In normal crystals like salt or diamond, atoms are arranged in patterns that repeat over and over in a grid. However, imagine a crystal where atoms follow a set of rules, but never repeat—like a tiled floor where the design keeps changing.
That’s the mystery of quasicrystals, a strange class of materials discovered four decades ago. For a long time, scientists weren’t sure if these structures were real, or just the frozen byproduct of rapid cooling.
For instance, when molten metal or another liquid cools down very quickly, the atoms might not have enough time to arrange themselves into a neat, repeating pattern. Instead, they freeze in place in a more disordered or irregular way. So, scientists once thought quasicrystals might just be this kind of accidental arrangement.
However, now, physicists at the University of Michigan have cracked the puzzle. Their latest study shows that some quasicrystals are not only real, they’re stable.
“The first step to understanding a material is knowing what makes it stable, but it has been hard to tell how quasicrystals were stabilized,” Woohyeon Baek, first author of the study and a doctoral student at the University of Michigan (UM), said.
The dilemma with quasicrystals
The story of quasicrystals began in the 1980s when scientists observed that certain alloys formed unexpected atomic structures with five-fold symmetry, like the shape of a starfish or a 20-sided die. These patterns had order, but didn’t repeat like normal crystals.
At the time, this discovery challenged what physicists believed to be a basic rule of nature that all solids with long-range order must exhibit a repeating pattern. Daniel Shechtman, whose discovery of quasicrystals challenged this rule, faced widespread skepticism before his work was finally accepted and earned him a Nobel Prize in 2011.
Even after their existence was confirmed, one big question remained: Are quasicrystals thermodynamically stable? Or are they just a result of rapid cooling, like how molten glass freezes into a disordered structure during cooling before the atoms can settle into a stable crystal?
To find the answers to these questions, scientists needed to calculate the internal energy of quasicrystals and compare it to that of other competing crystal structures, but there was a big challenge.
The standard tool for these calculations, called density functional theory (DFT), relies on modeling small repeating units of a material. However, since quasicrystals don’t repeat, the usual DFT approach breaks down. That’s where the new study comes up with an interesting solution.
What makes a quasicrystal stable?
Instead of trying to model an infinite quasicrystal, Baek and his team simulated tiny chunks, or nanoparticles, of the quasicrystal structure. By carefully calculating the energy of these small fragments and scaling up the results, they could estimate the bulk energy of a full quasicrystal.
If that energy is lower than the sum of possible competing phases, it means the quasicrystal is energetically favored and truly stable.
They applied this method to two well-known quasicrystals. One made of scandium and zinc, and the other of ytterbium and cadmium. Their calculations showed that both quasicrystals are stable because they have the lowest possible energy for those elements.
In other words, the atoms naturally prefer to arrange themselves in these unusual patterns, not just by chance, but because it’s the most stable option under the right conditions. However, running these simulations wasn’t easy.
Each time the researchers doubled the number of atoms in their model, the computational load increased roughly eightfold. To overcome this, they developed a new algorithm that reduced the need for communication between computer processors, dramatically speeding up the calculations. They also used GPU acceleration to handle the heavy lifting.
“In conventional algorithms, every computer processor needs to communicate with one another, but our algorithm is up to 100 times faster because only the neighboring processors communicate, and we effectively use GPU acceleration in supercomputers, Vikram Gavini, one of the study authors and a professor at UM, said.
Together, these innovations allowed them to simulate hundreds of atoms at a time, enough to see the energy trend and confirm the stability of the quasicrystals. “Our techniques broadly open the door to first-principles investigations into the structure–bonding–stability relationships of aperiodic materials,” the study authors added.
Time to think beyond ordered arrangements
This work settles a long-standing debate in condensed matter physics. It shows that quasicrystals, despite their aperiodic patterns, can be just as stable as ordinary crystals. That changes how scientists think about order in solid matter and opens new possibilities in designing materials with complex, non-repeating structures.
The implications also go beyond just quasicrystals. The team’s new method for calculating energy in non-repeating or disordered systems could be applied to solve many other challenges.
For example, it could help scientists understand the behavior of amorphous materials, glasses, and interfaces between different solids, areas where traditional modeling tools fall short. It could also help in quantum materials research, as many quantum devices, including sensors and potential quantum bits (qubits), rely on defects or irregularities in crystals.
“We can now simulate glass and amorphous materials, interfaces between different crystals, as well as crystal defects that can enable quantum computing bits,” Gavini said.
The study is published in the journal Nature Physics.
