An introduction to QUASICRYSTALS In The Name of God An introduction to QUASICRYSTALS 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) Quartz Glass (image source: http://www.benbest.com/cryonics/noncryst.gif)

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 OK OK pentagon FAIL!?! OK heptagon FAIL!?! overlap (source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)

Unit Cells & Filling 2D Space

Impossible Symmetries for Crystals 5 8 10 7

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:www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/shechtman-lecture.html)

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))

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.)

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. 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…

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

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 (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 Zn-Mg-Ho Al-Ni-Co (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: 𝟏𝟎 𝟓 ~ 𝟏𝟎 𝟗 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 JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777 (source: C.Janot- Quasicrystals A Primer-1994-Oxford University Press)

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 Cybernox Cookwares JM. Dubois, Chem. Soc. Rev., 2012, 41, 6760–6777 http://www.dvorsons.com/Sitram/Cybernox/CybernoxSet.jpg

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 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

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 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

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