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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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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:
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Polymers02:34

Polymers

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The word polymer is derived from the Greek words “poly” which means “many” and “mer” which means “parts”. Polymers are long chains of molecules composed of repeating units of smaller molecules, known as monomers. They either occur naturally, such as DNA and proteins, or can be constructed synthetically, like plastics. They have varied structural characteristics, such as linear chains, branched chains, or complex networks, that contribute to the...
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A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial concentration of acid. For example, 0.20 M hydrobromic acid will dissociate completely in water and produces 0.20 M of hydronium ions and 0.20 M of bromide ions.
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Updated: Feb 14, 2026

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Strong Cosserat Elasticity in a Transversely Isotropic Polymer Lattice.

Z Rueger1, R S Lakes1

  • 1Department of Engineering Physics, Department of Materials Science, University of Wisconsin, Madison, Wisconsin 53706-1687, USA.

Physical Review Letters
|February 27, 2018
PubMed
Summary

Large size effects in triangular lattices show significant increases in torsion and bending rigidity, consistent with Cosserat elasticity. These findings reveal a path to achieving substantial nonclassical mechanical effects in lattice structures.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Continuum Mechanics

Background:

  • Classical elasticity theory does not account for size effects in lattice structures.
  • Nonclassical phenomena, such as those described by Cosserat elasticity, are crucial for understanding complex material behaviors.
  • Previous studies on stretch-dominated lattices showed smaller nonclassical effects.

Purpose of the Study:

  • To experimentally quantify large size effects in triangular unit cell lattices.
  • To investigate the consistency of observed phenomena with Cosserat elasticity.
  • To explore the potential for achieving significant nonclassical mechanical effects in lattice structures.

Main Methods:

  • Experimental measurement of torsion and bending rigidity in triangular unit cell lattices.
  • Analysis of results in the context of classical and Cosserat elasticity theories.
  • Determination of Cosserat characteristic lengths for torsion and bending.

Main Results:

  • Observed a factor of 36 increase in torsion rigidity and 29 in bending rigidity due to size effects.
  • Cosserat characteristic lengths (ℓt = 9.4 mm, ℓb = 8.8 mm) were comparable to the unit cell size.
  • Nonclassical effects were significantly stronger than in previously studied stretch-dominated lattices.

Conclusions:

  • Large size effects are experimentally validated in triangular lattices, aligning with Cosserat elasticity.
  • The lattice structure facilitates the realization of substantial nonclassical mechanical behaviors.
  • Cosserat elasticity provides a suitable framework for describing the observed large size effects in these lattices.