Sound waves and other modes in the strong glass formerB2O3

We have investigated fast relaxational processes and the much debated boson peak in the strong glass former, ${\mathrm{B}}_2{\mathrm{O}}_3,$ from 60 to 1300 K (glass transition temperature 523 K) using coherent inelastic neutron scattering. The wave-vector dependence of the dynamic structure factor is different for energies below and above the boson peak, at $\sim 2.5\mathrm{meV},$ indicating a qualitative difference in the character of the respective modes. This finding demonstrates that the boson peak can be decomposed into an in-phase and a random-phase component. A quantitative analysis to separate these contributions has been carried out. At low temperatures the in-phase component extrapolates to the Debye level at low frequencies. It is then identified with the sound-wave contribution. At higher frequencies it increases to a maximum value at $\sim 2\mathrm{meV}$ and then the value decreases and becomes less than the Debye level at $\sim 4\mathrm{meV}.$ The density of states for the random-phase component reaches a maximum value at $\sim 3\mathrm{meV}$ and is similar to the boson peak observed in Raman scattering. The low-frequency behavior of the random-phase modes as well as the higher-frequency behavior of the total density of states are consistent with predictions of the soft potential model. At temperatures above the glass transition temperature we observe, in accordance with other glass formers, a strongly anharmonic behavior of the spectra. However for $T\gtrsim 800\mathrm{K}$ the system exhibits harmoniclike behavior and the dynamical properties of the system are essentially temperature independent up to the highest temperature of observation, an extraordinary finding.