Topological Approaches to the Structure of Crystalline and Amorphous Atom Assemblies

Crystalline assemblies of atoms possess not only symmetry and periodicity but also a topology that provides additional information not explicit in a conventional description. A topological description of structure is likewise shown to be the only sensible approach to the assessment of non-crystalline atom assemblies and to reveal useful similarities between crystalline and non-crystalline structures at intermediate range. Amorphizability of crystalline solids is shown to derive from topological properties of connectivity, and the defect structures of highly defective or amorphizing solids can be individually identified and categorized in model simulations using topological tools. Polyamorphic phase transformations between alternative amorphous arrangements can be similarly characterized. Examples of topological assessment tools are given for SiO₂, Si₃N₄, SiC, ZrSiO₄ and GeO₂ systems.