A Scientific Revolution on the Surface
In the world of materials science, they were once considered impossible. Today, they're revolutionizing our understanding of matter itself.
Imagine a mosaic so perfectly structured that it forms intricate, endless patterns, yet you will never find the same arrangement repeated anywhere. This isn't the work of a master artisan but the natural atomic structure of one of the most baffling materials ever discovered: the quasicrystal. For decades, scientists believed that all solid materials followed a simple rule—their atomic arrangements must form repeating patterns. Quasicrystals shattered this fundamental belief, revealing a hidden order that exists between the perfect repetition of crystals and the chaos of glass. The surface of these materials, where their exotic internal architecture meets the outside world, has become a frontier for discoveries that are reshaping technology and challenging our basic understanding of reality.
To understand why quasicrystals sent shockwaves through the scientific community, we need to revisit a basic principle of chemistry that stood for centuries: in crystalline materials, atoms are arranged in patterns that repeat periodically in all directions. This repeating structure allows crystals to possess only certain types of symmetry—specifically two-, three-, four-, and six-fold rotational symmetries. A five-fold symmetry, similar to the pattern on a die, was considered strictly impossible because you can't tile a surface with pentagons without leaving gaps4 8 .
Visualization of a quasicrystal pattern with five-fold symmetry
"The term 'quasicrystal' was coined to describe these new materials that display order without periodicity."
The unique atomic architecture of quasicrystals gives them a set of remarkable physical properties that distinguish them from conventional materials:
Their electrical resistivity increases as they are cooled to extremely low temperatures, the opposite behavior of conventional metals5 .
| Property | Traditional Crystals | Quasicrystals |
|---|---|---|
| Atomic Arrangement | Periodic repetition | Ordered but non-repeating |
| Allowed Symmetries | Two-, three-, four-, six-fold | Five-, eight-, ten-, twelve-fold |
| Electrical Conductivity | Good (if metallic) | Poor |
| Thermal Conductivity | Good (if metallic) | Poor |
| Surface Energy | Typically lower | Often higher |
The surface of any material is where it interacts with the environment, and for quasicrystals, these surfaces display extraordinary characteristics that have captivated researchers. Unlike conventional crystals with predictable surface patterns, quasicrystal surfaces maintain the complex, non-repeating order of their bulk structure. This creates unique environments for chemical reactions, light interaction, and electronic behavior.
Recent breakthroughs have revealed that the mysterious properties of quasicrystal surfaces are governed by their hidden higher-dimensional reality. Since quasicrystals can be described as three-dimensional "shadows" of periodic structures in higher dimensions, their surface properties also reflect this complex inheritance9 .
In 2025, a groundbreaking study led by Professor Guy Bartal and Dr. Shai Tsesses from the Technion, in collaboration with German universities, unveiled previously unknown topological properties of quasicrystal surfaces9 .
The research team employed sophisticated techniques to create and analyze the surface properties of quasicrystals:
The findings were remarkable. Although surface wave patterns appeared different at first glance, the researchers discovered that their two-dimensional topological properties were identical. The only way to distinguish them was by referring to the original higher-dimensional crystal from which the quasicrystal is theoretically derived9 .
Even more intriguing was the discovery of a bizarre temporal effect: two different topological patterns appeared identical when measured after specific attosecond-scale intervals. This phenomenon, described as a "competition" between topological and thermodynamic properties, suggests that the higher-dimensional nature of quasicrystals influences not just their spatial structure but also their temporal behavior9 .
| Aspect Investigated | Experimental Approach | Key Finding |
|---|---|---|
| Spatial Topology | Analysis of plasmon interference patterns | 2D topological properties were identical; distinction required higher-dimensional reference |
| Temporal Behavior | Attosecond-scale time measurements | Different patterns appeared identical at specific time intervals |
| Governing Principles | Comparison with theoretical models | Behavior explained by competition between topological and thermodynamic properties |
For four decades, a fundamental question plagued the field: are quasicrystals genuinely stable, or are they merely metastable artifacts formed under specific conditions? The answer came in 2025 when researchers at the University of Michigan developed a revolutionary approach to applying density functional theory (DFT)—the quantum-mechanical method for calculating a crystal's stability—to these non-repeating structures7 .
Traditional DFT calculations rely on patterns that repeat infinitely, making them incompatible with quasicrystals. The Michigan team, led by Wenhao Sun, ingeniously solved this by "nanoscooping"—extracting smaller nanoparticles from a larger simulated quasicrystal and calculating the energy in each nanoparticle3 7 . By repeating this for increasingly larger particles and extrapolating the results, they could determine the overall energy of the quasicrystal.
The results were definitive: the quasicrystals they studied were enthalpy-stabilized, meaning their atoms achieve the lowest possible energy state in this configuration, just like traditional crystals. This finding validated quasicrystals as genuine, stable forms of matter and explained why they form in nature7 .
| Research Tool | Primary Function | Application Example |
|---|---|---|
| Transmission Electron Microscopy | Revealing atomic structure and symmetry | Shechtman's initial discovery of 10-fold diffraction patterns4 |
| Density Functional Theory (DFT) | Calculating electronic structure and stability | Michigan team's stability proof via "nanoscooping"7 |
| Two-Photon Photoemission Electron Microscopy | Mapping surface wave propagation with high resolution | Technion team's topological studies9 |
| Dynabeads (micrometer-scale particles) | Simulating atomic assembly at observable scales | Studying quasicrystal formation processes3 |
| Rapid Cooling Apparatus | Creating metastable quasicrystals | Producing early aluminum-manganese quasicrystals4 |
The unique surface properties of quasicrystals have led to several practical applications, with more on the horizon:
Their unique structure allows them to absorb energy in unusual ways, offering potential for shock-absorbing materials1 .
Because they are poor thermal conductors, quasicrystals can serve as effective thermal barrier coatings3 .
The surface science of quasicrystals has journeyed from impossible discovery to Nobel Prize-winning revolution to a field that continues to challenge and expand our understanding of matter. What began with Shechtman's perplexing observation has evolved into a rich interdisciplinary field connecting mathematics, physics, chemistry, and materials science.
The recent discoveries of topological surface properties and definitive proof of quasicrystal stability represent more than just scientific milestones—they open the door to a new era of material design. By understanding how these exotic structures form and behave at their surfaces, scientists are now better equipped to engineer materials with tailored properties for specific applications.
"This understanding agrees with the explanation given by Levine and Steinhardt," connecting back to the theoretical foundation that made sense of Shechtman's impossible crystals decades earlier9 .
The story of quasicrystals reminds us that nature often harbors deeper complexities than our models can predict, and that scientific progress often begins when someone dares to question why the "impossible" might actually be possible.