The Nobel Prize in Chemistry 2011

1. The Nobel Prize in Chemistry 2011 Dan Shechtman Technion – Israel Institute of Technology, Haifa, Israel Prize motivation: "for the discovery of quasicrystals"

2. Matter Liquid Crystal Solid Liquid Gas Plasma Amorphous Crystalline 1984 QUASICRYSTALLINE

3. T Stable liquid Tm UnderCooled liquid L+ log t TTT Diagram for liquid-to-solid transformation Fine grained crystals Coarse grained crystals glass

4. SiO2 Amorphous Crystal

5. Amorphous Crystal 3D Periodic arrangement of atoms Random arrangement of atoms No Long-range order Long-range translational order Short-range order Short-range order Diffuse diffraction pattern Sharp diffraction pattern

6. Diffraction Patterns Sharp Crystalline Amorphous Diffuse

8. Electron Diffraction and symmetry Beam : <100> Beam : <111>

9. 7 crystal Systems Defining Crystal system Conventionalsymmunit cell a=b=c, ===90 4 Cubic a=bc,===90 1 Tetragonal abc, ===90 3 Orthorhombic a=bc, == 90, =120 Hexagonal 1 a=b=c, ==90 1 Rhombohedral abc, ==90 1 Monoclinic abc,  none Triclinic

11. Rotational Symmetries Z Angles: 180 120 90 72 60 45 Fold: 6 2 3 4 5 8 Graphic symbols

12. Crsytallographic Restriction 5-fold symmetry or Pentagonal symmetry is not possible for Periodic Tilings Symmetries higher than 6-fold also not possible Only possible rotational symmetries for periodic tilings 2 3 4 5 6 7 8 9…

14. A crystal with 10-Fold symmetry???

16. Icosahedral Symmetry Five-fold Two-fold Icosahedron Five-fold Three-fold Two-fold Three-fold

17. Regular Polygons: All sides equal all angles equal Triangle square pentagon hexagon… 3 4 5 6 How many regular polygons are possible? There are infinitely many regular polygons

18. 3D: Regular Polyhedra or Platonic Solids All faces regular congruent polygons, all corners identical. Tetrahedron Cube How many regular solids?

19. There are 5 and only 5 Platonic or regular solids ! Tetrahedron Cube Octahedron Dodecahedron Icosahedron

20. What is the structure of Quasicrystal?

21. One Dimensional Quasicrystal Fibbonacci Chain

22. Two-dimensional Quasicrystal Penrose Pattern

23. Hexagons always tile periodically Square can tile periodically or aperiodically. Is there a tile or a set of tile that will tile only aperiodically?

26. Thank you