SPACE FILLING MODELS OF AMORPHOUS STRUCTURES

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Abstract
The structure of amorphous systems is determined by the chemical bond between atoms and the topological constraints of the space filling requirement. Amorphous metallic systems show an icosahedrical local order incompatible with crystalline periodicity, but such a local order may exist in 3 dimensional spaces with non vanishing curvature. Hence it has been suggested to build up models of amorphous metallic structure by tiling curved spaces with icosahedra : the structure is subsequently decurved by methods that preserve the local order. The concept of disclination (or rotation-dislocation) plays a central role in the decurving procedure. At the opposite, another method consists of tiling a randomly corrugated space which remains euclidean in the average : regions of positive curvature are the nucleation centers of icosahedral environments. We define sum rules that relate the distribution of coordination numbers (defined by the Voronoi construction) to the curvature of the space. We discuss also the structure of "quasi-crystals" in which a fivefold (or tenfold) symmetry has been observed. An orientational order is still present but the translational order has disappeared. These "quasi-crystals" have to be related to the non-periodic structures invented by R. Penrose : both show a self-similar character. Endly, the structures of covalent fourfold coordinated amorphous systems are discussed as well as the structure of group V and VI elements

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