Push-Pull Alloys and the Legacy of Dan Shechtman.

Push-Pull Alloys and the Legacy of Dan Shechtman
Jean-Marie Dubois
Institut Jean Lamour
CNRS and Université de Lorraine
Nancy, France
Copyright © 2014 Jean-Marie Dubois.
All rights reserved.

Part 1
Push-Pull Alloys:
-Penrose tiling
-The discovery of non-periodic crystals
-A new paradigm in crystallography
-Push-Pull Alloys
-Complex metallic alloys (CMAs)
-One (essential) property of CMAs
-A typical application of a specific CMA
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Tiling 2D-space, like the floor of your kitchen
An integer number of tiles around each vertex:
No void, no overlap.
1/6 of 2p: 6 tiles
1/4 of 2p: 4 tiles
1/3 of 2p: 3 tiles
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Tiling a floor may not be that simple!
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 = 2(p- p /5)/2 = 4p/5 = 144°
1


The final result and its variety
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This logical problem was solved in 1974 by Sir Roger Penrose.

THE discovery in 1982
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Same point group symmetry as that of the icosahedron or of the pentagonal dodecahedron
Danny Shechtman, Technion, Haifa

Two main types of quasicrystals
Icosahedral:
Aperiodic in 3D Quasiperiodic planes stacked periodically
Decagonal: Aperiodic in 2D, Periodic in 1D
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Courtesy: P. A. Thiel, Ames Labs, USA.

Where are the atoms?
L
L
L
L
L
L
L
L
S
S
S
S
L  LS
S  L
L
LS
LSL
LSLLS
LSLLSLSL
…LSLLSLSLLSLLS…
Non-periodic if :
Num(L)/Num(S) =  =(1+5)/2 ≈ 1.618…
etc.
Courtesy : N. Takanura et al., NRIM, Japan
Although it is not periodic, the sequence of (red) planes is fully determined by an non-ambiguous algorithm: there is no disorder!
The same holds true for any other plane.
As a consequence, diffraction patterns show sharp diffraction spots, like periodic crystals do.
Copyright © 2014 Jean-Marie Dubois. All rights reserved.

5-fold, 8-fold, 10-fold and 12-fold
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All this implies a change of paradigm: sharp diffraction spots do not mean periodicity, but long range order!

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Nobel Prize for Chemistry in 2011
… for having forced the scientific community to change its paradigm about crystals …

Typical examples of quasicrystal-forming alloys
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Al-Cu-Fe Al-Pd-Mn Al-Cu-Ta Al-Ni-Co Al-Ni-Cu Al-Li-Cu Al-Mg-Zn Ti-Zr-Ni Ag-In-Yb Au-Sn-Yb Mg-Cd-Yb Hf-Mg-Zn … Cd-RE & Cd-Ca: the only known so far binary QCs
Immiscible elements
or
Weakly interacting species
Pd Cu

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CMAs in the Al-Cu-Fe system
Al62.5Cu25Fe12.5
-Al70Cu20Fe10
q-Al2Cu etc.
Cu & Fe form no compounds

Large size approximants
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Lei et al., Phil. Mag. 88-4 (2008) 279.
Quiquandon et al., JPCM 8 (1996) 2487
N=154
N≈2750
N≈300
N≈6125
Ω = 60-65 at/nm3

Al
Cu
Fe
?
push
pull
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B
C
A
push
Phase diagram of Push-Pull Alloy systems
immiscible
repulsive
A complexity amplifier
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To summarize at this stage
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Complexity: natural logarithm of Nunit cell or bC=Ln(Nuc)
∞
bC
Ln(2)
5
54
B2 CsCl type
Intermetallics
Complex metallic alloys
1 atom gram
10
Largest Al-based PERIODIC CMA known so far
Icosahedral quasicrystals

Electron transport
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Size of the unit cell
Conductivity:
Einstein type:   n(EF)-1
Conductivity: Mott type:   n(EF)-2
Belin-Ferré, Klanjšek, Jagličić, Dolinšek, Dubois, J. Phys. Cond. Matter (2005) 6911.
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Complexity determines the type of conductivity

An example of Self-Organised Criticality?
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Slope = - 1
Slope = 0
4,0
6,0
8,0
10,0
12,0
14,0
0,0
10,0
20,0
30,0
40,0
50,0
60,0
bC
Ln s
Earthquakes in California are another example of SOC: the frequency of occurrence of an earthquake of magnitude Am is f(m)/A if f(m) is the frequency of earthquakes of magnitude m.

Optical conductivity
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0
2 0 0 0
4 0 0 0
6 0 0 0
8 0 0 0
1 1 0
4
0 2 4 0 6 0 0 8 0 0 1 0 0 1 0 0 1 2 0 4 0 0 0 0 i - A l 0 % - 5 0 % 8 0 % 1 0 0 % 0 0 . 0 0 . 0 4 0 . 0 8 1 . 2 1 O s()p  t (i - 1 . c - 1
)
W a v e n - 1
)
E n e r g y 2000
4000
6000
8000
10000
g-Al-Cr-Fe
O1-Al-Cr-Fe
Ico-Al-Cu-Fe-B
Drude peak
No Drude peak
V. Demange et al. PRB 6-14 (2002) 144205 1.
High IR light
absorption 29 sept. 2014. 19

Selective Laser Sintering
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IR light
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A new, commercial technology based on CMAs
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Approx. 20 cm
Polyamide-matrix composite reinforced by atomized
Al-Cu-Fe-B icosahedral particules, which was assembled by Selective Laser Sintering.
Used for a Formula I race car by Renault.
S. Kenzari & V. Fournée, French Patent n°2950826 (2009), PCT n° WO2011/039469 (2011).
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Part 2: The Legacy of Dan Shechtman
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Part 2
The Legacy of Dan Shechtman:
-Soft-quasicrystals
-Quasiperiodic waves in hydrodynamics
-Quasicrystals in oxides
-Quasiperiodic cold atoms traps
-Quasiperiodic ensembles of microscopic particles
-Natural quasicrystal
-Quasiperiodic patterns in medieval islamic art
-Conclusion: What else?

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Part 2, revised
The Legacy of Dan Shechtman:
-Soft-quasicrystals
-Quasiperiodic waves in hydrodynamics
-Quasicrystals in oxides
-Quasiperiodic cold atoms traps
-Quasiperiodic ensembles of microscopic particles
-Natural quasicrystal
-Quasiperiodic patterns in medieval islamic art
-Conclusion: What else?

Soft quasicrystals
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Zeng et al., Nature 428 (2004) 157
Miscellar phases in
-lyotropic systems
-block co-polymers
-thermotropic liquid crystals X: weakly binding group

Non-periodic space groups in soft matter
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Defects as in metallic alloys
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A natural quasicrystal
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L. Bindi P.J. Steinhardt
See: L. Bindi et al.,
Science, 324 (2009) 1306

Natural quasicrystal : a meterorite
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Terrestrial origin
Extraterrestrial origin

Graphic arts
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R. Lück, MPG Stuttgart
Private communication

Not that new!
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Dürer (1471-1528)
Kepler (1571-1630)

Hans Ude Nissen c.a. 1996
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Lu and Steinhardt: Science, 315 (2007) 1106
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Conclusion: What else?
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A never ending story!
See for instance: hydrogen-bonded quasicrystals (Wasio et al., Nature 507 (6 March 2014) 86) in ferrocenecarboxylic acid.
20.5nm x 20.5 nm
11 nm x 10 nm

Templating artificially nanostructured materials
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Fournée et al., ACS Nano 8-4 (2014) 3646
Just one example: C60 balls ordered on an aperiodic surface

Shechtman's legacy is …
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A change of paradigm
AND
A full range of new discoveries, of unprecedented physics and chemistry of materials, of (???).

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Acknowledgements
Special thanks go to my great friend,
Prof. Dr Severino Jackson Guedes de Lima,
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who dedicated his life-long career to his University and to the Rapid Solidification Laboratory, for his invitation to this five-star conference, for the performance the whole of his group has achieved in bringing it to, and managing it in, Joao Pessoa and for the beautiful talks and events all of us will enjoy this week.

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And thanks to my sponsors:
Thank you to all those who worked hard to make this conference a reality, especially to the Chairlady,
Prof. Dr Iêda Maria Garcia dos Santos.

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Thank you for your kind attention!

Push-Pull Alloys and the Legacy of Dan Shechtman.

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Push-Pull Alloys and the Legacy of Dan Shechtman.