Abstract: The motivation for the present study is to be found in the recent experiments of Fuchizaki and Hamaya on GeI4. They observed a rapid increase in the melting temperature Tm in going from atmospheric pressure to p
~ 2.6 GPa. Tm was found to be largely independent of pressure above this value. In this paper, heuristic arguments are presented to support the idea that until some critical pressure, a crystalline phase of SnI4, CCl4 and GeI4 molecular solids melts into a low density liquid. However, at this critical pressure, a phase boundary intersects Tm(p), separating a low density liquid phase from a high density liquid. The new phase boundary is between the crystal and an amorphous molecular solid with increasing polymerisation as the pressure is increased.