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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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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Contractile rings are composed of microfilaments and are responsible for separating the daughter cells during cytokinesis. Contractile ring assembly proceeds along with other cell cycle events; however, very few mechanistic details are known about the timing and coordination of the contractile rings with the cell cycle.
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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 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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Three-dimensional patchy lattice model: ring formation and phase separation.

J M Tavares1, N G Almarza2, M M Telo da Gama3

  • 1Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal and Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal.

The Journal of Chemical Physics
|February 12, 2015
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Summary
This summary is machine-generated.

We studied particle self-assembly using simulations and theory, finding that particle geometry significantly impacts phase diagrams and structure. Unusual behavior near critical points is linked to ring formation.

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Area of Science:

  • Statistical mechanics
  • Soft matter physics
  • Computational chemistry

Background:

  • Understanding particle self-assembly is crucial for designing materials with targeted properties.
  • The phase behavior of associating particles is complex and depends on interaction parameters and geometry.
  • Existing theories may not fully capture systems with significant ring formation.

Purpose of the Study:

  • To investigate the structural and thermodynamic properties of a lattice model with specific particle patch configurations.
  • To explore the competition between chain, ring, and network self-assembly on the phase diagram.
  • To analyze the influence of interaction ratios and patch angles on system behavior.

Main Methods:

  • Utilized an extension of Wertheim's theory for associating fluids.
  • Employed Monte Carlo numerical simulations for systematic investigation.
  • Varied the ratio of interaction energies (r = εAB/εAA) and the angle (θ) between A patches.

Main Results:

  • Both interaction ratio (r) and A patch angle (θ) profoundly affect the phase diagram.
  • A reentrant phase diagram with a closed miscibility loop was observed in the empty fluid regime (r < 1/2).
  • Unusual behavior near the lower critical point is attributed to the formation of short rings.

Conclusions:

  • The geometry of associating particles, specifically the angle between interaction sites, plays a critical role in determining self-assembly pathways and phase behavior.
  • Theoretical models show excellent agreement with simulations for specific geometries (θ = 120°) but require refinement for others.
  • Further theoretical development is needed to accurately describe systems dominated by small ring structures.