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Palestra plenária do XI Encontro da SBPMat (Florianópolis, setembro de 2012). Palestrante: Jean Marie Dubois - Institut Jean Lamour (França).
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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
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
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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
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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
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(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
Sept. 23-27, 2012 MRS Brazil - Florianopolis 11
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
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Discoverers of quasicrystals
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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
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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
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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.
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βC
atoms
clusters
Hierarchical clusters
If glue atoms are omitted, fractal dimension < 3
Complexity in one, single number
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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
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Electron transport in CMAs
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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
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4K Conductivity: an example of SOC?
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Contains NO transition metal!
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RT thermal diffusity vs complexity
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κ = α ρ CP At 300K, CP ≈ 3R ; ρ ≈ Cte
κ ≈ A σ300K + B
Therefore: α α σ
Self-organised criticality (SOC)
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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
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Connectivity of the web
Earthquakes of magnitude m
SOC
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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
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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
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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
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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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SLSed Polymer matrix composites
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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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Selective Laser Sintering (2)
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IR light
Selective Laser Sintering (3)
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Selective Laser Sintering (4)
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Optical conductivity
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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
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Conclusion
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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!
Sept. 23-27, 2012 MRS Brazil - Florianopolis 48