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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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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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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
Metallic Solids02:37

Metallic Solids

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 malleability. Many...
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Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
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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 requirements are not imposed on the...

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Growing Protein Crystals with Distinct Dimensions Using Automated Crystallization Coupled with In Situ Dynamic Light Scattering
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From lumps to lattices: crystallized clusters made simple.

P Ziherl1, Randall D Kamien

  • 1Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia. primoz.ziherl@ijs.si

The Journal of Physical Chemistry. B
|March 16, 2011
PubMed
Summary
This summary is machine-generated.

This study reinterprets cluster mesophases in colloids using a minimal model. The research successfully rederived key properties and extended clustering criteria to include hard cores, impacting cluster formation at low densities.

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Area of Science:

  • Colloid science
  • Soft matter physics
  • Statistical mechanics

Background:

  • Colloids with soft shoulder-like repulsive interactions exhibit complex cluster mesophases.
  • Existing clustering criteria do not fully account for the influence of hard cores.

Purpose of the Study:

  • To reinterpret cluster mesophase features using a minimal model.
  • To rederive lattice spacing, binding energy, and phase diagrams.
  • To extend the clustering criterion to incorporate hard-core effects.

Main Methods:

  • Utilizing a minimal model based on continuum theory.
  • Analyzing a two-dimensional hard-core/square-shoulder ensemble.
  • Extending a previously established clustering criterion.

Main Results:

  • Successfully reinterpreted main features of cluster mesophases.
  • Lattice spacing, binding energy, and phase diagram were rederived.
  • The extended clustering criterion now includes hard-core effects.

Conclusions:

  • The minimal model effectively explains cluster mesophase behavior.
  • Hard cores play a crucial role in precluding cluster formation at low densities.
  • The extended criterion provides a more comprehensive understanding of colloidal clustering.