Topological modeling of reconstructive phase transitions through periodic hyperbolic surfaces: the β-quartz to keatite type transition

Abstract

Abstract The reconstructive transition β-quartz to keatite is evaluated by employing symmetry-adapted hyperbolic surfaces, i.e. periodic equi-surfaces (PES) as structural trial models. The PES descriptors reveal a transition model very close to the one discussed by Li et al. We can show that this model is associated with only a small shift of the principal structure factors in reciprocal space. We derive an intermediate structure halfway between quartz and keatite of P21 symmetry through symmetry considerations and group-subgroup relations. Atomic shifts are given. It is shown that topological modeling of reconstructive phase transitions by means of periodic hyperbolic surface descriptors is a valuable extension to MD methods in exploring possible transition coordinates. As the PES-method works strictly under symmetry control along group-subgroup relations it allows for a rationalization of both global structural changes and local chemical variations. The whole transition is described by means of only one significant set of structure factors for quartz and two sets for keatite.