Density of vibrational states in glasses

Abstract

A theory of the vibrational spectra of glasses, based on allowance for the statistical fluctuations of the local elastic constants, is proposed. The existence is established of two characteristic energies h, and h, , dividing the spectrum into regions of qualitatively different behavior of the density of states n (h). At low frequencices w 4 w, the increase of the density of states is determined by the additive contributions of phonons and mutually noninteracting quasilocal vibrations in random soft atomic potentials in the glass. In the intermediate region w , 5 w 5 w, the quasilocal vibrations interact strongly with phonons, and this makes their contributions superadditive. For w > w, the growth of n (h) slows down. As a result, n (h) increases at first more rapidly and then more slowly than the Debye density of states. An analytical expression for n (h) is obtained in the T-matrix formalism in the region w <a,, including the region of strong scattering. A numerical calculation of n (h) is performed in the coherent-potential approximation. The theory predicts qualitatively universal behavior of n (h) in different glasses.