Normal modes, and acoustic properties, of an elastic solid with line defects

Abstract

The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. As in amorphous materials, the attenuation as a function of frequency $\omega$ behaves as ${\omega }^4$ for low frequencies, and, as frequency increases, crosses over to ${\omega }^2$ and then to linear in $\omega$. Dispersion is negative in the frequency range where attenuation is quartic and quadratic in frequency. Explicit formulae are provided that relate these properties to the density of string states. { Continuum mechanics can thus be applied both to crystalline materials and their amorphous counterparts at similar length scales.} The possibility of linking this model with the microstructure of amorphous materials is discussed.

References in corpus (18)

• String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid
• Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
• Local elasticity map and plasticity in a model Lennard-Jones glass
• Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
• Continuum limit of amorphous elastic bodies (III): Three dimensional systems
• Inhomogeneous elastic response of silica glass
• The evolution of vibrational excitations in glassy systems
• Glass-specific behavior in the damping of acoustic-like vibrations
• Quantum hydrodynamics
• Anomalous properties of the acoustic excitations in glasses on the mesoscopic length-scale
• The Ioffe-Regel criterion and diffusion of vibrations in random lattices
• Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass
• Continuum limit of amorphous elastic bodies (II): Response to a point source
• Two-Gaussian excitations model for the glass transition
• Ultrasound as a probe of dislocation density in aluminum
• Universal Sound Absorption in Amorphous Solids: A Theory of Elastically Coupled Generic Blocks
• Atomistic Simulations of Elastic and Plastic Properties in Amorphous Silicon
• Measuring Dislocation Density in Aluminum with Resonant Ultrasound Spectroscopy

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• Clustering of negative topological charge precedes plastic failure in 3D glasses
• Stringlet Excitation Model of the Boson Peak
• Elastic anomalies in glasses: the string theory understanding in the case of Glycerol and Silica
• Phonons in stringlet-land and the boson peak
• Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations