The Ioffe-Regel criterion and diffusion of vibrations in random lattices

Abstract

We consider diffusion of vibrations in 3d harmonic lattices with strong force-constant disorder. Above some frequency w_IR, corresponding to the Ioffe-Regel crossover, notion of phonons becomes ill defined. They cannot propagate through the system and transfer energy. Nevertheless most of the vibrations in this range are not localized. We show that they are similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B 79, 1715 (1999) to describe heat transport in glasses. The crossover frequency w_IR is close to the position of the boson peak. Changing strength of disorder we can vary w_IR from zero value (when rigidity is zero and there are no phonons in the lattice) up to a typical frequency in the system. Above w_IR the energy in the lattice is transferred by means of diffusion of vibrational excitations. We calculated the diffusivity of the modes D(w) using both the direct numerical solution of Newton equations and the formula of Edwards and Thouless. It is nearly a constant above w_IR and goes to zero at the localization threshold. We show that apart from the diffusion of energy, the diffusion of particle displacements in the lattice takes place as well. Above w_IR a displacement structure factor S(q,w) coincides well with a structure factor of random walk on the lattice. As a result the vibrational line width Gamma(q)=D_u q^2 where D_u is a diffusion coefficient of particle displacements. Our findings may have important consequence for the interpretation of experimental data on inelastic x-ray scattering and mechanisms of heat transfer in glasses.

arXiv comment23 pages, 22 figures

References in corpus (25)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• The Kernel Polynomial Method
• Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
• Continuum limit of amorphous elastic bodies (III): Three dimensional systems
• Glass-specific behavior in the damping of acoustic-like vibrations
• Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy
• Anomalous properties of the acoustic excitations in glasses on the mesoscopic length-scale
• Bosonic Excitations in Random Media
• The Boson Peak and its Relation with Acoustic Attenuation in Glasses
• Electron-phonon interaction in the t-J model
• Energy transport in jammed sphere packings
• Heat transport in model jammed solids
• Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass
• Soft modes and elasticity of nearly isostatic lattices: randomness and dissipation
• Excess Modes in the Vibrational Spectrum of Disordered Systems and the Boson Peak
• Vibrations and Relaxations in a Soft Sphere Glass: Boson Peak and Structure Factors
• Vibrations in glasses and Euclidean Random Matrix theory
• Interaction of quasilocal harmonic modes and boson peak in glasses
• Frenkel-Kontorova Model of Vacancy-Line Interactions on Ga/Si(112): Formalism
• Dynamics of SiO${}_2$ glasses
• The dynamical structure factor in disordered systems
• Sparse random matrices and vibrational spectra of amorphous solids
• Vector vibrations and the Ioffe-Regel crossover in disordered lattices
• Density of states in random lattices with translational invariance
• Vibrational behaviour of a realistic amorphous-silicon model

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