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Band Theory02:35

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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
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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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There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Phononic band gap in random spring networks.

Kezhao Xiong1,2, Jie Ren3, Fabio Marchesoni3,4

  • 1Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China.

Physical Review. E
|November 18, 2023
PubMed
Summary
This summary is machine-generated.

We found a pseudodispersion relation to predict transitions in vibrational modes for networked materials. This allows controlling phonon and elastic wave propagation by tuning network properties like degree and assortativity.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Network Science

Background:

  • Understanding the interplay between topology and dynamics in disordered materials is crucial.
  • Predicting vibrational properties, such as phonon localization, remains a challenge.

Purpose of the Study:

  • To investigate the relationship between topological and vibrational properties in networked materials.
  • To develop a method for controlling phonon and elastic wave propagation.
  • To explore applications in phonon band engineering and energy harvesting.

Main Methods:

  • Numerical and analytical analysis of a random spring network model.
  • Establishment of a pseudodispersion relation.
  • Investigation of network parameters like average degree and assortativity.

Main Results:

  • A pseudodispersion relation was established, predicting transitions from extended to localized vibrational modes.
  • Phonon band gaps can be enhanced by increasing average degree or decreasing assortativity.
  • Demonstrated control over phonon and elastic wave propagation in disordered networks.

Conclusions:

  • Topological properties significantly influence vibrational modes in networked materials.
  • The pseudodispersion relation offers a predictive tool for material design.
  • Proposed methods provide avenues for advanced phonon band engineering and vibrational energy harvesting.