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

29 sept. 2014. MRS Brazil 2014 2 Copyright © 2014 Jean-Marie Dubois.

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MRS Brazil 2014

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

29 sept. 2014. 3 Copyright © 2014 Jean-Marie Dubois.

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Tiling a floor may not be that simple!

29 sept. 2014. MRS Brazil 2014 4

= 2(p- p /5)/2 = 4p/5 = 144°

1

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The final result and its variety

29 sept. 2014. MRS Brazil 2014 5

This logical problem

was solved in 1974

by Sir Roger

Penrose.

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THE discovery in 1982

29 sept. 2014. MRS Brazil 2014 6

Same point group symmetry as that

of the icosahedron or of the

pentagonal dodecahedron

Danny Shechtman,

Technion, Haifa

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Two main types of quasicrystals

Icosahedral:

Aperiodic in 3D

Quasiperiodic planes stacked periodically

Decagonal:

Aperiodic in 2D,

Periodic in 1D

29 sept. 2014. 7 MRS Brazil 2014

Courtesy: P. A. Thiel, Ames Labs, USA.

Copyright © 2014 Jean-Marie Dubois.

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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.

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5-fold, 8-fold, 10-fold and 12-fold

29 sept. 2014. MRS Brazil 2014 9

All this implies a change of

paradigm: sharp diffraction spots do

not mean periodicity, but long range

order!

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29 sept. 2014. MRS Brazil 2014 10

Nobel Prize for Chemistry in 2011

… for having forced the

scientific community to

change its paradigm

about crystals …

Copyright © 2014 Jean-Marie Dubois.

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Typical examples of quasicrystal-forming alloys

29 sept. 2014. MRS Brazil 2014 11

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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29 sept. 2014. MRS Brazil 2014 12

CMAs in the Al-Cu-Fe system

Al62.5Cu25Fe12.5

-Al70Cu20Fe10

q-Al2Cu etc.

Cu & Fe form no

compounds

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Large size approximants

29 sept. 2014. MRS Brazil 2014 13 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

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Al

Cu Fe

?

push

pull

29 sept. 2014. MRS Brazil 2014 14 Copyright © 2014 Jean-Marie Dubois.

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B C

A

push

Phase diagram of Push-Pull Alloy systems

immiscible

repulsive

A complexity amplifier

29 sept. 2014. MRS Brazil 2014 15 Copyright © 2014 Jean-Marie Dubois.

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To summarize at this stage

29 sept. 2014. MRS Brazil 2014 16

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

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Electron transport

MRS Brazil 2014

Siz

e o

f th

e u

nit c

ell

Conductivity:

Einstein type: n(EF)-1

Conductivity:

Mott type: n(EF)-2

Belin-Ferré, Klanjšek, Jagličić, Dolinšek, Dubois, J. Phys. Cond. Matter (2005) 6911.

29 sept. 2014. 17

Complexity determines the

type of conductivity

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An example of Self-Organised Criticality?

MRS Brazil 2014 29 sept. 2014. 18

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.

Copyright © 2014 Jean-Marie Dubois. All rights reserved.

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 04

0 2 0 04 0 06 0 08 0 01 0 0 01 2 0 01 4 0 0

i - A l - C u - F e - B0 % - A l - C r - F e5 0 % - A l - C r - F e8 0 % - A l - C r - F e1 0 0 % - A l - C r - F e

0 0 . 0 40 . 0 80 . 1 20 . 1 6O

pt

ic

al

c

on

du

ct

iv

it

y

s(

)

(

-1

.c

m-

1)

W a v e n u m b e r ( c m- 1

)

E n e r g y ( e V )

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

Copyright © 2014 Jean-Marie Dubois. All rights reserved.

Selective Laser Sintering

MRS Brazil 2014

IR light

29 sept. 2014. 20 Copyright © 2014 Jean-Marie Dubois.

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A new, commercial technology based on CMAs

MRS Brazil 2014

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).

29 sept. 2014. 21 Copyright © 2014 Jean-Marie Dubois.

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Part 2: The Legacy of Dan Shechtman

29 sept. 2014. MRS Brazil 2014 22 Copyright © 2014 Jean-Marie Dubois.

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29 sept. 2014. MRS Brazil 2014 23

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?

Copyright © 2014 Jean-Marie Dubois.

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29 sept. 2014. MRS Brazil 2014 24

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?

Copyright © 2014 Jean-Marie Dubois.

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Soft quasicrystals

29 sept. 2014. MRS Brazil 2014 25

Zeng et al., Nature 428 (2004) 157

Miscellar phases in

- lyotropic systems

- block co-polymers

- thermotropic liquid crystals

X: weakly binding group

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Non-periodic space groups in soft matter

29 sept. 2014. MRS Brazil 2014 26

Copyright © 2014 Jean-Marie Dubois. All rights reserved.

Defects as in metallic alloys

29 sept. 2014. MRS Brazil 2014 27 Copyright © 2014 Jean-Marie Dubois.

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A natural quasicrystal

29 sept. 2014. MRS Brazil 2014 28

L. Bindi P.J. Steinhardt

See: L. Bindi et al.,

Science, 324 (2009) 1306

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Natural quasicrystal : a meterorite

29 sept. 2014. MRS Brazil 2014 29

Terrestrial origin

Extraterrestrial origin

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Graphic arts

29 sept. 2014. MRS Brazil 2014 30

R. Lück, MPG Stuttgart

Private communication

Copyright © 2014 Jean-Marie Dubois. All rights reserved.

Not that new!

29 sept. 2014. MRS Brazil 2014 31

Dürer (1471-1528)

Kepler (1571-1630)

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Hans Ude Nissen c.a. 1996

29 sept. 2014. MRS Brazil 2014 32 Copyright © 2014 Jean-Marie Dubois.

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Lu and Steinhardt: Science, 315 (2007) 1106

29 sept. 2014. MRS Brazil 2014 33

Copyright © 2014 Jean-Marie Dubois. All rights reserved.

Conclusion: What else?

29 sept. 2014. MRS Brazil 2014 34

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 Copyright © 2014 Jean-Marie Dubois. All rights reserved.

Templating artificially nanostructured materials

29 sept. 2014. MRS Brazil 2014 35

Fournée et al.,

ACS Nano 8-4 (2014) 3646

Just one example: C60 balls ordered on an aperiodic surface

Copyright © 2014 Jean-Marie Dubois.

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Shechtman's legacy is …

29 sept. 2014. MRS Brazil 2014 36

A change of paradigm

AND

A full range of new discoveries, of unprecedented

physics and chemistry of materials, of (???).

Copyright © 2014 Jean-Marie Dubois.

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MRS Brazil 2014

Acknowledgements

Special thanks go to my great friend,

Prof. Dr Severino Jackson Guedes de Lima,

29 sept. 2014. 37

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. Copyright © 2014 Jean-Marie Dubois.

All rights reserved.

29 sept. 2014. MRS Brazil 2014 38

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.

Copyright © 2014 Jean-Marie Dubois.

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MRS Brazil 2014 29 sept. 2014. 39

Thank you for your

kind attention!

Copyright © 2014 Jean-Marie Dubois.

All rights reserved.