From the disordered via the quasicrystalline to the crystalline state

We report on structural similarities at short- and medium-range distances o f the amorphous and the quasicrystalline state and their consequences on st ructural stability and electronic transport. In the former the nearest neig hbour atoms are onion-shell-like radially ordered around any ad-atom. The s pacing between the concentrical shells is up to relatively large distances unique and matches the Friedel wavelength. Their occupation by the ions is random. We interpret this in terms of a resonance, based on spherical waves , between the conduction electrons and the static structure. The spherical arrangement of the atoms plays the role of mirror-spheres for spherical ele ctron waves at short and medium-range distances, quite similar to mirror-pl anes for the plane electron waves in a crystal. The conducting quasiparticl es become localised as there is better spherical correlation and hence the resonance condition is fulfilled. The quasicrystals are between the disorde red and the crystalline case. Radial order becomes more strict but lasts fo r shorter distances (cluster-like), and in addition exists only at particul ar sites. On the other hand, long-range orientational order, e.g. order at the spheres acid between the spheres has emerged, causing planar resonances between planar electron waves and mirror-planes. Long-range periodicity is still missing. The path from the disordered via the quasicrystalline to th e crystalline state seems to be triggered by the improvement of resonances between electrons and the forming static structure. (C) 2000 Elsevier Scien ce B.V. All rights reserved.