A quasicrystal is a solid whose atoms are arranged with long-range order but without the repeating pattern that defines a conventional crystal. When Daniel Shechtman first observed this arrangement in an aluminum-manganese alloy in 1982, the finding was so disruptive to established crystallography that it took years of heated debate before the scientific community accepted it. What makes quasicrystals strange is that they produce sharp, clean diffraction patterns (the hallmark of an orderly structure) while displaying rotational symmetries, like fivefold or tenfold, that are mathematically impossible in any repeating lattice. They occupy a previously unrecognized middle ground between crystalline order and amorphous disorder, and their unusual structure gives them a set of physical properties that no other class of material quite matches.
How Shechtman’s Discovery Overturned a Century of Crystallography
Before 1982, crystallography operated on a firm assumption: crystals are periodic. Their atoms repeat in a regular grid, the way tiles on a bathroom floor do. That periodicity constrains which rotational symmetries are allowed. You can tile a flat plane with shapes that have twofold, threefold, fourfold, or sixfold rotational symmetry, but fivefold symmetry is forbidden because regular pentagons cannot fill space without leaving gaps. This was not a guideline; it was treated as a mathematical law of crystal structure.
Daniel Shechtman, working at the National Bureau of Standards (now NIST) in Gaithersburg, Maryland, was examining rapidly cooled aluminum-manganese alloys when he saw an electron diffraction pattern with unmistakable tenfold symmetry. He reportedly wrote “10 Fold???” in his notebook, circled it, and spent the next two years trying to explain the result to skeptical colleagues. The resistance was intense. Linus Pauling, a two-time Nobel laureate, publicly dismissed the finding, reportedly quipping that “there is no such thing as quasicrystals, only quasi-scientists.”1Comptes Rendus Physique. Discovery of quasicrystals: The early days The hostility stemmed from how deeply periodicity was baked into the definition of a crystal. Accepting Shechtman’s result meant rewriting that definition entirely.
Which is exactly what happened. In 1992, the International Union of Crystallography revised the definition of “crystal” to mean any solid with an essentially discrete diffraction diagram, dropping the requirement for periodicity altogether.2arXiv. What is a crystal? Shechtman was awarded the 2011 Nobel Prize in Chemistry. It remains one of the clearest modern examples of a single observation forcing an entire field to rethink its foundations.
Order Without Repetition
The core puzzle of quasicrystals is how a material achieves long-range order without periodicity. In a regular crystal, knowing the position of one atom and the repeating unit cell lets you predict every other atom’s position. Quasicrystals have no unit cell that repeats. Yet they are emphatically not random. Their atoms follow precise mathematical rules that produce order across macroscopic distances, just not through repetition.
A useful analogy comes from two-dimensional geometry. In the 1970s, mathematician Roger Penrose discovered sets of two tile shapes that can cover an infinite plane without ever repeating. Penrose tilings have fivefold symmetry, local rules governing how tiles fit together, and long-range order despite the absence of periodicity. Quasicrystals are essentially a three-dimensional realization of this concept, built from atoms rather than tiles.3ScienceDirect. Aperiodic crystals: A contradictio in terminis? The mathematical framework used to describe quasicrystal structures involves projecting a higher-dimensional periodic lattice into three-dimensional space. A six-dimensional periodic lattice, sliced and projected at an irrational angle, can produce a three-dimensional pattern with icosahedral symmetry. This is not just an abstract trick; it is the standard working method crystallographers use to solve quasicrystal structures.
Along with the structural strangeness come distinctive dynamical features. Ordinary crystals have phonons, vibrations that propagate through the periodic lattice. Quasicrystals have phonons too, but they also support a second class of excitation called phasons. Phasons involve rearrangements of the local tiling pattern rather than displacements of atoms from their equilibrium positions. They do not cost energy in the long-wavelength limit and behave as diffusive modes rather than propagating waves.4PubMed. Phonons, phasons and atomic dynamics in quasicrystals5PubMed. What phasons look like: particle trajectories in a quasicrystalline potential Think of them as the structure locally shuffling which version of its aperiodic tiling it is expressing, without changing the overall character of the order.
Found in a Meteorite and a Nuclear Blast
For decades after Shechtman’s discovery, every known quasicrystal was made in a laboratory. That changed with the Khatyrka meteorite, a CV3 carbonaceous chondrite found in the Koryak Mountains of far-eastern Russia. Analysis revealed grains of an aluminum-copper-iron alloy with icosahedral symmetry, which researchers named icosahedrite (Al₆₃Cu₂₄Fe₁₃). Dating evidence placed the meteorite’s formation at roughly 4.5 billion years ago, making this quasicrystal older than the Earth itself.6PubMed Central. Evidence for the extraterrestrial origin of a natural quasicrystal
The meteorite had undergone violent impact events in space, with localized conditions exceeding 5 GPa of pressure and 1,200°C.7Nature Communications. Impact-induced shock and the formation of natural quasicrystals in the early solar system Those extreme, short-lived conditions appear to be what drove the quasicrystal’s formation. Further study of the Khatyrka meteorite turned up a second icosahedral quasicrystal with a composition (Al₆₂Cu₃₁Fe₇) that had never been synthesized in any lab, the first time a quasicrystal was discovered in nature before being made artificially.8Scientific Reports. Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory
The meteorite findings pointed to transient extreme conditions as a natural recipe for quasicrystals. Researchers then looked at another source of transient extremes: the Trinity nuclear test. In 2021, analysis of red trinitite, the glassy material fused from desert sand and copper transmission cables by the first atomic bomb detonation in July 1945, revealed a silicon-copper-calcium-iron icosahedral quasicrystal (Si₆₁Cu₃₀Ca₇Fe₂) with a composition never seen before. It is the oldest known human-made quasicrystal, its moment of creation pinned to 5:29 a.m. on July 16, 1945.9PubMed Central. Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test Both discoveries reinforced the same lesson: the extreme pressure-temperature conditions of impacts and explosions, followed by rapid cooling, provide a pathway for quasicrystal formation that works with a surprisingly wide range of elemental compositions.10PubMed Central. Extreme nonequilibrium synthesis of a Ca-Cu-Si clathrate during the Trinity nuclear test
Medieval Tile Makers Got There First
One of the more striking footnotes in quasicrystal history involves medieval Islamic architecture. The elaborate geometric tile patterns, known as girih, that decorate mosques and shrines across the Islamic world were long admired for their complexity. In 2007, physicists Peter Lu and Paul Steinhardt showed that around 1200 C.E., Islamic artisans underwent a conceptual shift: they began constructing their patterns not by drawing lines with compass and straightedge but by tessellating a set of equilateral polygon tiles. By the fifteenth century, this approach was combined with self-similar transformations to produce patterns that are nearly perfect quasicrystalline Penrose tilings, roughly five centuries before Penrose himself worked out the mathematics.11PubMed. Decagonal and quasi-crystalline tilings in medieval Islamic architecture The Darb-i Imam shrine in Isfahan, Iran, built in 1453, is the most celebrated example. Whether the artisans understood the deep mathematical properties of what they were creating remains unknown, but they clearly grasped the practical rules needed to tile a surface aperiodically with fivefold symmetry.
Properties That Do Not Behave Like Metals
Quasicrystals are made of metallic elements, but many of their properties are decidedly non-metallic. Their electrical conductivity is low and, oddly, gets worse as the structural quality improves, the opposite of what happens in normal metals where more order means better conductivity. The explanation lies in how electrons interact with the quasiperiodic structure: the aperiodic potential strongly scatters electrons and increases their effective mass, severely reducing their ability to carry current.12Journal of Non-Crystalline Solids. Optical conductivity of icosahedral quasicrystals Thermal conductivity is similarly poor, comparable to that of ceramic insulators rather than metals.
Quasicrystal surfaces also exhibit remarkably low friction and adhesion. This combination of hardness, low friction, and low surface energy was recognized early as commercially interesting, and led to one of the first consumer products: non-stick cookware coatings.13Progress in Surface Science. Toward theories of friction and adhesion on quasicrystals Quasicrystalline coatings for frying pans were briefly marketed in the 1990s, though they were eventually eclipsed by other non-stick technologies. The low-friction property remains scientifically intriguing because it arises from the aperiodic surface itself, not from a soft lubricating layer the way it does in most low-friction materials.
At macroscopic scales, quasicrystals are brittle, which limits their use as structural materials. But that brittleness turns out to be size-dependent. When quasicrystalline pillars are machined below about 500 nanometers in diameter, they become remarkably ductile, sustaining compressive strains above 50% at room temperature with strengths around 4.5 GPa. At that scale, the dominant mechanism of deformation shifts from dislocation climb, the usual route in quasicrystals, to dislocation glide.14Nature Communications. Superior room-temperature ductility of typically brittle quasicrystals at small sizes This finding is not just academic curiosity; it suggests that quasicrystalline thin films and nanostructures could be mechanically robust even though bulk pieces crack easily.
Applications Beyond the Lab Bench
The unusual thermal properties of quasicrystals have drawn the attention of aerospace engineers. A quasicrystalline approximant alloy based on aluminum, cobalt, iron, and chromium was explored as a thermal barrier coating for gas turbine components. Its thermal conductivity is comparable to yttria-stabilized zirconia, the standard material used to protect turbine blades from extreme heat, and it remains stable up to around 1,000°C. Coatings plasma-sprayed onto nickel superalloy substrates showed excellent quality in optimization trials.15MRS Proceedings. Application Of Quasicrystalline Materials As Thermal Barriers In Aeronautics And Future Perspectives Of Use For These Materials
In catalysis, the brittleness that makes bulk quasicrystals poor structural materials becomes an advantage: they can be crushed efficiently into fine powders, maximizing surface area. Aluminum-copper-iron quasicrystals, after treatment with an alkaline leaching solution that selectively dissolves aluminum from the surface, produce copper nanoparticles sitting on a skeletal quasicrystalline support. These catalysts show high activity for steam reforming of methanol, a reaction that produces hydrogen gas. One study reported hydrogen production rates of about 235 liters per kilogram per minute at 300°C, with the iron in the quasicrystal suppressing the sintering of copper particles that degrades conventional catalysts over time.16Applied Catalysis A: General. Highly active quasicrystalline Al-Cu-Fe catalyst for steam reforming of methanol Similar results have been demonstrated with aluminum-copper-cobalt decagonal quasicrystals, extending the approach beyond a single alloy system.17International Journal of Hydrogen Energy. Synthesis of fine skeletal structure on Al–Cu–Co decagonal quasicrystals for hydrogen production through steam reforming of methanol18International Journal of Hydrogen Energy. Quasicrystal derived catalyst for steam reforming of methanol
Quasicrystalline Order in Soft Matter
Quasicrystals are not limited to hard metallic alloys. In the past two decades, researchers have found quasicrystalline order in a range of soft-matter systems where the building blocks are not atoms but nanoparticles, micelles, or polymer domains. The structures that form tend to be dodecagonal (twelvefold symmetric) rather than icosahedral, reflecting the different geometry of self-assembly at much larger length scales.
Computer simulations demonstrated a design principle for assembling soft-matter quasicrystals: particles that interact through a potential with two characteristic length scales, one for the hard core and one for a softer repulsive shoulder, can spontaneously organize into quasicrystalline patterns. The thermodynamic stabilization in these systems appears to be largely entropic rather than driven by the specific energy of interparticle bonds.19PubMed Central. Self-assembly of soft-matter quasicrystals and their approximants On the experimental side, a dodecagonal quasicrystalline state was observed in a melt of diblock copolymer molecules (poly(isoprene-b-lactide)) that form spherical micelles. Rapid cooling from above the order-disorder transition temperature produced the quasicrystalline phase, which was characterized by X-ray scattering.20PubMed Central. Dodecagonal quasicrystalline order in a diblock copolymer melt
Soft-matter quasicrystals matter because they open the door to quasicrystalline structures at scales where metallic alloys cannot operate, potentially enabling photonic, phononic, and mechanical metamaterials built on quasiperiodic patterns tuned for specific applications.
Photonic Bandgaps and the Promise of Quasicrystalline Optics
Photonic crystals, periodic arrangements of dielectric materials, can block specific wavelengths of light from propagating in any direction, creating what is called a complete photonic bandgap. The higher rotational symmetry of quasicrystals gives them a structural advantage here. Because an icosahedral quasicrystal’s symmetry is closer to spherical than any periodic crystal can achieve, its bandgap frequencies are more uniform across different directions. Experiments on three-dimensional icosahedral quasicrystals confirmed sizeable stop gaps and demonstrated that the effective Brillouin zones (the boundaries in frequency space that define the bandgap) could be mapped out cleanly despite the aperiodicity.21Nature. Experimental measurement of the photonic properties of icosahedral quasicrystals In practical terms, a complete bandgap that is nearly the same in every direction means the material blocks light more evenly, regardless of the angle at which light hits it. This makes quasicrystalline photonic structures strong candidates for optical filters, waveguides, and other devices where directional uniformity matters.
Time Quasicrystals
The most recent extension of quasicrystalline order breaks away from spatial structure entirely and enters the time domain. In a time crystal, a driven quantum system spontaneously develops a response that oscillates at a different frequency from the drive, breaking the time-translation symmetry of the driving force. In a time quasicrystal, the system is driven with two or more frequencies whose ratio is irrational, and the system responds with a pattern in time that is ordered but aperiodic, the temporal analog of a spatial quasicrystal.
A 2025 experiment using strongly interacting nitrogen-vacancy spin ensembles in diamond demonstrated long-lived discrete time quasicrystals. When subjected to a quasiperiodic drive, the system showed robust responses at multiple frequencies that were not integer multiples of the drive frequencies, the signature of quasiperiodic time-translation symmetry breaking.22Physical Review X. Experimental Realization of Discrete Time Quasicrystals Theoretical work has also shown that such quasiperiodic temporal order can be stabilized in non-interacting spin chains through disorder and collective rigidity, and that controlled energy loss can actually help maintain the quasicrystalline time response rather than destroying it.23arXiv. Dissipation stabilizes Dicke Time Quasicrystals The field is young and largely theoretical, but it extends the idea of quasicrystalline order beyond material science and into fundamental questions about how driven quantum systems organize themselves.
How Quasicrystals Are Identified
If you were handed a metallic grain and asked to determine whether it was a quasicrystal, the primary tool would be diffraction. When X-rays or electrons pass through an ordered structure, they scatter to produce a pattern of bright spots. In a normal crystal, those spots form a periodic grid reflecting the lattice’s translational symmetry. In a quasicrystal, the diffraction pattern shows sharp spots arranged with a forbidden rotational symmetry, fivefold, tenfold, or icosahedral, and the spots are dense but discrete, meaning the underlying structure is ordered even though it is not periodic.
The sharpness of these spots is what distinguishes a quasicrystal from a disordered material. An amorphous solid or a glass gives broad, fuzzy diffraction rings. A quasicrystal gives pinpoints as sharp as those of any conventional crystal, but arranged in a pattern that no conventional crystal could produce. Electron microscopy, particularly transmission electron microscopy, was the technique Shechtman originally used and remains a standard identification method. For bulk samples, powder X-ray diffraction can reveal the characteristic spacing ratios. In soft-matter systems and polymer melts, small-angle X-ray scattering fills the same role, tuned to the much larger length scales involved.
One subtlety worth noting is the distinction between a true quasicrystal and a quasicrystal approximant. Approximants are periodic crystals with very large unit cells that locally resemble quasicrystalline arrangements. Their diffraction patterns look almost right but not quite, with spots appearing at positions close to, but not exactly at, the forbidden-symmetry positions. Approximants are useful materials in their own right (the thermal barrier coating alloy mentioned earlier is technically an approximant) and serve as a bridge between periodic and quasiperiodic worlds.