In a materials chemistry laboratory at National Taiwan University, a team of researchers has accomplished something that has frustrated materials scientists for years. Led by Mayumi Egashira with co-corresponding author Professor Chien-Lung Wang, the group has produced soft quasicrystals — materials whose patterns never repeat, yet never fall into disorder — with a single, uniform orientation stretching across millimeter-scale regions. The pattern they achieved carries the rare twelve-fold, or dodecagonal, symmetry that classical crystallography says should not exist at all.
The study, published in the *Journal of the American Chemical Society* (DOI: 10.1021/jacs.6c09814), introduces a strategy the team calls vapor-induced self-assembly, or VISA. Rather than mixing molecules and hoping they settle correctly, the researchers steered them through a normally inaccessible assembly pathway — a reverse structural transformation driven by vapor treatment and cooling. The result is the first highly oriented, face-on, single-domain dodecagonal quasicrystal of its kind, and it opens a new way of thinking about how complex materials are made.
What Makes a Quasicrystal "Impossible"?
To understand why this result matters, we have to go back to 1982. Working late in a laboratory, Israeli chemist Dan Shechtman examined an alloy of aluminum and manganese under an electron microscope and saw something that should not have been there: a diffraction pattern with ten-fold symmetry, like a star with ten perfect points. According to every textbook of the day, this was crystallographically impossible. In an ordinary crystal, atoms sit on a repeating grid, and geometry dictates that such grids can only show one, two, three, four, or six-fold rotational symmetry. Five-fold and ten-fold symmetry are forbidden, because regular pentagons cannot tile a flat surface without leaving gaps.
Shechtman's boss told him to go back and read the textbook. Linus Pauling, the double Nobel laureate, dismissed the finding, saying "there are no quasi-crystals, only quasi-scientists." But Shechtman was right, and the scientific establishment came around. In 2011, he received the Nobel Prize in Chemistry for discovering that matter can order itself in ways that are neither periodic crystals nor random glass: quasicrystals, whose patterns have long-range order but never exactly repeat. A decade earlier, Roger Penrose had already designed aperiodic tilings — covering a surface with two simple shapes and never repeating — that turned out to be the blueprint of a real quasicrystal.
What the Taiwanese team worked with is a newer cousin: the soft quasicrystal. Instead of hard metal alloys, soft quasicrystals are built from flexible building blocks — polymers, dendrimers, and engineered nanoparticles — that assemble themselves through the push and pull of weak molecular forces. They were first reported in the mid-2000s and immediately attracted attention, because soft matter can be processed into films and coatings at far lower cost and temperature than metallurgical quasicrystals. The catch is that soft building blocks are fidgety. Getting them to settle into one large, perfectly ordered quasicrystal — rather than a patchwork of small, competing orientations — has remained one of the field's toughest challenges.
The Twelve-Fold Pattern, Explained
Not all quasicrystals are created equal, and the twelve-fold pattern — dodecagonal symmetry — is special. Think of it this way: a snowflake has six-fold symmetry, so if you rotate it by 60 degrees it looks the same. A dodecagonal quasicrystal repeats its appearance twelve times in a full turn, every 30 degrees — something no periodic crystal can do.
Why does it matter? Twelve-fold symmetry sits closer to perfect circular symmetry than any achievable crystalline pattern, which gives dodecagonal quasicrystals a remarkable property: near-isotropic behavior. Light passing through them, or electrons moving across them, encounters nearly the same structure in every direction. For engineers, this is gold. Photonic materials built on dodecagonal patterns can guide or block light of certain colors from all directions at once — something ordinary photonic crystals struggle to do. That is why the race to produce large, uniform dodecagonal quasicrystals has been so competitive, and why the new result from Taipei drew immediate attention.
The Real Problem: Getting Every Tile to Face the Same Way
The molecules in Egashira's experiments know how to form twelve-fold quasicrystals — that part is not the problem. The problem is what happens when they do it on their own. Left to themselves, self-assembling molecules create quasicrystals the way frost creates ice on a window: dozens of small patches, each beautifully ordered, but each pointing in a different direction. At the boundaries where these patches meet, the order breaks down.
This domain problem is the central bottleneck of the field. A photonic device or a functional coating needs its pattern to be uniform over a large area — a "single domain." Previous methods could make large regions of soft quasicrystals, but the twelve-fold pattern pointed every which way inside them, and the competing orientations blurred the very properties that make the material useful.
The Taiwanese researchers started by watching this failure mode closely. Tracking their molecules over time, they found that the same molecules could travel down entirely different assembly pathways depending on temperature and molecular interactions. A freshly formed twelve-fold quasicrystal would gradually rearrange itself into different ordered structures — the well-known Frank–Kasper A15 and sigma phases — as conditions changed. Each pathway involved molecular shape optimization and volume redistribution.
How They Did It: Vapor-Induced Self-Assembly
The crucial insight was that these pathways do not have to be walked in only one direction. Having mapped how the quasicrystal fell apart into other phases, the team reasoned they could drive the process in reverse — back into the twelve-fold quasicrystal — if they could find a route through the energy landscape that molecules normally never take.
The Rugged Energy Landscape
Imagine a mountain range where every valley represents a different molecular arrangement, and the molecule is a ball rolling downhill toward the deepest valley. The twist is that the landscape is "rugged": full of pits and ridges, so a ball dropped casually will roll into the nearest shallow dip and stay there — a metastable state — rather than reaching the true bottom. In this analogy, the ordinary ways of preparing quasicrystals drop the ball randomly; it lands in scattered, misaligned domains.
The Taiwanese team's title phrase — "nonequilibrium navigation of a rugged energy landscape" — describes the opposite approach: instead of letting molecules roll downhill wherever they please, the researchers carefully tilted the landscape itself, guiding the molecules along a chosen route toward exactly one deep valley.
The Reverse Transformation
The vehicle for this navigation is vapor-induced self-assembly. By exposing the material to a carefully controlled solvent vapor and then cooling it in a precisely managed sequence, the team gave the molecules just enough mobility to rearrange, then froze them into place at exactly the right moment. The vapor treatment opened a pathway back from the A15 and sigma phases into the dodecagonal quasicrystal — a reverse structural transformation that conventional heating or cooling alone cannot reach.
Crucially, this reverse route passes through a state where only one orientation of the twelve-fold pattern is favored. Competing orientations — the domains that previously ruined the order — were suppressed as the molecules traveled through this narrow passage. When the transformation finished, the result was a face-on dodecagonal quasicrystal with a single, uniform twelve-fold orientation extending over millimeter-scale regions: enormous by the standards of molecular self-assembly, where uniformity usually collapses at the micrometer scale.
"By exploring assembly pathways that are normally difficult to access, we can guide molecules toward highly ordered structures that conventional methods struggle to produce," says Professor Wang. The sentence reads like a mission statement for a whole new direction in materials chemistry.
Why One Uniform Domain Changes Everything
A millimeter-scale, single-domain soft quasicrystal is not just a prettier microscope image — it crosses the threshold from laboratory curiosity to engineering material. Photonic components, for example, need optical uniformity across the entire device; a patchwork of misaligned domains scatters light and destroys the very band-gap effects designers want. With a single domain this large, researchers can now fabricate and test photonic materials with genuinely twelve-fold symmetric band gaps — a capability that was previously theoretical.
The applications the field is watching include:
- **Photonic materials:** waveguides, filters, and light-trapping layers that work identically in all in-plane directions, potentially improving solar cells and LEDs.
- **Protective coatings:** quasicrystalline structures are known for unusual hardness combined with low friction; large uniform domains make these properties predictable and consistent.
- **Nanoscale templates:** the non-repeating twelve-fold pattern is an ideal stamp for organizing other nanoparticles or biomolecules into arrangements no crystal could provide, useful for sensors and electronics.
Most importantly, the method is general: the same navigate-the-energy-landscape strategy could be adapted to other building blocks and symmetries — a recipe, not just a single dish.
The Bigger Lesson: Design the Pathway, Not Just the Product
Step back from the chemistry, and the message is philosophical as much as technical. For decades, materials science asked "what arrangement is most stable?" — find the deepest valley. The Taiwanese team asks instead: "which journey leads to the arrangement we want?" By controlling the *how* of assembly, they reached a structure equilibrium methods cannot produce at a useful scale.
This places the work in a remarkable season of materials breakthroughs. Our report on the ghost of superconductivity in quantum materials showed how fragile quantum states can be coaxed into revealing themselves, while our story on Bethe strings, the 95-year-old quantum prediction finally confirmed, showed how theory's most exotic predictions keep becoming laboratory reality. The quasicrystal advance belongs in the same conversation: another case of scientists refusing to accept that a hard-to-reach state of matter is unreachable, and engineering a path to it.
What Comes Next
The immediate next steps are clear. The researchers will need to show that vapor-induced self-assembly works at larger scales and with different molecular building blocks — and to explore whether the same nonequilibrium navigation can produce other "forbidden" symmetries in single-domain form. Industrial partners will be watching whether the process can be integrated into existing thin-film manufacturing, where vapor treatments are already routine.
Longer term, the prospect is a library of designer soft materials whose patterns are chosen for their function — photonic quasicrystals tuned to specific colors, templates with prescribed symmetries — all made by guiding molecules along hidden pathways. Four decades after Shechtman's ten-pointed star got him laughed out of the room, the "impossible" symmetries are becoming some of the most practical tools in materials science.
What began as a curiosity — a pattern that supposedly could not exist — has grown into an engineering discipline. With a puff of vapor and a carefully choreographed cooldown, the Taiwanese team has shown that even the most stubborn molecules can be guided to order, as long as you take them by the right road.