Tessellation patterns that have fascinated mathematicians since Johannes Kepler worked out their systematics 400 years ago – and that more recently have caught the eye of both artists and crystallographers – can now be seen in the laboratory.
They first took shape on a surface more perfectly two-dimensional than any sheet of writing paper, a single layer of atoms and molecules atop an atomically smooth substrate.
Physicists coaxed these so-called Kepler tilings "onto the page" through guided self-assembly of nanostructures.
The experiments were carried out by postdoctoral researcher David Ecija, PhD candidate Jose Ignacio Urgel and colleagues in the Physics Department of Technische Universitaet Muenchen (TUM), in collaboration with scientists in Karlsruhe and Zurich. They reported their findings in the Proceedings of the National Academy of Sciences.
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| The 2-D tessellation pattern known as the "semiregular snub square tiling" stands out clearly in this image, which combines scanning tunneling microscopy with computer graphics. The pattern, observed in a surface architecture just one molecule thick, was formed by self-assembly of linear organic linkers, imaged as rods, and lanthanide cerium centers, visualized as bright protrusions. The area shown measures less than 25 nanometers across. (Credit: Barth Lab, copyright TUM) |