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.

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.

2D oxide quasicrystals (OQCs) are recently discovered aperiodic, but well‐ordered oxide interfaces. In this topical review, an introduction to these new thin‐film systems is given. The concept of quasicrystals and their approximants is explained for and derived OQCs and related periodic structures in these 2D oxides. In situ microscopy unravels the high‐temperature formation process of OQCs on Pt(111). The dodecagonal structure is discussed regarding tiling statistics and tiling decoration based on the results of atomically resolved scanning tunneling microscopy and various diffraction techniques. In addition, angle‐resolved ultraviolet photoemission spectroscopy and X‐ray photoelectron spectroscopy results prove a metallic character of the 2D oxide.

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2D oxide quasicrystals (OQCs) are unique structures arising from atoms positioned at the vertices of a dodecagonal triangle–square–rhombus tiling. The prototypical example for OQCs is derived from BaTiO3 on Pt(111). Herein, scanning tunneling microscopy (STM) and low‐energy electron diffraction (LEED) investigations of 2D oxide layers derived from BaTiO3 on Pd(111) are reported. Upon ultrahigh vacuum (UHV) annealing, different long‐range ordered structures are observed with a base of four vertex atoms forming two edge‐sharing equilateral triangles. By a periodic repetition of this base in either quadratic or rectangular unit cells, a triangle–square tiling (known as σ‐phase approximant or 32.4.3.4 Archimedean tiling) or a triangle–rhombus tiling is formed. Both structures vary strongly in their vertex density. In addition, the formation of antiphase domain boundaries in the σ phase is observed resulting in a well‐ordered incorporation of rhombuses in the triangle–square tiling. A systematic variation of the frequency of these domain boundaries is identified as a mechanism for an incremental increase in the global vertex density, mediating between pure triangle–square and triangle–square–rhombus tilings.

Surface science studies of two‐dimensional Ba–Ti–O films on Pd(111) identify three different small unit cell structures (see article number http://doi.wiley.com/10.1002/pssb.202100389 by Stefan Förster and co‐workers). In scanning tunneling microscopy these structures exhibit an atomic base of four atoms of one species, decorating the vertices of two triangles. As depicted on the cover, this base rearranges upon atomic density variations. In a fully stretched‐out fashion (left side), corresponding to the lowest density state, a square lattice is formed. In the high‐density limit (right side) a rectangular structure forms, in which rhombuses fill the gaps. The medium density motif incorporates squares and rhombuses.

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