Quasicrystals (QC) in condensed matter are often accompanied by competing periodic structures with large unit cells that approximate the QC. Likewise for the dodecagonal Ba-Ti-O oxide quasicrystal that forms on Pt(111), approximants with square and oblique lattices have been reported. Here we report on the identification of a hexagonal approximant for this QC. Atomically-resolved scanning tunneling microscopy shows the characteristic vertex atoms, which form triangle, square, and rhombus tiling elements, which organize into more complex motifs that are building blocks of the aperiodic QC. Low-energy electron diffraction confirms the large-cell hexagonal structure and is well reproduced by a minimal single-scattering calculation. To accommodate the misfit, the hexagonal layer is twisted $4{}^{\circ }$ against the hexagonal Pt(111) substrate, which also lowers the overall symmetry of the system.

• Received 22 July 2021
• Accepted 9 August 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.084006