Anharmonic elasticity theory for sound attenuation in disordered solids with fluctuating elastic constants

Sound attenuation and anharmonic damping in solids with correlated disorder

We study via self-consistent Born approximation a model for sound waves in a disordered environment, in which the local fluctuations of the shear modulus G are spatially correlated with a certain correlation length The theory predicts an enhancement of the density of states over Debye's omega(2) law (boson peak) whose intensity increases for increasing correlation length, and whose frequency position is shifted downwards as lg. Moreover, the predicted disorder-induced sound attenuation coefficient r(k) obeys a universal scaling law F(k) = f (ke) for a given variance of G. Finally, the inclusion of the lowest-order contribution to the anharmonic sound damping into the theory allows us to rec…

Replica field theory for anharmonic sound attenuation in glasses

Abstract A saddle-point treatment of interacting phonons in a disordered environment is developed. In contrast to crystalline solids, anharmonic attenuation of density fluctuations becomes important in the hydrodynamic regime, due to a broken momentum conservation. The variance of the shear modulus Δ2 turns out to be the strength of the disorder enhanced phonon–phonon interaction. In the low-frequency regime (below the boson peak frequency) we obtain an Akhiezer-like sound attenuation law Γ ∝ Τω2. Together with the usual Rayleigh scattering mechanism this yields a crossover of the Brillouin linewidth from a ω2 to a ω4 regime. The crossover frequency ωc is fully determined by the boson peak …

Vibrational excitations in systems with correlated disorder

We investigate a $d$-dimensional model ($d$ = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's $\omega^{d-1}$ law (``boson peak'') as a result of disorder. This anomay becomes reinforced for increasing correlation length $\xi$. The theory predicts that $\xi$ times the width of the Brillouin line should be a universal …

High-frequency vibrational density of states of a disordered solid.

We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.