Quasicrystals: The Strange Order That Changed Crystallography

Gabrielle Birchak/ September 26, 2025/ Archive, Contemporary History, Modern History

Today, we’re exploring quasicrystals, what they are, how an “impossible” pattern was found in a lab, how it became the catalyst to rewriting textbooks, and why this exotic order matters for real‑world technologies from wear‑resistant coatings to photonics. I’m Gabrielle Birchak, and this is Math! Science! History!

Imagine holding a metal that seems to obey rules nature once forbid. You shine an electron beam through it and, on the detector, a perfect ring of ten bright dots appears, tenfold symmetry, crisp and clean. For more than a century, crystallography said that symmetry was impossible in a crystal. And yet there it is, staring back at you. It is order without repetition and a pattern that never tiles by marching the same unit cell across space. This is a quasicrystal.

What Exactly Is a Quasicrystal?

By Jgmoxness — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=63160388

When most people think of crystals, they picture something like salt or quartz: neat, geometric, and orderly. That’s because traditional crystals are built from tiny repeating patterns, like perfectly placed tiles on a bathroom floor. This repeating unit, called a unit cell, fits together over and over in all directions to fill space.

These crystals follow strict symmetry rules. So, imagine rotating a snowflake. It still looks the same at every 60° angle. That is called six-fold symmetry. Salt crystals, for example, can have four-fold symmetry, and diamonds follow a three-fold pattern. These regular symmetries leave a signature when scientists shine X‑rays through them: they create sharp, clear patterns, much like a fingerprint of repetition.

Quasicrystals are different. They are ordered but not periodic. Their atoms sit in a coordinated arrangement that exhibits long‑range order, yet the pattern never repeats by simple translation. In reciprocal space, quasicrystals still show sharp peaks, signatures of long‑range order, but those peaks arrange themselves in “forbidden” symmetries such as five-fold, eight-fold, ten-fold, or twelve-fold. Since I have Taylor Swift on the brain, I will give it a literary perspective: periodic crystals repeat, but quasicrystals rhyme.

If you want a mental picture, imagine a Penrose tiling, the famous kite‑and‑dart pattern that covers a plane with no repeating wallpaper motif, yet contains a hidden, hierarchical order.

By Inductiveload — Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=5839079

So, Penrose tiles were groundbreaking because they revealed two key ideas. First, non‑repeating order is possible. Second, the golden ratio appears again and again in the spacings of motifs. But, with quasicrystal structures, the distances between atomic clusters often occur in φ‑related ratios.

So, what is a φ‑related ratio and what is φ (Phi)?

Well, phi is a greek letter, that looks like a lower-case O with a line through it, like a backward facing p stuck to a forward facing p. It’s value is about 1.618.

Mathematically, φ is defined as:

It has the unique property that:

Where a > b and the segments a and b form what is called the golden ratio.

Here’s an audio analogy. Clap every two beats with one hand and every three beats with the other. The composite rhythm never exactly repeats, but it isn’t random, it’s structured. Quasicrystals are like that, except the “beats” are vectors in space and the interference creates a tapestry of order that never loops.

Another important point of quasicrystals is that they are definitional. The International Union of Crystallography eventually reframed the term crystal to emphasize diffraction, stating that a crystal is any solid that yields an essentially discrete diffraction pattern. That moves us away from “must have a unit cell” and toward “must exhibit long‑range order,” which is a definition quasicrystals satisfy perfectly. So, instead of insisting that a material must repeat the same tiny building block over and over, like tiles that all match, scientists began to focus on something broader. They focused on material that has an overall structure that stays consistent across large distances. That’s what we call long-range order.

And while quasicrystals don’t repeat like normal crystals, they still have this deep, elegant order, just without the strict repetition. In fact, quasicrystals are a perfect example of long-range order without periodicity. So, they don’t have that spatial repetition that we would see in regular crystals like salt or quartz where the atoms repeat in a very strict grid like pattern. That in regular crystals is called periodic spatial order. In quasicrystals, atoms are arranged in a way that is ordered but it doesn’t repeat. They still follow the mathematical rules and exhibit long range order, but you won’t find repeating tiles for a repeating unit cell.

The Discovery That Should Not Have Happened

It was a spring morning in 1982.

In a quiet lab at the National Bureau of Standards in Maryland, now known as National Institute of Standards and Technology, materials scientist Dan Shechtman was alone at his electron microscope, analyzing a rapidly cooled aluminum–manganese alloy. He wasn’t expecting a revolution. He was studying alloys like he had countless times before. Routine. Repetitive. Predictable.

But what he saw next changed everything.

The diffraction pattern staring back at him showed tenfold rotational symmetry, like a decagon etched in atomic light. That was impossible. According to the study of crystallography, you simply couldn’t have a crystal with tenfold symmetry. The laws were clear: only 2‑fold, 3‑fold, 4‑fold, and 6‑fold symmetries were allowed. Anything else? Forbidden.

Shechtman blinked. Recalibrated. Took another look. Still there.

He scribbled in his notebook:

“10-fold???”

Was it an error? A twinned crystal playing tricks? He checked again. And again. The pattern held.

In a 2011 interview, he told the story of how his colleagues reacted to his discovery. When Shechtman shared the data with colleagues, the response wasn’t celebration, it was disbelief. One colleague reportedly said, “Go read the textbook.” Another insisted he was wrong. Finally, his group leader told him, “Danny, you are a disgrace to my group and I want you to leave my group, I don’t want to be associated with this.” And so Dr. Schecthman was removed from his research group. I will post the link to the interview on the Math! Science! History! website. It’s an interesting read because doctor schechtman doesn’t take it too personally. He says it wasn’t traumatic period he said the reception was everything between encouragement and rejection. But when he was removed, though he didn’t feel good about it, he states he just became a scientific orphan and then found another group leader who would adopt him.

Still the vitriol continued even, from noneother than Linus Pauling. Pauling at a conference announced that “Danny Shechtman is talking nonsense, there are no quasi-crystals, just quasi-scientists.”

But Shechtman persevered. And he kept doing his research. He ignored the critics. He stood his ground. Quietly, methodically, he gathered more evidence. And two years later, in 1984, he published a paper with colleagues Ilan Blech, Denis Gratias, and John W. Cahn in Physical Review Letters. The title: “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry.”

This paper defined a quasicrystal.

By Holger Motzkau, Wikipedia/Wikimedia Commons (cc-by-sa‑3.0), CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=17637155

It took years for the community to accept the idea. But eventually, it did, and in 2011, Dan Shechtman received the Nobel Prize in Chemistry for discovering a new form of solid matter. It was an acknowledgement that quasicrystals had not only widened the map of crystallography but also reshaped their borders.

How “Impossible” Symmetries Became Thinkable

Dan Shechtman’s discovery in 1982 may have been the spark, but the kindling for that fire had been gathering for centuries.

Let’s travel back to the early 1600s. The great astronomer and mathematician Johannes Kepler was obsessed with patterns in nature. He marveled at five-pointed stars and the geometry of regular solids. He sketched intricate tilings with pentagons, elegant, mesmerizing, but never quite able to fit together perfectly without gaps. It was beautiful! But it was forbidden in the language of periodic repetition.

So, now when we fast forward to the twentieth century, the crystallographic restriction theorem had become gospel: only certain symmetries, twofold, threefold, fourfold, or sixfold, were allowed in a crystal that repeated in space. Fivefold was considered impossible. And as for icosahedral symmetry, like you’d find in a soccer ball or a virus shell? That couldn’t fill space with a repeating unit cell either.

But then in the 1970s, Mathematical Physicist Roger Penrose introduced something radical. He introduced tilings that never repeated, yet still had structure. His “aperiodic tilings” looked chaotic at first glance, but they followed strict rules, like a melody that never loops but always harmonizes. Soon after that, physicist Alan Mackay ran a simulation of X‑ray diffraction on a Penrose tiling, and he found sharp diffraction spots with fivefold symmetry. Clear evidence of order, without repetition.

So, by the time Shechtman saw that forbidden tenfold pattern in a rapidly cooled aluminum–manganese alloy, the groundwork had already been quietly laid. Some theorists scrambled to explain it. Some looked beyond our three dimensions, proposing quasiperiodicity, patterns that come from slicing through a higher-dimensional crystal and projecting the points into our world, like casting a shadow of a four-dimensional object.

What had once been mathematical musings and “impossible” geometries were suddenly staring back through the microscope, not as abstract art, but as reality.

Nature’s Plot Twist: Natural and Shock‑Made Quasicrystals

For a while it seemed quasicrystals were lab‑born oddities, fragile phases coaxed into existence by rapid quenching. Then in 2009, researchers reported natural icosahedral and decagonal quasicrystals in microscopic grains from a meteorite collected in Chukotka in the Russian Far East. Their compositions, Aluminum–Copper–Iron, matched known lab phases, and the diffraction patterns were unmistakable. The implication: the extreme conditions of space, shock, high pressure, rapid cooling, can drive matter into quasiperiodic order.

Shock can also come from human technology. Quasicrystals weren’t just found in a lab, they also showed up in one of the most violent human experiments in history. When scientists later examined the glassy debris left behind by the very first nuclear bomb test in the mid-twentieth century, they discovered tiny quasicrystals hidden inside. The blast had melted and then instantly cooled the surrounding sand and metal, and in that split second of extreme heat and rapid cooling, quasicrystals formed.

That discovery proved something remarkable: quasicrystals aren’t necessarily fragile lab creations. They can emerge even in the most chaotic environments. From that point on, quasicrystals were no longer dismissed as man-made oddities, they earned their place as genuine members of nature’s own library of materials.

And even though quasi crystals were now cemented into reality, there were still many myths and misconceptions that surrounded this discovery. Some people stated that quasi crystals are just disordered crystals. But they are not. The sharp Bragg peaks Mean that there is long range order. The order is quasi periodic, not random. Furthermore scientists believe that this forbidden symmetry broke the rules. But it didn’t. It revised our definition. Once we defined the crystals by diffraction rather than by translational periodicity, these five‑, eight‑, ten‑, and twelve‑fold symmetries became legitimate. Many material scientists believed they were too brittle to use. However, bulk brittleness is real but coatings, composites, approximates, and patterned metamaterials are already practical.

What Quasicrystals Feel Like

If you handle quasicrystalline materials (most often as coatings or fine‑grained composites), a distinctive engineering profile emerges.

Quasicrystals possess a unique set of properties that make them stand out from ordinary metals and alloys. Their complex atomic tilings give them exceptional hardness and wear resistance, because the structure prevents dislocations from moving easily and suppresses plastic deformation. As a result, quasicrystals perform superbly as thin protective wear layers. They also exhibit low friction and low surface energy, their surfaces resist wetting by molten metals, oils, and even some adhesives, which is why tribology tests often show them sliding with unusually low friction. In addition, aluminum-rich quasicrystals offer excellent corrosion resistance by forming stable oxide skins that protect the metal beneath, a feature especially valuable when applied to steel or aluminum. Unlike most metals, quasicrystals also show low thermal and electrical conductivity, which makes them useful as thermal barriers or for reducing eddy currents. Admittedly, bulk quasicrystals can be brittle at room temperature, but this drawback is often mitigated by design: large “approximant” crystals can be tougher, and composites that embed quasicrystalline particles in more ductile matrices can achieve practical durability. Finally, their unusual phason effects, subtle atomic rearrangements unique to quasiperiodic order, mean that careful processing, such as annealing to reduce phason strain, can significantly sharpen their mechanical and corrosion performance.

From Processing to Metamaterials: What Quasicrystals Are Good For Today

In the early days, quasicrystals were tricky to create. Scientists had to cool down molten metal extremely fast, so fast that the atoms couldn’t arrange themselves into the usual repeating crystal patterns. Instead, they “froze” into the unusual, almost-but-not-quite regular patterns we call quasicrystals. Later, researchers learned that by carefully reheating these materials, a process called annealing, they could turn unstable forms into more stable quasicrystals or related structures. This also helped smooth out flaws and release internal stresses.

Today, scientists have new ways to work with quasicrystals. Instead of just casting metals, they can make fine metal powders and press or fuse them together using special high-heat methods. Even though solid blocks of quasicrystals are still brittle, this powder approach lets engineers mix tiny quasicrystal particles into stronger materials, giving them useful toughness. At the same time, techniques like thermal spraying, vapor coating, and even 3D printing can spread thin layers of quasicrystals onto surfaces. That means quasicrystal coatings can now protect tools, valves, or pump parts, anywhere you need extra durability, resistance to corrosion, or strength in high heat.

With these processing advances, quasicrystals have moved from chalkboards to shop floors, and even into the realm of metamaterials. Their low surface energy and high hardness make them ideal for wear- and corrosion-resistant coatings that reduce friction, combat galling, and extend the life of industrial components. Their ability to stay non-stick at high temperatures has led to specialized applications in bakeware, release surfaces, and molds where conventional fluoropolymers would degrade.

Quasicrystals don’t just look unusual, they also behave in unusual ways. Their surfaces can act a bit like built-in catalysts, helping certain chemical reactions run more smoothly and with less wear. Some quasicrystals even “play well” with hydrogen, which makes scientists curious about whether they could be used in the future for things like purifying gases or building better membranes. And because quasicrystals don’t carry heat very well, they’re being studied as materials for things like heat-resistant coatings and energy devices that turn waste heat into electricity.

Quasicrystals have even inspired engineers to create special patterned materials that can shape light and sound in surprising ways. Imagine printing a design based on quasicrystal geometry into glass or plastic, suddenly you can bend, scatter, or block light in ways that ordinary materials can’t. For optics, that means clearer images in telescopes and microscopes, where tiny distortions can blur what you see. It also means better performance in everyday eyeglasses or camera lenses, where quasicrystal-inspired coatings can reduce glare and control how light passes through. These same patterns can even scatter sound more evenly, which is useful in technologies like ultrasound imaging or noise reduction.

Quasicrystals aren’t just about metals and coatings, they can also shape sound. “Acoustic quasicrystals” guide sound waves more smoothly, which makes them useful for things like clearer imaging devices or controlling unwanted noise. In mechanics, engineers are even 3D-printing quasicrystal-inspired patterns into metals and plastics. These unusual structures spread out stress in surprising ways, helping to stop cracks from growing. That means we can design lighter crash-absorbing materials for cars or even medical implants that mimic the natural stiffness of bone.

In short, the ability to process quasicrystals into metamaterials has turned them from fragile laboratory curiosities into versatile, high-performance tools, materials that not only withstand harsh environments but also shape light, sound, heat, and stress in ways that conventional crystals never could.

Dan Shechtman’s story is more than a tale about an unusual pattern of atoms, it is a lesson in scientific courage. He faced ridicule, isolation, and even expulsion from his research group, yet he trusted the evidence before his eyes. Decades later, the world validated his perseverance with the highest honor in science: the Nobel Prize in Chemistry. His journey reminds us that discovery often begins at the edge of what others say is impossible. No doubt, science changes and science advances when someone is stubborn about the truth.

Today, the “forbidden” symmetries that once got him laughed out of the lab are helping us build the future. Quasicrystals are finding their way into durable coatings, cleaner catalysts, hydrogen technologies, heat barriers, optics, acoustics, and even lightweight structures that mimic the resilience of bone. From the lens of a telescope to the surface of a jet engine, quasicrystals are no longer curiosities, they are tools.

So when we think of Shechtman peering into his microscope on that spring morning in 1982, seeing tenfold symmetry sparkle where none should exist, we are reminded of the power of persistence. Because sometimes, it takes one person refusing to look away from the evidence to reveal an entirely new order in nature, and open doors to innovations that can shape our world for generations to come.

Science is a living language. We refine our definitions as our measurements teach us new grammar. Quasicrystals remind us that nature doesn’t read our textbooks. When a tenfold pattern appeared on a screen in a small lab, it asked a simple question: will you trust your eyes?

Thank you for listening to Math! Science! History! Until next time carpe diem!

Math! Science! History!™

with Gabrielle Birchak