Localized low-frequency dynamics in SiO2 glass

Abstract

We have carried out ab initio molecular orbital calculations on a cluster of atoms modeling the medium-range structure in SiO2 glass to investigate its low-frequency vibrational properties. The model cluster is composed of several types of n-membered silica rings (n=3, 4, 5, and 6), and its geometry was completely optimized at the Hartree–Fock/3-21G(*) level. We have shown that the optimized structural parameters (the average Si–O, O–O, and Si–Si bond distances Si–O–Si and O–Si–O bond angles) are in good agreement with the observed ones. The three- and four-membered rings resulted in regular geometries, namely, a nearly planar and a puckered configuration, respectively, whereas the optimized geometries of the five- and six-membered rings were rather distorted. The frequency calculations on the cluster have demonstrated that relative rotations of the SiO4 tetrahedra occur in the low-frequency (⩽150 cm−1) vibrational region. The calculated vibrational density of states exhibits a maximum at ∼45 cm−1 that matches the observed “boson peak” of SiO2 glass. These rotational motions of the SiO4 tetrahedra have shown to be localized in the four-, five-, and six-membered rings, and the resonant frequencies increase with decreasing ring size. We have also found that collective rotations of the SiO4 tetrahedra exhibit transverse-type acoustic modes. These localized dynamics on the medium-range length scale is a possible mechanism for the anomalous low-frequency harmonic excitations in SiO2 glass called the boson peak.