1. An introduction to QUASICRYSTALS
In The Name of God
An introduction to QUASICRYSTALS
Editor: Eng. Mohamadreza Govahi

2. 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

3. Introduction
Classical view of Solid-State Physics: Materials Are Defined Into Two Types:
Crystals
Amorphous
(Non Crystalline)
Quartz
Glass
(image source:

4. 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

5. XRD Diagrams & Microstructure Comparison of Materials
(source: Jean-Marie Dubois, USEFUL QUASICRYSTALS, World Scientific, 2005)

6. 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!!

7. Unit Cells & Lattices in 2D spaceOK OK
pentagon
FAIL!?! OK
heptagon
FAIL!?!
overlap
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)

8. Unit Cells & Filling 2D Space

9. Impossible Symmetries for Crystals5 8 10 7

10. The Discovery Of Impossible Crystals
In 8April1982 Dr. Dan Shechtman Discover a Crystal with 10-fold (5-fold) Symmetry!
Shechtman’s NBS TEM logbook records
of the first observation of 10 (5)-fold symmetry!!!
(source:

11. 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:J.A. Jaszszak .The Mineralogical Record,25 (1994))
(source: Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984))

12. The First Quasicrystal
Dr.Shechtman and Dr.Blech published the famous paper named “The Microstructure of Rapidly Solidified Al6MN”.
Pentagonal
(5-fold)
Decagonal
(10-fold)
(source:D.Shechtman & I.A.Blech, Microstructure of Rapidly Solidified Al6Mn, Metallurgical TRANSACTIONS A, 1985.)

13. 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.)

14. 10-fold electron diffraction pattern
Electron diffraction from the Icosahedral Phase has 5-fold rotational axes and it is not periodic.
Inflation
Symmetry
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…

15. 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)

16. 2011 Chemistry Nobel Prize for Discovery of QCs
Dr. Dan Shechtman won the Nobel Prize for Chemistry in 2011

17. New Definition for Materials
Crystals
Quasicrytals
Amorphous
single-grain icosahedral Ho–Mg–Zn quasicrystal
(source: I.R. Fisher et al., Phil Mag B 77 (1998) 1601)

18. 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”

19. 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)

20. DIMENSION OF QUASIPERIODICITY (QP)
QC can have quasiperiodicity along 1,2 or 3 dimensions
At least one dimension should be quasiperiodic QP
QP/P
(source:

21. 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)

22. 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

23. The Most Common 2 Typs of QCs
Zn-Mg-Ho
Al-Ni-Co
(Source: Electrons in a strange sea, Patricia A. Thiel and Jean Marie Dubois Nature 406, (10 August 2000) doi: / )

24. Ex, Icosahedral QC & Atomic Order
(source:

25. Producing Methods Rapid Solidification (Melt Spinning)
Conventional Casting
Multilayer Deposition Technique
Mechanical Alloying (Ball Milling)
Laser or Electron Melting Method

26. Rapid Solidification (Melt Spinning)
Cooling Rate: 𝟏𝟎 𝟓 ~ 𝟏𝟎 𝟗 K/s
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)

27. Conventional Casting Can make large quasicrystalline grains
Can obtain stable quasicrystals
Can use as commersial method for producing QCs in large Quantities
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777
(source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)

28. 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) …

29. 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 …

30. Surface Non-Stick Coating and Thin Films
Thermal Spray
Plasma Spray
PVD
CVD
Multilayer Deposition
Cybernox Cookwares
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777

31. Quasicrystalline Nanoparticles
Reinforcement of razor blades and surgeon’s instruments by Nanocrystalline Nanoparticles.
Source:

32. 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

33. Nanoquasicrystalline Alloys
Comparison between 7075-T6 Alloy & Nanoquasicrystalline Alloy
JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777

34. 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”

35. 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.

36. The First Natural QC (Icosahedrite)
The 5-fold Diffraction Pattern
The 3-fold Diffraction Pattern
SEM image of
Khatyrka meteorite, The White part contains Natural QCs
The 2-fold Diffraction Pattern
Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal,L. Bindi,PJ. Steinhardt, N. Yao,PJ. Lu, American Mineralogist, Volume 96, pages 928–931, 2011

37. The Second Natural QC (Decagonal)
Natural quasicrystal with decagonal Symmetry, Luca Bindi et al, SCIENTIFIC REPORTS,5, 2015

38. Magics of Quasicrystals
To Be Continued …

39. 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
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
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

40. THANK YOU
FOR YOUR TIME