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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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Weak Base Solutions03:21

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Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
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Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...
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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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Bewley Lattice Diagram01:12

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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.
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Weak acids and bases do not undergo dissociation completely, and titrations between these two are rarely studied. When such studies are performed, say, for the titration of a weak acid with a weak base, the titration curve plots the change in pH as a function of the volume of base added. Take the titration of acetic acid with ammonia, for instance. During the titration, these two species form ammonium acetate and water, but the pH change is slow and gradual.
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Related Experiment Video

Updated: Feb 7, 2026

Visualizing Surface T-Cell Receptor Dynamics Four-Dimensionally Using Lattice Light-Sheet Microscopy
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Disorder-free weak dynamic localization in deformable lattices.

Alexander V Savin1, Yuri S Kivshar2, Mario I Molina3

  • 1Semenov Institute of Chemical Physics, Russian Academy of Science, Moscow 117977, Russia.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 4, 2018
PubMed
Summary

Electron transport in deformable lattices shows weak dynamic localization due to electron-phonon interactions. Thermal disorder prevents Anderson localization, revealing transitions between ballistic, diffusive, and soliton regimes based on temperature and nonlinearity.

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Area of Science:

  • Condensed matter physics
  • Theoretical physics
  • Materials science

Background:

  • Electron transport is crucial for material properties.
  • Phonons (lattice vibrations) can influence electron behavior.
  • Nonlinearity in lattice dynamics can lead to complex phenomena.

Purpose of the Study:

  • To investigate electron transport in a deformable lattice.
  • To understand the role of acoustic phonons and nonlinearity.
  • To determine the conditions for electron localization.

Main Methods:

  • Semiclassical approximation for electron transport.
  • Modeling the lattice as a discrete nonlinear elastic chain.
  • Analyzing thermal equilibrium of acoustic phonons at temperature T.

Main Results:

  • Thermalized phonons induce dynamic disorder, insufficient for Anderson localization.
  • Weak nonlinearity leads to a ballistic-to-diffusive transition with increasing temperature.
  • Strong nonlinearity shows a transition from localized solitons to diffusive transport with increasing temperature.

Conclusions:

  • Electron-phonon interaction causes weak, temperature-dependent dynamic localization.
  • The system exhibits distinct transport regimes (ballistic, diffusive, soliton) based on nonlinearity and temperature.
  • Anderson localization is not observed under these conditions.