NETWORK TOPOLOGY IN APERIODIC NETWORKS

Topological descriptions are an attractive alternative to conventional crystallographic formalism for describing crystals and are essential for describing aperiodic states lacking long-range translational and orientational order. In networks, topological connectivity approaches are usefully applied in making assessments of glass-forming ability and in providing a local description of network structure which can assess extendability. The structural freedom required to form aperiodic networks is directly related to connectivity, and the range of allowable structural possibilities can be enumerated using combinatorial geometry. Detailed applications to periodic and aperiodic network silicas are reviewed.