Vibrations and relaxations in a soft sphere glass: boson peak and structure factors

Abstract

The dynamics of a soft sphere model glass, studied by moleculardynamics, is investigated. The vibrational density of states divided byω2 shows a pronounced boson peak. Its shape is in agreement with the universal form derivedfor soft oscillators interacting with sound waves. The excess vibrations forming the bosonpeak have mainly transverse character. From the dynamic structure factor in the Brillouinregime pseudo dispersion curves are calculated. Whereas the longitudinal phonons are welldefined up to the pseudo zone boundary the transverse ones rapidly get over-dampedand go through the Ioffe–Regel limit near the boson peak frequency. In the highq regimeconstant-ω scans of the dynamic structure factor for frequencies around the boson peak areclearly distinct from those for zone boundary frequencies. Above the Brillouinregime, the scans for the low frequency modes follow closely the static structurefactor. This still holds after a deconvolution of the exact harmonic eigenmodes intolocal and extended modes. Also the structure factor for local relaxations at finitetemperatures resembles the static one. This semblance between the structurefactors mirrors the collective motion of chain-like structures in both low frequencyvibrations and atomic hopping processes, observed in the earlier investigations.