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

2. 2 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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.

3. 3 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang Also shown in… Selected Area Diffraction patterns of a crystal! [111] [112] [011] from a BCC phase in Mg 4 Zn 94 Y 2 alloy Source: NIST

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

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

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

7. 7 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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

8. 8 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang Images taken by (1) X – Ray Crystallography(2) Transmission Electron Microscopy Source: Life Sciences FoundationCredit: Louis Kang X-ray diffraction image of DNA Watson and Crick used to find its structure TEM image of the Al 6 Mn sample Shechtman sent to Prof. Gronsky of UC Berkeley MSE Deptartment

9. 9 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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

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

11. 11 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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

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

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

14. 14 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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!

15. 15 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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!

16. 16 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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’s X-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

17. 17 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang Beating the Skeptics Professor Gronsky provided the skeptics with the clearly labeled TEM images of Shechtman’s Al 6 Mn samples! Credit: Louis Kang

18. 18 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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

19. 19 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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)

20. 20 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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)Discovery of a Natural Quasicrystal From 4.5 billion years old ancient meteorite

21. 21 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang 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

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

23. 23 Physics 141A Spring 2013 Discovery of QuasicrystalsLouis Kang References http://www.nobelprize.org/nobel_prizes/chemistry/laureates/ 2011/advanced-chemistryprize2011.pdf 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