Low-frequency vibrational mode anomalies and glass transition: Thermal stability, phonon scattering, and pressure effects

The relationship between the excess of low-frequency vibrational modes observed in glasses and the stability against thermal fluctuations is explored. Such study is performed by calculating the correlation of atomic displacements inside the glass. As a result, it is proved that thermal stability requires that modes present in the boson or floppy peak (due to the flexibility or rigidity of the glass atomic network) should be localized or strongly scattered. The glass transition is thus determined by the size of the quadratic mean displacement. Also, the 2/3 relationship between melting and glass transition temperature is shown to have its origins in the differences between the mean-free path of phonons due to scattering. The size of this scattering is estimated using the Boson peak frequency and sound velocity. Finally, the change in the glass transition temperature with pressure is obtained from the displacement of low-frequency modes.