| Abstrakt: |
The local order is well defined in amorphous material, but filling all the space with a unit cluster involves distortions. This is due to an incompatibility between the local order symmetry and the properties of euclidian space. Nevertheless curved spaces can be tessellated with a given cell; in this paper we discuss the case of tetrahedral packing. It is well known that tetrahedra cannot fill euclidean space, but they can be packed together to build a regular structure (called a polytope) in a space of uniform positive curvature. The disorder in amorphous materials is then described in terms of defects occurring during the mapping of curved spaces on the euclidian space. This method of describing an amorphous structure provides a mathematical tool, similar to the crystallographic laws used to describe crystals. |
