Transition pathways connecting crystals and quasicrystals

TL;DR

This paper investigates the transition pathways from crystalline to quasicrystalline phases using computational methods on a Landau free-energy model, revealing one-stage and two-stage transition mechanisms.

Contribution

It introduces an efficient computational approach to identify transition pathways and saddle points connecting crystal and quasicrystal phases in a Landau model.

Findings

Identifies saddle points as critical nuclei for phase transitions.

Discovers two possible transition pathways: one-stage and two-stage.

Highlights the role of metastable lamellar quasicrystalline states.

Abstract

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.