Extraordinary defects on hyperbolic tessellations A contribution to the structural description of covalent glasses

Abstract

The structural description of amorphous states in terms of defects has essentially used up to now the {335} tessellation of the sphere S³ tiled with regular tetrahedra. This description is essentially valuable for amorphous metals. Here the advantages of the {663} tessellation of the hyperbolic space H3 for the description of tetravalent glasses are demonstrated. In particular, the Volterra process is used to classify the defects of dimension one in {663}: disclinations as in a spherical tessellation, but also dislocations and disvections. The core models are very unexpected. This large diversity of results leads to the belief that the analysis provides the tools necessary to understand plastic deformation in covalent glasses.