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