Quasicrystals, an unusual atomic structural form that falls between crystal and glass, may be the most stable form of matter, despite the fact that this unusual arrangement of atoms was once considered impossible by scientists.
According to University of Michigan researchers in a new study, what makes these materials so unique is that the atoms are arranged in lattices similar to those found in crystals. Yet unlike crystals, these lattices do not repeat.
The new work relied on simulations that demonstrated how, despite quasicrystals featuring irregular patterns similar to those found in glass caused by rapid heating and cooling, these unique materials are fundamentally stable.
The Enigma of Quasicrystals
“We need to know how to arrange atoms into specific structures if we want to design materials with desired properties,” said co-author Wenhao Sun, the new study’s corresponding author and a University of Michigan Dow Early Career Assistant Professor of Materials Science and Engineering. “Quasicrystals have forced us to rethink how and why certain materials can form. Until our study, it was unclear to scientists why they existed.”
Israeli scientist Daniel Shechtman was the first to describe quasicrystals in 1984, a discovery that seemed to defy known physics. He conceived of the arrangement when he observed that the structure of certain metals, such as aluminum and manganese, resembled a cluster of many 20-sided dice joined at their faces. From these metallic arrangements, Shechtman envisioned a five-fold symmetry, where a structure would be identical from five different views.
When Shechtman proposed the idea, scientists believed that crystal lattices must repeat in all directions, making the five-fold symmetry Shechtman suggested an impossibility. However, in the years following Shechtman’s description of quasicrystals, such materials were produced both synthetically in laboratories and discovered to occur naturally in billion-year-old meteorites. With his work validated, Shechtman was eventually awarded the Nobel Prize in Chemistry in 2011.
Properties That are Difficult to Quantify
Many questions remained about exactly how quasicrystals form, even after their formal recognition. Confusion arose mainly from the method used to calculate a crystal’s stability, involving what is known as density functional theory. The theory uses infinitely repeating patterns to determine a crystal’s stability, yet quasicrystals lack that fundamental feature.
“The first step to understanding a material is knowing what makes it stable, but it has been hard to tell how quasicrystals were stabilized,” said lead author Woohyeon Baek, a U-M doctoral student in materials science and engineering.
When crystals form, usually atoms arrange themselves into the lowest energy chemical bonds possible, known as enthalpy-stabilized crystals. Somewhat close to crystal’s enthalpy stabilization, glass is entropy-stabilized, but its rapid cooling freezes the atoms with no pattern. A slowed cooling can result in the formation of a sort of “middle ground” state where arrangements repeat locally, but vary throughout the substance at longer ranges.
Making Sense of Impossibility
When the researchers set out to determine whether quasicrystals are enthalpy-stabilized, like crystals, or entropy-stabilized, like glass, they removed small nanoparticles from a simulated chunk of quasicrystal. They next calculated the total energy present in each nanoparticle, which, because of the defined particle boundaries, allowed them to calculate stability with infinitely repeating patterns.
From their calculations, the team determined that both a scandium-zinc alloy and a ytterbium-cadmium alloy were enthalpy-stabilized.
One of the most significant challenges for the team was a massive computing bottleneck that arose in scaling up their calculation from nanoparticles to larger samples. Larger particles produce more accurate calculations, necessitating the team to scale up their findings; however, every doubling of atoms also increases computing time eightfold.
“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,” said co-author Vikram Gavini, a U-M professor of mechanical engineering and materials science and engineering.
“We can now simulate glass and amorphous materials, interfaces between different crystals, as well as crystal defects that can enable quantum computing bits,” Gavini concluded.
The paper, “Quasicrystal Stability and Nucleation Kinetics from Density Functional Theory,” appeared in Nature Physics on June 13, 2025.
Ryan Whalen covers science and technology for The Debrief. He holds an MA in History and a Master of Library and Information Science with a certificate in Data Science. He can be contacted at ryan@thedebrief.org, and follow him on Twitter @mdntwvlf.