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Related Concept Videos

Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
Structures of Solids02:22

Structures of Solids

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...
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
Imagine taking a large number of identical...
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
Space Trusses01:25

Space Trusses

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...
Structural Isomerism02:34

Structural Isomerism

Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula. Structural isomerism of coordination compounds can be divided into two subcategories, the linkage isomers and coordination-sphere isomers.
Linkage isomers occur when the coordination compound contains a ligand that can bind to the transition metal center through two different atoms. For example, the CN− ligand can bind through the carbon atom or through the nitrogen atom. Similarly, SCN− can be...

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Three-periodic nets and tilings: edge-transitive binodal structures.

Olaf Delgado-Friedrichs1, Michael O'Keeffe, Omar M Yaghi

  • 1Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|August 24, 2006
PubMed
Summary

This study identifies 28 unique three-periodic nets, detailing their crystallographic properties and natural tilings. It explores site symmetry and coordination number restrictions, providing examples from crystal structures.

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Area of Science:

  • Crystallography
  • Materials Science
  • Network Theory

Background:

  • Three-periodic nets are fundamental in understanding crystal structures and porous materials.
  • Characterizing these nets is crucial for predicting material properties and designing new frameworks.

Purpose of the Study:

  • To systematically identify and classify three-periodic nets with specific vertex and edge configurations.
  • To describe the crystallographic properties and natural tilings of these identified nets.
  • To investigate constraints on site symmetry and coordination numbers within these nets and provide real-world examples.

Main Methods:

  • Enumeration and classification of three-periodic nets based on topological and geometric criteria.
  • Analysis of crystallographic properties including site symmetry and coordination numbers.
  • Examination of natural tilings and comparison with known crystal structures.

Main Results:

  • Identification of 28 distinct three-periodic nets featuring two types of vertices and one type of edge.
  • Detailed description of the crystallographic properties and natural tiling characteristics for each identified net.
  • Discussion of site symmetry and coordination number limitations, supported by examples from existing crystal structures.

Conclusions:

  • The study provides a comprehensive catalog of a specific class of three-periodic nets.
  • Understanding the properties and constraints of these nets aids in the rational design of crystalline materials.
  • The findings offer valuable insights for researchers in crystallography, materials science, and network topology.