the nobel prize in chemistry 2011

The Nobel Prize in Chemistry 2011

Dan ShechtmanTechnion – Israel Institute of Technology, Haifa, IsraelPrize motivation: "for the discovery of quasicrystals"

Matter

Solid Liquid Gas PlasmaLiquid Crystal

AmorphousCrystalline

QUASICRYSTALLINE

1984

L+

TStable liquid

UnderCooled liquid

log t

Tm

TTT Diagram for liquid-to-solid transformation

Coarse grained crystals

Fine grained crystals

glass

Crystal AmorphousSiO2

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

Sharp

Crystalline Amorphous

Diffuse

Diffraction Patterns

Electron Diffraction and symmetry

Beam : <100>

Beam : <111>

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,

Rotational Symmetries

Z180 120 90 72 60

2 3 4 5 6

45

8

Angles:

Fold:

Graphic symbols

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…

A crystal with 10-Fold symmetry???

Five-fold

Two-fold

Five-fold

Two-fold Three-foldThree-fold

Icosahedral Symmetry

Icosahedron

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…

3D: Regular Polyhedra or Platonic Solids

Cube

How many regular solids?

Tetrahedron

All faces regular congruent polygons, all corners identical.

There are 5 and only 5 Platonic or regular solids !

Icosahedron

Octahedron

Tetrahedron

Cube

Dodecahedron

What is the structure of Quasicrystal?

One Dimensional Quasicrystal

Fibbonacci Chain

Two-dimensional Quasicrystal

Penrose Pattern

Hexagons always tile periodically

Square can tile periodically or aperiodically.

Is there a tile or a set of tile that will tile only aperiodically?

Thank you