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

Outline

• Some thermodynamic and theoretical limitations for thermoelectric refrigeration

• Material Classes:− Rare Earth intermetallics, Kondo insulators− Skutterudites− Clathrates− Cobaltites

• Conclusions

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

Thermoelectric Couples for Refrigeration or Power Generation.

ZT = T S2 σ/κ

For Power generation:

For Refrigeration:

where

Maximum Cooling vs ZT(Thot-Tcold)/ Thot

Th-Tc = 1/2 Z Tc2

Current Multistage Modules Using Bi-Sb-Te-Se Alloys can reach Tcold ≈ 160 K

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

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.

Rare Earth Intermetallics - Mixed Valence, Heavy Fermion

Compounds, Hybridization Gap

Seebeck Values for Ce (p-type) and Yb (n-type)Intermetallics

Data from Sthioul, Jaccard and Sierro- in Valence Instabilities p.

443, 1982.

Best “p-type” Rare Earth Intermetallic: CePd3

(first considered for TE by Gambino et al. APL 1973)

CePd3 (cont’d)

Best “n-type” Rare earth intermetallic: YbAl3

YbAl3 Cont’d

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

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

Electronic Structure and theoretical Seebeck of FeSi

T. Jarlborg, Phys. Rev. B. 51, 1106 (1995)

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)

Ir Doped FeSi (cont’d)

“Best” Thermoelectrics Among Mixed

Valence Intermetallics(Physics Today, March 1997)

“State-of-the-art” Thermoelectric Materials

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

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

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

“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

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)

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

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

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

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

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

NaxCoO2 Crystals Have Good

Thermoelectric Properties at High

Temperatures ! Why?

K. Fujita et al.Jpn. J. Appl. Phys.40 (2001) 4644

Layered Hexagonal Structure of Na0.75CoO2

Mixed Co Valence 3.25

Two Partially Occupied Na Sites (Na1 ≈ 0.25,Na2 ≈ 0.5)

Na1

Na2

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

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

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

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.

Maximum Cooling vs ZT(Thot-Tcold)/ Thot

Th-Tc = 1/2 Z Tc2

Correlated Electron GroupJin He, Brian Sales,Rongying Jin,

David Mandrus(Group Leader),PeterKhalifah and Kathleen Affholter (not shown)

Why finding a “good thermoelectric” (ZT > 1) is hard! ZT = T S2 /κρ (Physics Today, March1997)

Exceptions: RuAl2, NaTl, SrGa2, etc

Thermoelectric Modules are Used to PowerNASA’s Cassini Probe to Saturn and Jupiter

Some of amazing images from Cassini !(Lifted from NASA web page)

Thermoelectric Refrigerator (Igloo, Wallmart)

Holds 72 12-ouncecans-(44F below ambient)

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)

PbTe Superlattice with PbSeTe nanodots grown with Molecular Beam Epitaxy has ZT≈2

at room temperature

Harman et al. Science 297 (2002) 2229

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!

ZT ≈ 2.2 Bulk Sample of AgPb18SbTe20

(Kanatzidis group- Science, Feb 2004)

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

Phase Diagram for NaxCoO2

Foo,Cava,OngCond-Mat0312174

Only Na0.75CoO2 Crystals Grown by Floating

Zone Method Show Clear Magnetic Transition

Crystals of Na0.75CoO2

grown using optical furnace

Magnetic susceptibility changes systematically with Na content