Collective vibrational modes as signature of a static length accompanying the glass transition

I will present the results of a series of inelastic x-rays scattering experiments performed on vitreous silica at various densities [1-3] and on its parent polycrystalline aggregates [4], ?-quartz and ?-cristobalite. The main result of our work is the observation of a particularly large static length, ? ~ 20 interatomic distances, connected to the size of the elastic heterogeneities in the glass. The glass behaves elastically as a continuum medium at large wavelengths, ? >> ?. The atomic vibrations feel the microscopic details of the structure when ? ~ ? and their spectrum becomes almost indistinguishable from that of the corresponding polycrystal as the frequency is increased further. Here the glass shows a rich vibrational spectrum, which includes the three acoustics and the optic modes of the crystal averaged over the wave-vector orientations. I will discuss the connection between the length ? and the frequency of the excess vibrations at the boson peak, suggesting an increase of this length as the temperature is lowered below the glass transition.