physics 141a spring 2013
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Discovery of Quasicrystals. Source: NIST. Source: Physics Rev. Lett . 53. 1951 (1984). Discovery of QuasicrystalsLouis Kang. Physics 141A Spring 2013. What is a Crystal (before QCs). In Crystals, - PowerPoint PPT PresentationTRANSCRIPT
1Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Discovery of Quasicrystals
Source: NIST Source: Physics Rev. Lett. 53. 1951 (1984)
2Physics 141ASpring 2013
Discovery of Quasicrystals Louis 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.
3Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Also shown in…Selected Area Diffraction patterns of a crystal!
[111] [112]
[011]
from a BCC phase in Mg4Zn94Y2 alloy
Source: NIST
4Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Other rotations are forbidden!
Crystallographic Restriction Theorem
FIVE FOLD SYMMETRY IMPOSSIBLE!
SEVEN FOLD SYMMETRY IMPOSSIBLE!
Gaps!
5Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
The Discovery: Quasi-crystalsDiffracts 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
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Discovery of Quasicrystals Louis 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)
Al6Mn
1 mm
Source: Business Insider
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Discovery of Quasicrystals Louis 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
8Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Images taken by(1) X – Ray Crystallography
(2) Transmission Electron
Microscopy
Source: Life Sciences Foundation Credit: Louis Kang
X-ray diffraction image of DNA Watson and Crick used to find its structure
TEM image of the Al6Mn sample Shechtman sent to Prof. Gronsky of UC Berkeley MSE Deptartment
9Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
The Discovery: Quasi-crystalsLong-range ordered + aperiodic
The patterns of Quasicrystalscan be explained using thePenrose’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
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Discovery of Quasicrystals Louis Kang
My Favorite Penrose’s Tiling
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Discovery of Quasicrystals Louis 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
12Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
The Discovery: Quasi-crystalsThe 3-dimensional form of Quasicrystals: Icosahedron!
⬅ Three fold symmetry axis
⬇Five fold symmetry axis
⬅ Two fold symmetry axis
=
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Discovery of Quasicrystals Louis Kang
Quasicrystals and the Golden Ratio
Successive spots are at a distance inflated by
2 3 41
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Discovery of Quasicrystals Louis 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!
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Discovery of Quasicrystals Louis Kang
The Discovery: Quasi-crystalsQuick 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!
16Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Beating the SkepticsThe 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
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Discovery of Quasicrystals Louis Kang
Beating the Skeptics
Professor Gronsky provided the skeptics with the clearly labeled TEM images of Shechtman’s Al6Mn samples!
Credit: Louis Kang
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Discovery of Quasicrystals Louis 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
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Discovery of Quasicrystals Louis Kang
Properties and ApplicationsProperties • 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)
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Discovery of Quasicrystals Louis Kang
Occurrence of QuasicrystalsMostly 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
21Physics 141ASpring 2013
Discovery of Quasicrystals Louis Kang
Research on QuasicrystalsAbout 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
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Discovery of Quasicrystals Louis Kang
In Conclusion…
Be persistent and persevere!
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Discovery of Quasicrystals Louis Kang
References• http://www.nobelprize.org/nobel_prizes/chemistry/lau
reates/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