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Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant, with the aim of studying the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of a pseudo-Brillouin-zone in the quasicrystal. These results are compared with simulations on atomic models and using oscillating pair potentials, and the simulations reproduce in detail the experimental results. This paves the way for a detailed understanding of the physics of quasicrystals.

The origin of the light scattering observed at the alpha-beta transition of quartz is still a subject of controversy. We present structural studies performed during the coexistence of the alpha and the intermediate incommensurate (inc) phases using simultaneously synchrotron x-ray diffraction and optical techniques. The small and large angle light scatterings are due, respectively, to the orientation domains of the 3q inc phase and to the alpha phase twins revealed by diffuse x-ray scattering. In the vicinity of the interphase boundary, the two light scattering regions, both with perturbed properties, form a complex multiscale structure.