Phason-Driven Diversity of Nucleation Pathways in Icosahedral Quasicrystals

TL;DR

This paper reveals that phasons, unique to quasiperiodic structures, drive diverse nucleation pathways in icosahedral quasicrystals, affecting symmetry and energy barriers, and providing new insights into their formation.

Contribution

It introduces a model showing how phasons influence nucleation pathways and symmetry in icosahedral quasicrystals, a novel understanding of their formation mechanisms.

Findings

Low-temperature pathway is symmetry-preserving.

Higher temperatures favor a symmetry detour reducing nucleation barriers.

Bulk IQCs are thermodynamically degenerate despite different real-space symmetries.

Abstract

The nucleation of quasicrystals remains a fundamental puzzle, primarily due to the absence of a periodic translational template. Here, we demonstrate that phasons - hidden degrees of freedom unique to quasiperiodic order - drive diverse nucleation pathways in icosahedral quasicrystals (IQCs). Combining a Landau free-energy model with the spring pair method, we compute distinct critical nuclei and their corresponding minimum energy paths. At low temperatures, a direct, symmetry-preserving pathway dominates. In contrast, higher temperatures promote a "symmetry detour" that reduces the nucleation barrier via a lower-symmetry critical nucleus. Remarkably, while the resulting bulk IQCs exhibit distinct real-space symmetries, they remain thermodynamically degenerate with identical diffraction patterns. We resolve this paradox within the high-dimensional projection framework, showing that phason shifts modulate real-space symmetry without altering bulk thermodynamics. Our findings establish phasons as the structural origin of pathway diversity, offering a new physical picture for the emergence of quasiperiodic order.