Functional properties Stéphane Gorsse ICMCB gorsse@icmcb-bordeaux.cnrs.fr Action Nationale de Formation en Métallurgie 22-25/10/2012 - Aussois
Functional properties and microstructural features in ceramics [from M. Ashby]
Plan ❶ Thermoelectricity : applications, principle & materials ❷ How to tune transport properties? ❸ TE materials by design (microstructure engineering)
❶ Thermoelectricity - Applications, principle & materials Power generation Cooling
❶ Thermoelectricity - Applications, principle & materials Thermal power from exhaust = 10 kw 5% efficiency 500 W el Reduction of 7 g/km CO 2 [2012 Boris Mazar State of the Art Prototype Vehicle with a Thermoelectric Generator]
❶ Thermoelectricity - Applications, principle & materials V = S T Series-Parallel Arrangement U NS T P NσS 2 T 2 η max = T c T f T c 1 + ZT m 1 1 + ZT m + T c T f
❶ Thermoelectricity - Applications, principle & materials Squaring a circle S m n 2/3 σ = neμ Performance index: ZT = S2 σ κ T κ = κ l + κ e κ e = σl 0 T Ideal material: high S, high s and low k but when S increases s decreases and when s increases S decreases k increases Best compromise: semiconductors with high mobility and high effective mass of the carrier, and low lattice thermal conductivity
❶ Thermoelectricity - Applications, principle & materials [Vining, Nature Mater. 8 (2009) 83] From 1950 to 1990 : conventional TE materials [Tedenac] [M. Subramanian, DuPont Central Research and Development]
❷ Main strategies to tune transport properties Solid state physics Solid state chemistry ZT 2 S s T k S L 1 k C l 3 ph 2 0 1 3 k 1 kel 2 C ph ph 1 Metallurgy Materials science (Bottom-up app.) Colloidal nanocrystals Nanocomposites 20 20 nm nm
❷ Solid state chemistry phonon glass electron crystal Phonon Glass Electron Crystal [G. Slack, 1994] Nanocages and Rattlers Large unit cell and structural complexity k l k B ph V Clathrates, X 2 Y 6 E 46 (X & Y guest atoms encapsulated in polyhedra of E = Si, Ge or Sn) Filled skutterudites, 2 T 8 X 24 (guest atom inside a 12- coordinated cage surrounded by 8 TX 6 octahedra)
❷ Metallurgy nano to mesoscale engineering Nanograins Bi x Sb 2-x Te 3 [Poudel, Science 320 (2008) 634] Second phase Nanoparticules KPb m SbTe 2+m (PLAT-m) PbTe-rich matrix K/Sb-rich particles [Kanatzidis, Chem. Mater. 22 (2010) 648] [Acta Mater. 59 (2011) 7425]
❷ Main strategies to tune transport properties [Lenoir] 2D superlattices Nanoparticles /matrix Conventional TE materials Nanocages, large unit cells and structural complexity
❸ Toward a "material by design" approach ZT [Figure from Biswas, Nature 489 (2012) 414] Need a predictive tool that couples a description of the microstructure genesis and evolution to the various contributions to ZT
❸ Toward a "material by design" approach [Kozlov, JAllCom 509 (2011) 3326] 100 nm [Saravanan, JAllCom 479 (2009) 26] Mg 2 Si(Sn) SSSS Mg 2 Si(Sn) matrix + Mg 2 Sn(Si) precip. 100 nm [P. Bellanger s Thesis (ICMCB), collab. Redjaimia]
❸ Toward a "material by design" approach
❸ Toward a "material by design" approach Model development Development of Microstructure We need the knowledge of Grain size, d Second phase particle size, Rp Particle density, Np Amount of solute in solution, Xsol Need to develop a simple precipitation model Lattice thermal conductivity contributions Evaluate contributions to phonon scattering : Intrinsec lattice resistance Alloy disordering Grain boundary resistance Particule scattering Monitor : R p, N p, X sol
❸ "Material by design" : mstructure modeling Model development Microstructural genesis and evolution Continuous precipitation of Mg 2 Si from the supersaturated Mg 2 (Si,Sn) solid solution Thermodynamic assessment (sub-lattices) Classical nucleation Theory [Gibbs 1928, Becker 1935, Zeldovich 1943] Diffusion coefficients [Deschamps and Bréchet, Acta Mater. 47 (1999) 293]
❸ "Material by design" : prop. modeling Model development Lattice thermal conductivity Debye model : ω = vk Debye phonon spectrum - acoustic branch - Velocity, v=cst - Highest frequency w D Phonon scattering characterized by phonon life time. κ l = 1 3 C Vvλ = 1 3 C Vv 2 τ Phonon life time C V = U T V Heat capacity Debye frequency Speed of sound g ω = 3 ω2 2π 2 v 3 Phonon density of states U = ω D 0 ħωn ω dω ω D = ħω 0 g ω exp ħω k B T 1 dω Phonon energy Phonon distribution Bose-Einstein distribution function
❸ "Material by design" : prop. modeling Phonon life time (Mathiessen s rule) : τ 1 = τ 1 a + τ 1 ss + τ 1 p + τ 1 1 GB + τ D Normal phonon-phonon scattering τ n 1 = B n Tω a T b Anharmonic contribution [Mingo, PRB 68 (2003) 113308] Umklapp scattering τ u 1 = B u Tω 2 exp C T Results Phonon scattering by solute atoms τ 1 ss = x 1 x Αω 4 κ l Mg 2 Si κ l Mg 2 Sn Α AB = M A M B /M AB 2 + 2 K A K B /K AB 2 δ 3 4πv 3 [Abeles, PRB 131 (1963) 1906] κ l Mg 2 Si 1 x Snx
❸ "Material by design" : prop. modeling Results Second phase particle scattering τ p 1 = v σ s 1 + σ l 1 1 ρ Particles size comparable to the wavelength σ s = 2πR 2 Short and long wavelength cross sections [Kim & Majumdar, JAP 99 (2006) 084306] Combination of scattering due to difference in mass and force constant of a spherical nanoparticle in the Rayleigh regime (particles much smaller than the wavelength) σ l = 4πR2 9 ωr v 4 ΔD D 2 + 3 ΔK K 2 Mg 2 Si 0.4 Sn 0.6 "Exp." [P. Bellanger s Thesis (ICMCB)]
❸ "Material by design" : mstructure prop. coupling Results From the property to the process conditions [P. Bellanger s Thesis (ICMCB)]