Schlنfli cluster topological analysis of medium range order in paracrystalline amorphous semiconductor models

We show that topologically crystalline regions in computer models of amorphous materials can be identified by examining the Schläfli cluster associated with each atom. The Schläfli cluster contains those atoms that define the Schläfli circuit symbol. Different crystalline topologies that have the same Schläfli circuit symbol may be distinguished by considering the number of atoms in the Schläfli cluster. The diameter of the cubic diamond Schläfli cluster in Ge is ∼0.9 nm, which is typical of the shorter length scales associated with medium range order in amorphous materials. Regions of connected identical Schläfli clusters can be readily identified in models and their combined size provides an intrinsic length scale for describing the medium range order.