Schläfli 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 Schlafli cluster associated with each atom. The Schlafli cluster contains those atoms that define the Schlafli circuit symbol. Different crystalline topologies that have the same Schlafli circuit symbol may be distinguished by considering the number of atoms in the Schlafli cluster. The diameter of the cubic diamond Schlafli 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 Schlafli clusters can be readily identified in models and their combined size provides an intrinsic length scale for describing the medium range order.