Similarity of the Boson Peaks in Disordered Systems to the van Hove Singularities in Regular Crystals

Phonon spectra of solid substitutional solutions with finite concentrations of impurities were analyzed on the microscopic level. The local phonon densities of impurity atoms were calculated, in particular the formation of quasilocal vibrations and their evolution with increasing of the concentration of impurities were investigated. Modification of the local spectral densities of atoms of the host lattice by impurities and manifestation of the phonon Ioffe-Regel crossover (scattering of fast propagating phonons on quasi-localized vibrations) were analyzed. It is shown that such scattering causes the manifestation of the features such as "boson peak" in the phonon spectrum of solid substitutional solutions. A commonality of the physical nature of such singularities in disordered structures and van Hove singularities in ideal crystals was established, notably, reducing of the group velocity of acoustic phonons due to their scattering on slow phonons.