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.

The aluminum electromigration drift velocity was measured at the temperature range 250–400 °C. A threshold current density was found inversely proportional to the stripe length. An activation energy of 0.65 eV was found for the drift velocity. The occurrence of the threshold is explained by opposing chemical gradients created by the atom pile-up and depletion at the stripe ends. The threshold may explain several observations reported previously. The threshold is increased by decreasing the temperature or by enclosing the aluminum in silicon nitride. Virtually no electromigration is seen for very short aluminum stripes even at current densities above 106 A/cm2.

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...

Stresses in aluminum thin films on TiN were studied in situ by transmission x-ray topography. Stress gradients were seen to build up in thin aluminum films during passage of electrical currents. The stresses are more compressive in the anode regions. These stress gradients seem to be a concomitant of the backflow responsible for the reported threshold in electromigration, and can probably be correlated quantitatively with it.

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Experimental and theoretical results are presented on the evolution of large elastic deformation, non-uniform curvature, shape changes and geometric instability in substrates of Si wafers with metal films. The critical diameter and thickness of the Si wafer, for which large deformation and shape instability occur, are identified, as functions of the line tension in the film (which is the product of the biaxial stress in the film and the film thickness). Observations of the curvature and shape variations along the wafer diameter and geometry-dependence of the shape instability compare favorably with those predicted by detailed finite element analyses.

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Experimental and numerical results are presented on the evolution of stresses and the accompanying changes in the overall curvatures due to the patterning of silicon oxide lines on silicon wafers and subsequent thermal loading. The finite element analysis involves a generalized plane strain formulation, which is capable of predicting the wafer curvatures in directions parallel and perpendicular to the lines, for both the patterning and thermal cycling operations. The predictions compare reasonably well with systematic curvature measurements for several different geometrical combinations of the thickness, width and spacing of the patterned lines. The non-uniform stress fields within the fine lines and the substrate are also analyzed. It is shown both experimentally and theoretically that certain geometries of patterned lines on the substrate induce dramatic shape changes and reversals of curvature in the direction perpendicular to the lines. The mechanistic origin of this effect is identified to be the Poisson effect arising from the anisotropic strain coupling in the patterned structure.