the nobel prize in chemistry 2011 dan shechtman technion – israel institute of technology, haifa,...
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The Nobel Prize in Chemistry 2011
Dan ShechtmanTechnion – Israel Institute of Technology, Haifa, IsraelPrize motivation: "for the discovery of quasicrystals"
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Matter
Solid Liquid Gas PlasmaLiquid Crystal
AmorphousCrystalline
QUASICRYSTALLINE
1984
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L+
TStable liquid
UnderCooled liquid
log t
Tm
TTT Diagram for liquid-to-solid transformation
Coarse grained crystals
Fine grained crystals
glass
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Crystal AmorphousSiO2
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Crystal
3D Periodic arrangement of atoms
Amorphous
Random arrangement of atoms
Long-range translational order
Short-range order
No Long-range order
Short-range order
Sharp diffraction pattern
Diffuse diffraction pattern
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Sharp
Crystalline Amorphous
Diffuse
Diffraction Patterns
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Electron Diffraction and symmetry
Beam : <100>
Beam : <111>
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9/87 7 crystal Systems
Cubic
Defining Crystal system Conventional symm unit cell
4
1
3
1
1
1
none
Tetragonal
Orthorhombic
Hexagonal
Rhombohedral
Triclinic
Monoclinic
a=b=c, ===90
a=bc, ===90
abc, ===90
a=bc, == 90, =120
a=b=c, ==90
abc, ==90
abc,
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Rotational Symmetries
Z180 120 90 72 60
2 3 4 5 6
45
8
Angles:
Fold:
Graphic symbols
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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…
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A crystal with 10-Fold symmetry???
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Five-fold
Two-fold
Five-fold
Two-fold Three-foldThree-fold
Icosahedral Symmetry
Icosahedron
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Regular Polygons: All sides equal all angles equal
How many regular polygons are possible?
3 4 5 6
There are infinitely many regular polygons
Triangle square pentagon hexagon…
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3D: Regular Polyhedra or Platonic Solids
Cube
How many regular solids?
Tetrahedron
All faces regular congruent polygons, all corners identical.
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There are 5 and only 5 Platonic or regular solids !
Icosahedron
Octahedron
Tetrahedron
Cube
Dodecahedron
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What is the structure of Quasicrystal?
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One Dimensional Quasicrystal
Fibbonacci Chain
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Two-dimensional Quasicrystal
Penrose Pattern
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Hexagons always tile periodically
Square can tile periodically or aperiodically.
Is there a tile or a set of tile that will tile only aperiodically?
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Thank you
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