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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. Quasicrystals are perfectly ordered crystals lacking translational symmetry. Here the authors unravel the formation mechanism of two-dimensional dodecagonal quasicrystals that arise from systematic modifications of a hexagonal honeycomb structure. [ABSTRACT FROM AUTHOR]

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 structure 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. [ABSTRACT FROM AUTHOR]

Wills (1990, J. Phys., Paris, 51, 1061) found a method relating certain decagonal disc packings to decagonal sphere packings with high packing fractions. Applying this technique to the decagonal rectangle-triangle tiling generated by inflation, we obtain a sphere packing with decagonal symmetry and a packing fraction greater than 0.6953. This is the densest known stable quasicrystalline sphere packing. [ABSTRACT FROM AUTHOR]

Abstract We develop a model for Al-Co decagonal quasicrystals and approximants. Our model defines a large number of potential atomic positions. These sites are populated by two atomic species that interact with each other through electronicstructure-based pair potentials. Monte Carlo simulation of the model produces realistic atomic configurations for Al-Co alloys in the temperature and composition ranges where a metastable decagonal quasicrystal exists. The resulting structures generally consist of packings of space by pentagonal bipyramid clusters. Projections of the centres of these clusters form tilings of hexagons, boats and stars. We identify atomic displacements associated with phason fluctuations. We note a distinction between 'simple' phason hops involving predominantly Al atom motion and 'collective' phason flips that transport the Co atoms. [ABSTRACT FROM AUTHOR]