Group-theoretical and geometrical considerations of the phase transition between the high-temperature polymorphs of quartz and tridymite

A model was derived for the temperature-dependent phase transition between the high-temperature polymorphs of quartz (P6(4)22) and tridymite (P6(3)/mmc). Only the Si framework is considered, and the transformation can be described as a deformation of a homogeneous sphere packing with three contacts per sphere (type 3/10/h1) in the common subgroup P6(1)22 of P6(4)22 and P6(3)/mmc. The proposed model guarantees the three-dimensional connection of the crystal structure during the whole transformation process.