an introduction to quasicrystals, by mr.govahi
TRANSCRIPT
Editor: Eng. Mohamadreza Govahi
Content
Introduction (Solid State Physics, Crystallography)
Discovery of Impossible Crystals (QCs)
The Unique Structure
Producing Methods
Properties of QCs
Applications of QCs
Islamic Medieval Tiling & Discovery of Natural
QCs
References
Introduction
Classical view of Solid-State Physics: Materials Are Defined Into Two Types:
Crystals
Amorphous
(Non Crystalline)
(image source: http://www.benbest.com/cryonics/noncryst.gif)
Quartz Glass
Crystals Long Range Order
Holing a lattice which Contains atoms, ions or molecules with translational periodicity
With 1-,2-,3-,4-,6-fold rotational symmetries
Having sharp peaks in X-Ray Diffraction
XRD Diagrams & Microstructure Comparison of Materials
(source: Jean-Marie Dubois, USEFUL QUASICRYSTALS, World Scientific, 2005)
Symmetry in Crystallography
Crystals can only exhibit certain symmetries:
Only 1-,2-,3-,4-,6-fold symmetries are possible, a
lattice just can rotates and fill the space by 2π,
2π/2, 2π/3, 2π/4 and 2π/6 Radians.
5-fold, 7-fold, and higher fold symmetries are
forbidden!!
Unit Cells & Lattices in 2D space
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)
OK OK
OK
FAIL!?!
FAIL!?!
overlap
pentagon
heptagon
Unit Cells & Filling 2D Space Unit cell Filling 2D Space Unit cell Filling 2D Space
Impossible Symmetries for Crystals
5
7
8
10
The Discovery Of Impossible Crystals
In 8April1982 Dr. Dan Shechtman Discover a
Crystal with 10-fold (5-fold) Symmetry!
(source:www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/shechtman-lecture.html)
Shechtman’s NBS TEM
logbook records
of the first observation of 10
(5)-fold symmetry!!!
The First Quasicrystal In the nov.1984 Dr. Shechtman et al, Published a
paper at Physical Review Letters and He Claims that He has Observed a Icosahedral Single
Grain with 5-fold Symmetries!
(source: Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984))
(source:J.A. Jaszszak .The Mineralogical Record,25 (1994))
The First Quasicrystal
Dr.Shechtman and Dr.Blech published the famous paper named “The Microstructure of
Rapidly Solidified Al6MN”.
(source:D.Shechtman & I.A.Blech, Microstructure of Rapidly Solidified Al6Mn, Metallurgical TRANSACTIONS A, 1985.)
Pentagonal
(5-fold)
Decagonal
(10-fold)
Al6Mn Quasicrystal Microstructure
1 mm
(source:D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long range orientational order and no translational symmetry, Physical Review Letters 53(1984) 1951–1953.)
10-fold electron diffraction pattern
Electron diffraction from the
Icosahedral Phase has 5-fold
rotational axes and it is not
periodic.
The ratio of distances
between the central spot and
other spots is the Fibonacci
Number τ or φ
known also as the “Golden
Mean”.
τ=1+ 𝟓 /2 ≈ 𝟏. 𝟔𝟏𝟖 …
Inflation Symmetry
A New Definition for Crystal (1992)
“…… By crystal we mean any solid having an
essentially discrete diffraction diagram, and by
aperiodic crystal we mean any crystal in which three
dimensional lattice periodicity can be considered to
be absent.”
Reference: International Union of
Crystallography, “Report of the
executive Committee for 1991”, Acta
Cryst. A48 (1992) 922-946
2011 Chemistry Nobel Prize for Discovery of QCs
Dr. Dan Shechtman won the Nobel Prize for Chemistry in 2011
New Definition for Materials
Materials
Crystals
Amorphous
Quasicrytals
(source: I.R. Fisher et al., Phil Mag B 77 (1998) 1601)
single-grain
icosahedral Ho–Mg–Zn
quasicrystal
Qusicrystals (QCs)
The Quasicrystalline state is a third form of solid matter beside the crystalline and the amorphous.
The Atomic Positions are ordered, but with Rotational Symmetries, e.g. 5-,8-,10- or 12-fold, Which are not found in standard crystals.
These symmetries forbid a periodic structure and instead, enforce Quasiperiodicity.
“Hans-Rainer Trebin, Quasicrystals Structure and Physical Properties,
WILEY-VCH, 2003”
Differences Between QCs & Crystals
Material Ordered Periodic
Crystal
Quasicrystal
Amorphous
QCs ARE ORDERED
STRUCTURES WHICH
ARE NOT PERIODIC,
BUT QUASIPERIODICS.
t translation
Inflation (Golden Mean)
RC rotation crystallographic (2-,3-,4-,6-
fold)
RCQ RC + (5-,8-,10-,12-fold)
DIMENSION OF QUASIPERIODICITY (QP)
QC can have quasiperiodicity along 1,2 or 3 dimensions
At least one dimension should be quasiperiodic
QP QP/P
QP/P
(source: http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/shechtmanlecture.html)
QCs Types
There are two main groups of quasicrystals:
Quasiperiodic in two dimensions There is one
periodic direction perpendicular to the
quasiperodic layers.
Octagonal QCs with local 8-fold symmetry
Decagonal QCs with local 10-fold symmetry
Dodecagonal QCs with local 12-fold symmetry
Quasiperiodic in three dimensions, no periodic
direction
Icosahedral QCs(axes:12x5-fold, 20x3-fold, 30x2-fold)
Quasicrystals Examples Icosahedral QC Al-Mn
Al-Mn-Si
Al-Li-Cu *
Al-Pd-Mn *
Al-Cu-Fe
Al-Mg-Zn
Zn-Mg-RE (RE=La,Ce,Nd,Sm,Gd, Dy,Ho,Y)
Ti-TM (TM=Fe, Mn, Co, Ni)
Nb-Fe
V-Ni-Si
Pd-U-Si
Decagonal QC Al-Ni-Co *
Al-Cu-Mn
Al-Cu-Fe
Al-Cu-Ni
Al-Cu-Co *
Al-Cu-Co-Si *
Al-Mn-Pd *
V-Ni-Si
Cr-Ni
* - stable quasicrystals
The Most Common 2 Typs of QCs
Al-Ni-Co Zn-Mg-Ho
(Source: Electrons in a strange sea, Patricia A. Thiel and Jean Marie Dubois Nature 406, 570-573(10 August 2000) doi:10.1038/35020657)
Ex, Icosahedral QC & Atomic Order
(source:http://images.iop.org/objects/jio/labtalk/4/9/8/figure.jpg)
Producing Methods Rapid Solidification (Melt Spinning)
Conventional Casting
Multilayer Deposition Technique
Mechanical Alloying (Ball Milling)
Laser or Electron Melting Method
Rapid Solidification (Melt Spinning)
• Cooling Rate:
𝟏𝟎𝟓~𝟏𝟎𝟗 K/s
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)
Conventional Casting Can make large quasicrystalline
grains
Can obtain stable quasicrystals
Can use as commersial method for
producing QCs in large Quantities
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777
General Properties of QCs Light Absorption
Reduced Adhesion
Reduced Friction
Heat Resistance
High Corrosion Resistance
High Electric Resistance in Low Temperature
Brittleness
High Hardness (1000 HV)
…
Applications of QCs Surface Non-Stick Coating and Thin Films
Quasicrystalline Nanoparticles
Reinforcement of Composites
Hydrogen Storage
Infrared Light Absorption
Heat Insulation
Protection against Corrosion and Oxidation
Catalysis
Optic and Photonic QCs
…
Surface Non-Stick Coating and Thin Films
Thermal Spray
Plasma Spray
PVD
CVD
Multilayer Deposition
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777
http://www.dvorsons.com/Sitram/Cybernox/CybernoxSet.jpg
Cybernox Cookwares
Quasicrystalline Nanoparticles Reinforcement of razor blades and surgeon’s
instruments by Nanocrystalline Nanoparticles.
Source:www.designfax.net/cms/dfx/opens/article-view-dfx.php?nid=4&bid=117&et=featurearticle&pn=02
Reinforcement of Composites
Quasicrystalline
Particles are
Commercially
used for both
Metal Matrix
(Maraging Steel)
and Polymer
Matrix (Plyamide)
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777
Nanoquasicrystalline Alloys Comparison between 7075-T6 Alloy &
Nanoquasicrystalline Alloy
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777
Islamic Medieval Architecture & QCs
In 2007,Peter J. Lu and Paul J. Steinhardt
have proven that dodecagonal
Quasicrystalline were first came to
Islamic and Iranian Art as Islamic Girih
Tilings (500 years before discovery of
QCs)
“Lu and Steinhardt: Science, 315 (2007)
1106”
The First Natural QC (Icosahedrite)
Icosahedrite,
Al63Cu24Fe13,
the first natural
quasicrystal
Dicovered in
2009
Natural Quasicrystals, Luca Bindi, Paul J. Steinhardt, Nan Yao, Peter J. Lu, SCIENCE,324, 2009.
The First Natural QC (Icosahedrite)
The 5-fold
Diffraction Pattern
The 3-fold
Diffraction Pattern
The 2-fold
Diffraction Pattern
SEM image of
Khatyrka
meteorite, The
White part contains
Natural QCs
Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal,L. Bindi,PJ. Steinhardt, N. Yao,PJ. Lu, American Mineralogist, Volume 96, pages 928–931, 2011
The Second Natural QC (Decagonal)
Natural quasicrystal with decagonal Symmetry, Luca Bindi et al, SCIENTIFIC REPORTS,5, 2015
Magics of Quasicrystals
To Be Continued …
References Jean-Marie Dubois, USEFUL QUASICRYSTALS, World Scientific, 2005
C.Janot- Quasicrystals A Primer-Oxford University Press,1994
J.A. Jaszszak .The Mineralogical Record,25,1994
Shechtman et al. Phys. Rev. Lett., 53, 1951,1984
D.Shechtman & I.A.Blech, Microstructure of Rapidly Solidified Al6Mn, Metallurgical TRANSACTIONS A, 1985
D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long range orientational order and no translational symmetry, Physical Review Letters 53,1984
International Union of Crystallography, Report of the executive Committee for 1991, Acta
Cryst. A48 ,1992
I.R. Fisher et al., Phil Mag B 77,1998
Hans-Rainer Trebin, Quasicrystals Structure and Physical Properties, WILEY-VCH, 2003
Electrons in a strange sea, Patricia A. Thiel and Jean Marie Dubois Nature 406, 2000
JM. Dubois, Chem. Soc. Rev.,41, 2012
Lu and Steinhardt, Science, 315, 2007
Natural Quasicrystals, Luca Bindi, Paul J. Steinhardt, Nan Yao, Peter J. Lu, SCIENCE,324, 2009
Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal,L. Bindi,PJ. Steinhardt, N. Yao,PJ. Lu, American Mineralogist, 96, 2011
Natural quasicrystal with decagonal Symmetry, Luca Bindi et al, SCIENTIFIC REPORTS,5,
2015