Aperiodicity (EN)

Aperiodic crystals are a new state of matter which possess long range order without translational symmetry within the physical space.

Apériodiité

Aperiodic crystals are a new state of matter which possess long range order without translational symmetry within the physical space. Periodicity is recovered in higher dimensional spaces (up to 3+3 in the case of icosahedral quasicrystals). Contrary to conventional periodic crystals, it is no more possible to define a so-called Brillouin zone where all the properties could be expressed in terms of wave-vectors in the reciprocal spaces. In our lab, we mostly focus on structure determination, symmetry breakings, critical phenomena, atomic vibrations (phonons and phasons), free sliding and related effects in these crystals. Aperiodic crystals are usually divided in three families and these three families are considered: modulated incommensurate crystals (prototype: bis-chlorophenylsulfone), aperiodic composite (prototype: alkane/urea) and quasi-crystals (ZnAgSc and its approximant Zn6Sc). Very original other works are now in progress such as :

  • Generalization of the Landau description of structural phase transitions in N-dimensional crystallographic spaces.

  • Self-compression in composite materials.

  • Development of the new 3D-ΔPDF approach to aperiodic single crystals.

  • Understanding of the one-dimensional quasi-liquid ordering leading to three-dimensional long range ordered aperiodic crystals.

  • Determination of the specific collective dynamics in materials without translational symmetry.

  • Structure and dynamics of quasi-crystal and its approximant using high field solid state N.M.R. (en collaboration avec Christophe Odin).

  • Aperiodic ordering of molecular electronic states (spin state concentration waves)