Geometry and topology of structure in amorphous solids

The geometrical concept of an ideal solid and a method for its construction are presented as novel contributions to the understanding of atomic arrangements in amorphous solids. This ideal amorphous structure serves as a base-line model for atomic arrangements and as a universal reference from which any changes in atomic arrangement can be measured. The model is intended to represent the ideal structure of amorphous solids and not the way a real glass is formed. This provides for amorphous materials the same kind of base-line reference as an ideal crystal does for real crystalline materials, or tiling patterns for quasi-crystalline materials. Characteristic properties are described, including Debye X-ray scattering to show how relevant information can be derived about the presence of vacancies and compositional changes.