A tentative description of the crystallography of amorphous solids

Abstract

A number of continuous random lattices can be classified as specific one-to-one mappings of ordered lattices of spaces of constant curvature onto the usual 3-dimensional euclidean space. These mappings put emphasis on two types of lattice defects : surface defects for spaces of constant positive curvature (i.e. spherical spaces), disclinations for spaces of constant negative curvature (Lobatchewskian spaces). This method might provide clues for solving the difficulties encountered in the description of amorphous solids with metallic or covalent bonds