Polymorphism of Silica and Ice

The polymorphism of both silica and ice is described by a new chemical relationship between the different crystalline structures (cristobalite, etc.). This relationship is given by the set of admissible screw axes of a tetrahedrally coordinated crystal. The various winding numbers correspond to commensurate cylindrical superstructures calculated from a nonlinear model for both oxygen bonds (Si${\mathrm{O}}_2$) and hydrogen bonds (${\mathrm{H}}_2$O). Glass, in this description, is a strongly incommensurate ("chaotic") modification of cristobalite.