A SANS Approach to Possible Hierarchical Structures of Defects in Amorphous Alloys

Abstract

Amorphous systems are structurally characterized by a lack of long-range periodicity and the presence of a rather well defined short-range order. In amorphous metallic systems one satisfactory approximation proposed for the structure corresponds to close packing tetrahedra on the ground that a regular tetrahedron is the densest configuration for the packing of four equal spheres. As the dihedral angle of a tetrahedron is not a submultiple of 2π, a perfect tiling of the 3D Euclidean space with regular tetrahedra is not possible. SADOC [1] has first proposed a definition of an ideal amorphous structure by allowing for space curvature so that the local configuration can propagate without defect (a 2D example of this model is the perfect tiling of the surface of a sphere with regular pentagons). The so-called real amorphous structure would then be obtained by projection into our ordinary Euclidean 3D space. Obviously enough projection means distortions and introduces topological defects,among which disclination lines play an important role. Projection from curved to Euclidean space means also decurving. MOSSERI and SADOC [2] have shown that it is possible to remove the curvature using an iterative procedure which produces disclination networks, step by step.