Ring connectivity: Measuring network connectivity in network covalent solids

In atomistic models of amorphous materials, ring statistics provide a measure of medium-range order. However, while ring statistics tell us the number of rings present in the model, they do not give us any information about the arrangement of rings, e.g., whether the rings are clustered and how big the cluster is. In this work we present a method to calculate the ring connectivity, or clustering, of rings. We first calculate the rings present in the model using the shortest path criteria of Franzblau and then find the rings that are connected together and group them into clusters. We apply our method to a set of models of disordered carbons, obtained using a reverse Monte Carlo procedure developed in a recent work. We found that in these carbon models the five-, six-, and seven-membered rings are connected together, forming clusters. After isolating the clusters, we found that they resemble defective graphene segments twisted in a complex way. The clusters give further insight about the arrangement of carbon atoms in microporous carbons at a larger length scale. Moreover, the method can be applied to any network covalent solid that contains rings and thus gives information about the ring connectivity present in such materials.