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Discovery of Quasicrystals Source: NIST Physics 141A Spring 2013 Discovery of Quasicrystals Source: Physics Rev. Lett. 53. 1951 (1984) Louis Kang 1 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. Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 2 Also shown in… Selected Area Diffraction patterns of a crystal! Source: NIST [111] [112] [011] from a BCC phase in Mg4Zn94Y2 alloy Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 3 Other rotations are forbidden! Gaps! FIVE FOLD SYMMETRY IMPOSSIBLE! SEVEN FOLD SYMMETRY IMPOSSIBLE! Crystallographic Restriction Theorem Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 4 The Discovery: Quasi-crystals Diffracts electrons like a crystal ⬇ Twelve fold symmetry ⬆ Eight fold symmetry ⬅ Five fold symmetry Source: Physics Rev. Lett. 53. 1951 (1984) Source: Science but with symmetries strictly forbidden for crystals Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 5 The Discovery: Quasi-crystals 1 mm Source: Business Insider Al6Mn Source: Physics Rev. Lett. 53. 1951 (1984) Daniel Shechtman of the Technion–Israel Institute of Technology identified icosahedral symmetry from rapidly solidified alloys of Aluminum with 10-14% Manganese Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 6 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 Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 7 Images taken by (1) X – Ray Crystallography (2) Transmission Electron Microscopy Source: Life Sciences Foundation X-ray diffraction image of DNA Watson and Crick used to find its structure Physics 141A Spring 2013 Credit: Louis Kang TEM image of the Al6Mn sample Shechtman sent to Prof. Gronsky of UC Berkeley MSE Deptartment Discovery of Quasicrystals Louis Kang 8 The Discovery: Quasi-crystals Long-range ordered + aperiodic 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) The patterns of Quasicrystals can be explained using the Penrose’s tiling pictures (can tile non-periodically) Source: Wolfram Alpha Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 9 My Favorite Penrose’s Tiling Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 10 Fourier Transform of the Tile Fourier Transformation: the calculation of a discrete set of complex amplitudes The Fourier transformed image exhibits 5 and 10 fold symmetries similar to diffraction patterns of icosahedral Quasicrystals Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 11 The Discovery: Quasi-crystals The 3-dimensional form of Quasicrystals: Icosahedron! ⬅ Three fold symmetry axis ⬇Five fold symmetry axis = Physics 141A Spring 2013 ⬅ Two fold symmetry axis Discovery of Quasicrystals Louis Kang 12 Quasicrystals and the Golden Ratio 1 2 3 4 Successive spots are at a distance inflated by Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 13 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! Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 14 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! Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 15 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) The Interplanar angle between and is 70.5° - the difference is due to multiple twinning? which is very 1close to 72° of the 5F symmetry. The resolution of Shechtman’s X-Ray diffraction image was inadequate. But, the TEM image wasn’t! Source: Professor Ron Gronsky’s book on his shelf Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 16 Beating the Skeptics Credit: Louis Kang Professor Gronsky provided the skeptics with the clearly labeled TEM images of Shechtman’s Al6Mn samples! Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 17 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 Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 18 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) Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 19 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 Quasicrystal L Bindi, P. Steinhardt, N. Yao and P. Lu Science 324, 1306 (2009) From 4.5 billion years old ancient meteorite Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 20 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 Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 21 In Conclusion… Be persistent and persevere! Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 22 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 Physics 141A Spring 2013 Discovery of Quasicrystals Louis Kang 23