Unique Hierarchical Rotational Dynamics Induces Ultralow Lattice Thermal Conductivity in Cyanide-bridged Framework Materials

Heat is a restless traveler. In the solid world of materials, it moves not as a fluid, but as a chaotic jostling of atoms, a vibration that ripples through a structure like a wave through a crowd. For engineers and scientists, controlling this journey is a matter of survival. In devices that convert waste heat into electricity, or in the protective coatings of jet engines, the goal is often to stop the heat in its tracks. The best way to do this has traditionally been to build materials that are heavy and complicated, using dense atoms that act like speed bumps for these vibrations. But this approach hits a wall when we need materials that are light. A spacecraft component or a flexible electronic skin cannot afford the weight of lead or heavy metals; it needs to be built from the lightest elements available, like carbon, nitrogen, and oxygen. The challenge has been to find a way to make these lightweight structures just as good at blocking heat as their heavy counterparts, a feat that seemed impossible because light atoms usually let heat zip right through.

A team of researchers at Xiangtan University and Hunan Normal University in China has now found a way to break this rule. They discovered that by arranging light atoms in a very specific, flexible framework, they could create a material that is exceptionally good at stopping heat, even though it is made of the lightest ingredients. They focused on a family of materials known as cyanide-bridged frameworks. Imagine a structure built from tiny clusters of atoms connected by rigid rods of carbon and nitrogen. In these materials, the connections are not stiff and unyielding; they are flexible enough to allow the entire clusters to wobble and rotate. The researchers found that this specific kind of movement, combined with a unique internal architecture, creates a perfect storm of resistance for heat. The result is a material that conducts heat so poorly that it rivals the best heavy, complex materials known to science, despite being made of elements that are a fraction of the weight.

The secret lies in how the atoms move. In most solid materials, heat travels as sound waves, moving smoothly from one atom to the next. To stop this, you need to scatter those waves. The researchers found that in these cyanide frameworks, the atoms do not just vibrate in place; they rotate. Because the structure is built from super-atomic clusters—groups of atoms that act like single, larger units—these clusters have extra freedom to spin and twist. This rotation is not a simple, single motion. It happens in layers, with different parts of the structure moving in complex, hierarchical ways. When these clusters rotate, they create a chaotic environment for the heat waves. Instead of flowing smoothly, the heat waves are constantly bumped, twisted, and scattered in every direction.

This chaotic motion is so effective because it triggers a phenomenon called negative thermal expansion. In most materials, when you heat them up, they expand as the atoms push further apart. In these cyanide frameworks, the opposite happens: as the temperature rises, the material actually shrinks. This counterintuitive behavior is a sign that the atoms are moving in a highly unusual, non-linear way. The researchers observed that the rotation of the atomic clusters creates a specific kind of instability in the material's structure. As the clusters spin, they pull the structure inward rather than pushing it outward. This intense, non-linear motion makes it incredibly difficult for heat to find a clear path through the material. The heat waves are essentially trapped in a maze of spinning atoms, unable to travel far before being scattered back.

The researchers did not just observe this behavior; they quantified it with high precision. Using advanced computer simulations that modeled the behavior of billions of atoms, they calculated exactly how much heat these materials could conduct. They looked at several specific compounds, including ones made with cadmium, sodium, lithium, and silver, all linked with carbon and nitrogen. The results were striking. At room temperature, these materials conducted heat at rates between 0.35 and 0.81 watts per meter per kelvin. To put this in perspective, this is one to two orders of magnitude lower than other lightweight materials with similar weights, and it is even lower than many heavy, complex materials that have been studied for decades. For a material made of such light elements, this level of thermal resistance is unprecedented.

What makes this discovery particularly powerful is that it works through a combination of two different mechanisms that usually exist in separate types of materials. One mechanism comes from the hierarchical structure, where the large atomic clusters create a wide variety of vibration frequencies that block heat. The other comes from the rotational dynamics, similar to what is seen in perovskite materials, where the spinning of atomic units creates strong resistance. The researchers found that in these cyanide frameworks, these two mechanisms work together in a synergistic way. The rotation of the clusters creates a vast "phase space" for heat scattering, meaning there are countless ways for the heat energy to be dissipated. This leads to a situation where the scattering of heat is so intense that it dominates the material's behavior, effectively turning the material into a thermal insulator.

The team also explored how changing the specific atoms in the framework affected the heat flow. They found that as they transitioned the central atom from Boron to Indium within the same structural family, the heat conduction dropped even further. This was because the change in the specific element made the bonds between the clusters progressively weaker and more flexible. This increased flexibility allowed the clusters to rotate with even greater amplitude, creating more chaos for the heat waves. The most effective material in their study, a compound containing indium, showed the lowest thermal conductivity, confirming that the degree of atomic flexibility is directly linked to how well the material blocks heat.

This work challenges the long-held belief that you need heavy, complex atoms to stop heat effectively. By showing that light, flexible structures can achieve the same result through clever design, the researchers have opened a new path for material science. They have demonstrated that the key to stopping heat is not just about weight, but about how the atoms are arranged and how they move. The ability to create materials that are both light and thermally insulating could revolutionize fields that rely on temperature control, from aerospace engineering to next-generation electronics. The study provides a clear blueprint for how to design these materials: build a framework that allows for hierarchical rotation and embrace the resulting chaos. In doing so, they have turned a fundamental limitation of lightweight materials into a powerful new advantage.