Many crystalline ceramics can be amorphized within high-energy collision cascades whose overlap leads to global structural amorphization. Because the structural rearrangements amount to topological disordering, we have chosen to model these rearrangements using a topological modeling tool as an alternative to molecular dynamics simulations. We focus on the tetrahedral network compounds SiO2, Si3N4, and SiC, each compound comprising corner-sharing tetrahedral units, because they represent increasingly topologically constrained structures. SiO2 and SiC are easily amorphized experimentally, whereas Si 3N4 proves very difficult to amorphize. In this model, we consider the tetrahedron as the base unit, whose identity is largely retained throughout. In a collision cascade, all bonds in the neighborhood of a designated tetrahedron are broken, and we reform bonds in this region according to a set of local rules appropriate to crystalline assembly, each tetrahedron coordinating with available neighboring tetrahedra (insofar as is possible) in accordance with these rules. We generate fairly well connected amorphized structures for SiO2, but run into underconnected networks for Si3N4 and SiC which are irreparable without rebreaking and reforming primary tetrahedral bonds. The resulting structures are analyzed for ring content and bond angle distributions for comparison to the crystalline precursors.