Research led by Kimmo Mustonen at the University of Vienna is providing rare experimental insight into how melting unfolds when materials are reduced to just one or two atomic layers. By directly observing an atomically thin crystal as it transitions from solid to liquid, the team has captured evidence of an intermediate phase that challenges long-standing assumptions about how melting works at the smallest scales.
Bui, T. A., Lamprecht, D., Madsen, J., Kurpas, M., Kotrusz, P., Markevich, A., Mangler, C., Kotakoski, J., Filipovic, L., Meyer, J. C., Pennycook, T. J., Skákalová, V., & Mustonen, K. (2025). Hexatic phase in covalent two-dimensional silver iodide. Science, 390(6777), 1033–1037. https://doi.org/10.1126/science.adv7915
In everyday materials, melting is typically abrupt. Once the melting temperature is reached, the ordered structure of a solid collapses and becomes a liquid almost immediately. This behavior has shaped how phase transitions are taught and modeled in three-dimensional systems. However, theory has long suggested that materials confined to two dimensions may behave differently.
Kimmo Mustonen at the University of Vienna stated,
“Without the use of AI tools such as neural networks, it would have been impossible to track all these individual atoms.”
The new study focuses on silver iodide, a compound that can form atomically thin crystalline layers. When reduced to this scale, silver iodide becomes an ideal system for testing theories of two-dimensional melting. Using advanced electron microscopy, the researchers were able to watch individual atoms as the crystal was heated, providing a direct view of the transition process.
The experiments revealed that the crystal did not melt in a single step. Instead, it passed through a distinct intermediate state known as the hexatic phase. In this state, atoms lose their strict positional order, as in a liquid, but still retain a degree of angular order, a feature more typical of a solid. The existence of this phase was proposed decades ago, but until now it had only been observed in simplified model systems such as colloidal particles.
To make these observations possible, the team encapsulated the silver iodide crystal between layers of graphene, protecting it from damage during high-temperature imaging. A scanning transmission electron microscope equipped with a heating stage allowed precise control of temperature while recording atomic-resolution images. The experiments reached temperatures above 1,100 degrees Celsius, close to the material’s melting point.
Because the melting process involved tracking thousands of atoms across many images, the researchers combined microscopy with machine-learning analysis. Neural networks were trained on simulated data to identify atomic positions and follow their motion over time. This approach made it possible to distinguish subtle changes in order that would have been difficult to detect manually.
The analysis showed that the hexatic phase appeared within a narrow temperature window just below the full melting point. Electron diffraction measurements supported this finding, confirming that the intermediate state was a real physical phase rather than a transient artifact of the experiment.
One result stood out as unexpected. While theoretical models predict that both transitions, from solid to hexatic and from hexatic to liquid, should occur gradually, the researchers observed different behavior. The transition from solid to hexatic was continuous, but the shift from hexatic to liquid happened abruptly, resembling the sharp melting seen in bulk materials.
This observation suggests that melting in two-dimensional, strongly bonded materials may not follow existing theoretical descriptions as closely as previously thought. It points to the need for revised models that account for the role of chemical bonding and dimensional constraints in phase transitions.
Beyond fundamental physics, the findings are relevant to materials engineering at the nanoscale. As electronic, catalytic, and sensing devices increasingly rely on atomically thin materials, understanding how these materials behave near phase boundaries becomes more important. Stability, failure modes, and performance at high temperatures are all influenced by how atomic order is lost.
The study also highlights the growing role of advanced microscopy combined with data-driven analysis in materials science. By pairing atomic-resolution imaging with machine learning, researchers can now observe processes that were previously inferred only indirectly.
Rather than redefining melting outright, the work adds clarity to how phase transitions operate when materials are confined to two dimensions. It shows that even for well-studied concepts like melting, new behavior can emerge when systems are examined at the atomic scale, offering both challenges and opportunities for future materials research.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
