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Related Concept Videos

Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Trends in Lattice Energy: Ion Size and Charge02:54

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:
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

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Updated: Jun 29, 2026

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
06:34

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

Vacancy diffusion in the triangular-lattice dimer model.

Monwhea Jeng1, Mark J Bowick, Werner Krauth

  • 1Department of Physics, Syracuse University, Syracuse, New York 13244, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Vacancy diffusion in a triangular-lattice dimer model shows localized single monomers and delocalized pairs. Anomalous diffusion (exponent β≈0.46) is observed for monomers and small clusters, driven by coordinated pair motion.

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Theoretical Calculation and Experimental Verification for Dislocation Reduction in Germanium Epitaxial Layers with Semicylindrical Voids on Silicon
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Investigating particle diffusion is crucial for understanding material properties.
  • Kinetic constraints significantly impact diffusion dynamics in lattice models.
  • The triangular-lattice dimer model provides a simplified yet relevant system for studying diffusion.

Purpose of the Study:

  • To analyze vacancy diffusion in the triangular-lattice dimer model with translation-only kinetic constraints.
  • To characterize the behavior of single monomers, pairs, and small clusters.
  • To identify the underlying mechanisms responsible for anomalous diffusion.

Main Methods:

  • Simulations of the triangular-lattice dimer model.
  • Analysis of monomer and cluster localization and diffusion.
  • Calculation of diffusion exponents and average cluster sizes.

Main Results:

  • Single vacancies (monomers) form localized treelike structures with an average size of 8.16 sites.
  • Monomer pairs exhibit delocalization and anomalous diffusion (β=0.46±0.06).
  • The same anomalous diffusion exponent governs clusters of 3-4 monomers and dimers at low monomer densities.

Conclusions:

  • Coordinated motion of monomer pairs is key to large-scale transport at low densities.
  • A "swap-tunneling" mechanism involving swap and glide moves facilitates monomer pair diffusion.
  • The study reveals fundamental insights into constrained diffusion and transport phenomena.