How complexity can help: the case of Aluminum-based intermetallics.

How complexity can help: the case
of aluminum-based intermetallics
Jean-Marie DUBOIS
Institut Jean Lamour
UMR 7198 CNRS – Université de Lorraine
jean-marie.dubois@ijl.nancy-universite.fr
Esther BELIN-FERRÉ
Laboratoire Chimie-Physique Matière et Rayonnement
UMR 7614 CNRS Université Pierre et Marie Curie
esther.belin-ferre@upmc.fr

This lecture is dedicated to Prof.
Hans-Rainer Trebin, who retires
from his position as Professor of
the University of Stuttgart,
Germany, and head of the
Institute for Theoretical and
Applied Physics.

MRS Brazil - Florianopolis

Sept. 23-27, 2012

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1

Outline

1- The old paradigm of crystallography
2- Few old examples of periodic, complex metallic alloys
(CMAs)
3- The specific case of quasicrystals
4- Synthesis
5- Complexity in metallic alloys
6- Transport properties versus complexity
7- Few, complexity-dependent, applications of CMAs
8- Conclusion

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The old paradigm of crystallography


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2

The periodic tiling of 2D-space

1/6 of 2π: 6 tiles

1/4 of 2π: 4 tiles
4 tiles around each
vertex:

1/3 of 2π: 3 tiles

No void, no overlap.


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Not always that easy!
135°
α = 2(π- π /5)/2 = 4π/5 = 144°
1/5 of 2π
1
τ


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3

THE discovery in 1982

3D reciprocal space: same
symmetry as that of the
icosahedron or the pentagonal
dodecahedron

Danny Shechtman,
Technion, Haifa

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Few old examples of periodic,
complex metallic alloys (CMAs)


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4

The early days …
1930s to 60s

Al12Mo

Linus Pauling and
his collaborators
(Samson,
Schoemaker, etc.)

T-AlZnMg


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The example of the Bergman phase
(Al,Zn)49 Mg32

G. Bergman, J.L.T. Waugh, L. Pauling, Nature 169, 1057 (1952)

•  Cubic

structure Im3
•  Unit cell a = 14.16 Å,
•  ~162 atoms/cell
Al
Mg
Zn


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Another, even more complex, example: β-Al3Mg2
Feuerbacher et al.
Z. Krystallographie (2006)

Al
Al/Mg
Mg

1832 atomic positions,
but only 1178 occupied.
Lattice parameter:
Al
Mg

a = 2.824 nm.


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Two essential characteristics of complexity: 1
Atomic layers like Russian dolls:

The Al-Zn-Mg
Bergman phase
Drawings: courtesy of U. Mizutani

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Two essential characteristics of complexity: 2
Pronounced cluster structure

i- Large unit cell
cF1168-Al3Mg2 
 

a = 2.8239(1) nm 
V = 22.5189 nm3#
Courtesy Uichiro Mizutani, 2005.

ii- Significant amount of disorder

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10-fold symmetry: twinning ?


7

The specific case of quasicrystals


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Discoverers of quasicrystals

1982-1985
Not all co-discoverers
shown on this picture!

5 f

10 f

12 f


8 f

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8

No evidence of translation symmetry anymore
Perfect icosahedral
point group
symmetry in
reciprocal space
Perfect
pentagonal tiling
along specific
directions in real
space, with no
twinning!
Courtesy of P. A. Thiel,
Ames Labs, USA.

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Two main types of quasicrystals
Icosahedral:
Aperiodic in 3D

Decagonal:
Aperiodic in 2D,
Periodic in 1D

Quasiperiodic planes stacked periodically
Courtesy: P. A. Thiel, Ames Labs, USA.


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9

Where the atoms are in the bulk
A ⇒ AB
L
L
S
L
L
S
L
S
L
L
S
L

≈ 2 nm
Takakura et al., Acta Cryst. 2001

B⇒A
A
AB
ABA
ABAAB
ABAABABA
etc.

…
ABAABABAABAAB…
Non-periodic AND
Num(A)/Num(B) = τ =
(1+√5)/2 ≈ 1.618…

Synthesis


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Preparation of single crystals
Several techniques exist to grow single crystals
of complex metallic alloys with high structural
quality:
Czochralsky pulling technique
Flux growth method
≈ 8 cm

Courtesy:
M. Feuerbacher, Juelich

Courtesy: I. Fisher & P. Canfield, Ames

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Preparation by metallurgical methods
Not only laboratory samples:
Slowly solidified ingot

Composition: Al71Cu9Cr10Fe10 (at%)
PVD coating for thermal
insulation of a helicopter
turbine blade

Batches of up to 1 000 kg of atomized powder
produced in 1993-94

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Most CMAs are thermodynamically stable

Al62.5Cu25Fe12.5
ω-Al70Cu20Fe10


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Complexity

12

CMAs: Structure changes dramatically with conc.
βC

Hierarchical clusters
clusters
atoms

If glue atoms are omitted,
fractal dimension < 3

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Complexity in one, single number
In reciprocal space:

In real space:

Complexity index:

2kF

βC = Ln(Nunit cell)
Tri-Al Mn

Shannon entropy of a single 11 4
constituent compound: S = α βC + K

βC(bcc) = Ln(2)
βC(fcc) = 2 Ln(2)

βC(ico) << ∞
Jones zone

βC(ico) ≈ Ln(6.1023) ≈ 54

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Transport properties versus complexity


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Electron transport in CMAs
Belin-Ferré, Klanjšek, Jagličić, Dolinšek, Dubois, J. Phys. Cond. Matter 17 (2005) 6911.

Size of the unit cell

Conductivity:
Mott type: ρ ∝ n(EF)-2
2

( N ( E ) % S free e 2 
σ = & free F # F 3 F
' N ( EF ) $ 12π 
Mizutani, J. Phys. Cond. Matter
10 (1998) 4609.

Conductivity:
Einstein type: ρ ∝ n(EF)-1

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Electron conductivity at 4K


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4K Conductivity: an example of SOC?

Contains NO
transition metal!


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RT thermal diffusity vs complexity

κ = α ρ CP
ρ ≈ Cte
κ ≈ A σ300K + B
Therefore: α α σ

At 300K, CP ≈ 3R ;


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Self-organised criticality (SOC)
Frequency of the avalanche (Log of)

Slope ≈ -1

Size of the avalanche (Log of)
Per Bak 1948-2002

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Other examples of SOC
Connectivity
of the web

Earthquakes of
magnitude m


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SOC

SOC is an intermediate state, between order and disorder.
SOC is metastable, although it may last (nearly) for ever
(e.g. California’s earthquakes)
SOC is characterized by a power law:
N(m) = m-α
with α ≈ 1.
The SOC state in Al-based intermetallics is sampled thanks
to the formation of compounds of varying unit cell size.
In reminiscence of avalanches on a sand pile, it must be
related to hopping of electrons.

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Applications related to complexity


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Applications based on transport properties

There is a certain range of concentrations within which nearly
identical properties are found: industrial exploitation is feasible!

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Most CMAs applications exploit complexity
1988:
Frying pans (Dubois)
1992:
Solar light absorbers (Eisenhammer, Machizaud &
Dubois)
1993: Thermal barriers (Dubois)
High performance maraging steels (Nilsson)
ca 2000: Anti-fretting coatings (Dubois & Merstallinger)
Zero-TCR resistors (Dolinšek)
Advanced catalysts based on leached AlCuFe (Tsai)
…
2008:
Selective Laser Sintereded polymer-CMA composites
(Kenzari & Fournée)
Metal-matrix composites (Singh, Fleury, Eckert, …)
2010: Thermal memory cell (Dolinšek)
Dual thermo-electric rectifiers (Takeuchi)
2012: High-performance, low cost Al13Fe4 catalyst (Ambruster)

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A new, commercial technology based on CMAs
Polyamidematrix
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.

Approx. 20 cm

S. Kenzari & V. Fournée, French Patent n°2950826
(2009), PCT n° WO2011/039469 (2011).

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SLSed Polymer matrix composites
Pin-on-Disk test

Disk

Load Fn
Pin: e.g.
hard steel

Friction coefficient (µ)

Tangential force Ft

(a)

0,35

0,3

0,25

0,2

0,15

0,1

PA+AlCuFeB
PA+Al
PA

0

Friction coefficient: µ = Ft/Fn
Friction coefficient against hard
steel in air for various
composites

Friction coefficient (µ)

0,35

20

40

60

80

100

Sliding distance (m)

(b)

0,3

0,25

0,2
PA+AlCuFeB
Carbon fibers
Glass fibers
Glass
PA

0,15

0,1

0

20

40

60

80

100

Sliding distance (m)

S. Kenzari et al. Materials & Design, 35 (2011) 691.

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Selective Laser Sintering (1)


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IR light


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Optical conductivity
1 104

0

Energy (eV)

0.04

0.08

0.12

0.16

Optical conductivity σ(ω) (Ω-1.cm-1)

10000

i-Al-Cu-Fe-B
0%-Al-Cr-Fe
50%-Al-Cr-Fe
80%-Al-Cr-Fe
100%-Al-Cr-Fe

Drude peak

8000
8000

6000
6000

γ-Al-Cr-Fe

4000
4000

Ο1-Al-Cr-Fe

2000
2000

Ico-Al-Cu-Fe-B

0

0

200

400

600

800

1000
-1

1200

1400

Wavenumber (cm )

No Drude peak

V. Demange et al. PRB 6-14 (2002) 144205 1.

High IR light
absorption


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Conclusion


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Conclusion
Properties:
✿ Several properties of Al-based CMAs scale as power
laws of the complexity index βC : this is taken as an
example of Self-Organized Criticality (SOC).

Applications:
v 
Several applications may result:
ü  Thermal barriers for low (< 200 K) and high (800 < T
> 1200 K) applications
ü  Infra-red absorbers
ü  Low-stick coatings for frying pans
ü  Non-fretting parts for high vacuum technologies
ü  Etc.

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Acknowledgements
Special thanks to Hervé Combeau, IJL, for very interesting
discussions about SOC
And to our sponsors:


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Thank you for your attention!


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How complexity can help: the case of Aluminum-based intermetallics.

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