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.

A four-dimensional model for the Ba-Ti-O dodecagonal quasicrystal

A four-dimensional (4D) model is presented of the first oxide dodecagonal quasicrystal found in a Ba-Ti-O ultra-thin film on a Pt(111) single-crystal substrate. The 4D model, with a 4D dodecagonal lattice constant a_d = 8.39 Å, was derived by considering a tile decoration model of dodecagonal Niizeki-Gähler tiling composed of squares, triangles and 30° rhombuses. The model consists of four kinds of occupation domain, and 4D positional vectors defining the shape of each occupation domain are given. Moreover, the atomic arrangement of two Ba-Ti-O periodic approximants, the sigma-phase approximant and a 25.6 Å approximant were derived from the 4D model by the introduction of linear phason strains.

Structure of Periodic Crystals and Quasicrystals in Ultrathin Films of Ba-Ti-O

We model the remarkable thin-film Ba-Ti-O structures formed by heat treatment of an initial perovskite BaTiO₃ thin film on a Pt(111) surface. All structures contain a rumpled Ti-O network with all Ti threefold coordinated with O, and with Ba occupying the larger. mainly Ti₇O₇, pores. The quasicrystal structue is a simple decoration of three types of tiles: square, triangle and 30° rhombus, with edge lengths 6.85 Å, joined edge-to-edge in a quasicrystalline pattern; observed periodic crystals in ultrathin film Ba-Ti-O are built from these and other tiles. Simulated STM images reproduce the patterns seen experimentally, and identify the bright protrusions as Ba atoms. The models are consistent with all experimental observations.

Quasicrystalline structure formation in a classical crystalline thin-film system

The discovery of quasicrystals--crystalline structures that show order while lacking periodicity--forced a paradigm shift in crystallography. Initially limited to intermetallic systems, the observation of quasicrystalline structures has recently expanded to include 'soft' quasicrystals in the fields of colloidal and supermolecular chemistry. Here we report an aperiodic oxide that grows as a two-dimensional quasicrystal on a periodic single-element substrate. On a Pt(111) substrate with 3-fold symmetry, the perovskite barium titanate BaTiO3 forms a high-temperature interface-driven structure with 12-fold symmetry. The building blocks of this dodecagonal structure assemble with the theoretically predicted Stampfli-Gähler tiling having a fundamental length-scale of 0.69 nm. This example of interface-driven formation of ultrathin quasicrystals from a typical periodic perovskite oxide potentially extends the quasicrystal concept to a broader range of materials. In addition, it demonstrates that frustration at the interface between two periodic materials can drive a thin film into an aperiodic quasicrystalline phase, as proposed previously. Such structures might also find use as ultrathin buffer layers for the accommodation of large lattice mismatches in conventional epitaxy.