Turing structure with bismuth atoms

What giraffes, zebrafish and turtles have in common: These animals display neatly arranged patterns on their coats, scales, or shells. In 1952, to explain these geometric figures, the British mathematician Alan Turing developed a theory combining the phenomena of interaction and diffusion. By selecting the corresponding parameters, it is possible to describe all these patterns, whether it is several tens of centimeters in tigers or several millimeters in wasps. Recently, Yuki Fusya, from Chufu University in Japan, and his colleagues, notably Kamran Behnia, a CNRS researcher at ESPCI, in Paris, observed this Turing structure at the nanoscale, with bismuth atoms.

The researchers initially wanted to study the topology of one bismuth layer in two dimensions, on the support for niobium diselenide (NbSe).₂). But in 2018, they noticed that bismuth atoms clumped together in clusters, sometimes linking together to form Y-type branches. This arrangement reminded the team of the emperor angelfish, a tropical fish with yellow and blue stripes.

Bismuth is an element capable of self-organizing into many different solid structures, which change easily under pressure conditions and even more so in such a thin layer. But such an arrangement of atoms is unusual: niobium disilienide is usually a hexagonal crystal, which would impose very different restrictions on the shape of bismuth. Are these patterns controlled by the Turing equation? “The equations that support the Turing model don’t have different scales,” says Kamran Penhia. So it is not forbidden to use it on a microscopic scale. Nobody came up with the idea to use this approach to explain some complex structures at the nanoscale. “

To validate this geometric arrangement of bismuth atoms as a Turing structure, Yuki Foscia and Kamran Penhia and colleagues modeled the system by considering the angles between the covalent bonds of bismuth atoms to each other and to their supports. The obtained differential equations are related to the specific case of the Turing state, and are able to theoretically predict bismuth atomic patterns with high accuracy compared to observations.

By playing with the parameters of this model, the researchers noticed that the resulting pattern was the same size regardless of the initial conditions of the system: 1.7 nanometers long, or five bismuth atoms wide. In principle, the observed Y junctions between strokes disappear from the system when the composition reaches a state of equilibrium, but the team was able to reproduce it by introducing defects or inclusions into the structure.

Depending on the parameters selected, the bismuth layer can have hexagons, Y-connected lines, or even all parallel lines. This last arrangement is a state of stable equilibrium. The result: in the event of a crash, the entire system “repairs itself” and reconfigures the parallel band. In addition to the aesthetic aspects, the researchers hope to create, from Turing’s nanoscale shape and its ability to self-repair, materials with new properties, such as flawless ultra-thin films.

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