Two dimensional crystal reveals hexatic phase in real time

by Robert Schreiber
Vienna, Austria (SPX) Dec 05, 2025

When three dimensional materials melt, the transition from an ordered solid to a disordered liquid usually occurs abruptly once the melting temperature is reached. In atomically thin systems, theory predicts a more complex route in which an intermediate state known as the hexatic phase appears between solid and liquid.

An international team led by the University of Vienna has now directly observed this hexatic phase in an atomically thin crystal of silver iodide AgI, resolving a question that has remained open since the phase was first proposed in the 1970s. In the hexatic state, the material shows liquid like disorder in the spacing between atoms, while the angular arrangement of atoms retains a degree of order.

To probe this behavior in a real material, the researchers encapsulated a single layer of silver iodide between two graphene sheets, forming a protective graphene sandwich that stabilized the fragile crystal while still allowing it to melt. Using a scanning transmission electron microscope equipped with a heating holder, they increased the temperature of the encapsulated layer to more than 1100 C and recorded atomic scale movies of the melting process.

"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 first trained a neural network on large sets of simulated data and then applied it to thousands of high resolution images from the experiment to follow the motion and rearrangement of atoms during heating.

The analysis showed that, within a narrow temperature range about 25 C below the melting point of AgI, the crystal entered a distinct hexatic phase. Additional electron diffraction measurements supported this conclusion and provided independent evidence that an intermediate state exists in atomically thin, strongly bound silver iodide.

The observations also exposed a departure from standard theoretical expectations for two dimensional melting. While the transition from solid to hexatic followed a continuous evolution, the subsequent change from hexatic to liquid occurred abruptly, resembling the sudden melting familiar from bulk ice and other three dimensional systems.

"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, a lead author of the study alongside Thuy An Bui from the University of Vienna. The work indicates that real materials can follow melting pathways that differ from idealized models developed for two dimensional systems.

According to group leader Jani Kotakoski from the University of Vienna, "Kimmo and his colleagues have once again demonstrated how powerful atomic resolution microscopy can be." The combination of advanced electron microscopy, in situ heating and AI based image analysis allowed the team to identify phase behavior that had not been accessible in covalently bonded two dimensional materials.

The researchers report that the results deepen current understanding of phase transitions in two dimensions and show how atomic resolution experiments can refine or challenge long standing theories. They also argue that the approach used here can be extended to other two dimensional materials to test how general the observed melting scenario is and to explore how structural, bonding and environmental factors control hexatic phases and related states.

Research Report:Hexatic phase in covalent two-dimensional silver iodide.