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IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
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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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Localisation of vibrational modes in high-entropy oxides.

C M Wilson1, R Ganesh1, D A Crandles1

  • 1Department of Physics, Brock University, St. Catharines, Ontario L2S 3A1, Canada.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 4, 2024
PubMed
Summary

High-entropy oxides (HEOs) exhibit unique disorder and localized vibrational excitations. This study explores phonon localization in a prototypical HEO, revealing wave-like and localized modes, and suggesting HEOs as a platform for Anderson localization studies.

Keywords:
Anderson localisationhigh-entropy oxideslattice dynamicsphonons

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Area of Science:

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

Background:

  • High-entropy oxides (HEOs) present a novel class of materials with both crystalline order and significant atomic disorder.
  • Disordered solids like glasses and alloys are known to exhibit localized vibrational excitations.
  • Understanding phonon behavior in HEOs is crucial for their technological applications.

Purpose of the Study:

  • To investigate the phenomenon of disorder-induced phonon localization in the prototypical rock-salt structured HEO, Mg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$O.
  • To model and analyze the phononic excitation spectrum of this HEO.
  • To explore strategies for enhancing phonon localization in HEOs.

Main Methods:

  • Developed a model for cation-oxygen interatomic potentials by fitting to parent binary oxide properties.
  • Validated the model against experimental crystal structure and optical conductivity data.
  • Analyzed the phonon spectrum, including participation ratio and correlation amplitude, to identify localized modes.

Main Results:

  • The phonon spectrum of the HEO exhibits wave-like propagating modes at low energies and localized modes at high energies.
  • Signatures of localization, such as participation ratio and correlation amplitude, were identified.
  • A hypothetical high-entropy telluride-oxide demonstrated enhanced localization with additional modes in the mid-spectrum.

Conclusions:

  • Disorder in HEOs can induce localized vibrational excitations, distinct from traditional disordered materials.
  • Increasing mass disorder offers a route to enhance phonon localization in HEOs.
  • HEOs serve as a promising experimental platform for studying Anderson localization of phonons.