Applications of solid state physics: Thermoelectric materials. Eric S. Toberer Physics Dept, Colorado School of Mines
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1 Applications of solid state physics: Thermoelectric materials Eric S. Toberer Physics Dept, Colorado School of Mines
2 CSM Physics: Experimental energy materials (NREL) Condensed matter theory (NIST) Femtosecond optics Nuclear/particle/astrophysics Mountains Golden NREL
3 Post- docs: Grad students: Undergrads: NREL
4 Group research interests Advanced materials for energy: Thermoelectrics, photovoltaics, H 2 storage, combinatorial synthesis and characterizadon Condensed ma?er physics: Transport in crystalline solids: electrons, phonons, ions Chemical structure property reladonships Postdoc: Materials Science, Caltech PhD: Materials Science, UCSB BS: Chemistry, Harvey Mudd College Teaching: Solid State Physics
5 Goals for this talk: PracDcal applicadon of QM, solid state, thermal phys. Understanding how a thermoelectric generator works Example - controlling semiconductor charge transport Example controlling phonons and heat flow
6 Space power
7 Galileo: Volcano erupdon on Io, moon of Jupiter
8 How do you generate electricity in space? Galileo
9 Space power: Thermoelectric effect Thermoelectrics directly convert the flow of heat into electrical power Seebeck effect " =! V! T Voltage Temperature gradient
10 Space power: Thermoelectric effect Thermoelectrics directly convert the flow of heat into electrical power Seebeck effect " =! V! T Voltage Temperature gradient
11 Space power: Wait, we need a temperature gradient?? How do we get a temperature gradient in space?
12 Space power: How do we get a temperature gradient in space? 238 PuO 2
13 Space power: How do we get a temperature gradient in space? Neptunium-237 Plutonium-238 Uranium-234 Lead-206 irradiation decay, 90 year half-life alpha-emitter (He 2+ ) Power supply: Plutonium Cooling: Space
14 Galileo
15
16 Seebeck effect Seebeck effect " =! V! T Voltage Temperature gradient Gas filled tube hot ΔT Pressure equalizadon! cold Density gradient!
17 From the Seebeck effect to TE generators " =! V! T Voltage Temperature gradient i hot Sign of voltage depends on doping type (n or p) e - h + To create a circuit, need both n and p-type materials. n p A thermoelectric generator has the legs electrically in series but thermally in parallel. cold TE module: Heat absorbed load Heat rejected
18 Material efficiency: Transport Efficiency: Want maximum power for a given transfer of heat (heat is our fuel) Seebeck coefficient leads to requisite voltage. Maximize: P = I x V = V 2 /R Maximize voltage V = α T e - i hot n cold load p h + Figure of merit (z) = Seebeck coefficient 2 electrical resistivity Minimize Ohmic losses (V=IR)
19 Material efficiency: Transport hot Efficiency: Want maximum power for a given transfer of heat (heat is our fuel) Two sources of loss: electrical resistance thermal shorting e - i n cold p h + load Figure of merit (z) = zt = " 2 T #$ Seebeck coefficient 2 electrical resistivity thermal conductivity Avoid parasitic heat loss. All heat transferred should be creating current.
20 Revolution in thermoelectric generator performance Historically, efficiency record set by NASA-JPL radioisotope thermoelectric generators Curiosity Hot side: Pu oxide core Cold side: black-body radiation to space 20
21 Revolution in thermoelectric generator performance Last 6 years: new materials have let to demonstrated modules with nearly x3 efficiency of heritage generators! Not just high zt, demonstrated efficiency! Brown et al, Chem Mater 2006 May et al Phys Rev B 2008 Calait et al Nuclear Emerg Tech. Space
22 Couple under test 22
23 Seebeck effect and electrical conductivity Seebeck coefficient maximized at low carrier densities for simple semiconductors. zt = " 2 #T $ Thus, degenerate semiconductors Snyder & Toberer, Nature Mater
24 Thermal conductivity zt = " 2 #T $ " = " lattice + " elect " elect = LT# L - Lorenz number (not constant) σ - electrical conducdvity 24
25 Heat transport Copper bar - e- carry heat Enormous Diamond: Lattice vibrations carry heat Glass - not so much heat transfer
26 Design principles for thermoelectrics Figure of merit: zt =! 2 " T # α σ κ Seebeck coef Electrical cond. Thermal cond. 26 Snyder & Toberer Nature Mater 2008
27 Case example 1: Yb 14 AlSb 11 Yb 14 AlSb 11 La 3-x Te 4 XCo 4 Sb 12 27
28 Electronic properties of Yb 14 AlSb 11 Yb 14 AlSb 11 has 104 atoms in the primitive cell (4 x formula) Formula breakdown: 14 Yb 2+ cations Isolated, covalently bound anionic moieties: AlSb 4 9- tetrahedra Sb 3 7- linear trimer 4 isolated Sb 3- Expect intrinsic semiconductor! 28 Toberer et al, Adv. Funct. Mater. (2008)
29 Electronic properties of Yb 14 AlSb 11 Observation: Large, decreasing electrical resistance with increasing T carrier acdvadon E Density of states 29 Toberer et al, Adv. Funct. Mater. (2008)
30 Electronic properties of Yb 14 AlSb 11 Observation: Large, decreasing electrical resistance with increasing T carrier acdvadon E e - Density of states 30 Toberer et al, Adv. Funct. Mater. (2008)
31 Electronic properties of Yb 14 AlSb 11 Observation: Large, decreasing electrical resistance with increasing T carrier acdvadon 31 Toberer et al, Adv. Funct. Mater. (2008)
32 Yb 14 Mn x Al 1-x Sb 11 Hall effect Hall effect measurements: Increase in hole concentration with Mn 2+ substitution for Al 3+ agrees with doping level (dashed line) 32 Toberer et al, Adv. Funct. Mater. (2008)
33 Yb 14 Mn x Al 1-x Sb 11 Hall effect Resistivity: Extrinsic semiconductor (fixed carrier conc) with mobility = T Toberer et al, Adv. Funct. Mater. (2008)
34 Yb 14 AlSb 11 mobility and m* DOS Mixture of ionic and covalent substructure in unit cell, mobility low but not terrible. (5 cm 2 /Vs at 300K) m* DOS = 3 m e zt = " 2 #T $ 34 Toberer et al, Adv. Funct. Mater. (2008)
35 Yb 14 AlSb 11 mobility and m* DOS Mixture of ionic and covalent substructure in unit cell, mobility low but not terrible. (5 cm 2 /Vs at 300K) m* DOS = 3 m e zt = " 2 #T $? 35 Toberer et al, Adv. Funct. Mater. (2008)
36 Thermal conductivity overview " = " lattice + " elect " lattice = 1 3 C vvl Thermal conductivity in solids can be as low as ~ 0.1 W/mK at room temperature (plastics). Window glass: ~1 W/mK Typical semiconductors: W/mK Toberer, Baranowski, Dames, ARMR 2012
37 Yb 14 AlSb 11 - κ L amorphous SiO 2 Incredibly low thermal conductivity!! Yb 14 AlSb 11 glass limit Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 37 J. Mater. Chem 2011
38 Understanding low thermal conductivity in Yb 14 AlSb 11 a) n = 1 Frequency (") v g Plane wave descripdon of lamce vibradons. Each allowed mode has wavevector k and an associated freq. Group velocity: v g = dw/dk 0!/a k 0 Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 38 J. Mater. Chem 2011
39 Understanding low thermal conductivity in Yb 14 AlSb 11 a) n = 1 2 Frequency (") v g opdcal acousdc 0!/a k 0!/a k Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 39 J. Mater. Chem 2011
40 Understanding low thermal conductivity in Yb 14 AlSb 11 a) n = Frequency (") v g 0!/a k 0!/a k 0!/a k 0 Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 40 J. Mater. Chem 2011
41 Understanding low thermal conductivity in Yb 14 AlSb 11 a) n = Frequency (") v g 0!/a k 0!/a k 0!/a k 0!/a k Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 41 J. Mater. Chem 2011
42 Understanding low thermal conductivity in Yb 14 AlSb 11 Frequency (") a) n = v g 0!/a k 0!/a k 0!/a k 0!/a k Theory: κ L proportional to n -2/3 n: # atoms primidve cell Expectation that structurally complex crystalline materials will have incredibly low thermal conductivity. Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 42 J. Mater. Chem 2011
43 Yb 14 AlSb 11 - κ L Incredibly low thermal conductivity!! amorphous SiO 2 Scattering? Group velocity? Both? glass limit Yb 14 AlSb 11 Theory: κ L proportional to n -2/3 n: # atoms primidve cell n = 104 for Yb 14 AlSb 11 Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 43 J. Mater. Chem 2011
44 Understanding low thermal conductivity in Yb 14 AlSb 11 Structural complexity proves to be a good predictor of κ L for similar compounds (e.g. antimonides)! Roufosse & Klemens PRB 1973 Toberer, Zevalkink, Snyder, 44 J. Mater. Chem 2011
45 Yb 14 AlSb 11 : Inspiring Zintl thermoelectrics Factors contributing to good thermoelectric performance of Yb 14 Mn x Al 1-x Sb 11 (and many other Zintl compounds): robust carrier concentration control large DOS effective mass (leading to a large Seebeck coefficient). extremely low lattice thermal conductivity (structural complexity) Yb 14 Mn x Al 1- x Sb 11 Heavily doped Undoped x Targeting other Zintl compounds from this understanding: Ca 3 AlSb 3 Ca 5 Al 2 Sb 6 Yb 9 Mn 4.2 Sb 9 SrZn 2 Sb 2 Sr 3 GaSb 3 45
46 Case example 3: XCo 4 Sb 12 Yb 14 AlSb 11 La 3-x Te 4 XCo 4 Sb 12 46
47 Filled skutterudites XCo 4 Sb 12 Intermetallic Co 4 Sb 12 XCoSb 3 X atom in void space Robust carrier concentration control through guest and framework substitution 47 Koza et al Nature Mater. 2008
48 Filled skutterudites Low thermal conductivity Traditionally understood as uncoupled, local vibrational modes for rattlers that scattered phonons Koza et al Nature Mater Toberer et al J. Mater Chem. 2012
49 Filled skutterudites Low thermal conductivity More recently, understood as coupled oscillators: Model with ball/springs: Weak spring Heavy mass Koza et al Nature Mater Toberer et al J. Mater Chem. 2012
50 Filled skutterudites Low thermal conductivity Avoided crossing yields low-velocity region in acoustic branch: Toberer et al J. Mater Chem. 2012
51 Goals for this talk: PracDcal applicadon of QM, solid state, thermal phys. Understanding how a thermoelectric generator works Example - controlling semiconductor charge transport Example controlling phonons and heat flow
52 Path forward From these materials: Electronic properties: Band degeneracy Nested bands Thermal conductivity: Structural complexity Point defects Rattling Grand challenges standard transport : Electronic band degeneracy (m* DOS ) Earth abundant analogs Implement high throughput techniques Grand challenges beyond standard transport : Non-parabolic electronic bands Tailoring E-dependent e - scattering Yb 14 AlSb 11 La 3-x Te 4 XCo 4 Sb 12
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