A team of physicists has characterized an exotic class of matter that defies the fundamental rules of crystal behavior, demonstrating that crystals composed of rotating particles can spontaneously shatter into fragments and then reassemble themselves. The discovery, made by a joint German-American research group, reveals a bizarre microscopic world where materials possess strange properties, such as twisting when they are pulled, and exhibit defects that can be controlled in a targeted manner. This counter-intuitive dynamic behavior opens a new frontier for materials science and challenges long-held theories of solid-state physics.
This phenomenon, detailed in the Proceedings of the National Academy of Sciences, is not confined to synthetic laboratory materials but also appears in biological systems. The researchers from Aachen, Düsseldorf, Mainz, and Wayne State University developed a comprehensive theory to predict and explain the crystals’ unique characteristics, which are governed by previously poorly understood transverse forces. Observations of starfish embryos swimming in concert, organizing themselves into a rotating crystalline structure, confirm that these forces operate in the natural world, suggesting a fundamental law of nature that connects the microscopic behavior of particles with the collective function of living organisms.
A New Class of Crystalline Solids
Conventional crystals, from salt grains to diamonds, are defined by a static, repeating lattice of atoms. In stark contrast, roto-crystals are solids made of components that are in a state of constant rotation. This intrinsic motion gives rise to material properties that are, in the words of one researcher, “downright odd.” One of the most striking of these is known as “odd elasticity.” While normal materials will stretch or compress along the direction of a force, odd elastic materials respond by twisting. This unusual quality is a direct result of the transverse, or sideways, forces that the rotating building blocks exert on one another.
The internal structure of these solids is also highly unusual. The boundaries between different crystalline fragments, or grains, do not follow conventional energetic rules. Furthermore, the research team found that defects within the crystal lattice—interruptions in the repeating pattern—can be precisely controlled. This level of control over material imperfections is a significant step, as defects often dictate a material’s most important electronic and physical properties. Understanding how to manipulate them in roto-crystals could pave the way for novel materials engineered with specific, dynamic functions.
The Paradoxical Growth of Roto-Crystals
Perhaps the most revolutionary finding is the way roto-crystals grow and shrink. For centuries, it has been understood that under favorable conditions, crystals grow larger, with smaller crystals merging into bigger ones. The new research demonstrates that roto-crystals behave in the exact opposite manner. When a large roto-crystal forms, it becomes unstable and spontaneously decays, breaking apart into an aggregation of smaller, rotating crystallites. Conversely, smaller fragments will only grow up to a certain critical size before the process reverses.
This behavior is directly linked to the speed of the rotating components. The research team’s work established a fundamental law for these systems: the size of the crystal fragments is intrinsically tied to their rotation speed. This self-limiting growth mechanism, where stability is found in fragmentation rather than consolidation, represents a paradigm shift in crystallography and suggests that the principles governing these active materials are fundamentally different from those of passive, static matter.
From Biological Systems to New Materials
Observation in Living Organisms
The theoretical framework for roto-crystals found stunning validation in the biological realm. An earlier experiment conducted at MIT revealed that a dense group of starfish embryos, each spinning and swimming, collectively organizes into a large, rotating crystalline structure. The embryos, through their individual movements, influence each other via hydrodynamic forces that are mathematically equivalent to the transverse interactions seen in synthetic systems. According to Professor Hartmut Löwen of Heinrich Heine University Düsseldorf, a system with many rotating elements behaves in ways that defy normal intuition, forming a solid mass with peculiar properties. The purpose of this collective crystalline behavior in the embryos is not yet known, but its existence confirms that roto-crystals are a feature of the natural world, not just an artificial curiosity.
Synthetic and Future Applications
Beyond the living world, transverse forces are known to occur in certain synthetic materials, such as specific magnetic solids. The new, comprehensive theory developed by the research team, led by Professor Zhi-Feng Huang of Wayne State University, provides a powerful tool for predicting the behavior of these systems. The model calculations suggest a range of exciting applications, from advanced colloid research to the development of new biological models. For example, the property of odd elasticity could be harnessed to create innovative technical switching elements that respond to force in novel ways, while the ability to control defects could lead to new classes of smart materials with tunable properties.
A Unifying Cross-Scale Theory
A key achievement of the international collaboration was the development of a cross-scale theory that explains the full spectrum of roto-crystal phenomena, from the interactions of individual building blocks to the behavior of the bulk material. This theoretical model successfully predicts the spontaneous disintegration and reassembly, the unusual growth laws, and the odd material properties that the physicists observed. It serves as a foundational framework for a new area of physics focused on “active matter”—systems whose constituent parts consume energy and exhibit motion. The theory provides scientists with the tools to explore and ultimately engineer these complex systems, bridging the gap between fundamental physics and practical application.