A new way to evaluate x-ray Brillouin scattering data

Making use of the classical second moment sum rule, it is possible to convert a series of constant-Q x-ray Brillouin scattering scans (Q momentum transfer) into a series of constant frequency scans over the measured $Q$ range. The method is applied to literature results for the phonon dispersion in liquid vitreous silica and in glassy polybutadiene. It turns out that the constant frequency scans are again well fitted by the damped harmonic oscillator function, but now in terms of a Q-independent phonon damping depending exclusively on the frequency. At low frequency, the sound velocity and the damping of both evaluations agree, but at higher frequencies one gets significant differences. The results in silica suggest a new interpretation of x-ray Brillouin data in terms of a strong mixing of longitudinal and transverse phonons toward higher frequencies. The results in polybutadiene enlighten the crossover from Brillouin to Umklapp scattering.