considered neighbors if they share an edge. Paths in the grid are sequences of triangles where each triangle (except the first) follows one of its neighbors. Digital distance is defined and calculated based on the number of steps in a shortest path between any pair of triangles.

Ultrathin selenium nanorods from helical phases: a quantum chemical study using line group theory

The torsion instability of chiral selenium nanorods from the trigonal bulk phase was theoretically predicted. Two types (chiral/achiral) of selenium nanorods from the tetragonal bulk phase were constructed and studied.

The separation of the effects of atomic displacement and local resolution in crystallographic and cryo-electron microscopy maps

Shell-based density modeling allows us to separate the effects of atomic displacements and of resolution cutoffs on crystallographic and cryo-electron microscopy maps during the refinement of atomic models in real space.