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Related Concept Videos

π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...
π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds01:14

π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds

In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as annulenes. In...
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:
Debye–Huckel–Onsager Conductance Equation01:28

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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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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...
Lattice Energies of Ionic Crystals01:27

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...

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Dimensional Effect on the Lattice Anharmonicity in Graphene and Graphite.

Xiao-Ping Yao1,2, Yu-Wen Zhang1,2, Han-Pu Liang3

  • 1Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo, China.

Small (Weinheim an Der Bergstrasse, Germany)
|July 3, 2026
PubMed
Summary

Dimensionality reduction in graphene unexpectedly enhances phonon anharmonicity, leading to broader phonon linewidths. This effect, driven by increased phonon population and anharmonicity in flexural acoustic phonons, challenges conventional expectations.

Keywords:
anharmonic broadeningdimensionality effectgraphene and graphitelattice anharmonicity

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid-State Physics

Background:

  • Dimensionality reduction typically slows phonon anharmonic decay by reducing phase space for interactions.
  • The Raman-active E2g phonon in graphene exhibits anharmonic scattering behavior that deviates from this expectation when compared to graphite.

Purpose of the Study:

  • To investigate the reasons behind the anomalous anharmonic scattering behavior of phonons in graphene compared to graphite.
  • To elucidate the role of dimensionality in lattice anharmonicity within the graphene-graphite system.

Main Methods:

  • Systematic theoretical analysis of phonon-phonon interactions.
  • Investigation of phonon population and anharmonicity in flexural acoustic (ZA) phonons.
  • Analysis of interlayer coupling effects on phonon anharmonicity in graphite.

Main Results:

  • Dimensionality reduction in graphene enhances both phonon population and anharmonicity of ZA phonons.
  • This enhancement overrides the reduced scattering phase space, resulting in a broader phonon linewidth.
  • Phonon anharmonicity in graphite's ZA phonons can be tuned by altering interlayer coupling.

Conclusions:

  • The study provides fundamental insights into lattice anharmonicity and the critical role of dimensionality.
  • The findings highlight how dimensionality reduction can lead to unexpected increases in phonon anharmonicity.