Related Experiment Video
Updated: Mar 7, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
B7 as a supergroup of crystal and quasicrystal symmetries
1Faculty of Computer Science and Material Sciences, University of Silesia, Katowice, Poland.
Abstract:
In sharp contrast to the generation of a finite group that includes all the 14 types of Bravais lattices as its subgroups [Hosoya (2000). Acta Cryst. A56, 259-263; Hosoya (2002). Acta Cryst. A58, 208], it was proved that a signed permutation group Bk may be interpreted as the supergroup of both crystal and quasicrystal symmetries. Minimal dimension k = 6 is adequate for lattices referred to their three non-coplanar shortest vectors, or for symmetry groups of most quasicrystal types. If one prefers complete, well defined semi-reduced lattice descriptions or needs a dodecagonal group, the B7 supergroup is necessary. All considered matrix groups correspond to isometric transformations in extended k-bases and may be easily derived from B7 and projected onto three-dimensional crystallographic space. Three models of extended bases are proposed: semi-reduced, cyclic and axial. In all cases additional basis vectors are strictly (functionally) related to three original basis vectors.
More Related Videos
06:35Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
09:15Combining X-Ray Crystallography with Small Angle X-Ray Scattering to Model Unstructured Regions of Nsa1 from S. Cerevisiae
Published on: January 10, 2018
Related Concept Videos
The Seven Crystal Systems: Overview
Crystallographic Point Groups
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Imperfections in Crystal Structure: Stoichiometric Point Defects
Imperfections in Crystal Structure: Point, Line and Plane Defects