From the disordered via the quasicrystalline to the crystalline state

We report on structural similarities at short- and medium-range distances of the amorphous and the quasicrystalline state and their consequences on structural stability and electronic transport. In the former the nearest neighbour atoms are onion-shell-like radially ordered around any ad-atom. The spacing 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 electron waves at short and medium-range distances, quite similar to mirror-planes for the plane electron waves in a crystal. The conducting quasiparticles become localised as there is better spherical correlation and hence the resonance condition is fulfilled. The quasicrystals are between the disordered and the crystalline case. Radial order becomes more strict but lasts for shorter distances (cluster-like), and in addition exists only at particular sites. On the other hand, long-range orientational order, e.g. order at the spheres and 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 the crystalline state seems to be triggered by the improvement of resonances between electrons and the forming static structure.