Transition pathways connecting crystals and quasicrystals.

Area of Science:

• Condensed matter physics
• Materials science
• Computational physics

Background:

• The formation of quasicrystals from crystalline phases presents a significant challenge in computational physics due to structural incommensurability.
• Understanding the nucleation mechanisms is crucial for controlling the synthesis and properties of quasicrystalline materials.

Purpose of the Study:

• To investigate the nucleation pathways of quasicrystals using an efficient computational method.
• To identify critical nuclei and understand the transition dynamics between crystalline and quasicrystalline phases.

Main Methods:

• Application of an efficient computational method to a Landau free-energy functional.
• Utilizing high-index saddle dynamics to obtain transition pathways between local minima of the Lifshitz-Petrich model.
• Identification of saddle points as critical nuclei for 6-fold crystals and 12-fold quasicrystals.

Main Results:

• Two distinct pathways for phase transitions between crystalline and quasicrystalline phases were identified.
• These pathways include a direct one-stage transition and a two-stage transition involving a metastable lamellar quasicrystalline state.
• The study successfully identified critical nuclei for both crystalline and quasicrystalline structures.

Conclusions:

• The findings provide a detailed mechanism for quasicrystal nucleation and growth.
• The identified pathways offer valuable insights into the complex phase transitions in condensed matter systems.
• This research advances the computational understanding of quasicrystal formation.