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
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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
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In Conclusion…
Be persistent and persevere!
Physics 141A
Spring 2013
Discovery of Quasicrystals
Louis Kang
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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
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