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 reconstru ctive phase transitions is proposed. To screen the simplest pathways out of the infinite manifold in configurational space, a Fourier function approac h is used, based on periodic nodal (PNS) and periodic equi-surface (PES) de scriptors. The simplicity of the chosen functions representing the structur es in question and the linear transition approach provide for most simple r elevant transition models. Here it is shown that the tetrahedral networks o f quartz and tridymite are represented topologically and transformed into e ach other by this approach. A trigonal network related to alpha-ThSi2 and B 2O3 appears as intermediate during the transition model of the periodic fun ctions. The transition path found in this way seems to be of exciting direc tness and of fundamental topological interest. The presented approach is no t restricted to this specific case and is expected to be applicable to a wi de variety of reconstructive phase transitions of solids.