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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.
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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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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.
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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.
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Crystal Field Theory
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Ring structure of selected two-dimensional procrystalline lattices.

David Ormrod Morley1, Andrew L Goodwin2, Mark Wilson1

  • 1Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.

Physical Review. E
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Procrystalline lattices, lacking translational symmetry but possessing underlying order, exhibit unique ring distributions and assortativities. These systems display fundamentally different behaviors compared to traditional disordered and crystalline materials.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Network Theory

Background:

  • Introduction of the term "procrystalline" for systems with high-symmetry lattices but no translational symmetry.
  • Existing research often focuses on fully ordered crystalline or completely disordered systems.

Purpose of the Study:

  • To investigate the properties of five two-dimensional (2D) procrystalline lattices.
  • To analyze ring topologies, size distributions, and assortativities within these lattices.
  • To compare procrystalline behavior with traditional disordered and crystalline systems.

Main Methods:

  • Generation of configurations using a Monte Carlo algorithm for lattices with coordination numbers four, five, and six.
  • Analytical derivation of ring size distributions for square and trihexagonal nets.
  • Comparison of distributions with a maximum entropy method and analysis against the Lemaître curve.
  • Calculation of assortativities to quantify ring ordering.

Main Results:

  • Procrystalline lattices generate varied ring distributions influenced by underlying lattice constraints.
  • Three lattices deviate from the near-universal Lemaître curve, indicating unique topological properties.
  • Procrystalline systems exhibit systematically higher assortativities than those from standard bond-switching methods.
  • Distinctive behavior in ring size distributions and assortativities compared to crystalline motifs.

Conclusions:

  • Procrystalline lattices possess fundamentally different characteristics than traditional disordered and crystalline systems.
  • The partial ordering of underlying lattices significantly impacts topological properties and ordering of rings.
  • These findings highlight procrystalline structures as a distinct class of materials with unique ordering principles.