From crystal color symmetry to quantum spacetime

This perspective article elucidates both the importance and the implications of relativistic spacetime crystals as well as the renormalized blended coordinates transformation. It alludes to possible applications in materials science, condensed matter physics and quantum gravity.

Relativistic spacetime crystals

By appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown. Using this mapping, hidden symmetries in relativistic spacetime crystals are uncovered.

Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain

A new method is presented combining multiwavelength anomalous diffraction and Bragg coherent diffractive imaging. Combining the advantages of both approaches, it opens the possibility of simultaneously probing the strain and the unit-cell configuration.

Polarization effects of X-ray monochromators modeled using dynamical scattering theory

Treatment of the effects of a single-crystal incident-beam monochromator in a powder diffraction experiment must be carried out using dynamical diffraction to obtain the correct intensities for reflections, due to the modification of the beam polarization by the monochromator. Theory and data are presented to verify the effect.

Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon

The resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.

A reference-based multi-lattice indexing method integrating prior information correction and iterative refinement in protein crystallography

A new multi-lattice indexing method based on the principle of whole-pattern matching given cell dimensions and space-group symmetry is presented for macromolecular crystallography. The proposed method features a local correction for prior information accompanied by iterative refinement of experimental parameters, both of which are numerically and experimentally demonstrated to be critical for accurately identifying multiple crystal lattices.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

A new strategy for improving precision and sensitivity in the refinement of crystal structure factors is proposed. This technique will help to precisely determine the chemical bonding states of crystalline materials, which are closely related to their physical properties.

On symmetry breaking of dual polyhedra of non-crystallographic group H₃

The ubiquity of the icosahedral symmetry among various spherical molecules, fullerenes and viruses motivates the current study. The structures of dual polytopes with the H₃ symmetry obtained for seven types of dominant points are described in detail. The existence of the corresponding nanotubes is explained using a symmetry-breaking mechanism. The structure of the fullerene C₂₀ is expanded into the nanotubes C_20+6N and C_20+10N, using the reduction of the icosahedral symmetry to the subgroups A₂ and H₂, respectively.

A topological proof of the modified Euler characteristic based on the orbifold concept

The vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler characteristic is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.

Magnetic modes compatible with the symmetry of crystals

The magnetic point groups are classified into 32 categories which lead to a total of 64 unique magnetic modes with the same set of directions of M. This classification gives hints on the neutron powder diffraction analysis of collinear magnetic ordering.

A new density-modification procedure extending the application of the recent |ρ|-based phasing algorithm to larger crystal structures

The insertion of a peakness-enhancing fast Fourier transform compatible module in the novel S_M,_|ρ| phasing algorithm improves its efficiency for larger crystal structures as shown with a collection of representative X-ray diffraction data sets taken from the Protein Data Bank.

Sidney C. Abrahams (1924–2021)

Obituary for Sidney C. Abrahams

An Invitation to Applied Category Theory. Seven Sketches in Compositionality

Space Group Visualizer