The Ioffe-Regel criterion and diffusion of vibrations in random lattices
arXiv:1210.2257 · doi:10.1103/PhysRevB.87.134203
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.
23 pages, 22 figures
References in corpus (7)
- Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
- The Kernel Polynomial Method
- Electron-phonon interaction in the t-J model
- Energy transport in jammed sphere packings
- Sparse random matrices and vibrational spectra of amorphous solids
- Density of states in random lattices with translational invariance
- Vibrational behaviour of a realistic amorphous-silicon model