Heating through the glass transition: A rigidity approach to the boson peak

Using molecular dynamics, we study the relationship between the excess of low-frequency vibrational modes (Boson peak, BP) and the glass transition for a bidispersive glass interacting through a truncated Lennard-Jones potential. The evolution of the BP with increasing temperature is correlated with the average coordination, as predicted by rigidity theory. This is due to a lack of atomic ?contacts,? as is confirmed by taking a crystal with broken bonds. We show how the quadratic mean displacement (?u2?) is enhanced by the BP. When ?u2? is obtained on short time scales or measured on inherent structures, the glass transition temperature Tg is determined by the position and height of the BP. Between the melting temperature Tm and Tg, the nature of the relaxation processes exhibit phase separation, where the backbone increases its rigidity while the smaller atoms diffuse away to form separate crystals.