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.
Results open a new line of research
Organic molecules equipped with functional groups to express distinct linkages to metal atoms were deposited onto a smooth silver substrate under vacuum conditions. Subsequently the organic layer on this platform was exposed to an atomic flux of the lanthanide cerium. At a certain ratio of cerium atoms to molecules, self-assembly produced a symmetrical complex 2-D pattern described originally by Kepler and known today as the snub square tiling. Clearly identifiable through scanning tunneling microscopy was a recurring, five-vertex connecting element less than one nanometer across, a cerium-ligand coordination unit.
Read more at: Phys.org