The topological density of a three-dimensional net is currently available after determining its entire coordination sequence. This paper shows that its value can be obtained directly from the set of cycles of the quotient graph of the net. A geometrical tool, the cycles figure of the net has been developed for this purpose. Its construction as a convex polyhedron with triangular faces is described as well as its use for topological density calculations. An exact expression is derived for three-dimensional nets and extended to arbitrary n-dimensional nets. Additionally, this paper describes applications to three-dimensional lattices and nets, n-dimensional diamonds and lonsdaleites.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1107/s0108767303022037 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
In confluent cell monolayers, patterns of cell forces and motion are systematically altered near topological defects in cell shape. In turn, defects have been proposed to alter cell density, extrusion, and invasion, but it remains unclear how the defects form and how they affect cell forces and motion. Here, we studied +1/2 defects, and, in contrast to prior studies, we observed both tail-to-head and head-to-tail defect motion occurring at the same time in the same cell monolayer.
View Article and Find Full Text PDFMechanistic Pathways in Cyanide-Mediated Benzoin Condensation: A Comprehensive Electron Localisation Function (ELF) and Catastrophe Theory Analysis of the Umpolung Reaction.
Molecules
January 2025
Faculty of Chemistry, University of Wroclaw, 50-383 Wroclaw, Poland.
This research investigates the mechanism of the cyanide-type umpolung reaction in benzoin condensation using topological analysis of ELF and catastrophe theory. The study achieves a comprehensive understanding of the evolution of chemical bonds and non-bonding electron density in the reaction of benzaldehyde and cyanide ions. The results reveal that the reaction proceeds through five transition state structures, with the formation of Lapworth's cyanohydrin being the rate-determining step.
View Article and Find Full Text PDFStructural and topological analysis of thiosemicarbazone-based metal complexes: computational and experimental study of bacterial biofilm inhibition and antioxidant activity.
BMC Chem
January 2025
Chemistry Department, Faculty of Science, Alexandria University, Alexandria, Egypt.
The structural and electronic behavior of thiosemicarbazone (TSC)-based metal complexes of Mn (II), Fe (II), and Ni (II) have been investigated. The synthesized metal complexes were characterized using elemental analysis, magnetic susceptibility, molar conductivity, FTIR, and UV-Vis spectroscopy, the computational path helped with further structural investigation. The solubility test on the TSC and its complexes revealed their solubility in most organic solvents.
View Article and Find Full Text PDFAnisotropic Elasticity, Spin-Orbit Coupling, and Topological Properties of ZrTe and NiTe: A Comparative Study for Spintronic and Nanoscale Applications.
Nanomaterials (Basel)
January 2025
Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27606, USA.
The present work investigates the interfacial and atomic layer-dependent mechanical properties, SOC-entailing phonon band structure, and comprehensive electron-topological-elastic integration of ZrTe and NiTe. The anisotropy of Young's modulus, Poisson's ratio, and shear modulus are analyzed using density functional theory with the TB-mBJ approximation. NiTe has higher mechanical property values and greater anisotropy than ZrTe.
View Article and Find Full Text PDFAltermagnetism in two-dimensional CaRuO perovskite.
Nanoscale
January 2025
Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile.
We propose and characterize a novel two-dimensional material, 2D-CRO, derived from bulk calcium-based ruthenates (CROs) of the Ruddlesden-Popper family, CaRuO ( = 1 and 2). Using density functional theory, we demonstrate that 2D-CRO maintains structural stability down to the monolayer limit, exhibiting a tight interplay between structural and electronic properties. Notably, 2D-CRO displays altermagnetic behavior, characterized by zero net magnetization and strong spin-dependent phenomena, stabilized through dimensionality reduction.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!