Thermal Nanoquakes: Terahertz Frequency Surface Rayleigh Waves in Diamond Nanocrystals

Everything we touch, from the air we breathe to the ground beneath our feet, is made of atoms that are never truly still. Even in a solid block of material, these tiny building blocks vibrate constantly, jiggling in place like a crowd of people shifting their weight. In large, solid objects, these vibrations travel through the material in predictable waves, much like sound moving through a room. However, when scientists shrink a piece of material down to the size of a speck of dust, known as a nanocrystal, the rules change. The surface of the object becomes just as important as the inside, and the vibrations behave in ways that are difficult to predict. Understanding these tiny movements is crucial because they dictate how heat moves through materials, how sensors work, and how future quantum computers might be built. For a long time, scientists knew that the surface of these tiny particles played a special role, but they did not have a clear picture of exactly what kind of vibrations were happening there or why they mattered.

A team of researchers has now filled in this missing picture by looking at nanodiamonds, which are tiny particles of diamond only a few billionths of a meter across. By combining powerful computer simulations with real-world experiments using neutron beams, they discovered that the surface of these particles is constantly undergoing violent, earthquake-like shaking. These are not the slow, rolling tremors that move the ground during a major quake, but rather ultra-fast, high-frequency ripples that race along the surface of the particle. The researchers call these "thermal nanoquakes." They found that these surface waves are so intense that, relative to the size of the particle, the shaking is far more dramatic than the largest earthquakes ever recorded on Earth. This discovery explains a long-standing mystery about why the energy of vibrations in these tiny crystals increases in a straight line rather than following the curved pattern seen in larger materials.

To uncover this secret, the scientists first turned to computer models to watch the atoms in a single nanodiamond move. They simulated a perfect sphere of diamond and another version with a slightly messy, disordered outer layer to see how the vibrations changed. The simulations revealed a distinct pattern of movement that appeared only on the surface. While the atoms in the center of the particle vibrated in a way that matched the behavior of a large, solid block of diamond, the atoms on the outside moved differently. They created waves that traveled along the surface, fading away quickly as they moved deeper into the particle. These waves, known as Rayleigh waves, are the same type of seismic wave that causes the most damage during an earthquake, but here they are happening at a scale so small that they occur trillions of times faster. The computer models showed that these waves are responsible for a specific, straight-line increase in the number of low-energy vibrations, a feature that had been observed in experiments for years but never fully explained.

To prove that these computer models reflected reality, the researchers turned to the Australian Nuclear Science and Technology Organisation to perform experiments with neutron beams. They took two samples: one made of the tiny nanodiamonds and another made of larger, microscopic diamonds. By firing neutrons at these samples, they could measure how the atoms inside were vibrating. The results from the real-world samples matched the computer predictions almost perfectly. The larger diamonds showed the expected curved pattern of vibrations, but the tiny nanodiamonds showed the straight-line pattern, confirming the presence of the surface waves. The data also showed that the vibrations in the tiny particles were broader and softer, suggesting that the atoms were moving with more freedom and less restriction than in the larger crystals. This confirmed that the surface waves were not just a quirk of the computer code but a genuine physical phenomenon occurring in the real material.

The researchers also tested whether these waves could exist if the surface was not free to move. In their simulations, they locked the outer atoms in place, preventing them from shifting. When they did this, the strange straight-line pattern of vibrations disappeared, and the material behaved like a normal, solid block again. This proved that the waves rely entirely on the surface being free to move, just like a real earthquake needs the ground to be unconfined to travel. They further checked if the particles were behaving like a liquid, which can also show similar vibration patterns, but found no evidence of liquid-like movement. Instead, the behavior was consistent with solid atoms shaking in a specific, surface-bound way. The study also looked at how the size of the particle changed the effect. As the particles got smaller, the surface waves became more dominant, and the vibrations of the atoms inside the particle shifted to lower energies, likely due to the tension created by the surface pulling on the core.

This work provides a complete map of how vibrations behave in nanodiamonds, showing that they are a mix of the standard vibrations found in large solids and these unique, surface-bound waves. The discovery of these "thermal nanoquakes" suggests that the surface of nanocrystals is a highly active place, constantly shaking with energy that could influence how heat is transferred or how the particles interact with their surroundings. For scientists designing new materials for electronics, sensors, or medical tools, this means that the surface is not just a boundary but a dynamic region that drives the material's properties. The findings offer a new framework for understanding how tiny objects vibrate, moving beyond the old ideas that treated them simply as small versions of large solids. By recognizing the unique role of these surface waves, researchers can better predict and control the behavior of nanomaterials in the future.