For decades crystallography defined a crystal as matter whose lattice repeats periodically in three dimensions. Shechtman’s electron-diffraction pattern, showing tenfold symmetry that repeats every 36°, contradicted that dogma and revealed solids with quasiperiodic order. By ruling out twins and other artefacts, he connected the atomic arrangement to Penrose tilings, an aperiodic mathematical mosaic. Quasicrystals possess striking properties—high hardness, low thermal conductivity and very smooth, non-stick surfaces—leading to uses in frying-pan coatings and wear-resistant steels. The study is also a celebrated lesson that questioning authority and verifying results experimentally are essential parts of scientific progress.

Quasicrystals are solids that lack translational symmetry yet display long-range order and sharp Bragg peaks in diffraction experiments. When Shechtman rapidly solidified an Al-Mn alloy, the resulting electron-diffraction pattern exhibited tenfold symmetry, forbidden by conventional space-group theory. Subsequent structural analysis employed higher-dimensional (e.g., six-dimensional) superspace lattices projected into 3-D physical space, enabling quantitative descriptions of quasiperiodicity. Comparisons with Penrose tilings and amorphous phases revealed quasicrystals as a novel state of matter situated between crystalline and glassy order. Reported properties include low electrical and thermal conductivity due to electron localization, pseudo-gap formation that confers metastability, and almost friction-free surfaces. Diverse quasicrystal phases have been discovered in Al–Cu–Fe, Al–Pd–Mn, Cd–Yb and many other multicomponent alloys; stabilization has been discussed in terms of Hume-Rothery electron concentration rules and cluster-packing models. These findings forced an expansion of crystallography’s framework, culminating in the International Union of Crystallography’s 1992 redefinition of “crystal.” Quasicrystal research continues to grow as an interdisciplinary field intersecting condensed-matter physics, materials science and mathematical topology.

The tenfold electron-diffraction pattern observed in the i-Al-Mn phase corresponds to long-range order describable by a five-/six-dimensional superspace group such as P10/mmm. High-resolution TEM and single-crystal X-ray intensity mapping revealed Mackay-type icosahedral clusters (Al20Mn12) as the fundamental structural motifs. Structural modelling employed Elser’s cut-and-project algorithm, with extensive discussion of dynamic diffuse scattering arising from phason degrees of freedom. First-principles calculations (FLAPW, LMTO) indicated the formation of a pseudo-gap near Ef whose steep density-of-states gradient suppresses thermal and hot-electron transport. In-situ DSC experiments documented metastable sequences i-phase → relaxed state → μ-phase, governed kinetically by phason-stress relaxation mediated via dislocation motion. Mechanical studies attribute the high hardness (>HV1000) to bimodal interatomic distance distributions and the sharing of Bergman clusters with approximant crystals. Alloying-induced adjustment of electron concentration e/a broadens the stability range of the i-phase via FS–BZ interactions consistent with the Hume-Rothery mechanism. Recent SAXS/SANS and anisotropic phonon-spectra analyses have experimentally confirmed phonon–phason coupling responsible for unusual thermal-diffusion anisotropy. These insights directly inform design guidelines for complex metallic alloys, approximant crystals and the exploitation of quasicrystals as high-temperature thermoelectric materials.