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In this Lecture, we introduce the notion of the Brillouin zonesBrillouinzone of the inverse latticeLatticeinverse lattice and consider the behavior of the group velocityVelocitygroup velocity on the zone’s boundary. We discuss the density of the phonon states in general case and in the Debye approximationApproximationDebye approximationDebyeDebye approximation. We analyze Van Hove singularities in the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum for crystals of different spatial dimensions. We consider one-dimensional chain with two atoms in the elementary cellCellelementary cell and illustrate an emergence of acoustic and optical branches of the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum in it.

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Lecture 7. Density of the Phonon States. Debye Approximation

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  • 发表日期：

    2026年

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  • Maxim Kagan

摘要

In this Lecture, we introduce the notion of the Brillouin zonesBrillouinzone of the inverse latticeLatticeinverse lattice and consider the behavior of the group velocityVelocitygroup velocity on the zone’s boundary. We discuss the density of the phonon states in general case and in the Debye approximationApproximationDebye approximationDebyeDebye approximation. We analyze Van Hove singularities in the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum for crystals of different spatial dimensions. We consider one-dimensional chain with two atoms in the elementary cellCellelementary cell and illustrate an emergence of acoustic and optical branches of the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum in it.