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Ionic Crystal Structures02:42

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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Structures of Solids02:22

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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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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.
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Metallic Solids02:37

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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Crystal Field Theory
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Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
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Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry.

Andrew J Archer1, Tomonari Dotera2, Alastair M Rucklidge3

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Researchers designed new aperiodic tilings with hexagonal symmetry using rectangles and triangles. This advances the design of general quasicrystals in soft matter systems beyond common dodecagonal types.

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Area of Science:

  • Materials Science
  • Crystallography
  • Soft Matter Physics

Background:

  • Aperiodic tilings, like Penrose tilings, exhibit non-repeating patterns with specific symmetries.
  • Most quasicrystals in soft matter display dodecagonal symmetry.
  • Designing novel quasicrystalline structures is crucial for advanced materials.

Purpose of the Study:

  • To investigate aperiodic tilings with hexagonal symmetry using rectangle and triangle tiles.
  • To demonstrate the design of soft-matter systems forming stable aperiodic states with these tilings.
  • To explore general quasicrystal design beyond dodecagonal symmetry.

Main Methods:

  • Utilized pair potentials with two length scales to guide particle interactions.
  • Designed soft-matter systems capable of self-assembling into specific aperiodic tilings.
  • Investigated tilings composed of rectangles and two types of equilateral triangles.

Main Results:

  • Successfully designed soft-matter systems forming stable aperiodic states with hexagonal symmetry.
  • Identified two distinct rectangle-triangle tiling examples, including the bronze-mean tiling.
  • Demonstrated the formation of aperiodic structures beyond dodecagonal symmetry.

Conclusions:

  • Soft-matter systems can be engineered to form novel aperiodic tilings with hexagonal symmetry.
  • This research provides a pathway for designing more general quasicrystals in soft matter.
  • The findings expand the possibilities for quasicrystal structures in materials science.