We have observed a metallic solid (Al -14-at. /o-Mn) with long-range orientationai order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice.

CWY), hand@kias.re.kr (YWS) † These authors contributed equally to this work.2 ABSTRACT Quantum states of quasiparticles in solids are dictated by symmetry. Thus, a discovery of unconventional symmetry can provide a new opportunity to reach a novel quantum state. Recently, Dirac and Weyl electrons have been observed in crystals with discrete translational symmetry. Here we experimentally demonstrate Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystal was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°.The graphene quasicrystal was grown up to a millimeter scale on SiC(0001) surface while maintaining the single rotation angle over an entire sample and was successfully isolated from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cone replicated with the 12-fold rotational symmetry were observed in angle resolved photoemission spectra, showing its unique electronic structures with anomalous strong interlayer coupling with quasi-periodicity.Our study provides a new way to explore physical properties of relativistic fermions with controllable quasicrystalline orders. ONE SENTENCE SUMMARY:A Dirac fermion quasicrystal with 12-fold rotational symmetry and without any translational symmetry can be realized from twisted bilayer graphene rotated exactly 30°. Microscopy, Graphene. by ×10 9 . (B-D) Umklapp scattering paths from the Dirac point of the upper layer with the shortest three wave vectors |q| involved in the Umklapp process (see text). Each panel shows the scattering involving different G. (E) A schematic drawing of the locations of Dirac cones in calculations, where the Dirac cones were ranked by the length of |q| and the size of circle is proportional to the intensity calculated theoretically (see Figs. S8 and S9 in SI also). (F) A schematic drawing of the locations of Dirac cones in ARPES measurements, where the Dirac cones were also ranked by the length of |q| and the intensity and size of circle is proportional to the intensity measured experimentally. (G) The theoretical calculations of the contribution to the ARPES intensity from the single (multiple) scattering plotted as a function of |q|. Red (grey) circles in (G) show the contribution from the single (multiple) scattering (see SI and Fig. S8 also). (H) The experimental intensities of Dirac cones plotted as a function of |q|. 19 FIGURE 4. ARPES spectra and Fermi velocities of graphene quasicrystal. (A) Constant energy maps of ARPES spectra of graphene quasicrystal with different binding energies. (B) Energy-momentum dispersions of Dirac cones at the K points of the upper and lower layer graphene. (C) The fitted lines of energy-momentum dispersions of Dirac cones used to extract Fermi velocities (see Fig. S4F in SI also for detailed comparison between the experimental dispersions and the fitted lines), where the Fermi velocities of the A, B, C and D Dirac cones (see Fig. 3(A) for the notations of the Dirac cones) a...

Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

No abstract

The tensile properties of the intermetallic compound TiAl have been determined at several temperatures in the range 25 to 1000°C. Additional variables studied were the influence of strain rate and the effect of exposure to oxidizing conditions prior to testing. The modes of deformation under the various testing conditions were studied in the electron microscope, the modes of fracture were studied in the scanning electron microscope, and these data were correlated with the mechanical properties. The results indicate that the ductilebrittle transition behavior of TiAl at about 700°C is controlled by the trailing a/6 [112] partial dislocation components of the a [011] superdislocations overcoming their pinning barriers. It was also shown that prior exposure to oxidizing conditions does not markedly influence the mechanical properties of TiA1.

No abstract

No abstract

No abstract