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Physics 141A Spring 2013

Discovery of Quasicrystals. Source: NIST. Source: Physics Rev. Lett . 53. 1951 (1984). Discovery of Quasicrystals Louis Kang. Physics 141A Spring 2013. What is a Crystal (before QCs). In Crystals,

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Physics 141A Spring 2013

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  1. Discovery of Quasicrystals Source: NIST Source: Physics Rev. Lett. 53. 1951 (1984) Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  2. What is a Crystal (before QCs) In Crystals, Atoms or atomic clusters repeat periodically, analogues to a tessellation in 2D constructed from a single type of tile Try tiling the plane with identical units! Only 2, 3, 4 and 6 fold symmetries are possible. Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  3. Also shown in… Selected Area Diffraction patterns of a crystal! [111] [112] [011] from a BCC phase in Mg4Zn94Y2 alloy Source: NIST Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  4. Other rotations are forbidden! Crystallographic Restriction Theorem Gaps! FIVE FOLD SYMMETRY IMPOSSIBLE! SEVEN FOLD SYMMETRY IMPOSSIBLE! Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  5. The Discovery: Quasi-crystals Diffracts electrons like a crystal but with symmetries strictly forbidden for crystals ⬇ Twelve fold symmetry ⬆ Eight fold symmetry ⬅ Five fold symmetry Source: Physics Rev. Lett. 53. 1951 (1984) Source: Science Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  6. The Discovery: Quasi-crystals Daniel Shechtmanof the Technion–Israel Institute of Technology identified icosahedral symmetry from rapidly solidified alloys of Aluminum with 10-14% Manganese Al6Mn 1 mm Source: Business Insider Source: Physics Rev. Lett. 53. 1951 (1984) Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  7. The Imaging Instruments (1) X – Ray Crystallography (2) Transmission Electron Microscopy Source: Vanderbilt Source: Pittsburgh Determine the atomic and molecular structure of a crystal (1) crystalline atoms cause a beam of X-rays to diffract + measure the angles and intensities of these diffracted beams (2) a beam of electrons is transmitted through a specimen + an image is formed on a layer of photographic film or detected by a sensor Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  8. Images taken by (1) X – Ray Crystallography (2) Transmission Electron Microscopy Source: Life Sciences Foundation Credit: Louis Kang X-ray diffraction image of DNA Watson and Crick used to find its structure TEM image of the Al6Mn sample Shechtmansent to Prof. Gronsky of UC Berkeley MSE Deptartment Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  9. The Discovery: Quasi-crystals Long-range ordered + aperiodic The patterns of Quasicrystals can be explained using the Penrose’s tiling pictures (can tile non-periodically) Only one point of global 5-fold symmetry (the center of the pattern) Regions of local 5-forld symmetry 10-fold symmetry with respect to the center (aperiodic) Source: Wolfram Alpha Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  10. My Favorite Penrose’s Tiling Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  11. Fourier Transform of the Tile The Fourier transformed image exhibits 5 and 10 fold symmetries similar to diffraction patterns of icosahedral Quasicrystals Fourier Transformation: the calculation of a discrete set of complex amplitudes Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  12. The Discovery: Quasi-crystals The 3-dimensional form of Quasicrystals: Icosahedron! ⬅ Three fold symmetry axis ⬇Five fold symmetry axis = ⬅ Two fold symmetry axis Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  13. 3 2 4 1 Quasicrystals and the Golden Ratio Successive spots are at a distance inflated by  Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  14. so is the Fibonacci Sequence! 1, 1, 2, 3, 5, 8, 13, 21, … The ratio between any two succesive terms is very close to the Golden Ratio: and many other things! Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  15. The Discovery: Quasi-crystals Quick review! Quasicrystals are similar to crystals, BUT… (1) Orderly arrangement QUASIPERIODIC instead of PERIODIC (2) Rotational Symmetry FORBIDDEN symmetry + short-range (3) Consists of a finite number of repeating units With Quasiperiodicity, any symmetry in any number of dimensions is possible! Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  16. Beating the Skeptics The claim: Aluminum’s FCC structure is responsible for the 5-fold symmetry (even Linus Pauling agreed to this at that time) which is very close to 72° of the 5F symmetry. The resolution of Shechtman’sX-Ray diffraction image was inadequate. But, the TEM image wasn’t! The Interplanar angle between and is 70.5° - the difference is due to multiple twinning? Source: Professor Ron Gronsky’s book on his shelf Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  17. Beating the Skeptics Professor Gronsky provided the skeptics with the clearly labeled TEM images of Shechtman’s Al6Mn samples! Credit: Louis Kang Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  18. The new definition of Crystals After Quasicrystals: “Any solid having an essentially discrete diffraction diagram. The word essentially means that most of the intensity of the diffraction is concentrated in relatively sharp Bragg peaks, besides the always present diffuse scattering. By 'aperiodic crystal' we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent.” from the International Union of Crystallography Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  19. Properties and Applications • Properties • Hard and brittle! -> usually considered defects • Lacking periodicity -> poor thermal and electronic transport modes (which are usually enhanced by phonons developed as a consequence of the periodic nature of crystals) • Low surface energy -> corrosion- and adhesion-resistant • Applications • Wear resistant coating (Al-Cu-Fe-Cr) • Non-stick coating (Al-Cu-Fe) • Thermal barrier coating (Al-Co-Fe-Cr) Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  20. Occurrence of Quasicrystals • Mostly synthetic • Synthetic intermetallics • Liquid Crystals • Copolymers • Self-assemblies of nanoparticles • Recently discovered the naturally occurring quasicrystalline From: Discovery of a Natural QuasicrystalL Bindi, P. Steinhardt, N. Yao and P. Lu Science 324, 1306 (2009) From 4.5 billion years old ancient meteorite Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  21. Research on Quasicrystals About 23,700 results on Quasicrystals on Google Scholar Mostly on their mathematical properties but more than 2 million results on graphene…! Click the image below for the link to the original paper of Shechtman Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  22. In Conclusion… Be persistent and persevere! Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

  23. References • http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/advanced-chemistryprize2011.pdf • http://www.jcrystal.com/steffenweber/qc.html • http://www.jewelinfo4u.com/Quasicrystals.aspx • http://www.tau.ac.il/~ronlif/symmetry.html Discovery of Quasicrystals Louis Kang Physics 141A Spring 2013

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