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Related Concept Videos

Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral 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,...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
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...
Unit Cells01:18

Unit Cells

A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...

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Related Experiment Video

Updated: Jul 7, 2026

Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source
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Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source

Published on: April 23, 2021

Higher-dimensional point groups in superspace crystallography.

A Janner1

  • 1Theoretical Physics, Radboud University Nijmegen, Toernooiveld 1, Nijmegen, The Netherlands. a.janner@science.ru.nl

Acta Crystallographica. Section A, Foundations of Crystallography
|February 21, 2008
PubMed
Summary
This summary is machine-generated.

Extending superspace crystallography to higher dimensions can solve complex crystallographic puzzles. This approach includes finite subgroups of O(n), offering new explanations for biomacromolecules and viral capsids.

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Last Updated: Jul 7, 2026

Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source
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Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source

Published on: April 23, 2021

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Microcrystallography of Protein Crystals and In Cellulo Diffraction

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Area of Science:

  • Crystallography
  • Structural Biology
  • Mathematical Physics

Background:

  • Current crystallography models struggle with complex structures like biomacromolecules and viral capsids.
  • Integral indexing and scaling present significant challenges within existing crystallographic frameworks.

Purpose of the Study:

  • To propose an extension of (n,d)-dimensional superspace crystallography.
  • To address crystallographic puzzles not explained by current methods, including integral indexing and scaling.
  • To incorporate finite subgroups of the higher-dimensional orthogonal group O(n).

Main Methods:

  • Extending (n,d)-dimensional superspace crystallography.
  • Including finite subgroups of O(n) beyond those restricted by physical dimension d.
  • Applying the extended framework to axial-symmetric biomacromolecules and icosahedral viral capsids.

Main Results:

  • The extended superspace crystallography framework offers potential solutions for integral indexing and scaling problems.
  • This approach provides a theoretical basis for understanding complex crystallographic structures.
  • Demonstrates the applicability to axial-symmetric biomacromolecules and icosahedral viral capsids.

Conclusions:

  • The proposed extension of superspace crystallography can resolve current limitations in the field.
  • Incorporating higher-dimensional orthogonal groups enhances the explanatory power of crystallographic models.
  • This framework opens new avenues for studying complex biological macromolecules and viral structures.