Vector vibrations and the Ioffe-Regel crossover in disordered lattices

Abstract

The spectral density for vector vibrations in the f.c.c. lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and compared with that for electrons. The weak-scattering regime for external long-wavelength vibrational plane waves is shown to be due to sum-rule correlations in the dynamical matrix. A secondary peak below the Brillouin peak for sufficiently large wavevectors is found for the lattice models. The results obtained are supported by precise numerical solutions.

21 pages, 13 figures

References in corpus (4)

• Vibrational spectrum of topologically disordered systems
• Excess Modes in the Vibrational Spectrum of Disordered Systems and the Boson Peak
• Disorder-induced zero-energy spectral singularity for random matrices with correlations
• Nature of vibrational eigenmodes in topologically disordered solids

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• Atomic vibrations in disordered systems: Comparison of disordered diamond lattices and a realistic amorphous silicon model