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Related Concept Videos

Crystallographic Point Groups01:29

Crystallographic Point Groups

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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...
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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
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Determination of Crystal Structures

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In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Crystal Field Theory - Octahedral Complexes

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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...
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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
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Brillouin-zone database on the Bilbao Crystallographic Server.

Mois I Aroyo1, Danel Orobengoa1, Gemma de la Flor1

  • 1Departamento Física de la Materia Condensada, Universidad del País Vasco (UPV/EHU), Bilbao, Spain.

Acta Crystallographica. Section A, Foundations and Advances
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Summary

The Bilbao Crystallographic Server

Keywords:
Bilbao Crystallographic ServerBrillouin-zone databasereciprocal-space groups

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Area of Science:

  • Crystallography
  • Solid-state physics
  • Materials science

Background:

  • The Bilbao Crystallographic Server provides a comprehensive Brillouin-zone database.
  • This database includes k-vector tables and figures essential for classifying irreducible representations of space groups.

Purpose of the Study:

  • To present a classification of irreducible representations for all 230 space groups.
  • To compare this classification with existing schemes, such as Cracknell et al.'s.
  • To address issues of uniqueness and completeness in space-group representations.

Main Methods:

  • Utilizing k-vector tables and figures from the Brillouin-zone database.
  • Describing wavevector symmetry properties using reciprocal-space groups.
  • Specifying independent parameter ranges for general and special k vectors.

Main Results:

  • A detailed classification of irreducible representations for all 230 space groups.
  • A comparison with Cracknell et al.'s classification scheme.
  • Solutions for uniqueness and completeness problems in space-group representations.

Conclusions:

  • The Brillouin-zone database offers a robust framework for understanding space-group representations.
  • Recent updates enhance the database with new data for specific crystal systems.
  • The database serves as a valuable resource for researchers in crystallography and related fields.