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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.
Types of Unit Cells
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The Seven Crystal Systems: Overview01:24

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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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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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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 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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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...
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Polydispersed rods on the square lattice.

Jürgen F Stilck1, R Rajesh2

  • 1Instituto de Física and National Institute of Science and Technology for Complex Systems, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-346-Niterói, RJ, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This study on hard polydispersed rods found no disordered phase at high density. Critical behavior aligns with the Ising universality class, differing from monodispersed systems.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Phase transitions

Background:

  • Understanding phase transitions in systems with varying particle sizes is crucial.
  • Hard polydispersed rods on a lattice provide a simplified model for complex fluid behavior.

Purpose of the Study:

  • To investigate the phase behavior of hard polydispersed rods on a square lattice.
  • To determine the critical line between isotropic and nematic phases.
  • To compare the phase transitions with monodispersed rod systems.

Main Methods:

  • Grand-canonical ensemble calculations.
  • Transfer matrix technique.
  • Finite-size scaling analysis.

Main Results:

  • A critical line separating isotropic and nematic phases was identified.
  • No second transition to a disordered phase was observed at high densities.
  • Critical exponents and central charge were estimated.

Conclusions:

  • The behavior of polydispersed rods differs from monodispersed rods, notably lacking a high-density disordered phase.
  • The observed critical phenomena are consistent with the Ising universality class.