Chemical patterns proposed by British mathematician Alan Turing in 1952 were discovered at the atomic level. The patterns appear as stripes in a single atomic layer of bismuth adsorbed on crystalline niobium selenide and are only 2 nm (about five atoms) wide – much smaller than any other Turing pattern.

The study shows “that we can control and shape patterns as required on surfaces under certain interface conditions,” comments chemical engineer Kourosh Kalantar-Zadeh from the University of New South Wales in Australia.

Turing proposed his theoretical pattern formation scheme as an explanation of how shape and structure can arise spontaneously in embryos, which begin as a uniform cell sphere. He suggested that pattern formation could result from competition between reaction and diffusion of molecules he called morphogens (formers). Turing noted the similarity of the mottled patterns his scheme brought out and the pigmentation on animal skins and pelts, like the leopard spots and the zebra crossings.

An image that shows a regular pattern of larger green and smaller blue spheres

Turing patterns in an artificial chemical system were first described more than 30 years ago. Usually the patterns are large enough to be seen with the naked eye. However, some studies have described them on a smaller scale – for example in polymer membranes and solidifying metals.

The surface scientist Aharon Kapitulnik and his colleagues at Stanford University saw wave-shaped surface nanopatterns in their monolayers of bismuth, which were based on niobium selenide (NbSe2) three years ago. Due to a mismatch between the equilibrium lattice spacing of the substrate and the adsorbed film, the bismuth atoms can be displaced both horizontally and vertically by stretching.

Condensed matter physicist Yuki Fuseya from the University of Electrical Communication in Chofu, Japan, met Kapitulnik at a meeting in Paris. “Aharon showed me his data and I suddenly had the idea of ​​Turing patterns,” he says. However, proving this was a different matter as there are several other processes that could lead to the formation of islands and patterns.

Fuseya, Kapitulnik, and their colleagues developed equations to predict the outcome of film growth and found conditions under which different patterns such as simple stripes or labyrinthine networks would form. It turned out that their computer simulations of such a process came very close to the patterns observed experimentally under comparable conditions.

Bismuth deserves its streak

Turing’s original patterning scheme later required two morphogens: an activator that catalyzes its own production and an inhibitor that disrupts the activator’s autocatalysis. The patterns depend on the two components having very different diffusion rates, resulting in the formation of localized spots of the activator with areas in between where its production is suppressed.

The surface process described by Fuseya and colleagues, on the other hand, has only one chemical component: bismuth atoms. However, their vertical and horizontal shifts can be different and serve as an activator or inhibitor.

In Turing patterns, which are formed by the diffusion of chemical or biochemical morphogens, the length scale of the resulting features depends on density differences, which typically comprise many trillions of molecules, explains Fuseya. This leads to macroscopic patterns. In contrast to this, the length scale in this case is only determined by the nanoscale lattice constant of the surface.

An image that shows a series of squares with different blue and white patterns.  The patterns in the lower left of the picture are simple, mostly striped, while the patterns in the upper right become more complicated and labyrinthine

“I would expect this phenomenon to be fairly common on solid surfaces,” says Rodolfo Cuerno of the Carlos III University of Madrid in Spain, who has studied pattern formation in surface deposition processes. “Perhaps additional effects play a role, such as crystalline anisotropies, which cause faster diffusion in some directions compared to others.”

Fuseya agrees that the process could well be common. Kalantar-Zadeh and colleagues recently reported both spot and stripe nanopatterns on the surface of solidifying alloys, particularly bismuth and gallium, which he suggested might be Turing-like.

“If we can make nanoscale dots with Turing patterns, it would be a new way to make quantum dots,” says Fuseya. Nanoscale strips could act as quantum wires. Both structures could be valuable for electronic and optical devices whose properties are determined by the quantum mechanical consequences of trapping electrons or other charge carriers in such a small space.

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