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

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How complexity can help: the case of aluminum-based intermetallics

Jean-Marie DUBOIS Institut Jean Lamour

UMR 7198 CNRS – Université de Lorraine [email protected]

Esther BELIN-FERRÉ

Laboratoire Chimie-Physique Matière et Rayonnement UMR 7614 CNRS Université Pierre et Marie Curie

[email protected]

Sept. 23-27, 2012 MRS Brazil - Florianopolis 2

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.

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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

The old paradigm of crystallography


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The periodic tiling of 2D-space

4 tiles around each vertex:

No void, no overlap.

1/6 of 2π: 6 tiles

1/4 of 2π: 4 tiles

1/3 of 2π: 3 tiles


Not always that easy!

135°

α = 2(π- π /5)/2 = 4π/5 = 144°

1

τ

1/5 of 2π

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THE discovery in 1982

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

Danny Shechtman, Technion, Haifa

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


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The early days …

1930s to 60s

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

Al12Mo

T-AlZnMg

The example of the Bergman phase


(Al,Zn)49 Mg32 G. Bergman, J.L.T. Waugh, L. Pauling, Nature 169, 1057 (1952)

Al

Mg

Zn

•  Cubic structure Im3 •  Unit cell a = 14.16 Å,

•  ~162 atoms/cell

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Another, even more complex, example: β-Al3Mg2


Al Mg

1832 atomic positions, but only 1178 occupied.

Lattice parameter:

a = 2.824 nm.

Feuerbacher et al. Z. Krystallographie (2006)

Al

Mg Al/Mg

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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Pronounced cluster structure

ii- Significant amount of disorder

i- Large unit cell

cF1168-Al3Mg2

a = 2.8239(1) nmV = 22.5189 nm3 #

Courtesy Uichiro Mizutani, 2005.

Two essential characteristics of complexity: 2

10-fold symmetry: twinning ?


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The specific case of quasicrystals


Discoverers of quasicrystals


1982-1985

12 f

10 f

8 f

5 f Not all co-discoverers shown on this picture!

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

Sept. 23-27, 2012 17 MRS Brazil - Florianopolis

Perfect icosahedral point group symmetry in reciprocal space

Perfect pentagonal tiling

along specific directions in real

space, with no twinning!

No evidence of translation symmetry anymore

Two main types of quasicrystals

Icosahedral: Aperiodic in 3D

Quasiperiodic planes stacked periodically

Decagonal: Aperiodic in 2D, Periodic in 1D

Sept. 23-27, 2012 18 MRS Brazil - Florianopolis Courtesy: P. A. Thiel, Ames Labs, USA.

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Takakura et al., Acta Cryst. 2001

Where the atoms are in the bulk

L L

L L

L

L

L

L

S

S

S

S

A ⇒ AB

B ⇒ A A

AB ABA

ABAAB ABAABABA

…ABAABABAABAAB… Non-periodic AND

Num(A)/Num(B) = τ = (1+√5)/2 ≈ 1.618…

etc.

≈ 2 nm


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

Preparation by metallurgical methods


Not only laboratory samples: Slowly solidified ingot

PVD coating for thermal insulation of a helicopter turbine blade

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

Composition: Al71Cu9Cr10Fe10 (at%)

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Most CMAs are thermodynamically stable

Al62.5Cu25Fe12.5

ω-Al70Cu20Fe10

Complexity


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CMAs: Structure changes dramatically with conc.


βC

atoms

clusters

Hierarchical clusters

If glue atoms are omitted, fractal dimension < 3

Complexity in one, single number


Tri-Al11Mn4

Jones zone

2kF

In reciprocal space: In real space:

βC = Ln(Nunit cell)

βC(bcc) = Ln(2)

βC(fcc) = 2 Ln(2)

βC(ico) << ∞

βC(ico) ≈ Ln(6.1023) ≈ 54

Complexity index:

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

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Transport properties versus complexity


Electron transport in CMAs


Siz

e of

the

unit

cell

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

Conductivity: Mott type: ρ ∝ n(EF)-2

3

22

12)()(

πσ F

freeF

Ffree

F eSENEN

#$

%&'

(=

Mizutani, J. Phys. Cond. Matter 10 (1998) 4609.

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

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Electron conductivity at 4K


4K Conductivity: an example of SOC?


Contains NO transition metal!

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RT thermal diffusity vs complexity


κ = α ρ CP At 300K, CP ≈ 3R ; ρ ≈ Cte

κ ≈ A σ300K + B

Therefore: α α σ

Self-organised criticality (SOC)


Per Bak 1948-2002

Frequency of the avalanche (Log of)

Size of the avalanche (Log of)

Slope ≈ -1

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Other examples of SOC


Connectivity of the web

Earthquakes of magnitude m

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


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)

A new, commercial technology based on CMAs


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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SLSed Polymer matrix composites


Friction coefficient against hard steel in air for various

composites

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

0,1

0,15

0,2

0,25

0,3

0,35

0 20 40 60 80 100

PA+AlCuFeBPA+AlPA

Sliding distance (m)

Frict

ion co

effic

ient (µ)

0,1

0,15

0,2

0,25

0,3

0,35

0 20 40 60 80 100

PA+AlCuFeBCarbon fibersGlass fibersGlassPA

Frict

ion co

effic

ient (µ)

Sliding distance (m)

(a)

(b)

Pin-on-Disk test

Load Fn

Pin: e.g. hard steel

Tangential force Ft

Disk

Friction coefficient: µ = Ft/Fn

Selective Laser Sintering (1)


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IR light



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Optical conductivity


0

2000

4000

6000

8000

1 104

0 200 400 600 800 1000 1200 1400

i-Al-Cu-Fe-B0%-Al-Cr-Fe50%-Al-Cr-Fe80%-Al-Cr-Fe100%-Al-Cr-Fe

0 0.04 0.08 0.12 0.16

Opt

ical

con

duct

ivity

σ(ω

) (Ω

-1.c

m-1

)

Wavenumber (cm-1)

Energy (eV)

2000

4000

6000

8000

10000

γ-Al-Cr-Fe

Ο1-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

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Conclusion


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:

Thank you for your attention!


Technology

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