physics 141a spring 2013

1Physics 141ASpring 2013

Discovery of Quasicrystals Louis Kang

Discovery of Quasicrystals

Source: NIST Source: Physics Rev. Lett. 53. 1951 (1984)



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.



Also shown in…Selected Area Diffraction patterns of a crystal!

[111] [112]

[011]

from a BCC phase in Mg4Zn94Y2 alloy

Source: NIST



Other rotations are forbidden!

Crystallographic Restriction Theorem

FIVE FOLD SYMMETRY IMPOSSIBLE!

SEVEN FOLD SYMMETRY IMPOSSIBLE!

Gaps!



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



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



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



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



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



My Favorite Penrose’s Tiling



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



The Discovery: Quasi-crystalsThe 3-dimensional form of Quasicrystals: Icosahedron!

⬅ Three fold symmetry axis

⬇Five fold symmetry axis

⬅ Two fold symmetry axis

=



Quasicrystals and the Golden Ratio

Successive spots are at a distance inflated by

2 3 41



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!



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!



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



Beating the Skeptics

Professor Gronsky provided the skeptics with the clearly labeled TEM images of Shechtman’s Al6Mn samples!

Credit: 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



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)



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

http://www.sciencemag.org/cgi/content/full/324/5932/1306?ijkey=M.9o1c.ng5mcg&keytype=ref&siteid=sci

http://www.sciencemag.org/cgi/content/full/324/5932/1306?ijkey=M.9o1c.ng5mcg&keytype=ref&siteid=sci



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

http://www.tdsb.on.ca/libraries/library_files/3440/PhysRevLett.53.1951.pdf



In Conclusion…

Be persistent and persevere!



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

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/advanced-chemistryprize2011.pdf

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/advanced-chemistryprize2011.pdf

http://www.jcrystal.com/steffenweber/qc.html

http://www.jcrystal.com/steffenweber/qc.html

http://www.jewelinfo4u.com/Quasicrystals.aspx

http://www.jewelinfo4u.com/Quasicrystals.aspx

http://www.tau.ac.il/~ronlif/symmetry.html

http://www.tau.ac.il/~ronlif/symmetry.html

physics 141a spring 2013

Documents

icosahedral symmetry

fold symmetrysource

forld symmetry

fold symmetries similar

nist source

manganese source

mg4zn94y2 alloy source

image exhibits