The range and kind of order in random tetrahedral structures

A hypothetical model for amorphous silicon was obtained by simple deletion of the 2-connected points in a random network construction of vitreous silica. The distribution of atom pair separations has five distinguishable peaks, the first two of which are essentially Gaussian. Detailed asymmetry of the third peak is largely associated with the variable geometry of 6-membered rings. Topological analysis of neighbors, in terms of the number of bonds traversed in a connected path, yields the shape of individual components which are overlapped in the pair distribution curve. Mathematical manipulation of the atom coordinates can be made in physically reasonable ways without breaking connections or significantly changing the structural details in peaks at the larger distances. Coordination or packing numbers for the average atom have been obtained from topological analysis. These are in remarkable agreement with the numbers obtained by the same analysis of the diamond lattice.