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How do quasicrystalline solids differ from ordinary crystals?

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Diagram showing four physical states of matter: solid with tightly packed molecules, liquid with loosely packed molecules, gas with widely spaced molecules, and plasma with free electrons and nuclei, each labeled with descriptions and an arrow indicating increasing energy. — phase States of matter.

Quasicrystalline solids differ from ordinary crystals primarily in their atomic arrangement and symmetry. While ordinary crystals are characterized by translational periodicity—a repeating lattice structure that allows for specific rotational symmetries (twofold, threefold, fourfold, and sixfold)—quasicrystals lack this periodicity.12

Instead, quasicrystals exhibit a quasiperiodic structure, where atoms are arranged in patterns that do not repeat at regular intervals. This allows them to display symmetries that are strictly forbidden in ordinary crystals, such as fivefold, eightfold, tenfold, and twelvefold rotational symmetry.21

Despite lacking translational periodicity, quasicrystals are distinguished from amorphous solids by their long-range order, which is confirmed by sharp Bragg diffraction peaks. In contrast, amorphous solids lack both translational periodicity and long-range order, resulting in diffuse rings in their diffraction patterns. In summary, quasicrystals occupy a unique structural space, possessing the long-range order of crystals but the non-repeating, high-symmetry patterns that defy traditional crystalline classification.134