The structure of real icosahedral quasicrystals of the Al± Pd± Mn system can be described in terms of a hierarchical self-similar packing of overlapping atomic clusters. An in¯ation scale factor ¿ 3 preserves long-range order but generates a hierarchy of holes and a fractal structure. Such holes have actually been observed and they might be of basic importance in the growth mechanism and stability of quasicrystals. § 1. IntroductionQuasicrystals are a form of the solid state which possesses a long-range translational order despite a non-crystallographic point group of symmetries (Janot 1994). The debate concerning structure and stability of quasicrystals very often revolves about the relative roles of energy and entropy (Henley 1991) but in both cases the description of the structure is based on tiles representing the short-range order in the material. Perfect quasiperiodic structures can be obtained via several geometrical methods including in¯ation± de¯ation of prototiles, tiling with at least two di erent prototiles plus matching rules and also a physical cut of a higher-dimensional periodic structure. These perfectly quasiperiodic models are irreplaceable when one needs to approach experimentally the structure of real quasicrystals for which they give at least a very useful average description (Cornier-Quiquandon et al. 1991Boudard et al. 1992), but space tiling requires a choice of a small number of prototiles together with the de® nition of rules to ® ll space without overlap nor holes. This is intuitively simple for crystals; it is actually easy to imagine a single building block arising as a low-energy atomic cluster of the given elements and, then, periodicity is obtained by adding identical clusters again and again. The procedure works quite well as long as the building block has proper crystallographic symmetries. The physical conditions required to emulate, say, a Penrose (1974) tiling appear to be much more complex. The energetics must be delicately balanced to allow two distinct clusters to be almost equally stable so that they intermix with a speci® c ratio of densities and according to matching rules. The entropic view point (Henley 1991, Joseph andElser 1997) allows phason defects to stabilize the structure, relaxes the

Single grains of real quasicrystals have been investigated using X-ray imaging techniques at a third-generation synchrotron radiation source (ESRF). Facetted microholes have been observed. The experimental results are discussed with reference to a description of the quasicrystal structure in terms of overlapping atomic clusters (self-similar packing or random covering modifications). Relations between holes and quasicrystal formation are also discussed.

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