Elucidation of simple pathways for reconstructive phase transitions using periodic equi-surface (PES) descriptors. The silica phase system. I. Quartz–tridymite

A method of estimating short topological pathways for solid–solid reconstructive phase transitions is proposed. To screen the simplest pathways out of the infinite manifold in configurational space, a Fourier function approach is used, based on periodic nodal (PNS) and periodic equi-surface (PES) descriptors. The simplicity of the chosen functions representing the structures in question and the linear transition approach provide for most simple relevant transition models. Here it is shown that the tetrahedral networks of quartz and tridymite are represented topologically and transformed into each other by this approach. A trigonal network related to α-ThSi₂ and B₂O₃ appears as intermediate during the transition model of the periodic functions. The transition path found in this way seems to be of exciting directness and of fundamental topological interest. The presented approach is not restricted to this specific case and is expected to be applicable to a wide variety of reconstructive phase transitions of solids.