Beyond the Usefulness of Quasicrystals

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BEYOND THE USEFULNESS OF QUASICRYSTALS J.M. DUBOIS Laboratoire de Science et Génie des Matériaux Métalliques (UMR 7584 CNRS-INPL), Ecole des Mines, Parc de Saurupt, F-54042 Nancy. This article is dedicated to Dr André Simon on the occasion of his 60th birthday. ABSTRACT For more than a decade, quasicrystals were considered to exhibit only fundamental interest in so far that they have raised basic questions regarding the organization and stability of condensed matter. As well, they addressed the mechanisms of wave propagation in aperiodic solids. In more recent years, they turned to become useful materials in various mechanical devices, in solar absorbers or in heat insulation coatings. Nowadays, the science of quasicrystals, and especially the relevant high-dim crystallography techniques, have issued quite useful concepts and methods that prove useful in neighboring domains of condensed matter physics, of mechanics, of low temperature physics, etc. Hence, this article puts more emphasis on a few of the new subjects that quasicrystals science has helped us to study rather than on the few possible breakthroughs of quasicrystalline materials identified yet on the market. INTRODUCTION The discovery by D. Shechtman on April 8, 1982 afternoon [1] of an unexpected diffraction pattern showing simultaneously sharp diffraction spots and ten-fold symmetry has arose quite some criticism from the world of conventional crystallography [2]. The first authors, who were right on track from early beginning, could not unambiguously demonstrate the existence of genuine aperiodic icosahedral quasicrystals until the discovery of facetted, stable, monodomain samples [3]. Even more important in this respect was the existence, established systematically in the years following the discovery, of approximant crystals [4]. Such crystals of similar compositions and crystalline structures than the parent quasicrystal are clearly distinct from it in reciprocal space and exhibit very large, when not giant, unit cells. Hence, the quasicrystal appears as the limit to infinite size of the unit cell of these approximants, which in turn prove the existence - within accuracy of our instruments - of true quasicrystals. A tremendous research effort was generated in order to put this knowledge on a firm theoretical basis [5]. The notion of phasons flips has appeared as a natural by-product of this generalized crystallography. On top of the experimental detection of such localized atom jumps, both at high [6] and at low [7] temperatures, it turns out that this concept is at the heart of our current interpretation of the physical and mechanical properties of quasicrystals. Nearly twenty years after the breakthrough by Shechtman et al. [8], it happens that the robust concepts worked out in order to understand the unique crystalline structures of quasicrystals have already opened, or are in my opinion close to opening, new domains of research in quasicrystal science. They have contributed in an original way to solve ancient problems in mechanics. As well, recen