Elastic excitations in colloidal crystals

Summary form only given. The dispersion of sound waves in a fcc colloidal crystal consisting of silica spheres (diameter d=226 nm) immersed in cyclohexane was measured using Brillouin light scattering. Five distinct vibrational modes are observed. The dispersion curve of the lowest frequency mode corresponds to an acoustic wave which propagates almost exclusively through the cyclohexane, with a velocity slightly higher than that of the solvent. The next two modes are mainly due to the MS effects. Their energy density is spreaded in the solvent and it is zero or very small inside the spheres. Such modes should interfere very strongly with similar modes associated with neighboring silica spheres, making thus possible the MS effects. In the two highest-frequency modes, the single-scattering character seems to prevail, being related to sharp resonances (i.e. peaks) in the "scattering cross section" of sound by a single particle. The above resonances are revealed by substracting from the silica scattering amplitude the hard sphere amplitude. The last but one mode arises from a d-type single-scattering resonance (i.e. peak in the l=2 spherical harmonic component), while the last one from a combination between a p-type (l=1) and an f-type (l=3) resonance. We calculated the energy density distribution of these d, p and f modes and we found that it is well localized inside the spheres with a weak leakage outside. The density energy, which escapes in the solvent is small, so, very weak interference with similar modes is expected. This localization in the real space is in agreement with the flatness in q-space, as suggested by the experiment. In a perfect crystal, propagation of these modes takes place through their slight overlap. Even weak disorder may keep them localized.