2D honeycomb transformation into dodecagonal quasicrystals driven by electrostatic forces.

Dodecagonal oxide quasicrystals are well established as examples of long-range aperiodic order in two dimensions. However, despite investigations by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), low-energy electron microscopy (LEEM), photoemission spectroscopy as well as density functional theory (DFT), their structure is still controversial. Furthermore, the principles that guide the formation of quasicrystals (QCs) in oxides are elusive since the principles that are known to drive metallic QCs are expected to fail for oxides. Here we demonstrate the solution of the oxide QC structure by synchrotron-radiation based surface x-ray diffraction (SXRD) refinement of its largest-known approximant. The oxide QC formation is forced by large alkaline earth metal atoms and the reduction of their mutual electrostatic repulsion. It drives the n = 6 structure of the 2D Ti2O3 honeycomb arrangement via Stone-Wales transformations into an ordered structure with empty n = 4, singly occupied n = 7 and doubly occupied n = 10 rings, as supported by DFT.

Full real-space analysis of a dodecagonal quasicrystal.

The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki-Gähler tiling. Although the Niizeki-Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.