Structure, odd lines and topological entropy of disorder of amorphous silicon

A continuous random network model of amorphous silicon, subject to periodic boundary conditions, is partitioned into cells bounded by irreducible rings. An algorithm has been developed to find the cells and the rings that bound them. A thread can be imagined to pass through odd rings (rings containing an odd number of atoms) without passing through even rings. Such a thread is an algorithmic realization of an odd line, which is the only topological defect in glass or amorphous condensed matter. The topological entropy of disorder associated with these odd lines is found to be approximately 80% of the value for an ideal tetrahedrally bonded random network of atoms for which the rings that bound the cells are statistically independent.