Finally, a strange intermediate state of matter is observed

Extremely thin materials behave very differently. Instead of melting all at once, they can go through an unusual transition state that lies between a solid and a liquid. This rare state is known as the hexatic phase. Scientists from the University of Vienna have now directly observed this phase in an atomically thin crystal, which has never been confirmed before.

By combining advanced electron microscopy with neural networks, the team recorded a silver iodide crystal as it melted while being protected by layers of graphene. These ultra-thin, two-dimensional materials allowed the researchers to observe how melting unfolds at the level of individual atoms. The results greatly improve the scientific understanding of how phase transitions work in two dimensions. The findings also contradict long-standing theoretical expectations and have now been published in Science.

Why two-dimensional materials melt differently

Common materials melt suddenly. Once the melting point is reached, the ordered solid structure quickly changes to a disordered liquid. This behavior is shared by metals, minerals, ice, and many other three-dimensional substances.

When the material is reduced to nearly two dimensions, melting follows a different path. A distinct interphase may appear between the solid and liquid states. This state, known as the hexatic phase, was first proposed in the 1970s, but has been difficult to confirm in real materials.

At this stage, the material exhibits mixed behavior. The spacing between the particles becomes irregular, liquid-like, while the angles between them remain partially ordered, a feature usually associated with solids. This combination makes the hexatic phase a hybrid state with properties of both forms of matter.

Solving a long-standing mystery in real materials

So far, the hexatic phase has only been observed in simplified model systems such as tightly packed polystyrene spheres. Scientists weren’t sure if the same behavior could exist in everyday materials held together by strong chemical bonds.

An international research team led by the University of Vienna has now answered this question. By studying atomically thin crystals of silver iodide (AgI), scientists were able to observe the hexatic phase directly in the strongly bound material for the first time. This achievement resolves a question that has remained open for decades.

The discovery confirms that this elusive phase can occur in real two-dimensional crystals and reveals new details about how melting works when materials are reduced to atomic thickness.

Melting of atoms inside a graphene sandwich

To observe this fragile process, the researchers designed a specialized experimental setup. A single layer of silver iodide was placed between two layers of graphene, creating a protective ‘sandwich’. This structure prevented the fine crystal from collapsing while allowing it to melt naturally.

The team then used a scanning transmission electron microscope (STEM) equipped with a heating holder to gradually increase the temperature of the sample above 1100°C. This setup made it possible to record the melting process in real time and at atomic resolution.

How artificial intelligence made atomic-scale surveillance possible

Tracking the movement of individual atoms during melting produces a huge amount of data. According to Kimm Mustonen of the University of Vienna, lead author of the study, this task would not be possible without artificial intelligence. “Without the use of artificial intelligence tools like neural networks, it would be impossible to track all these individual atoms,” he explains.

The researchers trained their neural network using large sets of simulated data. Once trained, the system analyzed thousands of high-resolution microscopic images generated during the experiment.

A narrow temperature window reveals the hexatic phase

The analysis revealed a surprising result. In a small temperature range – approximately 25 °C below the melting point of AgI – the crystal entered a well-defined hexatic phase. Additional electron diffraction measurements confirmed this behavior and provided strong evidence that this transition state exists in atomically thin, strongly bound materials.

Rethinking how melting works in two dimensions

The study also revealed behavior that challenges existing theory. Models previously suggested that both transitions, from solid to hexatic and from hexatic to liquid, should occur sequentially. Instead, the researchers found that only the first transition followed this pattern.

While the transition from solid to hexatic occurred smoothly, the change from hexatic to liquid occurred suddenly, similar to when ice changes to water. “This suggests that melting in covalent two-dimensional crystals is much more complex than previously thought,” says David Lamprecht of the University of Vienna and the Vienna University of Technology (TU Wien), one of the study’s lead authors along with Thuy An Bui, also of the University of Vienna.

Breaking new ground in materials science

This decade-long discovery challenges theoretical assumptions and opens new directions for the study of matter at the smallest scale. Jani Kotakoski, head of the research group at the University of Vienna, emphasizes the importance of this work, saying: “Kimmo and his colleagues have once again shown how powerful atomic resolution microscopy can be.”

In addition to improving our understanding of melting in two dimensions, the study also shows how advanced microscopy and artificial intelligence can work together to explore new frontiers in materials science.

Key things

• When materials are only a few atoms thick, they do not melt in the usual way. Instead of jumping directly from solid to liquid, they go through a rare transition state called the “hexatic phase.” Scientists from the University of Vienna have now for the first time observed this process directly in atomically thin crystals of silver iodide (AgI).
• To do this, the researchers enclosed a single layer of silver iodide in a protective ‘graphene sandwich’. Advanced electron microscopy and neural networks were then used to track how individual atoms moved as the crystal heated up and began to melt.
• This approach showed a clear result. In a very narrow temperature range, about 25 °C below the melting point of AgI, the crystal entered a distinct hexatic phase that exists between a solid and a liquid.
• The team also discovered an unexpected twist. While the change from solid to hexatic occurred gradually, exactly as theory predicted, the final transition from hexatic to liquid occurred suddenly, similar to the melting of ice into water. This contradicts long-held assumptions about how two-dimensional materials should melt.
• Together, these findings reshape scientists’ understanding of phase transitions in real materials and provide a stronger foundation for future advances in materials science, especially at the atomic scale.