An Experimentalists Overview of the role of Electron Correlations - - PowerPoint PPT Presentation

An Experimentalist’s Overview of the role

• f Electron Correlations in the

Thermoelectric Performance of Various Materials

Brian Sales Correlated Electron Materials Group Oak Ridge National Laboratory Oak 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 Tc

2

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

• r ZT = S2/ L0

which means that for ZT=1,

• r 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 Chemistry

And 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

clathrate from Latin “clathro” meaning “to enclose with bars”

A B 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 Filled with a CH4 molecule

Can Make Semiconducting Clathrate Compounds With Type I Ice Clathrate Structure: X8Ga16Ge30, X= Ba, Sr, Eu Sr Semiconducting clathrates Have ZT ≈ 1 at 700K

No obvious role of electron 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 intriguing as 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

• f CE materials for thermoelectric

refrigeration is unlikely.

Maximum Cooling vs ZT (Thot-Tcold)/ Thot Th-Tc = 1/2 Z Tc

2

Correlated Electron Group

Jin He, Brian Sales,Rongying Jin, David Mandrus(Group Leader),Peter Khalifah 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 Power NASA’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-ounce cans-(44F below ambient)

Another Approach: Thin Films, Wires and Superlattices Proposed by Dresselhaus group starting ≈1993 Lower 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 at www.cemg.ornl.gov

Phase Diagram for NaxCoO2

Foo,Cava,Ong Cond-Mat 0312174

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