Watching a Crystal Melt One Atom at a Time: Capturing an Unexpected Phase in Two Dimensions

Melting is one of the most familiar phase transitions in physics. In three dimensional materials, the process is usually abrupt. Once a critical temperature is reached, the ordered structure of a solid collapses and gives way to a liquid. This behavior is so consistent that it has long shaped how engineers and physicists think about thermal stability and material limits.

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

Recent work led by Kimmo Mustonen at the University of Vienna, however, shows that this intuition does not always apply. By directly observing an atomically thin crystal as it melted, researchers have captured a fleeting intermediate state that exists neither as a conventional solid nor as a liquid. The findings provide the clearest experimental evidence so far that melting in two dimensional materials follows different rules, with implications for materials science, nanotechnology, and device engineering.

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 study focused on silver iodide, a compound known for its well defined crystal structure and relevance in solid state physics. When reduced to a single atomic layer, silver iodide behaves as a two dimensional material, meaning atomic motion is constrained to a plane. In such systems, theory has long suggested that melting might occur in stages rather than all at once, passing through a so called hexatic phase.

The hexatic phase was proposed decades ago as an intermediate state unique to two dimensions. In this phase, atoms lose their fixed positions, as they would in a liquid, but retain a degree of angular order typically associated with a solid. Until recently, convincing evidence for this state came mainly from simplified model systems, such as colloidal particles or soft matter experiments. Whether the same behavior could occur in real, chemically bonded crystals remained an open question.

To address this, the Vienna team developed an experimental setup that allowed them to watch melting unfold at atomic resolution. The researchers encapsulated an atomically thin silver iodide crystal between protective layers of graphene, forming what they describe as a stable “sandwich.” This configuration prevented contamination and structural damage while allowing the crystal to be heated to extreme temperatures.

Using a scanning transmission electron microscope equipped with a precision heating stage, the team gradually raised the temperature above 1100 degrees Celsius. This made it possible to record thousands of high resolution images as the crystal evolved. Each image captured the positions of individual atoms, creating an unprecedented dataset of atomic motion during melting.

Analyzing this volume of data posed a major challenge. Tracking every atom across thousands of frames is not feasible using conventional image processing alone. To overcome this, the researchers employed neural network based analysis, trained on large sets of simulated atomic configurations. This allowed them to reliably identify atomic positions and correlations throughout the heating process.

The results revealed a narrow but clearly defined temperature window, roughly 25 degrees below the melting point, in which the crystal entered the hexatic phase. In this regime, atomic spacing became disordered, while angular relationships between neighboring atoms remained partially intact. Electron diffraction measurements independently confirmed this behavior, strengthening the conclusion that the observed state was not an artifact of imaging or analysis.

One of the most striking aspects of the study was how the phase transitions unfolded. Existing theories predicted that both the transition from solid to hexatic and from hexatic to liquid would occur smoothly. Instead, the researchers found a mixed picture. The transition from solid to hexatic was gradual, consistent with theoretical expectations. The transition from hexatic to liquid, however, was abrupt, resembling the sudden melting seen in bulk materials.

This observation suggests that melting in covalently bonded two dimensional crystals is more complex than previously assumed. It also highlights the limits of simplified theoretical models when applied to real materials with strong chemical interactions.

From an engineering perspective, these findings matter because two dimensional materials are increasingly used in electronic, optical, and sensing devices. Thermal stability at the atomic scale can determine device performance, reliability, and failure modes. Understanding that melting may proceed through intermediate states opens new questions about how heat, defects, and mechanical stress interact in ultra thin systems.

More broadly, the work demonstrates how advances in microscopy and data analysis are changing what can be observed directly. Atomic resolution imaging combined with machine learning is making it possible to study phase transitions not as averaged bulk processes, but as sequences of individual atomic events.

As researchers continue to explore materials at reduced dimensions, discoveries like this are likely to become more common. What was once treated as a simple, universal transition now appears to depend strongly on dimensionality and bonding. For engineers designing the next generation of nanoscale devices, these details may prove just as important as the materials themselves.