How might entropy help stabilize quasicrystal structures near their melting points?

Quasicrystals are thermodynamically stable phases that often exist only within a limited temperature range near their melting point. Because the stable structure of a material is determined by minimizing its free energy—calculated as energy minus the product of temperature and entropy—entropy plays a critical role in this stability.1

Entropy, which serves as a measure of fluctuations around an ideal structure, becomes increasingly significant at higher temperatures. In the context of quasicrystals, this is linked to the presence of phasons, which are elastic deformations corresponding to rearrangements of atomic positions. While phason strain can be frozen into the structure at low temperatures, these deformations fluctuate continually near the melting point as atoms jump between positions. These high-temperature fluctuations increase the entropy of the system, which helps lower the overall free energy and stabilizes the quasicrystalline phase relative to ordinary crystal structures.12