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.


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.


Tiling a floor may not be that simple!

29 sept. 2014. MRS Brazil 2014 4

= 2(p- p /5)/2 = 4p/5 = 144°

1



The final result and its variety


This logical problem

was solved in 1974

by Sir Roger

Penrose.



THE discovery in 1982


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

29 sept. 2014. 7 MRS Brazil 2014

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.



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


All this implies a change of

paradigm: sharp diffraction spots do

not mean periodicity, but long range

order!



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 …



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



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



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



Al

Cu Fe

?

push

pull



B C

A

push

Phase diagram of Push-Pull Alloy systems

immiscible

repulsive

A complexity amplifier



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



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



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

MRS Brazil 2014

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


Selective Laser Sintering

MRS Brazil 2014

IR light



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).



Part 2: The Legacy of Dan Shechtman



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?



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?



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



Non-periodic space groups in soft matter

29 sept. 2014. MRS Brazil 2014 26


Defects as in metallic alloys



A natural quasicrystal

29 sept. 2014. MRS Brazil 2014 28

L. Bindi P.J. Steinhardt

See: L. Bindi et al.,

Science, 324 (2009) 1306



Natural quasicrystal : a meterorite

29 sept. 2014. MRS Brazil 2014 29

Terrestrial origin

Extraterrestrial origin



Graphic arts

29 sept. 2014. MRS Brazil 2014 30

R. Lück, MPG Stuttgart

Private communication


Not that new!

29 sept. 2014. MRS Brazil 2014 31

Dürer (1471-1528)

Kepler (1571-1630)



Hans Ude Nissen c.a. 1996



Lu and Steinhardt: Science, 315 (2007) 1106

29 sept. 2014. MRS Brazil 2014 33


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



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 (???).



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.


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.



MRS Brazil 2014 29 sept. 2014. 39

Thank you for your

kind attention!



push-pull alloys and the legacy of dan shechtman

Science

crystals copyright

mn alcu

cu alli

electron transportmrs

optical conductivitymrs

fe alpd

ta alni

periodic cma