Why do quasicrystal diffraction patterns have sharp spots despite lacking periodicity?

Quasicrystals produce sharp diffraction spots because they possess long-range order in their atomic positions, despite lacking the translational periodicity found in ordinary crystals.1

While amorphous materials produce only diffuse rings in diffraction patterns due to a lack of coherent atomic arrangement, the deterministic nature of quasicrystalline structures ensures that atoms are placed according to specific, non-repeating rules. This structure is described as quasiperiodic, meaning that while the pattern never repeats itself and lacks a traditional unit cell, it maintains a high degree of structural coherence over long distances.12

In crystallography, the presence of sharp Bragg diffraction peaks is a direct consequence of this long-range coherence. Because the atoms in a quasicrystal are arranged in a deterministic, quasiperiodic fashion—often following sequences like the Fibonacci sequence—they scatter waves in a manner that results in discrete, sharp spots rather than the blurred patterns seen in disordered materials.12