Relation between the boson peak in glasses and van Hove singularity in crystals

Abstract

We analysed the relation between the boson peak in glasses and the van Hove singularity in crystals. The comparison of the experimental results obtained for amorphous iron to the published data for two different iron crystals suggests that the appearance of the pseudo-Brillouin zone with corresponding flattening of the dispersion relations and the resulting boson peak in glasses are the fundamental effects caused by a finite and well-defined value of interatomic distance, i.e. simply by an atomistic character of nature. Accordingly, the Brillouin zone and the van Hove singularities in crystals can be considered as the crystalline counterparts, or ‘derivatives’, of these ‘glassy’ quantities. In addition, we analyse the options for observing the excess states in glasses caused by another effect, i.e. by phonon scattering. Possibly, this is indeed seen in the reduced DOS of ambient silica glass and amorphous iron in the 1–2 meV energy range.