an experimentalist’s overview of the ... -...
TRANSCRIPT
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An Experimentalist’s Overview of the role
of Electron Correlations in the
Thermoelectric Performance of Various
Materials
Brian SalesCorrelated Electron Materials Group
Oak Ridge National LaboratoryOak Ridge, TN
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Outline
• Some thermodynamic and theoretical limitations for thermoelectric refrigeration
• Material Classes:− Rare Earth intermetallics, Kondo insulators− Skutterudites− Clathrates− Cobaltites
• Conclusions
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Basic Facts About Thermoelectric Devices
• All solid-state devices (no moving parts except electrons)
• Can be used for refrigeration or power generation
• Refrigeration with no chemical refrigerant (such as Freon)
• Major advantage: reliable and quiet
• Major disadvantage: poor efficiency
• Efficiency determined by figure of merit ZT, depends only on material properties
• ZT = S2Tσ/κ , where S = Seebeck coefficient, σ is electrical
conductivity, and κ is the thermal conductivity
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Thermoelectric Couples for Refrigeration or Power Generation.
ZT = T S2 σ/κ
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For Power generation:
For Refrigeration:
where
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Maximum Cooling vs ZT(Thot-Tcold)/ Thot
Th-Tc = 1/2 Z Tc2
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Current Multistage Modules Using Bi-Sb-Te-Se Alloys can reach Tcold ≈ 160 K
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Limitations of “True Intermetallic Compounds” (≈good metals) as Thermoelectric Elements:
ZT = T S2 /κρ κ ≈ κel + κLattice
Best Case, Suppose κLattice = 0
Then ZT = T S2 /κel ρ But for a good metal the Wiedemann-Franz law holds and L0 = κel ρ/T= 2.4 x 10-8 V2/K2
or ZT = S2/ L0
which means that for ZT=1, or S > 156 µV/K
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Theoretically the “Best Thermoelectric” results from a very narrow energy distribution of electrons participating in the transport process Mahan and Sofo, Proc. U.S. National Acad.
Sciences, 93, 7436 1996
ZT = 14
We think these values are achievable in rare-earth compounds.
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Rare Earth Intermetallics - Mixed Valence, Heavy Fermion
Compounds, Hybridization Gap
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Seebeck Values for Ce (p-type) and Yb (n-type)Intermetallics
Data from Sthioul, Jaccard and Sierro- in Valence Instabilities p.
443, 1982.
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Best “p-type” Rare Earth Intermetallic: CePd3
(first considered for TE by Gambino et al. APL 1973)
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CePd3 (cont’d)
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Best “n-type” Rare earth intermetallic: YbAl3
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YbAl3 Cont’d
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Hybridization Gap Materials “Kondo Insulators”T. Takabatke et al. Physica B 328 (2003) 53
ZT ≈ 0.017 at 10K and ZT ≈ 0.1 at 100 K
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Seebeck and Resistivity Data from FeSi Single Crystal- ZT ≈ 0.02
Unusual Transport and Magnetic properties first reported by Jaccarino et al. Phys. Rev. 160 (1967) 476
Data from Sales et al. PRB 1994
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Electronic Structure and theoretical Seebeck of FeSi
T. Jarlborg, Phys. Rev. B. 51, 1106 (1995)
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FeSi Doped with a large number of elements (Ir, Ru, Re, Co, Ge, Al, B etc.) in an attempt to maximize ZT- Ir doping resulted in largest ZT
Sales et al. PRB 50, 8207 (1994)
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Ir Doped FeSi (cont’d)
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“Best” Thermoelectrics Among Mixed
Valence Intermetallics(Physics Today, March 1997)
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“State-of-the-art” Thermoelectric Materials
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Cubic Filled Skutterudites as Thermoelectrics:
RxM4X12 , x <1
R fillers: Ce, Pr, Nd,Sm, Eu Gd and Yb, Tl, Ca, Sr, Ba, Na. K, etc
M(transition metals) Fe, Ru, Os, Co,Rh, Ir
X (pnictides) = P, As, Sb
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Filled Skutterudites
• Large number of interesting correlated ground states at low temperatures- but as far as I am aware none of these skutterudites are promising for thermoelectric refrigeration
• Filled skutterudites are of interest for thermoelectric power generation at elevated temperatures (≈1000 K) No clear evidence for ZT enhancement as a result of correlations (magnetism).
B. C. Sales “Filled Skutterudites” chapter 211 (2003) in Handbook of ChemistryAnd Physics of Rare Earths- Ed. By Gschneider. PDF file of chapter from
www.cemg.ornl.gov
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Ce Compound Has Slightly Higher ZT than La analog- but may be related to quality of sample (density, impurity phases) rather than correlations
Sales et al. PRB 56 (1997) 15081
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“n-type” skutterudites with large ZT can be made with Yb, or Ba with no obvious
improvement due to Yb 4f shell
Nolas et al. APL, 77 (2000) 1855
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What is a “clathrate” crystal?clathrate from Latin “clathro”
meaning “to enclose with bars”
AB
Type I “Ice Clathrate”
A : (H2O)24 (CH4)
B : (H2O)20 (CH4)
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Ice Clathrates Cage Large amounts of Methane and CO2 on the sea floor and in the frozen
tundra (2 x 1016 kg carbon)
Ice Clathrate with Methane[H2O]20 Cage Filledwith a CH4 molecule
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Can Make Semiconducting Clathrate Compounds With Type I Ice Clathrate Structure:
X8Ga16Ge30, X= Ba, Sr, Eu
Sr Semiconducting clathratesHave ZT ≈ 1 at 700K
No obvious role ofelectron correlations
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New Classes of Promising Metalloid Thermoelectric Materials (bulk) Most ZT values good above room temp: • Filled skutterudites, e.g. CeFe4Sb12, Ybx
CoSb3 - ZT ≈ 1.2, T≈ 600-900K• Half-Heusler Alloys: e.g. TiNiSn, ZrNiSn ZT ≈ 0.7 , 800 K • Semiconducting Clathrates, e.g Sr8Ga16Ge30 , ZT ≈
1 , T ≈700 K• Complex Bi chalcogenides CsBi4Te6, ZT≈0.8 , T =
225 K• Cubic Ag-Pb-Sb-Te bulk compounds-may have ≈
epitaxial nanocrystal inclusions, ZT ≈ 2.2 at 800 K
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Recent Interest in NaxCoO2 Materials as
Thermoelectrics Terasaki et al. Phys. Rev. B56, R12685 (1997)
• This material violates most of the “traditional rules” for finding a good thermoelectric (heavy atoms, small electronegativity differences, no magnetic elements)
• However oxides are attractive since they are stable in air at elevated temperatures
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Data on Na0.7CoO2 from Terasaki’s Original
Paper. Good oxide thermoelectric ! Violates “conventional wisdom”
Oxides are very intriguingas thermoelectrics for power generation : relatively cheap and stable in air
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NaxCoO2 Crystals Have Good
Thermoelectric Properties at High
Temperatures ! Why?
K. Fujita et al.Jpn. J. Appl. Phys.40 (2001) 4644
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Layered Hexagonal Structure of Na0.75CoO2
Mixed Co Valence 3.25
Two Partially Occupied Na Sites (Na1 ≈ 0.25,Na2 ≈ 0.5)
Na1
Na2
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Is this structure important for a good CoO2
based thermoelectric material ? Apparently YES since several other layered hexagonal
Cobalt oxides also have high ZT values :
Bi2-xPbxSr2Co2Oy
Ca3Co4O9
TlSr2Co2Oy
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Possible origin of high Thermopower in
Hexagonal CoO2 Layers: Entropy current
as carrier moves between Co+3 and Co+4
configurations.
t2g
levels
Co+
3
Co+4
S=0, g3 =1 S =1/2, g4 =6
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Thermopower at high temperature due to configurational Entropy Current Calculated By:
Koshibe et al. PRB 62, 6869 (2000)
S = -kB/e ln{( g3/g4) (x/1-x)}, where x is fraction of Co4+ ions
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Conclusions:
• Basic thermodynamics and a survey of several families of correlated electron compound indicate that the practical use of CE materials for thermoelectric refrigeration is unlikely.
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Maximum Cooling vs ZT(Thot-Tcold)/ Thot
Th-Tc = 1/2 Z Tc2
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Correlated Electron GroupJin He, Brian Sales,Rongying Jin,
David Mandrus(Group Leader),PeterKhalifah and Kathleen Affholter (not shown)
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Why finding a “good thermoelectric” (ZT > 1) is hard! ZT = T S2 /κρ (Physics Today, March1997)
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Exceptions: RuAl2, NaTl, SrGa2, etc
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Thermoelectric Modules are Used to PowerNASA’s Cassini Probe to Saturn and Jupiter
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Some of amazing images from Cassini !(Lifted from NASA web page)
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Thermoelectric Refrigerator (Igloo, Wallmart)
Holds 72 12-ouncecans-(44F below ambient)
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Another Approach: Thin Films, Wires and Superlattices
Proposed by Dresselhaus group starting ≈1993Lower dimensionality can result in:
• Enhancement in density of states near Fermi energy which leads to larger Seebeck coefficient
• Exploit anisotropic Fermi surfaces in cubic multivalley semiconductors
• In nano-structured superlattices, boundary scattering can effect phonons more than electrons (or holes)
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PbTe Superlattice with PbSeTe nanodots grown with Molecular Beam Epitaxy has ZT≈2
at room temperature
Harman et al. Science 297 (2002) 2229
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High ZT values may be related to nanocrystal inclusions. Implication: It may be possible to reproduce the high ZT values of MBE films
using bulk processing techniques!
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ZT ≈ 2.2 Bulk Sample of AgPb18SbTe20
(Kanatzidis group- Science, Feb 2004)
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References
• “Recent Trends in Thermoelectric Materials” Semiconductor and Semimetals, Edited by Terry Tritt, Volumes 69,70,71, Academic Press (2001)
• T. C. Harman et al. Science 297 (2002) 2229 • K. F. Hsu et al. Science 303 (2004) 818 • R. Venkatasubramanian et al. Nature 413 (2001) 597• B. C. Sales Science 295 (2002) 1248• G. Mahan, B. Sales and J. Sharp, Physics Today, March 1997, p.42
Power Point Presentation Available atwww.cemg.ornl.gov
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Phase Diagram for NaxCoO2
Foo,Cava,OngCond-Mat0312174
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Only Na0.75CoO2 Crystals Grown by Floating
Zone Method Show Clear Magnetic Transition
Crystals of Na0.75CoO2
grown using optical furnace
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Magnetic susceptibility changes systematically with Na content