New research offers clearer insight into how phase transitions unfold at the atomic scale in real materials.

When ice turns into water, the change happens almost instantly. Once the melting temperature is reached, the rigid structure of the solid collapses and becomes a flowing liquid. This abrupt shift is typical for most materials in three dimensions. Extremely thin materials, however, behave very differently. Instead of switching directly from solid to liquid, they can pass through an unusual intermediate state known as the hexatic phase.

Researchers at the University of Vienna have now directly observed this rare state in an atomically thin crystal. By combining advanced electron microscopy with neural network analysis, the team recorded a silver iodide crystal, protected by graphene, as it melted. These ultra‑thin, two‑dimensional materials made it possible to watch atomic‑scale melting as it unfolded. The results deepen scientific understanding of phase transitions and, unexpectedly, challenge earlier theoretical predictions. The work has now been published in Science.

In everyday experience, melting is sudden. Ice, metals, minerals, and other three‑dimensional materials lose their orderly structure as soon as the melting point is reached, becoming disordered liquids almost immediately. This rapid transformation has long been considered a universal feature of melting in bulk materials.

That picture changes when materials are reduced to nearly two dimensions. At this extreme thinness, melting can proceed in stages. Between the solid and liquid states, a distinct intermediate form of matter can appear, called the hexatic phase. First proposed in the 1970s, this phase combines properties of both states. Particle spacing becomes irregular, similar to a liquid, while the angles between neighboring particles remain relatively well organized, resembling a solid.

The Protochips Fusion heating stage and chip used in the Nion electrical module, which enabled the scientists to conduct controlled high‑temperature studies in the vacuum of the microscope. Credit: Jani Kotakoski

Until now, evidence for the hexatic phase had been limited to large‑scale model systems, such as tightly packed plastic spheres. Whether the same behavior could exist in real materials held together by strong chemical bonds was an open question. The international team led by the University of Vienna has now answered it.

By observing atomically thin silver iodide (AgI) crystals as they melted, the researchers demonstrated for the first time that the hexatic phase can occur in a covalently bonded material. This resolves a long‑standing scientific puzzle and reveals new details about how melting works in two dimensions.

Melting atoms in a protective ‘graphene sandwich’

Using an advanced scanning transmission electron microscope (STEM) equipped with a heating stage, the team slowly raised the temperature to more than 1100 °C. This approach made it possible to record the melting process directly, capturing atomic‑scale changes as they happened. By combining these high‑resolution images with neural network analysis, the researchers were able to track how the solid crystal passed through the hexatic phase before fully becoming a liquid, offering a rare, real‑time view of melting at the level of individual atoms.

“Without the use of AI tools such as neural networks, it would have been impossible to track all these individual atoms,” explains Kimmo Mustonen from the University of Vienna, senior author of the study. The team trained the network with huge amounts of simulated data sets before processing the thousands of high‑resolution images generated by the experiment.

Kimmo Mustonen in front of the Nion UltraSTEM 100 microscope used for the study. Credit: Jani Kotakoski

Their analysis yielded a remarkable result: within a narrow temperature window – approximately 25 °C below the melting point of AgI – a distinct hexatic phase occurred. Supplementary electron diffraction measurements confirmed this finding and provided strong evidence for the existence of this intermediate state in atomically thin, strongly bound materials.

A new chapter in the physics of melting

The study also revealed an unexpected twist. According to previous theories, the transitions from solid to hexatic and from hexatic to liquid should be continuous. However, the researchers observed that while the transition from solid to hexatic was indeed continuous, the transition from hexatic to liquid was abrupt, similar to the melting of ice into water.

Artistic illustration of a silver iodide crystal as it approaches its melting temperature. Credit: 2025 Thuy An Bui, David Lamprecht, and Kimmo Mustonen, CC BY 4.0

“This suggests that melting in covalent two‑dimensional crystals is far more complex than previously thought,” says David Lamprecht from the University of Vienna and the Vienna University of Technology (TU Wien), one of the main authors of the study alongside Thuy An Bui, also from the University of Vienna.

This discovery not only challenges long‑standing theoretical predictions, but also opens up new perspectives in the study of materials at the atomic level. “Kimmo and his colleagues have once again demonstrated how powerful atomic‑resolution microscopy can be,” says Jani Kotakoski, head of the research group at the University of Vienna.

The results of the study not only deepen our understanding of melting in two dimensions, but also highlight the potential of advanced microscopy and AI in exploring the frontiers of materials science.

Reference

“Hexatic phase in covalent two‑dimensional silver iodide” by Thuy An Bui, David Lamprecht, Jacob Madsen, Marcin Kurpas, Peter Kotrusz, Alexander Markevich, Clemens Mangler, Jani Kotakoski, Lado Filipovic, Jannik C. Meyer, Timothy J. Pennycook, Viera Skákalová and Kimmo Mustonen, 4 December 2025, Science.

DOI: https://doi.org/10.1126/science.adv7915