Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Bewley Lattice Diagram

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.

Lattice Centering and Coordination Number

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...

Lattice Energies of Ionic Crystals

Lattice Energies of Ionic Crystals

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...

Structures of Solids

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...

Graphical Representation of Inequalities

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...

Trends in Lattice Energy: Ion Size and Charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Symmetric vertex- and edge-transitive 3-periodic nets.

Acta crystallographica. Section A, Foundations and advances·2026

Same author

Minimal-transitivity finite tangles and catenated polyhedra.

Acta crystallographica. Section A, Foundations and advances·2026

Same author

Towards a taxonomy of nets: supersymmetric 2- and 3-periodic structures in three-dimensional Euclidean space.

Acta crystallographica. Section A, Foundations and advances·2025

Same author

3-Periodic weavings: piecewise linear embeddings of symmetric structures.

Acta crystallographica. Section A, Foundations and advances·2025

Same author

Isogonal 1-periodic polycatenanes (chains). Transitivity and intransitivity of links.

Acta crystallographica. Section A, Foundations and advances·2025

Same author

Symmetric 3-periodic polycatenanes: catenated rings, polyhedra and rods.

Acta crystallographica. Section A, Foundations and advances·2025

Search research articles

Related Experiment Video

Updated: Jun 20, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Edge-transitive lattice nets.

Olaf Delgado-Friedrichs¹, Michael O'Keeffe

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

Acta Crystallographica. Section A, Foundations of Crystallography

|August 19, 2009

Summary

This study describes edge-transitive lattice nets, focusing on two- and three-periodic structures. Researchers identified simple density expressions for 2D nets and cataloged 13 families of 3D cubic, hexagonal, trigonal, and tetragonal lattice nets.

More Related Videos

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Related Experiment Videos

Last Updated: Jun 20, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Area of Science:

Crystallography
Materials Science
Geometry

Background:

Lattice nets are fundamental structures in understanding crystal packing and material properties.
Characterizing periodic nets is crucial for designing new materials with specific topological and physical attributes.

Purpose of the Study:

To describe two- and three-periodic lattice nets, specifically those that are edge-transitive.
To derive empirical expressions for the topological density of two-periodic nets.
To identify and classify infinite families of three-periodic lattice nets.

Main Methods:

Systematic enumeration and description of edge-transitive lattice nets.
Empirical derivation of mathematical expressions for topological density.
Classification of three-periodic nets into families based on symmetry and topology.

Main Results:

Description of several two- and three-periodic edge-transitive lattice nets.
Empirically derived simple expressions for the topological density of two-periodic nets.
Identification of thirteen infinite families of three-periodic cubic, hexagonal, trigonal, and tetragonal lattice nets.

Conclusions:

The study provides a comprehensive catalog of specific types of lattice nets.
The findings contribute to the topological classification of periodic nets.
This work can inform the design and understanding of crystalline materials.