issue contents

Journal logoFOUNDATIONS
ADVANCES
ISSN: 2053-2733

July 2021 issue

Highlighted illustration

Cover illustration: The study of spacetime crystals, where space and time can mix, could usher in an entirely new class of metamaterials with exotic properties otherwise not available in nature. By blending two separate observations of the same event, Venkat Gopalan [Acta Cryst. (2021), A77, 242–256] also develops a new mathematical formalism that may solve a decades-old problem in understanding spacetime, the fabric of the universe proposed in Einstein's theories of relativity. It may also provide a fresh starting point for unifying quantum mechanics and gravity, as an accompanying commentary on this work discusses [Bojowald & Saxena (2021), Acta Cryst. A77, 239–241]. The cover image shows four 3D holohedral renormalized blended spacetime (RBS) point groups for periodic RBS crystals.

advances

scientific commentaries


link to html
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.

research papers


link to html
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.

short communications


link to html
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.

foundations

research papers


link to html
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.

link to html
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.

link to html
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.

link to html
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.

link to html
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 C20+6N and C20+10N, using the reduction of the icosahedral symmetry to the subgroups A2 and H2, respectively.

link to html
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.

link to html
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.

link to html
The insertion of a peakness-enhancing fast Fourier transform compatible module in the novel SM,|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.

obituaries


book reviews



Follow Acta Cryst. A
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds