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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

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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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Ionic Crystal Structures

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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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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,...
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Lattice Centering and Coordination Number02:33

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Metallic Solids

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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Updated: Jan 13, 2026

Fabrication of Spatially Confined Complex Oxides
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Published on: July 1, 2013

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Exploring oxide quasicrystals in internal space.

Sebastian Schenk1, Martin Haller1, Stefan Förster1

  • 1Institute of Physics, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany.

Acta Crystallographica. Section A, Foundations and Advances
|January 9, 2026
PubMed
Summary
This summary is machine-generated.

Researchers quantitatively assessed quasicrystal structural quality using scanning tunneling microscopy. They analyzed internal space and found acceptance domains increase logarithmically, revealing phason disorder in oxide quasicrystals (OQCs).

Keywords:
hyperspaceparallel spaceperpendicular spacephason elastic constantphason flipsquasicrystalsrandom tilingtiling analysis

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Crystallography

Background:

  • Quantitative assessment of quasicrystal structural quality is challenging.
  • Diffraction techniques are limited to coherently scattering regions.
  • Diffuse scattering and local imaging offer insights into inhomogeneities and tiling.

Purpose of the Study:

  • To analyze atomically resolved scanning tunneling microscopy (STM) images of dodecagonal oxide quasicrystal (OQC) systems.
  • To investigate the internal space perspective for structural analysis.
  • To determine effective phason elastic constants and assess phason disorder.

Main Methods:

  • Atomically resolved scanning tunneling microscopy (STM) imaging.
  • Uplifting 2D coordinates to a 4D hyperspace for analysis in internal and physical spaces.
  • Statistical evaluation of tiling elements and acceptance domain expansion.

Main Results:

  • The quasicrystal acceptance domain in internal space increases logarithmically with system size for all three OQCs studied.
  • Effective phason elastic constants were determined from the acceptance domain expansion.
  • Phason disorder within the square-triangle-rhombus tiling was quantified.

Conclusions:

  • Inspecting the internal space provides a sensitive perspective for quasicrystal structural analysis.
  • STM imaging and 4D hyperspace analysis enable quantitative assessment of phason disorder.
  • The findings offer a new method for evaluating the structural quality of oxide quasicrystals.